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Review work and force and energy

abstract:
reference:

step	inference rule	input	feed	output	step validity (as per SymPy)
1	111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			1590774089 $dW=F dx$	no validation is available for declarations
2	111408: integrate number of inputs: 1; feeds: 0; outputs: 1 Integrate Eq.~ref{eq:#1}; yields Eq.~ref{eq:#2}.	1590774089 $dW=F dx$		5542528160 $\int dW=F \int_0^x dx$	recognized infrule but not yet supported
3	111662: evaluate definite integral number of inputs: 1; feeds: 0; outputs: 1 Evaluate definite integral Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	5542528160 $\int dW=F \int_0^x dx$		3512166162 $W=F x$	Type Tuple cannot be instantiated; use tuple() instead
4	111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	5345738321 $F=m a$ 3512166162 $W=F x$		8953094349 $W=m a x$	valid
5	111236: change three variables in expression number of inputs: 1; feeds: 6; outputs: 1 Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\\ref{eq:#7}; yields Eq.~\\ref{eq:#8}.	5611024898 $d=\frac{1}{2 a} (v^2 - v_0^2)$	9623791270 $d$ 6701855578 $v_2$ 3183197515 $v_1$ 3652511721 $v$ 5398681502 $v$ 8111389082 $x$	3253234559 $x=\frac{v_2^2 - v_1^2}{2 a}$	list index out of range
6	111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3253234559 $x=\frac{v_2^2 - v_1^2}{2 a}$ 8953094349 $W=m a x$		9413699705 $W=m a \frac{v_2^2 - v_1^2}{2 a}$	valid
7	111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	9413699705 $W=m a \frac{v_2^2 - v_1^2}{2 a}$		4811121942 $W=\frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2$	valid
8	111732: substitute LHS of two expressions into expression number of inputs: 3; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} and LHS of Eq.~\\ref{eq:#2} into Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	7676652285 $KE_2=\frac{1}{2} m v_2^2$ 4811121942 $W=\frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2$ 4928007622 $KE_1=\frac{1}{2} m v_1^2$		3360172339 $W=KE_2 - KE_1$	recognized infrule but not yet supported
9	111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	3360172339 $W=KE_2 - KE_1$			no validation is available for declarations

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timing of Neo4j queries:

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step	inference rule	input	feed	output	step validity (as per SymPy)
1	111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			1590774089 \(dW=F dx\)	no validation is available for declarations
2	111408: integrate number of inputs: 1; feeds: 0; outputs: 1 Integrate Eq.~ref{eq:#1}; yields Eq.~ref{eq:#2}.	1590774089 \(dW=F dx\)		5542528160 \(\int dW=F \int_0^x dx\)	recognized infrule but not yet supported
3	111662: evaluate definite integral number of inputs: 1; feeds: 0; outputs: 1 Evaluate definite integral Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	5542528160 \(\int dW=F \int_0^x dx\)		3512166162 \(W=F x\)	Type Tuple cannot be instantiated; use tuple() instead
4	111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	5345738321 \(F=m a\) 3512166162 \(W=F x\)		8953094349 \(W=m a x\)	valid
5	111236: change three variables in expression number of inputs: 1; feeds: 6; outputs: 1 Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\\ref{eq:#7}; yields Eq.~\\ref{eq:#8}.	5611024898 \(d=\frac{1}{2 a} (v^2 - v_0^2)\)	9623791270 \(d\) 6701855578 \(v_2\) 3183197515 \(v_1\) 3652511721 \(v\) 5398681502 \(v\) 8111389082 \(x\)	3253234559 \(x=\frac{v_2^2 - v_1^2}{2 a}\)	list index out of range
6	111556: substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3253234559 \(x=\frac{v_2^2 - v_1^2}{2 a}\) 8953094349 \(W=m a x\)		9413699705 \(W=m a \frac{v_2^2 - v_1^2}{2 a}\)	valid
7	111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	9413699705 \(W=m a \frac{v_2^2 - v_1^2}{2 a}\)		4811121942 \(W=\frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2\)	valid
8	111732: substitute LHS of two expressions into expression number of inputs: 3; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} and LHS of Eq.~\\ref{eq:#2} into Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	7676652285 \(KE_2=\frac{1}{2} m v_2^2\) 4811121942 \(W=\frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2\) 4928007622 \(KE_1=\frac{1}{2} m v_1^2\)		3360172339 \(W=KE_2 - KE_1\)	recognized infrule but not yet supported
9	111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	3360172339 \(W=KE_2 - KE_1\)			no validation is available for declarations