%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM134+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 : n013.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 12:11:38 PM UTC 2026
% Result : Theorem 1.30s 0.63s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 21 unt; 0 def)
% Number of atoms : 192 ( 97 equ)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 205 ( 63 ~; 96 |; 36 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 161 ( 14 sgn 94 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof('T-subst-app',conjecture,
! [X15,X20,X9,X11,X34] :
( ( vtcheck(vbind(X9,X15,X20),vapp(ve1,ve2),X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,vapp(ve1,ve2)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-app') ).
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-app',axiom,
! [X1,X4,X6] : vvar(X1) != vapp(X4,X6),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
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-app',axiom,
! [X4,X6,X7,X8] :
( ( ( X6 = X8
& X4 = X7 )
=> vapp(X4,X6) = vapp(X7,X8) )
& ( vapp(X4,X6) = vapp(X7,X8)
=> ( X6 = X8
& X4 = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-app') ).
fof('T-subst-IH-app1',axiom,
! [X15,X20,X9,X11,X34] :
( ( vtcheck(vbind(X9,X15,X20),ve1,X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,ve1),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-IH-app1') ).
fof('T-subst-IH-app2',axiom,
! [X15,X20,X9,X11,X34] :
( ( vtcheck(vbind(X9,X15,X20),ve2,X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,ve2),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-IH-app2') ).
fof('T-app',axiom,
! [X10,X20,X12,X13,X15] :
( ( vtcheck(X20,X13,X10)
& vtcheck(X20,X12,varrow(X10,X15)) )
=> vtcheck(X20,vapp(X12,X13),X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-app') ).
fof(subst2,axiom,
! [X1,X4,X6,X19,X12,X9,X11,X13] :
( ( X6 = vapp(X12,X13)
& X4 = X11
& X1 = X9 )
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vapp(vsubst(X9,X11,X12),vsubst(X9,X11,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst2) ).
fof(c_0_9,negated_conjecture,
~ ! [X15,X20,X9,X11,X34] :
( ( vtcheck(vbind(X9,X15,X20),vapp(ve1,ve2),X34)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,vsubst(X9,X11,vapp(ve1,ve2)),X34) ),
inference(assume_negation,[status(cth)],['T-subst-app']) ).
fof(c_0_10,plain,
! [X1,X3,X4,X6,X7] : vabs(X1,X3,X4) != vapp(X6,X7),
inference(fof_simplification,[status(thm)],['DIFF-abs-app']) ).
fof(c_0_11,plain,
! [X1,X4,X6] : vvar(X1) != vapp(X4,X6),
inference(fof_simplification,[status(thm)],['DIFF-var-app']) ).
fof(c_0_12,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_13,negated_conjecture,
( ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vapp(ve1,ve2)),esk36_0)
& vtcheck(vbind(esk34_0,esk32_0,esk33_0),vapp(ve1,ve2),esk36_0)
& vtcheck(esk33_0,esk35_0,esk32_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,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_10])]) ).
fof(c_0_15,plain,
! [X51,X52,X53] : vvar(X51) != vapp(X52,X53),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
fof(c_0_16,plain,
! [X43,X44,X45,X46] :
( ( vapp(X43,X44) = vapp(X45,X46)
| X44 != X46
| X43 != X45 )
& ( vapp(X43,X44) != vapp(X45,X46)
| X44 = X46 )
& ( vapp(X43,X44) != vapp(X45,X46)
| X43 = X45 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['EQ-app'])])])]) ).
cnf(c_0_17,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_12]) ).
cnf(c_0_18,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),vapp(ve1,ve2),esk36_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
vabs(X1,X2,X3) != vapp(X4,X5),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
vvar(X1) != vapp(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( vapp(X1,X3) != vapp(X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
vapp(esk29_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)),esk30_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0))) = vapp(ve1,ve2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( vapp(ve1,ve2) != vapp(X1,X2)
| esk29_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
esk29_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)) = ve1,
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_25,plain,
( vapp(X3,X1) != vapp(X4,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
vapp(ve1,esk30_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0))) = vapp(ve1,ve2),
inference(rw,[status(thm)],[c_0_22,c_0_24]) ).
fof(c_0_27,plain,
! [X311,X312,X313,X314,X315] :
( vtcheck(X312,vsubst(X313,X314,ve1),X315)
| ~ vtcheck(vbind(X313,X311,X312),ve1,X315)
| ~ vtcheck(X312,X314,X311) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-subst-IH-app1'])])]) ).
cnf(c_0_28,plain,
( ~ vtcheck(X1,X2,X3)
| X2 = vvar(esk24_3(X2,X3,X1))
| X2 = vabs(esk25_3(X2,X3,X1),esk27_3(X2,X3,X1),esk26_3(X2,X3,X1))
| vtcheck(X1,esk29_3(X2,X3,X1),varrow(esk31_3(X2,X3,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
( vapp(ve1,ve2) != vapp(X2,X1)
| esk30_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)) = X1 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ vtcheck(vbind(X4,X3,X1),ve1,X5)
| ~ vtcheck(X1,X2,X3)
| vtcheck(X1,vsubst(X4,X2,ve1),X5) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),ve1,varrow(esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)),esk36_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_19]),c_0_20]),c_0_24]) ).
fof(c_0_32,plain,
! [X316,X317,X318,X319,X320] :
( vtcheck(X317,vsubst(X318,X319,ve2),X320)
| ~ vtcheck(vbind(X318,X316,X317),ve2,X320)
| ~ vtcheck(X317,X319,X316) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-subst-IH-app2'])])]) ).
cnf(c_0_33,plain,
( ~ vtcheck(X1,X2,X3)
| X2 = vvar(esk24_3(X2,X3,X1))
| X2 = vabs(esk25_3(X2,X3,X1),esk27_3(X2,X3,X1),esk26_3(X2,X3,X1))
| vtcheck(X1,esk30_3(X2,X3,X1),esk31_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
esk30_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)) = ve2,
inference(er,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X280,X281,X282,X283,X284] :
( vtcheck(X281,vapp(X282,X283),X284)
| ~ vtcheck(X281,X283,X280)
| ~ vtcheck(X281,X282,varrow(X280,X284)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-app'])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ vtcheck(esk33_0,X1,esk32_0)
| vtcheck(esk33_0,vsubst(esk34_0,X1,ve1),varrow(esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)),esk36_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
vtcheck(esk33_0,esk35_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,plain,
( ~ vtcheck(vbind(X4,X3,X1),ve2,X5)
| ~ vtcheck(X1,X2,X3)
| vtcheck(X1,vsubst(X4,X2,ve2),X5) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),ve2,esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0))),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_19]),c_0_20]),c_0_34]) ).
fof(c_0_40,plain,
! [X161,X162,X163,X164,X165,X166,X167,X168] :
( X164 = vapp(vsubst(X166,X167,X165),vsubst(X166,X167,X168))
| X164 != vsubst(X161,X162,X163)
| X163 != vapp(X165,X168)
| X162 != X167
| X161 != X166 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst2])])]) ).
cnf(c_0_41,plain,
( ~ vtcheck(X1,X5,X3)
| ~ vtcheck(X1,X2,varrow(X3,X4))
| vtcheck(X1,vapp(X2,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
vtcheck(esk33_0,vsubst(esk34_0,esk35_0,ve1),varrow(esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)),esk36_0)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( ~ vtcheck(esk33_0,X1,esk32_0)
| vtcheck(esk33_0,vsubst(esk34_0,X1,ve2),esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( X8 != vsubst(X1,X3,X5)
| X5 != vapp(X6,X7)
| X3 != X4
| X1 != X2
| X8 = vapp(vsubst(X2,X4,X6),vsubst(X2,X4,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( ~ vtcheck(esk33_0,X1,esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0)))
| vtcheck(esk33_0,vapp(vsubst(esk34_0,esk35_0,ve1),X1),esk36_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
vtcheck(esk33_0,vsubst(esk34_0,esk35_0,ve2),esk31_3(vapp(ve1,ve2),esk36_0,vbind(esk34_0,esk32_0,esk33_0))),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_47,plain,
vapp(vsubst(X1,X2,X3),vsubst(X1,X2,X4)) = vsubst(X1,X2,vapp(X3,X4)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_44])])])]) ).
cnf(c_0_48,negated_conjecture,
~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vapp(ve1,ve2)),esk36_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM134+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 14:17:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.30/0.63 % Version: 3.5.1
% 1.30/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.30/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.30/0.63 % Starting sh5l with 300s (1) cores
% 1.30/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 977004 completed with status 0
% 1.30/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.30/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.30/0.63 % No SInE strategy applied
% 1.30/0.63 % Search class: FGHSF-FSLF32-MFFFFFNN
% 1.30/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.30/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.30/0.63 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 1.30/0.63 % Starting new_bool_3 with 136s (1) cores
% 1.30/0.63 % Starting new_bool_1 with 136s (1) cores
% 1.30/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 977017 completed with status 0
% 1.30/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.30/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.30/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.30/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.30/0.63 % No SInE strategy applied
% 1.30/0.63 % Search class: FGHSF-FSLF32-MFFFFFNN
% 1.30/0.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.30/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.30/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.30/0.63 % Preprocessing time : 0.008 s
% 1.30/0.63 % Presaturation interreduction done
% 1.30/0.63
% 1.30/0.63 % Proof found!
% 1.30/0.63 % SZS status Theorem
% 1.30/0.63 % SZS output start CNFRefutation
% See solution above
% 1.30/0.63 % Parsed axioms : 60
% 1.30/0.63 % Removed by relevancy pruning/SinE : 0
% 1.30/0.63 % Initial clauses : 426
% 1.30/0.63 % Removed in clause preprocessing : 13
% 1.30/0.63 % Initial clauses in saturation : 413
% 1.30/0.63 % Processed clauses : 1083
% 1.30/0.63 % ...of these trivial : 39
% 1.30/0.63 % ...subsumed : 77
% 1.30/0.63 % ...remaining for further processing : 967
% 1.30/0.63 % Other redundant clauses eliminated : 307
% 1.30/0.63 % Clauses deleted for lack of memory : 0
% 1.30/0.63 % Backward-subsumed : 0
% 1.30/0.63 % Backward-rewritten : 42
% 1.30/0.63 % Generated clauses : 2725
% 1.30/0.63 % ...of the previous two non-redundant : 2521
% 1.30/0.63 % ...aggressively subsumed : 0
% 1.30/0.63 % Contextual simplify-reflections : 0
% 1.30/0.63 % Paramodulations : 2454
% 1.30/0.63 % Factorizations : 0
% 1.30/0.63 % NegExts : 0
% 1.30/0.63 % Equation resolutions : 323
% 1.30/0.63 % Disequality decompositions : 0
% 1.30/0.63 % Total rewrite steps : 213
% 1.30/0.63 % ...of those cached : 174
% 1.30/0.63 % Propositional unsat checks : 0
% 1.30/0.63 % Propositional check models : 0
% 1.30/0.63 % Propositional check unsatisfiable : 0
% 1.30/0.63 % Propositional clauses : 0
% 1.30/0.63 % Propositional clauses after purity: 0
% 1.30/0.63 % Propositional unsat core size : 0
% 1.30/0.63 % Propositional preprocessing time : 0.000
% 1.30/0.63 % Propositional encoding time : 0.000
% 1.30/0.63 % Propositional solver time : 0.000
% 1.30/0.63 % Success case prop preproc time : 0.000
% 1.30/0.63 % Success case prop encoding time : 0.000
% 1.30/0.63 % Success case prop solver time : 0.000
% 1.30/0.63 % Current number of processed clauses : 458
% 1.30/0.63 % Positive orientable unit clauses : 43
% 1.30/0.63 % Positive unorientable unit clauses: 0
% 1.30/0.63 % Negative unit clauses : 23
% 1.30/0.63 % Non-unit-clauses : 392
% 1.30/0.63 % Current number of unprocessed clauses: 2213
% 1.30/0.63 % ...number of literals in the above : 8223
% 1.30/0.63 % Current number of archived formulas : 0
% 1.30/0.63 % Current number of archived clauses : 415
% 1.30/0.63 % Clause-clause subsumption calls (NU) : 43088
% 1.30/0.63 % Rec. Clause-clause subsumption calls : 9532
% 1.30/0.63 % Non-unit clause-clause subsumptions : 55
% 1.30/0.63 % Unit Clause-clause subsumption calls : 3793
% 1.30/0.63 % Rewrite failures with RHS unbound : 0
% 1.30/0.63 % BW rewrite match attempts : 61
% 1.30/0.63 % BW rewrite match successes : 5
% 1.30/0.63 % Condensation attempts : 0
% 1.30/0.63 % Condensation successes : 0
% 1.30/0.63 % Termbank termtop insertions : 113588
% 1.30/0.63 % Search garbage collected termcells : 4039
% 1.30/0.63
% 1.30/0.63 % -------------------------------------------------
% 1.30/0.63 % User time : 0.159 s
% 1.30/0.63 % System time : 0.015 s
% 1.30/0.63 % Total time : 0.174 s
% 1.30/0.63 % Maximum resident set size: 4512 pages
% 1.30/0.63
% 1.30/0.63 % -------------------------------------------------
% 1.30/0.63 % User time : 0.818 s
% 1.30/0.63 % System time : 0.054 s
% 1.30/0.63 % Total time : 0.872 s
% 1.30/0.63 % Maximum resident set size: 4608 pages
% 1.30/0.63 % E exiting
%------------------------------------------------------------------------------