%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM124+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 : n004.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 12:11:36 PM UTC 2026
% Result : Theorem 16.66s 2.65s
% Output : CNFRefutation 16.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 17 unt; 0 def)
% Number of atoms : 237 ( 99 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 270 ( 105 ~; 98 |; 37 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 269 ( 23 sgn 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('alpha-equiv-subst-abs',axiom,
! [X10,X9,X21,X11] :
( ~ visFreeVar(X21,X11)
=> valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-subst-abs') ).
fof('T-Weak-FreeVar-abs-2',conjecture,
! [X9,X10,X20,X21,X36,X15] :
( ( vtcheck(X20,vabs(X21,X36,veabs),X15)
& ~ visFreeVar(X9,vabs(X21,X36,veabs))
& X9 = X21 )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-2') ).
fof('alpha-equiv-typing',axiom,
! [X11,X20,X12,X15] :
( ( valphaEquivalent(X11,X12)
& vtcheck(X20,X11,X15) )
=> vtcheck(X20,X12,X15) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-typing') ).
fof('alpha-equiv-sym',axiom,
! [X13,X12] :
( valphaEquivalent(X12,X13)
=> valphaEquivalent(X13,X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-sym') ).
fof('T-Weak-FreeVar-abs-1-gen',axiom,
! [X9,X10,X20,X21,X36,X12,X15] :
( ( vtcheck(X20,vabs(X21,X36,X12),X15)
& ~ visFreeVar(X9,vabs(X21,X36,X12))
& X9 != X21 )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,X12),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1-gen') ).
fof('alpha-equiv-FreeVar',axiom,
! [X11,X9,X12] :
( ( valphaEquivalent(X11,X12)
& ~ visFreeVar(X9,X11) )
=> ~ visFreeVar(X9,X12) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+1.ax','alpha-equiv-FreeVar') ).
fof(isFreeVar1,axiom,
! [X15,X1,X4,X9,X14,X11] :
( ( X4 = vabs(X9,X15,X11)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X11)
& X9 != X14 ) )
& ( ( visFreeVar(X14,X11)
& X9 != X14 )
=> visFreeVar(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).
fof(isFreeVar2,axiom,
! [X1,X4,X12,X14,X13] :
( ( X4 = vapp(X12,X13)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X13)
| visFreeVar(X14,X12) ) )
& ( ( visFreeVar(X14,X13)
| visFreeVar(X14,X12) )
=> visFreeVar(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).
fof(isFreeVar0,axiom,
! [X1,X4,X9,X14] :
( ( X4 = vvar(X9)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> X9 = X14 )
& ( X9 = X14
=> visFreeVar(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).
fof('gensym-is-fresh',axiom,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','gensym-is-fresh') ).
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(subst0,axiom,
! [X9,X21,X1,X4,X6,X19,X11] :
( ( X6 = vvar(X21)
& X4 = X11
& X1 = X9 )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst0) ).
fof(c_0_12,plain,
! [X10,X9,X21,X11] :
( ~ visFreeVar(X21,X11)
=> valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
inference(fof_simplification,[status(thm)],['alpha-equiv-subst-abs']) ).
fof(c_0_13,negated_conjecture,
~ ! [X9,X10,X20,X21,X36,X15] :
( ( vtcheck(X20,vabs(X21,X36,veabs),X15)
& ~ visFreeVar(X9,vabs(X21,X36,veabs))
& X9 = X21 )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
inference(assume_negation,[status(cth)],['T-Weak-FreeVar-abs-2']) ).
fof(c_0_14,plain,
! [X308,X309,X310,X311] :
( vtcheck(X309,X310,X311)
| ~ valphaEquivalent(X308,X310)
| ~ vtcheck(X309,X308,X311) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-typing'])])]) ).
fof(c_0_15,plain,
! [X304,X305,X306,X307] :
( valphaEquivalent(vabs(X305,X304,X307),vabs(X306,X304,vsubst(X305,vvar(X306),X307)))
| visFreeVar(X306,X307) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X9,X10,X20,X21,X36,X15] :
( ( vtcheck(X20,vabs(X21,X36,veabs),X15)
& ~ visFreeVar(X9,vabs(X21,X36,veabs))
& X9 = X21 )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X299,X300] :
( valphaEquivalent(X299,X300)
| ~ valphaEquivalent(X300,X299) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-sym'])])]) ).
fof(c_0_18,plain,
! [X9,X10,X20,X21,X36,X12,X15] :
( ( vtcheck(X20,vabs(X21,X36,X12),X15)
& ~ visFreeVar(X9,vabs(X21,X36,X12))
& X9 != X21 )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,X12),X15) ),
inference(fof_simplification,[status(thm)],['T-Weak-FreeVar-abs-1-gen']) ).
cnf(c_0_19,plain,
( ~ valphaEquivalent(X2,X4)
| ~ vtcheck(X1,X2,X3)
| vtcheck(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( valphaEquivalent(vabs(X3,X4,X2),vabs(X1,X4,vsubst(X3,vvar(X1),X2)))
| visFreeVar(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,negated_conjecture,
( ~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0)
& vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0)
& ~ visFreeVar(esk32_0,vabs(esk35_0,esk36_0,veabs))
& esk32_0 = esk35_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_22,plain,
( ~ valphaEquivalent(X1,X2)
| valphaEquivalent(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X325,X326,X327,X328,X329,X330,X331] :
( vtcheck(vbind(X325,X326,X327),vabs(X328,X329,X330),X331)
| ~ vtcheck(X327,vabs(X328,X329,X330),X331)
| visFreeVar(X325,vabs(X328,X329,X330))
| X325 = X328 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_24,plain,
( ~ vtcheck(X1,vabs(X4,X3,X5),X6)
| visFreeVar(X2,X5)
| vtcheck(X1,vabs(X2,X3,vsubst(X4,vvar(X2),X5)),X6) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X11,X9,X12] :
( ( valphaEquivalent(X11,X12)
& ~ visFreeVar(X9,X11) )
=> ~ visFreeVar(X9,X12) ),
inference(fof_simplification,[status(thm)],['alpha-equiv-FreeVar']) ).
cnf(c_0_27,plain,
( visFreeVar(X1,X4)
| valphaEquivalent(vabs(X1,X2,vsubst(X3,vvar(X1),X4)),vabs(X3,X2,X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,plain,
( ~ vtcheck(X5,vabs(X2,X3,X4),X6)
| vtcheck(vbind(X1,X7,X5),vabs(X2,X3,X4),X6)
| visFreeVar(X1,vabs(X2,X3,X4))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( visFreeVar(X1,veabs)
| vtcheck(esk34_0,vabs(X1,esk36_0,vsubst(esk35_0,vvar(X1),veabs)),esk37_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X15,X1,X4,X9,X14,X11] :
( ( X4 = vabs(X9,X15,X11)
& X1 = X14 )
=> ( ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X11)
& X9 != X14 ) )
& ( ( visFreeVar(X14,X11)
& X9 != X14 )
=> visFreeVar(X1,X4) ) ) ),
inference(fof_simplification,[status(thm)],[isFreeVar1]) ).
fof(c_0_31,plain,
! [X312,X313,X314] :
( ~ visFreeVar(X313,X314)
| ~ valphaEquivalent(X312,X314)
| visFreeVar(X313,X312) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_32,negated_conjecture,
~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,negated_conjecture,
esk32_0 = esk35_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
( ~ vtcheck(X1,vabs(X6,X3,vsubst(X2,vvar(X6),X4)),X5)
| visFreeVar(X6,X4)
| vtcheck(X1,vabs(X2,X3,X4),X5) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( visFreeVar(X2,veabs)
| visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)))
| vtcheck(vbind(X1,X3,esk34_0),vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)),esk37_0)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_36,plain,
! [X74,X75,X76,X77,X78,X79] :
( ( X76 != vabs(X77,X74,X79)
| X75 != X78
| ~ visFreeVar(X75,X76)
| visFreeVar(X78,X79) )
& ( X76 != vabs(X77,X74,X79)
| X75 != X78
| ~ visFreeVar(X75,X76)
| X77 != X78 )
& ( X76 != vabs(X77,X74,X79)
| X75 != X78
| visFreeVar(X75,X76)
| ~ visFreeVar(X78,X79)
| X77 = X78 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
fof(c_0_37,plain,
! [X80,X81,X82,X83,X84] :
( ( X81 != vapp(X82,X84)
| X80 != X83
| visFreeVar(X83,X84)
| visFreeVar(X83,X82)
| ~ visFreeVar(X80,X81) )
& ( X81 != vapp(X82,X84)
| X80 != X83
| visFreeVar(X80,X81)
| ~ visFreeVar(X83,X84) )
& ( X81 != vapp(X82,X84)
| X80 != X83
| visFreeVar(X80,X81)
| ~ visFreeVar(X83,X82) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar2])])])]) ).
fof(c_0_38,plain,
! [X70,X71,X72,X73] :
( ( X71 != vvar(X72)
| X70 != X73
| X72 = X73
| ~ visFreeVar(X70,X71) )
& ( X71 != vvar(X72)
| X70 != X73
| visFreeVar(X70,X71)
| X72 != X73 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar0])])])]) ).
fof(c_0_39,plain,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
inference(fof_simplification,[status(thm)],['gensym-is-fresh']) ).
cnf(c_0_40,plain,
( ~ visFreeVar(X1,X3)
| ~ valphaEquivalent(X2,X3)
| visFreeVar(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
~ vtcheck(vbind(esk35_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( visFreeVar(X2,veabs)
| visFreeVar(X1,vabs(X2,esk36_0,vsubst(esk35_0,vvar(X2),veabs)))
| vtcheck(vbind(X1,X3,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( X4 != vabs(X1,X5,X6)
| X3 != X2
| ~ visFreeVar(X3,X4)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( X4 != vapp(X2,X5)
| X3 != X1
| ~ visFreeVar(X1,X2)
| visFreeVar(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( X4 != vvar(X1)
| X3 != X2
| X1 != X2
| visFreeVar(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_46,plain,
! [X147,X148] :
( ~ visFreeVar(X147,X148)
| vgensym(X148) != X147 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
cnf(c_0_47,plain,
( ~ visFreeVar(X1,vabs(X5,X3,vsubst(X2,vvar(X5),X4)))
| visFreeVar(X5,X4)
| visFreeVar(X1,vabs(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_48,negated_conjecture,
( visFreeVar(X1,veabs)
| visFreeVar(esk35_0,vabs(X1,esk36_0,vsubst(esk35_0,vvar(X1),veabs)))
| esk35_0 = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
~ visFreeVar(X1,vabs(X1,X2,X3)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_43])])]) ).
cnf(c_0_50,plain,
( X4 != vapp(X5,X2)
| X3 != X1
| ~ visFreeVar(X1,X2)
| visFreeVar(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
( ~ visFreeVar(X1,X2)
| visFreeVar(X1,vapp(X2,X3)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_44])]) ).
cnf(c_0_52,plain,
visFreeVar(X1,vvar(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_45])])]) ).
fof(c_0_53,plain,
! [X163,X164,X165,X166,X167,X168,X169,X170] :
( X166 = vapp(vsubst(X168,X169,X167),vsubst(X168,X169,X170))
| X166 != vsubst(X163,X164,X165)
| X165 != vapp(X167,X170)
| X164 != X169
| X163 != X168 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst2])])]) ).
fof(c_0_54,plain,
! [X149,X150,X151,X152,X153,X154,X155] :
( X154 = X155
| X154 != vsubst(X151,X152,X153)
| X149 != X150
| X153 != vvar(X150)
| X152 != X155
| X151 != X149 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst0])])]) ).
cnf(c_0_55,plain,
( ~ visFreeVar(X2,X1)
| vgensym(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( visFreeVar(X1,veabs)
| esk35_0 = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_57,plain,
( ~ visFreeVar(X1,X3)
| visFreeVar(X1,vapp(X2,X3)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])]) ).
cnf(c_0_58,plain,
visFreeVar(X1,vapp(vvar(X1),X2)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,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_53]) ).
cnf(c_0_60,plain,
( X7 != vsubst(X1,X3,X5)
| X2 != X6
| X5 != vvar(X6)
| X3 != X4
| X1 != X2
| X7 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
~ visFreeVar(vgensym(X1),X1),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( visFreeVar(X1,vapp(veabs,X2))
| esk35_0 = X1 ),
inference(spm,[status(thm)],[c_0_51,c_0_56]) ).
cnf(c_0_63,plain,
visFreeVar(X1,vapp(X2,vapp(vvar(X1),X3))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,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_59])])])]) ).
cnf(c_0_65,plain,
vsubst(X1,X2,vvar(X1)) = X2,
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])])])])]) ).
cnf(c_0_66,negated_conjecture,
vgensym(vapp(veabs,X1)) = esk35_0,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
visFreeVar(X1,vapp(X2,vapp(X3,vapp(vvar(X1),X4)))),
inference(spm,[status(thm)],[c_0_57,c_0_63]) ).
cnf(c_0_68,plain,
vapp(vsubst(X1,X2,X3),X2) = vsubst(X1,X2,vapp(X3,vvar(X1))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
~ visFreeVar(esk35_0,vapp(veabs,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_66]) ).
cnf(c_0_70,plain,
visFreeVar(X1,vapp(X2,vsubst(X3,vapp(vvar(X1),X4),vapp(X5,vvar(X3))))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_69,c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM124+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:17:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 16.66/2.65 % Version: 3.5.1
% 16.66/2.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.66/2.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.66/2.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.66/2.65 % Starting new_bool_3 with 300s (1) cores
% 16.66/2.65 % Starting new_bool_1 with 300s (1) cores
% 16.66/2.65 % Starting sh5l with 300s (1) cores
% 16.66/2.65 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3354332 completed with status 0
% 16.66/2.65 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 16.66/2.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.66/2.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.66/2.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.66/2.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.66/2.65 % No SInE strategy applied
% 16.66/2.65 % Search class: FGHSF-FSLF32-MFFFFFNN
% 16.66/2.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.66/2.65 % Starting SubtermCWHack with 136s (1) cores
% 16.66/2.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 16.66/2.65 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 16.66/2.65 % Starting new_bool_3 with 136s (1) cores
% 16.66/2.65 % Starting new_bool_1 with 136s (1) cores
% 16.66/2.65 % new_bool_3 with pid 3354349 completed with status 0
% 16.66/2.65 % Result found by new_bool_3
% 16.66/2.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.66/2.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.66/2.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.66/2.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.66/2.65 % No SInE strategy applied
% 16.66/2.65 % Search class: FGHSF-FSLF32-MFFFFFNN
% 16.66/2.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.66/2.65 % Starting SubtermCWHack with 136s (1) cores
% 16.66/2.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 16.66/2.65 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 16.66/2.65 % Starting new_bool_3 with 136s (1) cores
% 16.66/2.65 % Preprocessing time : 0.013 s
% 16.66/2.65 % Presaturation interreduction done
% 16.66/2.65
% 16.66/2.65 % Proof found!
% 16.66/2.65 % SZS status Theorem
% 16.66/2.65 % SZS output start CNFRefutation
% See solution above
% 16.66/2.65 % Parsed axioms : 64
% 16.66/2.65 % Removed by relevancy pruning/SinE : 0
% 16.66/2.65 % Initial clauses : 431
% 16.66/2.65 % Removed in clause preprocessing : 13
% 16.66/2.65 % Initial clauses in saturation : 418
% 16.66/2.65 % Processed clauses : 5724
% 16.66/2.65 % ...of these trivial : 133
% 16.66/2.65 % ...subsumed : 2796
% 16.66/2.65 % ...remaining for further processing : 2795
% 16.66/2.65 % Other redundant clauses eliminated : 1892
% 16.66/2.65 % Clauses deleted for lack of memory : 0
% 16.66/2.65 % Backward-subsumed : 165
% 16.66/2.65 % Backward-rewritten : 106
% 16.66/2.65 % Generated clauses : 75259
% 16.66/2.65 % ...of the previous two non-redundant : 66893
% 16.66/2.65 % ...aggressively subsumed : 0
% 16.66/2.65 % Contextual simplify-reflections : 8
% 16.66/2.65 % Paramodulations : 73285
% 16.66/2.65 % Factorizations : 10
% 16.66/2.65 % NegExts : 0
% 16.66/2.65 % Equation resolutions : 1971
% 16.66/2.65 % Disequality decompositions : 0
% 16.66/2.65 % Total rewrite steps : 11807
% 16.66/2.65 % ...of those cached : 9169
% 16.66/2.65 % Propositional unsat checks : 0
% 16.66/2.65 % Propositional check models : 0
% 16.66/2.65 % Propositional check unsatisfiable : 0
% 16.66/2.65 % Propositional clauses : 0
% 16.66/2.65 % Propositional clauses after purity: 0
% 16.66/2.65 % Propositional unsat core size : 0
% 16.66/2.65 % Propositional preprocessing time : 0.000
% 16.66/2.65 % Propositional encoding time : 0.000
% 16.66/2.65 % Propositional solver time : 0.000
% 16.66/2.65 % Success case prop preproc time : 0.000
% 16.66/2.65 % Success case prop encoding time : 0.000
% 16.66/2.65 % Success case prop solver time : 0.000
% 16.66/2.65 % Current number of processed clauses : 2008
% 16.66/2.65 % Positive orientable unit clauses : 267
% 16.66/2.65 % Positive unorientable unit clauses: 4
% 16.66/2.65 % Negative unit clauses : 53
% 16.66/2.65 % Non-unit-clauses : 1684
% 16.66/2.65 % Current number of unprocessed clauses: 60027
% 16.66/2.65 % ...number of literals in the above : 227995
% 16.66/2.65 % Current number of archived formulas : 0
% 16.66/2.65 % Current number of archived clauses : 693
% 16.66/2.65 % Clause-clause subsumption calls (NU) : 309408
% 16.66/2.65 % Rec. Clause-clause subsumption calls : 132877
% 16.66/2.65 % Non-unit clause-clause subsumptions : 1927
% 16.66/2.65 % Unit Clause-clause subsumption calls : 10096
% 16.66/2.65 % Rewrite failures with RHS unbound : 118
% 16.66/2.65 % BW rewrite match attempts : 4791
% 16.66/2.65 % BW rewrite match successes : 44
% 16.66/2.65 % Condensation attempts : 0
% 16.66/2.65 % Condensation successes : 0
% 16.66/2.65 % Termbank termtop insertions : 2652825
% 16.66/2.65 % Search garbage collected termcells : 4103
% 16.66/2.65
% 16.66/2.65 % -------------------------------------------------
% 16.66/2.65 % User time : 2.033 s
% 16.66/2.65 % System time : 0.062 s
% 16.66/2.65 % Total time : 2.095 s
% 16.66/2.65 % Maximum resident set size: 4784 pages
% 16.66/2.65
% 16.66/2.65 % -------------------------------------------------
% 16.66/2.65 % User time : 10.051 s
% 16.66/2.65 % System time : 0.353 s
% 16.66/2.65 % Total time : 10.404 s
% 16.66/2.65 % Maximum resident set size: 4864 pages
% 16.66/2.65 % E exiting
%------------------------------------------------------------------------------