%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM131+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:11:37 PM UTC 2026
% Result : Theorem 6.82s 1.38s
% Output : CNFRefutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 26 unt; 0 def)
% Number of atoms : 246 ( 132 equ)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 264 ( 83 ~; 109 |; 54 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-3 aty)
% Number of variables : 247 ( 29 sgn 149 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof('T-subst-abs-2',conjecture,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& ~ visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2') ).
fof('DIFF-abs-app',axiom,
! [X1,X3,X4,X6,X7] : vabs(X1,X3,X4) != vapp(X6,X7),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-abs-app') ).
fof('DIFF-var-abs',axiom,
! [X1,X2,X3,X4] : vvar(X1) != vabs(X2,X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-abs') ).
fof('T-inv',axiom,
! [X11,X15,X20] :
( vtcheck(X20,X11,X15)
=> ( ? [X12,X13,X10] :
( vtcheck(X20,X13,X10)
& vtcheck(X20,X12,varrow(X10,X15))
& X11 = vapp(X12,X13) )
| ? [X9,X13,X33,X34] :
( vtcheck(vbind(X9,X33,X20),X13,X34)
& X15 = varrow(X33,X34)
& X11 = vabs(X9,X33,X13) )
| ? [X9] :
( vlookup(X9,X20) = vsomeType(X15)
& X11 = vvar(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-inv') ).
fof('EQ-abs',axiom,
! [X1,X3,X4,X2,X5,X6] :
( ( ( X4 = X6
& X3 = X5
& X1 = X2 )
=> vabs(X1,X3,X4) = vabs(X2,X5,X6) )
& ( vabs(X1,X3,X4) = vabs(X2,X5,X6)
=> ( X4 = X6
& X3 = X5
& X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-abs') ).
fof('T-Weak-FreeVar',axiom,
! [X9,X10,X20,X11,X15] :
( ( vtcheck(X20,X11,X15)
& ~ visFreeVar(X9,X11) )
=> vtcheck(vbind(X9,X10,X20),X11,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar') ).
fof(subst5,axiom,
! [X1,X4,X6,X19,X21,X15,X9,X11,X12] :
( ( X6 = vabs(X21,X15,X12)
& X4 = X11
& X1 = X9 )
=> ( ( ~ visFreeVar(X21,X11)
& X9 != X21 )
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vabs(X21,X15,vsubst(X9,X11,X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst5) ).
fof('T-Context-Swap',axiom,
! [X21,X22,X9,X23,X20,X11,X15] :
( ( vtcheck(vbind(X9,X23,vbind(X21,X22,X20)),X11,X15)
& X9 != X21 )
=> vtcheck(vbind(X21,X22,vbind(X9,X23,X20)),X11,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-Context-Swap') ).
fof('T-subst-IH-abs',axiom,
! [X15,X20,X9,X11,X34] :
( ( vtcheck(vbind(X9,X15,X20),veabs,X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,veabs),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-IH-abs') ).
fof('T-abs',axiom,
! [X20,X9,X11,X10,X15] :
( vtcheck(vbind(X9,X10,X20),X11,X15)
=> vtcheck(X20,vabs(X9,X10,X11),varrow(X10,X15)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-abs') ).
fof(c_0_10,negated_conjecture,
~ ! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& ~ visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(assume_negation,[status(cth)],['T-subst-abs-2']) ).
fof(c_0_11,negated_conjecture,
~ ! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34)
& vtcheck(X20,X11,X15)
& ~ visFreeVar(X21,X11)
& X9 != X21 )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_12,plain,
! [X1,X3,X4,X6,X7] : vabs(X1,X3,X4) != vapp(X6,X7),
inference(fof_simplification,[status(thm)],['DIFF-abs-app']) ).
fof(c_0_13,plain,
! [X1,X2,X3,X4] : vvar(X1) != vabs(X2,X3,X4),
inference(fof_simplification,[status(thm)],['DIFF-var-abs']) ).
fof(c_0_14,plain,
! [X285,X286,X287] :
( ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| vlookup(esk24_3(X285,X286,X287),X287) = vsomeType(X286)
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| vtcheck(vbind(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),X287),esk26_3(X285,X286,X287),esk28_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X286 = varrow(esk27_3(X285,X286,X287),esk28_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| vtcheck(X287,esk30_3(X285,X286,X287),esk31_3(X285,X286,X287)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| vtcheck(X287,esk29_3(X285,X286,X287),varrow(esk31_3(X285,X286,X287),X286)) )
& ( ~ vtcheck(X287,X285,X286)
| X285 = vvar(esk24_3(X285,X286,X287))
| X285 = vabs(esk25_3(X285,X286,X287),esk27_3(X285,X286,X287),esk26_3(X285,X286,X287))
| X285 = vapp(esk29_3(X285,X286,X287),esk30_3(X285,X286,X287)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-inv'])])])])]) ).
fof(c_0_15,negated_conjecture,
( ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0)
& vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0)
& vtcheck(esk33_0,esk35_0,esk32_0)
& ~ visFreeVar(esk36_0,esk35_0)
& esk34_0 != esk36_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_16,plain,
! [X54,X55,X56,X57,X58] : vabs(X54,X55,X56) != vapp(X57,X58),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
fof(c_0_17,plain,
! [X47,X48,X49,X50] : vvar(X47) != vabs(X48,X49,X50),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])]) ).
fof(c_0_18,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( vabs(X37,X38,X39) = vabs(X40,X41,X42)
| X39 != X42
| X38 != X41
| X37 != X40 )
& ( vabs(X37,X38,X39) != vabs(X40,X41,X42)
| X39 = X42 )
& ( vabs(X37,X38,X39) != vabs(X40,X41,X42)
| X38 = X41 )
& ( vabs(X37,X38,X39) != vabs(X40,X41,X42)
| X37 = X40 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['EQ-abs'])])])]) ).
cnf(c_0_19,plain,
( ~ vtcheck(X3,X1,X2)
| X1 = vvar(esk24_3(X1,X2,X3))
| X1 = vabs(esk25_3(X1,X2,X3),esk27_3(X1,X2,X3),esk26_3(X1,X2,X3))
| X1 = vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
vabs(X1,X2,X3) != vapp(X4,X5),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
vvar(X1) != vabs(X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( vabs(X1,X3,X4) != vabs(X2,X5,X6)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
vabs(esk25_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)),esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)),esk26_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))) = vabs(esk36_0,esk37_0,veabs),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( vabs(esk36_0,esk37_0,veabs) != vabs(X1,X2,X3)
| esk25_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
esk25_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = esk36_0,
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_27,plain,
( vabs(X3,X4,X1) != vabs(X5,X6,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
vabs(esk36_0,esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)),esk26_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))) = vabs(esk36_0,esk37_0,veabs),
inference(rw,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( vabs(esk36_0,esk37_0,veabs) != vabs(X2,X3,X1)
| esk26_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
esk26_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = veabs,
inference(er,[status(thm)],[c_0_29]) ).
fof(c_0_31,plain,
! [X9,X10,X20,X11,X15] :
( ( vtcheck(X20,X11,X15)
& ~ visFreeVar(X9,X11) )
=> vtcheck(vbind(X9,X10,X20),X11,X15) ),
inference(fof_simplification,[status(thm)],['T-Weak-FreeVar']) ).
cnf(c_0_32,plain,
( vabs(X3,X1,X4) != vabs(X5,X2,X6)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
vabs(esk36_0,esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)),veabs) = vabs(esk36_0,esk37_0,veabs),
inference(rw,[status(thm)],[c_0_28,c_0_30]) ).
fof(c_0_34,plain,
! [X1,X4,X6,X19,X21,X15,X9,X11,X12] :
( ( X6 = vabs(X21,X15,X12)
& X4 = X11
& X1 = X9 )
=> ( ( ~ visFreeVar(X21,X11)
& X9 != X21 )
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vabs(X21,X15,vsubst(X9,X11,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[subst5]) ).
fof(c_0_35,plain,
! [X306,X307,X308,X309,X310] :
( vtcheck(vbind(X306,X307,X308),X309,X310)
| ~ vtcheck(X308,X309,X310)
| visFreeVar(X306,X309) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
fof(c_0_36,plain,
! [X21,X22,X9,X23,X20,X11,X15] :
( ( vtcheck(vbind(X9,X23,vbind(X21,X22,X20)),X11,X15)
& X9 != X21 )
=> vtcheck(vbind(X21,X22,vbind(X9,X23,X20)),X11,X15) ),
inference(fof_simplification,[status(thm)],['T-Context-Swap']) ).
cnf(c_0_37,negated_conjecture,
( vabs(esk36_0,esk37_0,veabs) != vabs(X2,X1,X3)
| esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = X1 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_38,plain,
! [X188,X189,X190,X191,X192,X193,X194,X195,X196] :
( X191 = vabs(X192,X193,vsubst(X194,X195,X196))
| X191 != vsubst(X188,X189,X190)
| visFreeVar(X192,X195)
| X194 = X192
| X190 != vabs(X192,X193,X196)
| X189 != X195
| X188 != X194 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_39,plain,
! [X311,X312,X313,X314,X315] :
( vtcheck(X312,vsubst(X313,X314,veabs),X315)
| ~ vtcheck(vbind(X313,X311,X312),veabs,X315)
| ~ vtcheck(X312,X314,X311) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-subst-IH-abs'])])]) ).
cnf(c_0_40,plain,
( ~ vtcheck(X3,X2,X4)
| vtcheck(vbind(X1,X5,X3),X2,X4)
| visFreeVar(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
vtcheck(esk33_0,esk35_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_42,plain,
! [X138,X139,X140,X141,X142,X143,X144] :
( vtcheck(vbind(X138,X139,vbind(X140,X141,X142)),X143,X144)
| ~ vtcheck(vbind(X140,X141,vbind(X138,X139,X142)),X143,X144)
| X140 = X138 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_43,plain,
( ~ vtcheck(X3,X1,X2)
| X1 = vvar(esk24_3(X1,X2,X3))
| vtcheck(vbind(esk25_3(X1,X2,X3),esk27_3(X1,X2,X3),X3),esk26_3(X1,X2,X3),esk28_3(X1,X2,X3))
| X1 = vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_44,negated_conjecture,
esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)) = esk37_0,
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( X9 != vsubst(X1,X3,X5)
| X5 != vabs(X6,X7,X8)
| X3 != X4
| X1 != X2
| X9 = vabs(X6,X7,vsubst(X2,X4,X8))
| visFreeVar(X6,X4)
| X2 = X6 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( ~ vtcheck(vbind(X4,X3,X1),veabs,X5)
| ~ vtcheck(X1,X2,X3)
| vtcheck(X1,vsubst(X4,X2,veabs),X5) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( visFreeVar(X1,esk35_0)
| vtcheck(vbind(X1,X2,esk33_0),esk35_0,esk32_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( ~ vtcheck(vbind(X1,X3,vbind(X2,X4,X5)),X6,X7)
| vtcheck(vbind(X2,X4,vbind(X1,X3,X5)),X6,X7)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
vtcheck(vbind(esk36_0,esk37_0,vbind(esk34_0,esk32_0,esk33_0)),veabs,esk28_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_20]),c_0_26]),c_0_44]),c_0_30]),c_0_21]),c_0_22]) ).
cnf(c_0_50,negated_conjecture,
esk34_0 != esk36_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,plain,
( ~ vtcheck(X3,X1,X2)
| X1 = vvar(esk24_3(X1,X2,X3))
| X2 = varrow(esk27_3(X1,X2,X3),esk28_3(X1,X2,X3))
| X1 = vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
~ visFreeVar(esk36_0,esk35_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_53,plain,
( visFreeVar(X3,X2)
| X1 = X3
| vsubst(X1,X2,vabs(X3,X4,X5)) = vabs(X3,X4,vsubst(X1,X2,X5)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_45])])])]) ).
fof(c_0_54,plain,
! [X275,X276,X277,X278,X279] :
( vtcheck(X275,vabs(X276,X278,X277),varrow(X278,X279))
| ~ vtcheck(vbind(X276,X278,X275),X277,X279) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-abs'])])]) ).
cnf(c_0_55,negated_conjecture,
( ~ vtcheck(vbind(X3,esk32_0,vbind(X1,X2,esk33_0)),veabs,X4)
| visFreeVar(X1,esk35_0)
| vtcheck(vbind(X1,X2,esk33_0),vsubst(X3,esk35_0,veabs),X4) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,vbind(esk36_0,esk37_0,esk33_0)),veabs,esk28_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,negated_conjecture,
varrow(esk27_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0)),esk28_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))) = esk38_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_58,negated_conjecture,
~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_59,negated_conjecture,
( X1 = esk36_0
| vsubst(X1,esk35_0,vabs(esk36_0,X2,X3)) = vabs(esk36_0,X2,vsubst(X1,esk35_0,X3)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
( ~ vtcheck(vbind(X1,X2,X3),X4,X5)
| vtcheck(X3,vabs(X1,X2,X4),varrow(X2,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
vtcheck(vbind(esk36_0,esk37_0,esk33_0),vsubst(esk34_0,esk35_0,veabs),esk28_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52]) ).
cnf(c_0_62,negated_conjecture,
varrow(esk37_0,esk28_3(vabs(esk36_0,esk37_0,veabs),esk38_0,vbind(esk34_0,esk32_0,esk33_0))) = esk38_0,
inference(rw,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_63,negated_conjecture,
~ vtcheck(esk33_0,vabs(esk36_0,esk37_0,vsubst(esk34_0,esk35_0,veabs)),esk38_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_50]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM131+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:12:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.82/1.38 % Version: 3.5.1
% 6.82/1.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.82/1.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.82/1.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.82/1.38 % Starting new_bool_3 with 300s (1) cores
% 6.82/1.38 % Starting new_bool_1 with 300s (1) cores
% 6.82/1.38 % Starting sh5l with 300s (1) cores
% 6.82/1.38 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2529285 completed with status 0
% 6.82/1.38 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.82/1.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.82/1.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.82/1.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.82/1.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.82/1.38 % No SInE strategy applied
% 6.82/1.38 % Search class: FGHSF-FSLF32-MFFFFFNN
% 6.82/1.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.82/1.38 % Starting SubtermCWHack with 136s (1) cores
% 6.82/1.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.82/1.38 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 6.82/1.38 % Starting new_bool_3 with 136s (1) cores
% 6.82/1.38 % Starting new_bool_1 with 136s (1) cores
% 6.82/1.38 % new_bool_3 with pid 2529295 completed with status 0
% 6.82/1.38 % Result found by new_bool_3
% 6.82/1.38 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.82/1.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.82/1.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.82/1.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.82/1.38 % No SInE strategy applied
% 6.82/1.38 % Search class: FGHSF-FSLF32-MFFFFFNN
% 6.82/1.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.82/1.38 % Starting SubtermCWHack with 136s (1) cores
% 6.82/1.38 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.82/1.38 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 6.82/1.38 % Starting new_bool_3 with 136s (1) cores
% 6.82/1.38 % Preprocessing time : 0.008 s
% 6.82/1.38 % Presaturation interreduction done
% 6.82/1.38
% 6.82/1.38 % Proof found!
% 6.82/1.38 % SZS status Theorem
% 6.82/1.38 % SZS output start CNFRefutation
% See solution above
% 6.82/1.38 % Parsed axioms : 60
% 6.82/1.38 % Removed by relevancy pruning/SinE : 0
% 6.82/1.38 % Initial clauses : 428
% 6.82/1.38 % Removed in clause preprocessing : 13
% 6.82/1.38 % Initial clauses in saturation : 415
% 6.82/1.38 % Processed clauses : 2466
% 6.82/1.38 % ...of these trivial : 17
% 6.82/1.38 % ...subsumed : 948
% 6.82/1.38 % ...remaining for further processing : 1501
% 6.82/1.38 % Other redundant clauses eliminated : 1172
% 6.82/1.38 % Clauses deleted for lack of memory : 0
% 6.82/1.38 % Backward-subsumed : 23
% 6.82/1.38 % Backward-rewritten : 35
% 6.82/1.38 % Generated clauses : 31402
% 6.82/1.38 % ...of the previous two non-redundant : 29633
% 6.82/1.38 % ...aggressively subsumed : 0
% 6.82/1.38 % Contextual simplify-reflections : 6
% 6.82/1.38 % Paramodulations : 30254
% 6.82/1.38 % Factorizations : 4
% 6.82/1.38 % NegExts : 0
% 6.82/1.38 % Equation resolutions : 1196
% 6.82/1.38 % Disequality decompositions : 0
% 6.82/1.38 % Total rewrite steps : 1809
% 6.82/1.38 % ...of those cached : 1358
% 6.82/1.38 % Propositional unsat checks : 0
% 6.82/1.38 % Propositional check models : 0
% 6.82/1.38 % Propositional check unsatisfiable : 0
% 6.82/1.38 % Propositional clauses : 0
% 6.82/1.38 % Propositional clauses after purity: 0
% 6.82/1.38 % Propositional unsat core size : 0
% 6.82/1.38 % Propositional preprocessing time : 0.000
% 6.82/1.38 % Propositional encoding time : 0.000
% 6.82/1.38 % Propositional solver time : 0.000
% 6.82/1.38 % Success case prop preproc time : 0.000
% 6.82/1.38 % Success case prop encoding time : 0.000
% 6.82/1.38 % Success case prop solver time : 0.000
% 6.82/1.38 % Current number of processed clauses : 973
% 6.82/1.38 % Positive orientable unit clauses : 81
% 6.82/1.38 % Positive unorientable unit clauses: 2
% 6.82/1.38 % Negative unit clauses : 42
% 6.82/1.38 % Non-unit-clauses : 848
% 6.82/1.38 % Current number of unprocessed clauses: 25312
% 6.82/1.38 % ...number of literals in the above : 93870
% 6.82/1.38 % Current number of archived formulas : 0
% 6.82/1.38 % Current number of archived clauses : 433
% 6.82/1.38 % Clause-clause subsumption calls (NU) : 126456
% 6.82/1.38 % Rec. Clause-clause subsumption calls : 66986
% 6.82/1.38 % Non-unit clause-clause subsumptions : 546
% 6.82/1.38 % Unit Clause-clause subsumption calls : 1502
% 6.82/1.38 % Rewrite failures with RHS unbound : 40
% 6.82/1.38 % BW rewrite match attempts : 1199
% 6.82/1.38 % BW rewrite match successes : 15
% 6.82/1.38 % Condensation attempts : 0
% 6.82/1.38 % Condensation successes : 0
% 6.82/1.38 % Termbank termtop insertions : 700856
% 6.82/1.38 % Search garbage collected termcells : 4098
% 6.82/1.38
% 6.82/1.38 % -------------------------------------------------
% 6.82/1.38 % User time : 0.799 s
% 6.82/1.38 % System time : 0.033 s
% 6.82/1.38 % Total time : 0.832 s
% 6.82/1.38 % Maximum resident set size: 4780 pages
% 6.82/1.38
% 6.82/1.38 % -------------------------------------------------
% 6.82/1.38 % User time : 4.163 s
% 6.82/1.38 % System time : 0.194 s
% 6.82/1.38 % Total time : 4.358 s
% 6.82/1.38 % Maximum resident set size: 4864 pages
% 6.82/1.38 % E exiting
%------------------------------------------------------------------------------