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Review Schwarzschild radius for non-rotating black hole

abstract:
reference: https://en.wikipedia.org/wiki/Derivation_of_the_Schwarzschild_solution

step	inference rule	input	feed	output	validity (as per SymPy)
2	ID: 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}.	8946383937 $v_{\rm escape}^2=2 G \frac{m}{r}$	2660368546 $r$ 9933742680 $r_{\rm Schwarzschild}$ 8362338572 $v_{\rm escape}$ 1238593037 $c$	4275004561 $c^2=2 G \frac{m}{r_{\rm Schwarzschild}}$	list index out of range
4	ID: 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}.	2883079365 $r_{\rm Schwarzschild} c^2=2 G m$	7263534144 $c^2$	6800170830 $r_{\rm Schwarzschild}=\frac{2 G m}{c^2}$	valid
1	ID: 111483; raise both sides to power number of inputs: 1; feeds: 1; outputs: 1 Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.	5404822208 $v_{\rm escape}=\sqrt{2 G \frac{m}{r}}$	3663007361 $2$	8946383937 $v_{\rm escape}^2=2 G \frac{m}{r}$	recognized infrule but not yet supported
3	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4275004561 $c^2=2 G \frac{m}{r_{\rm Schwarzschild}}$	7194432406 $r_{\rm Schwarzschild}$	2883079365 $r_{\rm Schwarzschild} c^2=2 G m$	valid

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timing of Neo4j queries:

0.011 seconds for pdg_app/to_review_derivation: node_properties, derivation2018336
0.014 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation4733182
0.01 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule6816524
0.011 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT6816524
0.01 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_FEED6816524
0.011 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_OUTPUT6816524
0.005 seconds for compute/get_dict_of_steps_in_derivation: step_has_sequence_index4733182
0.008 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule5915980
0.007 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT5915980
0.006 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_FEED5915980
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0.007 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule1707844
0.005 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT1707844
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0.005 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule2770227
0.012 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT2770227
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0.003 seconds for pdg_app/to_review_derivation: get_list_of_step_dicts_in_this_derivation2018336
0.005 seconds for pdg_app/to_review_derivation: get_list_of_sequence_values_for_derivation_id2018336142831
0.037 seconds for pdg_app/to_review_derivation: get_list_node_dicts_of_type inference_rule2018336
0.004 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule8323456
0.003 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT8323456
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0.003 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule2958288
0.003 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT2958288
0.004 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_FEED2958288
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0.003 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule6791019
0.003 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT6791019
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0.004 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule7598455
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0.004 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_OUTPUT7598455
0.004 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule3695218
0.003 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT3695218
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0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_OUTPUT3695218
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule8192137
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0.003 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule4685454
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT4685454
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_FEED4685454
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_OUTPUT4685454
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_has_inference_rule4788931
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_INPUT4788931
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_FEED4788931
0.002 seconds for compute/get_dict_of_steps_in_derivation: step_id_has_expressions, HAS_OUTPUT4788931

step	inference rule	input	feed	output	validity (as per SymPy)
2	ID: 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}.	8946383937 \(v_{\rm escape}^2=2 G \frac{m}{r}\)	2660368546 \(r\) 9933742680 \(r_{\rm Schwarzschild}\) 8362338572 \(v_{\rm escape}\) 1238593037 \(c\)	4275004561 \(c^2=2 G \frac{m}{r_{\rm Schwarzschild}}\)	list index out of range
4	ID: 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}.	2883079365 \(r_{\rm Schwarzschild} c^2=2 G m\)	7263534144 \(c^2\)	6800170830 \(r_{\rm Schwarzschild}=\frac{2 G m}{c^2}\)	valid
1	ID: 111483; raise both sides to power number of inputs: 1; feeds: 1; outputs: 1 Raise both sides of Eq.~\\ref{eq:#2} to $#1$; yields Eq.~\\ref{eq:#3}.	5404822208 \(v_{\rm escape}=\sqrt{2 G \frac{m}{r}}\)	3663007361 \(2\)	8946383937 \(v_{\rm escape}^2=2 G \frac{m}{r}\)	recognized infrule but not yet supported
3	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4275004561 \(c^2=2 G \frac{m}{r_{\rm Schwarzschild}}\)	7194432406 \(r_{\rm Schwarzschild}\)	2883079365 \(r_{\rm Schwarzschild} c^2=2 G m\)	valid