\documentclass[a4paper]{article}
\usepackage{gclc_proof}


\begin{document}


	Let $P_{cd}^{0}$ be the point such that lines $P_{cd}^{0}C$ and $AB$ are parallel (and {\tt PRATIO} $P_{cd}^{0}$ $C$ $A$ $B$ $1$).


	Let $P_{ad}^{1}$ be the point such that lines $P_{ad}^{1}A$ and $BC$ are parallel (and {\tt PRATIO} $P_{ad}^{1}$ $A$ $B$ $C$ $1$).


\vspace*{2mm} \hrule \vspace*{2mm} 


\begin{displayproof}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  S_{ABA_2}\right)}{by the statement}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  \frac{ \left( \left( S_{ABB_1} \cdot  S_{ABA_1}\right) +  \left( -1  \cdot  \left( S_{A_1BB_1} \cdot  S_{ABA}\right)\right)\right)}{ S_{ABA_1B_1}}\right)}{by Lemma 30 (point $A_2$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  \frac{ \left( \left( S_{ABB_1} \cdot  S_{ABA_1}\right) +  \left( -1  \cdot  \left( S_{A_1BB_1} \cdot  0 \right)\right)\right)}{ S_{ABA_1B_1}}\right)}{by Lemma 2 (equal)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  \frac{ \left( \left( S_{ABB_1} \cdot  S_{ABA_1}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ABA_1B_1}}\right)}{by multiplication by 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  \frac{ \left( \left( S_{ABB_1} \cdot  S_{ABA_1}\right) +  0 \right)}{ S_{ABA_1B_1}}\right)}{by multiplication by 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \left( 13  \cdot  \frac{ \left( S_{ABB_1} \cdot  S_{ABA_1}\right)}{ S_{ABA_1B_1}}\right)}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( S_{ABB_1} \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by multiplication of fractions}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( S_{ABD} +  \left( 0.333333  \cdot  \left( S_{ABA} +  \left( -1  \cdot  S_{ABD}\right)\right)\right)\right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by Lemma 29 (point $B_1$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( S_{ABD} +  \left( 0.333333  \cdot  \left( 0  +  \left( -1  \cdot  S_{ABD}\right)\right)\right)\right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by Lemma 2 (equal)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( S_{ABD} +  \left( 0.333333  \cdot  \left( -1  \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( S_{ABD} +  \left( -0.333333  \cdot  S_{ABD}\right)\right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( \left( 0.666667  \cdot  S_{ABD}\right) +  0 \right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( \left( 0.666667  \cdot  S_{ABD}\right) \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 13  \cdot  \left( 0.666667  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)\right)}{ S_{ABA_1B_1}}}{by right association}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ S_{ABA_1B_1}}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( S_{ABA_1D} +  \left( 0.333333  \cdot  \left( S_{ABA_1A} +  \left( -1  \cdot  S_{ABA_1D}\right)\right)\right)\right)}}{by Lemma 29 (point $B_1$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{AA_1D}\right) +  \left( 0.333333  \cdot  \left( S_{ABA_1A} +  \left( -1  \cdot  S_{ABA_1D}\right)\right)\right)\right)}}{by Definition 4}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( 0.333333  \cdot  \left( S_{ABA_1A} +  \left( -1  \cdot  S_{ABA_1D}\right)\right)\right)\right)}}{by Lemma 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( 0.333333  \cdot  \left( \left( S_{ABA_1} +  S_{AA_1A}\right) +  \left( -1  \cdot  S_{ABA_1D}\right)\right)\right)\right)}}{by Definition 4}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( 0.333333  \cdot  \left( \left( S_{ABA_1} +  S_{AAA_1}\right) +  \left( -1  \cdot  S_{ABA_1D}\right)\right)\right)\right)}}{by Lemma 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( 0.333333  \cdot  \left( \left( S_{ABA_1} +  S_{AAA_1}\right) +  \left( -1  \cdot  \left( S_{ABA_1} +  S_{AA_1D}\right)\right)\right)\right)\right)}}{by Definition 4}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( 0.333333  \cdot  \left( \left( S_{ABA_1} +  S_{AAA_1}\right) +  \left( -1  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)\right)}}{by Lemma 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  \left( S_{ABA_1} +  S_{AAA_1}\right)\right) +  \left( 0.333333  \cdot  \left( -1  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  \left( S_{ABA_1} +  S_{AAA_1}\right)\right) +  \left( -0.333333  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( \left( \left( 0.333333  \cdot  S_{ABA_1}\right) +  \left( 0.333333  \cdot  S_{AAA_1}\right)\right) +  \left( -0.333333  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( \left( 1.333333  \cdot  S_{ABA_1}\right) +  S_{DAA_1}\right) +  \left( \left( 0  +  \left( 0.333333  \cdot  S_{AAA_1}\right)\right) +  \left( -0.333333  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( \left( 1.333333  \cdot  S_{ABA_1}\right) +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  \left( -0.333333  \cdot  \left( S_{ABA_1} +  S_{DAA_1}\right)\right)\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( \left( 1.333333  \cdot  S_{ABA_1}\right) +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  \left( \left( -0.333333  \cdot  S_{ABA_1}\right) +  \left( -0.333333  \cdot  S_{DAA_1}\right)\right)\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( \left( 1  \cdot  S_{ABA_1}\right) +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  \left( 0  +  \left( -0.333333  \cdot  S_{DAA_1}\right)\right)\right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  \left( 0  +  \left( -0.333333  \cdot  S_{DAA_1}\right)\right)\right)\right)}}{by multiplication by 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  S_{DAA_1}\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  \left( -0.333333  \cdot  S_{DAA_1}\right)\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right) +  \left( \left( 0.333333  \cdot  S_{AAA_1}\right) +  0 \right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABA_1}\right)\right)}{ \left( \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right) +  \left( 0.333333  \cdot  S_{AAA_1}\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  \left( S_{ABC} +  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right) +  \left( 0.333333  \cdot  S_{AAA_1}\right)\right)}}{by Lemma 29 (point $A_1$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  \left( S_{ABC} +  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right) +  \left( 0.333333  \cdot  0 \right)\right)}}{by Lemma 2 (equal)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  \left( S_{ABC} +  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right) +  0 \right)}}{by multiplication by 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( S_{ABD} \cdot  \left( S_{ABC} +  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( \left( S_{ABD} \cdot  S_{ABC}\right) +  \left( S_{ABD} \cdot  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( 8.666671  \cdot  \left( \left( S_{ABD} \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  \left( S_{ABD} \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by associativity and commutativity}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 8.666671  \cdot  \left( 0.333333  \cdot  \left( S_{ABD} \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( \left( S_{ABD} \cdot  S_{ABD}\right) +  \left( S_{ABD} \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( \left( S_{ABD} \cdot  S_{ABD}\right) +  \left( -1  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by associativity and commutativity}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right) +  \left( 2.888887  \cdot  \left( -1  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 8.666671  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right) +  \left( -2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right) +  0 \right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( S_{ABA_1} +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( S_{ABC} +  \left( 0.333333  \cdot  \left( S_{ABD} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by Lemma 29 (point $A_1$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( S_{ABC} +  \left( \left( 0.333333  \cdot  S_{ABD}\right) +  \left( 0.333333  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( S_{ABC} +  \left( \left( 0.333333  \cdot  S_{ABD}\right) +  \left( -0.333333  \cdot  S_{ABC}\right)\right)\right) +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( \left( 0.333333  \cdot  S_{ABD}\right) +  0 \right)\right) +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  S_{DAA_1}\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{DAC} +  \left( 0.333333  \cdot  \left( S_{DAD} +  \left( -1  \cdot  S_{DAC}\right)\right)\right)\right)\right)\right)}}{by Lemma 29 (point $A_1$ eliminated)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{DAC} +  \left( 0.333333  \cdot  \left( 0  +  \left( -1  \cdot  S_{DAC}\right)\right)\right)\right)\right)\right)}}{by Lemma 2 (equal)}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{ACD} +  \left( 0.333333  \cdot  \left( 0  +  \left( -1  \cdot  S_{DAC}\right)\right)\right)\right)\right)\right)}}{by Lemma 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{ACD} +  \left( 0.333333  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACD}\right)\right)\right)\right)\right)\right)}}{by Lemma 1}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{ACD} +  \left( 0.333333  \cdot  \left( -1  \cdot  S_{ACD}\right)\right)\right)\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( S_{ACD} +  \left( -0.333333  \cdot  S_{ACD}\right)\right)\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( \left( 0.666667  \cdot  S_{ACD}\right) +  0 \right)\right)\right)}}{by similar summands}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.666667  \cdot  \left( 0.666667  \cdot  S_{ACD}\right)\right)\right)}}{by addition with 0}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  S_{ABCD}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( 3  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)}}{by Lemma 30 (point $D$ eliminated)}{4500=4500.000865}
\proofstep{ \frac{ \left( 3  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)}}{by multiplication of fractions}{4500=4500.000865}
\proofstep{ \frac{ \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( 3  \cdot  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)}}{by distribution of multiplication over addition}{4500=4500.000865}
\proofstep{ \frac{ \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)}{ \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)}}{by multiplication of constants}{4500=4500.000865}
\proofstep{ \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right) +  \left( 0.444445  \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by fractions on two sides}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( 0.444445  \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( \left( 0.666667  \cdot  S_{ABC}\right) +  \left( 0.333333  \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( 0.666667  \cdot  S_{ABC}\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( 0.333333  \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( 0.666667  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABC}\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  \left( 0.333333  \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( 0.666667  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABC}\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( 0.666667  \cdot  \left( \left( S_{ABC} \cdot  \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( 0.666667  \cdot  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( 0.666667  \cdot  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 0.666667  \cdot  \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( 0.666667  \cdot  \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( 0.666667  \cdot  \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ABD}\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( S_{ABD} \cdot  \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABD} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( 3  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABD} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( \left( 3  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -3  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.333333  \cdot  \left( 3  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( 0.333333  \cdot  \left( -3  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( 0.333333  \cdot  \left( -3  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) +  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACD}\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( S_{ACD} \cdot  \left( 3  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ACD} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( 3  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( S_{ACD} \cdot  \left( -3  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( \left( 3  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -3  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.444445  \cdot  \left( 3  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( 0.444445  \cdot  \left( -3  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( 0.444445  \cdot  \left( -3  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)}{by multiplication of constants}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( 5.777784  \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by distribution of multiplication over addition}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( 2.888887  \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000295=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \frac{ \left( 0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \frac{ \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \frac{ \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by sum of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \frac{ \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \frac{ \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \frac{ \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by sum of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \frac{ \left( \left( \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by distribution of multiplication over addition}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \frac{ \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000299=-3656251828.124995}
\proofstep{ \left( \frac{ \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} +  \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by sum of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( 1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by distribution of multiplication over addition}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( -1.333335  \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ABD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by associativity and commutativity}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  1 \right)\right)\right)}{ 1 }\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by ratio cancellation}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)}{ 1 }\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 1}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by fraction with number denominator}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000299=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ACA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \frac{ \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \frac{ \left( 1  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)}{ 1 }\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by ratio cancellation}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)}{ 1 }\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 1}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by fraction with number denominator}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ACD} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ACA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \frac{ \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \frac{ \left( 1  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)}{ 1 }\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by ratio cancellation}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)}{ 1 }\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 1}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by fraction with number denominator}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000305=-3656251828.124995}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABC}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \frac{ \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABC}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \frac{ \left( 1  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABC}\right)\right)}{ 1 }\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by ratio cancellation}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABC}\right)}{ 1 }\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 1}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABC}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by fraction with number denominator}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABD} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000305=-3656251828.125008}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABD}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABD}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}} \cdot  S_{ABD}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABD}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \frac{ \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABD}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \frac{ \left( 1  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABD}\right)\right)}{ 1 }\right)\right)}{by ratio cancellation}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABD}\right)}{ 1 }\right)\right)}{by multiplication by 1}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) \cdot  S_{ABD}\right)\right)\right)}{by fraction with number denominator}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABD}\right)\right)\right)\right)}{by right association}{-3656251125.000305=-3656251828.125014}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABA}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{by Lemma 30 (point $D$ eliminated)}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  0 \right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  \left( -1  \cdot  0 \right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \frac{ \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right) +  0 \right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{by multiplication by 0}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \frac{ \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)\right)}{by addition with 0}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \frac{ \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \left( 2.888887  \cdot  \frac{ \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) +  \frac{ \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}\right)}{by multiplication of fractions}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{by sum of fractions}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right)\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{by right association}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABP_{ad}^{1}} \cdot  S_{ABC}\right) \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{by right association}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ S_{ACP_{ad}^{1}P_{cd}^{0}}}}{by right association}{-3656251125.000305=-3656251828.125021}
\proofstep{ \frac{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{ 1 }}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ 1 }}{by fractions on two sides}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \frac{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{ 1 }}{by fraction with number denominator}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by fraction with number denominator}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{AP_{ad}^{1}P_{cd}^{0}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Definition 4}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{ad}^{1}P_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{AP_{ad}^{1}P_{cd}^{0}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Definition 4}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{P_{ad}^{1}CP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{AP_{ad}^{1}P_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Definition 4}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) \cdot  S_{ACP_{ad}^{1}}\right) +  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right) \cdot  S_{ACP_{ad}^{1}}\right)\right) +  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.224609=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right) \cdot  S_{ACP_{ad}^{1}}\right) +  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right) \cdot  S_{ACP_{ad}^{1}}\right)\right) +  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{ad}^{1}} +  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right) +  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.762207}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right) +  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} +  \left( 1  \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right) \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} +  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right) \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right) +  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right) +  \left( S_{ACP_{ad}^{1}} \cdot  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right) +  \left( -1  \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCP_{ad}^{1}} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} +  \left( 1  \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} +  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right) \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right) +  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right) +  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right) +  \left( -1  \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.225098=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABCA} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right) \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABCC} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right) \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABCB} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.236816=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( S_{CP_{cd}^{0}C} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  S_{ACP_{cd}^{0}}\right) +  \left( \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{ad}^{1}}\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 0  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 0  +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.239258=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( S_{CP_{cd}^{0}C} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right) \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  S_{ACP_{cd}^{0}}\right) +  \left( \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by right association}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ABCA} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 0  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.228027=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( 0  +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.228027=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.228027=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.228027=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( 0  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( 0  +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 0  +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{P_{cd}^{0}AP_{ad}^{1}} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.228516=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right) \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{CP_{cd}^{0}B} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ABCA} \cdot  \left( -1  \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ABC} +  0 \right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} +  0 \right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} +  \left( 1  \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} +  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right) +  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.234375=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0  +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  0 \right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ABC} +  0 \right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} +  0 \right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.233887=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( S_{CP_{cd}^{0}C} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABCA} \cdot  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  0 \right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -0.999999  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  0 \right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 0  +  0 \right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  0 \right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCP_{ad}^{1}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} +  \left( 1  \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCA} +  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right) +  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} +  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( 0  +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -3  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  0 \right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{ad}^{1}} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 1  \cdot  S_{ABC}\right) \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{CP_{cd}^{0}P_{ad}^{1}} \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.232422=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( S_{CP_{cd}^{0}C} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{CP_{cd}^{0}A} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( 0  +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right) \cdot  S_{ABCA}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABCA} \cdot  \left( -1  \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 3  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.230957=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  0 \right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  \left( -1.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 0  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABCA}\right)\right)\right)\right) +  0 \right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by similar summands}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 0  +  0 \right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  0 \right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ABC} +  0 \right)\right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} +  0 \right) \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{ad}^{1}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( S_{ACA} +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACC} +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 1  \cdot  S_{ABC}\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.762695}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ABC} +  0 \right)\right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} +  0 \right) \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AP_{ad}^{1}}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.761719}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( S_{P_{cd}^{0}AA} +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{P_{cd}^{0}AC} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 1}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( 0  +  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} +  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( S_{ABC} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by distribution of multiplication over addition}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABP_{ad}^{1}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication of constants}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 0}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( 0  +  \left( S_{ABC} +  0 \right)\right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( S_{ABC} +  0 \right) \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.778320}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABC} \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by addition with 0}{2742188343750.231445=2742188871093.778320}
\end{displayproof}


\vspace*{2mm} \hrule \vspace*{2mm} 


Proving lemma...(level 1)

\begin{displayproof}
\proofstep{ S_{ABC}}{=}{ 0 }{by the statement}{750=0}
\end{displayproof}


\proveddisproved{2}


\begin{displayproof}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by cancellation rule (assuming $ S_{ABC} \neq  0 $)}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( 1  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{ad}^{1}}\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125039}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABA} +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{ad}^{1}$ eliminated)}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABB}\right)\right)\right)\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ABC} +  0 \right)\right)\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 0  +  \left( S_{ABC} +  0 \right)\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} +  0 \right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  \left( 2.888887  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABC}\right)\right)\right)\right)}{by addition with 0}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right) +  0 \right)}{by similar summands}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{CP_{cd}^{0}B}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{CP_{cd}^{0}B} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{P_{cd}^{0}AB}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000308=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABC} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABC}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( -5.777784  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 8.666671  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{by right association}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -5.777784  \cdot  \left( -1  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000312=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000304=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( 0  +  \left( S_{ACB} +  0 \right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 0  +  \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by similar summands}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000297=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000293=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( S_{ABB} +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  0 \right)\right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 0  +  0 \right)\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  0 \right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( -1  \cdot  \left( S_{ABCC} \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCC} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 0  +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by similar summands}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( 0  +  \left( S_{ACB} +  0 \right)\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  S_{ACB}\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 0  +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by similar summands}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( S_{ABB} +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  0 \right)\right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 0  +  0 \right)\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  0 \right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( S_{ACB} \cdot  \left( -1  \cdot  \left( S_{ABCB} \cdot  S_{ACB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( 2.000001  \cdot  \left( -1  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  S_{ACB}\right)\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by associativity and commutativity}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -2.333334  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ACB} \cdot  \left( S_{ABCB} \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  0 \right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by similar summands}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{BCP_{cd}^{0}}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( S_{BCC} +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{BCC} +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( \left( 1  \cdot  S_{ACB}\right) \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000290=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( S_{ACB} +  0 \right)\right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( 0  +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by similar summands}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{BCP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( S_{BCC} +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{BCB} +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{BCA}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by Lemma 1}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 0  +  \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  \left( -1  \cdot  S_{ACB}\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by addition with 0}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( 1  \cdot  S_{ACB}\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication of constants}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{3656251125.000283=3656251828.125038}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( 1  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right)\right) +  \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by cancellation rule}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( 1  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACB}\right)\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ACP_{cd}^{0}}\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( S_{ABB} +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  0 \right)\right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 0  +  0 \right)\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  0 \right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( S_{ABCA} \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( -2.000001  \cdot  \left( -1  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by associativity and commutativity}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 2.333334  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  \left( 2.000001  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication of constants}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right) +  0 \right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by similar summands}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  S_{ACP_{cd}^{0}}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( 0  +  \left( S_{ACB} +  0 \right)\right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  \left( S_{ACB} +  0 \right)\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( \left( -8.666671  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 0  +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)\right)}{by similar summands}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACP_{cd}^{0}} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( S_{ACC} +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  S_{ACA}\right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  \left( -1  \cdot  0 \right)\right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by Lemma 2 (equal)}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( 0  +  \left( 1  \cdot  \left( S_{ACB} +  0 \right)\right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( 0  +  \left( S_{ACB} +  0 \right)\right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 1}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( \left( S_{ACB} +  0 \right) \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ACB} \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  S_{ACB}\right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( S_{ACB} \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( S_{ACB} \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by addition with 0}{-4875001.500000=-4875002.437500}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( 1  \cdot  S_{ABCC}\right)\right) +  \left( -4.333335  \cdot  \left( 1  \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  1 \right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( 1  \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by cancellation rule}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  \left( 1  \cdot  S_{ABCB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  1 \right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( 1  \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABCA} \cdot  1 \right)\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( 1  \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  \left( 1  \cdot  S_{ACB}\right)\right) +  \left( 5.777784  \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( 1  \cdot  S_{ABP_{cd}^{0}}\right)\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  S_{ABP_{cd}^{0}}\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( S_{ABB} +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)}{by Lemma 29 (point $P_{cd}^{0}$ eliminated)}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  S_{ABA}\right)\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( S_{ABC} +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)}{by Lemma 2 (equal)}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  \left( -1  \cdot  0 \right)\right)\right)\right)\right)\right)}{by Lemma 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 1  \cdot  \left( 0  +  0 \right)\right)\right)\right)\right)}{by multiplication by 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  \left( 0  +  0 \right)\right)\right)\right)}{by multiplication by 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( \left( -1  \cdot  S_{ACB}\right) +  0 \right)\right)\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( 5.777784  \cdot  \left( -1  \cdot  S_{ACB}\right)\right)\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -2.888887  \cdot  S_{ACB}\right) +  \left( -5.777784  \cdot  S_{ACB}\right)\right)}{by multiplication of constants}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( \left( -8.666671  \cdot  S_{ACB}\right) +  0 \right)}{by similar summands}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABCC}\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  S_{ACC}\right)\right) +  \left( -4.333335  \cdot  S_{ABCB}\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Definition 4}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  S_{ACC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  S_{ACB}\right)\right)\right) +  \left( 4.333335  \cdot  S_{ABCA}\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Definition 4}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  S_{ACC}\right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  S_{ACB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  S_{ACA}\right)\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Definition 4}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  S_{ACB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  S_{ACA}\right)\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Lemma 2 (equal)}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  S_{ACB}\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Lemma 2 (equal)}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right)\right)}{=}{ \left( -8.666671  \cdot  S_{ACB}\right)}{by Lemma 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right)\right)}{=}{ \left( -8.666671  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)}{by Lemma 1}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 4.333335  \cdot  \left( S_{ABC} +  0 \right)\right)\right)}{=}{ \left( -8.666671  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 4.333335  \cdot  S_{ABC}\right)\right)}{=}{ \left( -8.666671  \cdot  \left( -1  \cdot  S_{ABC}\right)\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 4.333335  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  \left( 4.333335  \cdot  S_{ABC}\right)\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by multiplication of constants}{6500.002000=6500.003250}
\proofstep{ \left( \left( \left( 8.666669  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right) +  0 \right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by similar summands}{6500.002000=6500.003250}
\proofstep{ \left( \left( 8.666669  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( S_{ABC} +  \left( -1  \cdot  S_{ABC}\right)\right)\right)\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( 8.666669  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( \left( 0  \cdot  S_{ABC}\right) +  0 \right)\right)\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by similar summands}{6500.002000=6500.003250}
\proofstep{ \left( \left( 8.666669  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  \left( 0  +  0 \right)\right)\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by multiplication by 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( 8.666669  \cdot  S_{ABC}\right) +  \left( -4.333335  \cdot  0 \right)\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( \left( 8.666669  \cdot  S_{ABC}\right) +  0 \right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by multiplication by 0}{6500.002000=6500.003250}
\proofstep{ \left( 8.666669  \cdot  S_{ABC}\right)}{=}{ \left( 8.666671  \cdot  S_{ABC}\right)}{by addition with 0}{6500.002000=6500.003250}
\proofstep{ \left( 0  \cdot  S_{ABC}\right)}{=}{ 0 }{by similar summands on two sides}{0=0}
\proofstep{ 0 }{=}{ 0 }{by multiplication by 0}{0=0}
\end{displayproof}


\proveddisproved{1}


NDG conditions are:

$ S_{ACP_{cd}^{0}}\neq S_{P_{ad}^{1}CP_{cd}^{0}}$ i.e., lines $AP_{ad}^{1}$ and $CP_{cd}^{0}$ are not parallel (construction based assumption)

$ S_{ABB_1}\neq S_{A_1BB_1}$ i.e., lines $AA_1$ and $BB_1$ are not parallel (construction based assumption)

$ S_{ABC}\neq 0 $ i.e., points $A$, $B$ and $C$ are not collinear (cancellation assumption)


\vspace*{2mm} \hrule \vspace*{2mm} 


Number of elimination proof steps:     62

Number of geometric proof steps:      152

Number of algebraic proof steps:      582

Total number of proof steps:          796


Time spent by the prover: 2.337 seconds


\end{document}

