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In[]:=
RowFormatLemma/@DeleteCasesCasesValuesNormalProofObject
Logic: EquationalLogic
Steps: 508
Theorems:
a.
(a.·a.)·(a.·a.)a.
["ProofDataset"][All,"Statement"],HoldForm[_==_],HoldForm[x_==x_],
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In[]:=
TextTraditionalFormGridWithpg=ProofGraph2ProofObject
Logic: EquationalLogic
Steps: 307
Theorems:
a.
(a.·a.)·(a.·a.)a.
,"Events"->False,{#,VertexOutDegree[pg,#]}&/@TakeLargestBy[VertexList[pg],VertexOutDegree[pg,#]&,6],Frame->All
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a.·b.b.·a.
43
a.((b.·c.)·a.)·(b.·((b.·a.)·b.))
34
a.·b.a.·((a.·b.)·a.)
23
a.·(a.·(a.·b.))a.·b.
10
(a.·b.)·c.c.·(b.·a.)
10
a.(b.·a.)·((c.·b.)·(((c.·b.)·a.)·(c.·b.)))
9
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First/@Withpg=ProofGraph2ProofObject
Logic: EquationalLogic
Steps: 307
Theorems:
a.
(a.·a.)·(a.·a.)a.
,"Events"->False,{#,VertexOutDegree[pg,#]}&/@TakeLargestBy[VertexList[pg],VertexOutDegree[pg,#]&,6]
Out[]=
{a.·b.b.·a.,a.((b.·c.)·a.)·(b.·((b.·a.)·b.)),a.·b.a.·((a.·b.)·a.),a.·(a.·(a.·b.))a.·b.,(a.·b.)·c.c.·(b.·a.),a.(b.·a.)·((c.·b.)·(((c.·b.)·a.)·(c.·b.)))}
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ResourceFunction["UnformalizeSymbols"]/@%268
Out[]=
{a·bb·a,a((b·c)·a)·(b·((b·a)·b)),a·ba·((a·b)·a),a·(a·(a·b))a·b,(a·b)·cc·(b·a),a(b·a)·((c·b)·(((c·b)·a)·(c·b)))}
In[]:=
FEPp·q==q·p,
{a.,b.,c.}
((a.·b.)·c.)·(a.·((a.·c.)·a.))c.
Out[]=
ProofObject
Logic: EquationalLogic
Steps: 104
Theorem: p·qq·p
In[]:=
SelectProofObject
Logic: EquationalLogic
Steps: 104
Theorem: p·qq·p
["ProofDataset"][All,"Statement"],LeafCount[#]<20&
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Axiom
1
a.((b.·c.)·a.)·(b.·((b.·a.)·b.))
Hypothesis
1
p·qq·p
CriticalPairLemma
19
a.(a.·((a.·a.)·a.))·(a.·((a.·a.)·a.))
SubstitutionLemma
15
a.·a.a.·((a.·a.)·a.)
SubstitutionLemma
17
a.·a.a.·((a.·a.)·a.)
SubstitutionLemma
19
(a.·a.)·a.a.·(a.·((a.·a.)·a.))
SubstitutionLemma
20
(a.·a.)·a.a.·(a.·a.)
SubstitutionLemma
21
(a.·a.)·(a.·((a.·a.)·a.))a.
SubstitutionLemma
22
(a.·a.)·(a.·a.)a.
CriticalPairLemma
42
a.((a.·b.)·a.)·(a.·(a.·(a.·a.)))
SubstitutionLemma
23
a.·a.a.·(a.·(a.·a.))
SubstitutionLemma
24
a.((a.·b.)·a.)·(a.·a.)
CriticalPairLemma
43
a.·a.(((a.·a.)·b.)·(a.·a.))·a.
CriticalPairLemma
44
a.(b.·((b.·a.)·b.))·(a.·a.)
CriticalPairLemma
45
a.·a.(b.·((b.·(a.·a.))·b.))·a.
CriticalPairLemma
46
a.·a.a.·(b.·((b.·(a.·a.))·b.))
CriticalPairLemma
47
a.(a.·a.)·(b.·((b.·a.)·b.))
SubstitutionLemma
26
a.·((a.·((a.·b.)·(a.·b.)))·a.)a.·b.
SubstitutionLemma
29
a.((a.·b.)·a.)·(a.·((a.·b.)·a.))
SubstitutionLemma
31
(a.·b.)·a.(a.·((a.·b.)·a.))·a.
rows 120 of 35
In[]:=
NeighborhoodGraphProofGraph2ProofObject
Logic: EquationalLogic
Steps: 104
Theorem: p·qq·p
,a.·a.a.·((a.·a.)·a.),3,VertexLabels->Automatic
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In[]:=
ProofGraph2ProofObject
Logic: EquationalLogic
Steps: 104
Theorem: p·qq·p
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Sizes of Input & Output Lemmas

Unrolling to Axioms

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