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Review total electrical resistance for circuit with two resistors in parallel

abstract:
reference: http://www.dfcd.net/articles/derivations/resistors.html

step	inference rule	input	feed	output	step validity (as per SymPy)
1	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 $V=I R$	1323602089 $I_1$ 7191277455 $R$ 2867848403 $I$ 5258419993 $R_1$	4128500715 $V=I_1 R_1$	list index out of range
2	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 $V=I R$	5585739998 $I$ 5463275819 $I_2$ 9746066299 $R_2$ 1377431959 $R$	9243879541 $V=I_2 R_2$	list index out of range
3	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	9243879541 $V=I_2 R_2$	3031116098 $R_2$	7002609475 $\frac{V}{R_2}=I_2$	valid
4	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4128500715 $V=I_1 R_1$	5181421075 $R_1$	2051901211 $\frac{V}{R_1}=I_1$	valid
5	111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			6753224061 $I_{\rm total}=I_1 + I_2$	no validation is available for declarations
6	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 $V=I R$	7410124465 $R_{\rm total}$ 7798615279 $I_{\rm total}$ 1100332145 $R$ 9053099840 $I$	2271186630 $V=I_{\rm total} R_{\rm total}$	list index out of range
7	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2271186630 $V=I_{\rm total} R_{\rm total}$	6546594355 $R_{\rm total}$	2809345867 $\frac{V}{R_{\rm total}}=I_{\rm total}$	valid
8	111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} and LHS of Eq.~\\ref{eq:#2} and LHS of Eq.~\\ref{eq:#3} into Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}.	7002609475 $\frac{V}{R_2}=I_2$ 6753224061 $I_{\rm total}=I_1 + I_2$ 2051901211 $\frac{V}{R_1}=I_1$ 2809345867 $\frac{V}{R_{\rm total}}=I_{\rm total}$		4866160902 $\frac{V}{R_{\rm total}}=\frac{V}{R_1} + \frac{V}{R_2}$	recognized infrule but not yet supported
9	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4866160902 $\frac{V}{R_{\rm total}}=\frac{V}{R_1} + \frac{V}{R_2}$	3433441359 $V$	1457415749 $\frac{1}{R_{\rm total}}=\frac{1}{R_1} + \frac{1}{R_2}$	valid
10	111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	1457415749 $\frac{1}{R_{\rm total}}=\frac{1}{R_1} + \frac{1}{R_2}$			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	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 \(V=I R\)	1323602089 \(I_1\) 7191277455 \(R\) 2867848403 \(I\) 5258419993 \(R_1\)	4128500715 \(V=I_1 R_1\)	list index out of range
2	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 \(V=I R\)	5585739998 \(I\) 5463275819 \(I_2\) 9746066299 \(R_2\) 1377431959 \(R\)	9243879541 \(V=I_2 R_2\)	list index out of range
3	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	9243879541 \(V=I_2 R_2\)	3031116098 \(R_2\)	7002609475 \(\frac{V}{R_2}=I_2\)	valid
4	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4128500715 \(V=I_1 R_1\)	5181421075 \(R_1\)	2051901211 \(\frac{V}{R_1}=I_1\)	valid
5	111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			6753224061 \(I_{\rm total}=I_1 + I_2\)	no validation is available for declarations
6	111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\\ref{eq:#5}; yields Eq.~\\ref{eq:#6}.	4087145886 \(V=I R\)	7410124465 \(R_{\rm total}\) 7798615279 \(I_{\rm total}\) 1100332145 \(R\) 9053099840 \(I\)	2271186630 \(V=I_{\rm total} R_{\rm total}\)	list index out of range
7	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2271186630 \(V=I_{\rm total} R_{\rm total}\)	6546594355 \(R_{\rm total}\)	2809345867 \(\frac{V}{R_{\rm total}}=I_{\rm total}\)	valid
8	111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} and LHS of Eq.~\\ref{eq:#2} and LHS of Eq.~\\ref{eq:#3} into Eq.~\\ref{eq:#4}; yields Eq.~\\ref{eq:#5}.	7002609475 \(\frac{V}{R_2}=I_2\) 6753224061 \(I_{\rm total}=I_1 + I_2\) 2051901211 \(\frac{V}{R_1}=I_1\) 2809345867 \(\frac{V}{R_{\rm total}}=I_{\rm total}\)		4866160902 \(\frac{V}{R_{\rm total}}=\frac{V}{R_1} + \frac{V}{R_2}\)	recognized infrule but not yet supported
9	111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4866160902 \(\frac{V}{R_{\rm total}}=\frac{V}{R_1} + \frac{V}{R_2}\)	3433441359 \(V\)	1457415749 \(\frac{1}{R_{\rm total}}=\frac{1}{R_1} + \frac{1}{R_2}\)	valid
10	111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	1457415749 \(\frac{1}{R_{\rm total}}=\frac{1}{R_1} + \frac{1}{R_2}\)			no validation is available for declarations