%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM127+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 : Fri Sep 25 01:04:28 PM UTC 2026
% Result : Theorem 58.40s 18.81s
% Output : CNFRefutation 58.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 108 ( 30 unt; 3 def)
% Number of atoms : 417 ( 184 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 294 ( 97 ~; 133 |; 49 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 266 ( 0 sgn 210 !; 56 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( X0 = X1
=> vvar(X0) = vvar(X1) )
& ( vvar(X0) = vvar(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-var') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( X3 = vabs(X0,X1,X2)
=> visValue(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isValue0) ).
fof(f8,axiom,
! [X0,X1] :
( X1 = vvar(X0)
=> ~ visValue(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isValue1) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( ( X1 = vvar(X2)
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> X2 = X3 )
& ( X2 = X3
=> visFreeVar(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).
fof(f24,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X3 = vbind(X1,X0,X6)
& X2 = X5 )
=> ( X5 != X1
=> ( X4 = vlookup(X2,X3)
=> X4 = vlookup(X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',lookup2) ).
fof(f51,axiom,
! [X0,X1,X2] :
( vlookup(X1,X0) = vsomeType(X2)
=> vtcheck(X0,vvar(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-var') ).
fof(f54,axiom,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X7,X4,X8] :
( vtcheck(X2,X4,X8)
& vtcheck(X2,X7,varrow(X8,X1))
& X0 = vapp(X7,X4) )
| ? [X3,X4,X5,X6] :
( vtcheck(vbind(X3,X5,X2),X4,X6)
& X1 = varrow(X5,X6)
& X0 = vabs(X3,X5,X4) )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-inv') ).
fof(f57,conjecture,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) )
=> vtcheck(vbind(X0,X1,X2),vvar(X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-var') ).
fof(f58,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) )
=> vtcheck(vbind(X0,X1,X2),vvar(X3),X4) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f65,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ) ),
inference(rectify,[],[f54]) ).
fof(f66,plain,
! [X0,X1] :
( ( X0 != X1
| vvar(X0) = vvar(X1) )
& ( vvar(X0) != vvar(X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1] :
( vvar(X0) != X1
| ~ visValue(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( vvar(X2) != X1
| X0 != X3
| ( ( ~ visFreeVar(X0,X1)
| X2 = X3 )
& ( X2 != X3
| visFreeVar(X0,X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( vvar(X2) != X1
| X0 != X3
| ( ( ~ visFreeVar(X0,X1)
| X2 = X3 )
& ( X2 != X3
| visFreeVar(X0,X1) ) ) ),
inference(flattening,[],[f74]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vbind(X1,X0,X6) != X3
| X2 != X5
| X1 = X5
| vlookup(X2,X3) != X4
| X4 = vlookup(X5,X6) ),
inference(ennf_transformation,[],[f24]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vbind(X1,X0,X6) != X3
| X2 != X5
| X1 = X5
| vlookup(X2,X3) != X4
| X4 = vlookup(X5,X6) ),
inference(flattening,[],[f91]) ).
fof(f137,plain,
! [X0,X1,X2] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) ),
inference(ennf_transformation,[],[f51]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(flattening,[],[f141]) ).
fof(f147,plain,
? [X0,X1,X2,X3,X4] :
( vtcheck(X2,vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3))
& ~ vtcheck(vbind(X0,X1,X2),vvar(X3),X4) ),
inference(ennf_transformation,[],[f58]) ).
fof(f148,plain,
? [X0,X1,X2,X3,X4] :
( vtcheck(X2,vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3))
& ~ vtcheck(vbind(X0,X1,X2),vvar(X3),X4) ),
inference(flattening,[],[f147]) ).
fof(f210,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| ( vtcheck(vbind(sK83(X0,X1,X2),sK85(X0,X1,X2),X2),sK84(X0,X1,X2),sK86(X0,X1,X2))
& varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
& vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0 )
| ( vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2)
& vvar(sK82(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82,sK83,sK84,sK85,sK86]),skolemize(X3,sK82(X0,X1,X2)),skolemize(X4,sK83(X0,X1,X2)),skolemize(X5,sK84(X0,X1,X2)),skolemize(X6,sK85(X0,X1,X2)),skolemize(X7,sK86(X0,X1,X2))],[f165]) ).
fof(f211,plain,
( vtcheck(sK89,vvar(sK90),sK91)
& ~ visFreeVar(sK87,vvar(sK90))
& ~ vtcheck(vbind(sK87,sK88,sK89),vvar(sK90),sK91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90,sK91]),skolemize(X0,sK87),skolemize(X1,sK88),skolemize(X2,sK89),skolemize(X3,sK90),skolemize(X4,sK91)],[f148]) ).
fof(f213,plain,
! [X0,X1] :
( vvar(X0) != vvar(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f222,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(cnf_transformation,[],[f71]) ).
fof(f225,plain,
! [X0,X1] :
( vvar(X0) != X1
| ~ visValue(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( vvar(X2) != X1
| X0 != X3
| X2 != X3
| visFreeVar(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f250,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vbind(X1,X0,X6) != X3
| X2 != X5
| X1 = X5
| vlookup(X2,X3) != X4
| vlookup(X5,X6) = X4 ),
inference(cnf_transformation,[],[f92]) ).
fof(f348,plain,
! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) ),
inference(cnf_transformation,[],[f137]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
| vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f210]) ).
fof(f356,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0
| vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f210]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
| vvar(sK82(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f210]) ).
fof(f359,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0
| vvar(sK82(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f210]) ).
fof(f362,plain,
vtcheck(sK89,vvar(sK90),sK91),
inference(cnf_transformation,[],[f211]) ).
fof(f363,plain,
~ visFreeVar(sK87,vvar(sK90)),
inference(cnf_transformation,[],[f211]) ).
fof(f364,plain,
~ vtcheck(vbind(sK87,sK88,sK89),vvar(sK90),sK91),
inference(cnf_transformation,[],[f211]) ).
fof(f371,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f224]) ).
fof(f372,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f225]) ).
fof(f374,plain,
! [X3,X0,X1] :
( vvar(X3) != X1
| X0 != X3
| visFreeVar(X0,X1) ),
inference(equality_resolution,[],[f228]) ).
fof(f375,plain,
! [X3,X1] :
( vvar(X3) != X1
| visFreeVar(X3,X1) ),
inference(equality_resolution,[],[f374]) ).
fof(f376,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f375]) ).
fof(f407,plain,
! [X2,X3,X0,X1,X6,X5] :
( vbind(X1,X0,X6) != X3
| X2 != X5
| X1 = X5
| vlookup(X2,X3) = vlookup(X5,X6) ),
inference(equality_resolution,[],[f250]) ).
fof(f408,plain,
! [X3,X0,X1,X6,X5] :
( vbind(X1,X0,X6) != X3
| X1 = X5
| vlookup(X5,X6) = vlookup(X5,X3) ),
inference(equality_resolution,[],[f407]) ).
fof(f409,plain,
! [X0,X1,X6,X5] :
( X1 = X5
| vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6)) ),
inference(equality_resolution,[],[f408]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( vvar(X0) != vvar(X1) ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : vapp(X0,X1) != vvar(X2),
inference(cnf_transformation,[],[f222]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : visValue(vabs(X0,X1,X2)),
inference(cnf_transformation,[],[f371]) ).
tcf(c_59,plain,
! [X0: $i] : ~ visValue(vvar(X0)),
inference(cnf_transformation,[],[f372]) ).
tcf(c_61,plain,
! [X0: $i] : visFreeVar(X0,vvar(X0)),
inference(cnf_transformation,[],[f376]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( vlookup(X0,vbind(X1,X2,X3)) = vlookup(X0,X3) ) ),
inference(cnf_transformation,[],[f409]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] :
( vtcheck(X1,vvar(X0),X2)
| ( vlookup(X0,X1) != vsomeType(X2) ) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP12(X1,X2,X0)
| ( vvar(sK82(X1,X2,X0)) = X1 )
| ( vabs(sK83(X1,X2,X0),sK85(X1,X2,X0),sK84(X1,X2,X0)) = X1 )
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[],[f359]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP12(X1,X2,X0)
| ( vvar(sK82(X1,X2,X0)) = X1 )
| ( varrow(sK85(X1,X2,X0),sK86(X1,X2,X0)) = X2 )
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[],[f358]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP12(X1,X2,X0)
| ( vlookup(sK82(X1,X2,X0),X0) = vsomeType(X2) )
| ( vabs(sK83(X1,X2,X0),sK85(X1,X2,X0),sK84(X1,X2,X0)) = X1 )
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP12(X1,X2,X0)
| ( vlookup(sK82(X1,X2,X0),X0) = vsomeType(X2) )
| ( varrow(sK85(X1,X2,X0),sK86(X1,X2,X0)) = X2 )
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[],[f355]) ).
tcf(c_189,negated_conjecture,
~ vtcheck(vbind(sK87,sK88,sK89),vvar(sK90),sK91),
inference(cnf_transformation,[],[f364]) ).
tcf(c_190,negated_conjecture,
~ visFreeVar(sK87,vvar(sK90)),
inference(cnf_transformation,[],[f363]) ).
tcf(c_191,negated_conjecture,
vtcheck(sK89,vvar(sK90),sK91),
inference(cnf_transformation,[],[f362]) ).
tcf(c_13196,definition,
iPr_def_10 = vvar(sK90),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13197,definition,
iPr_def_11 = vbind(sK87,sK88,sK89),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_13198,negated_conjecture,
vtcheck(sK89,iPr_def_10,sK91),
inference(demodulation,[status(thm)],[c_191,c_13196]) ).
tcf(c_13199,negated_conjecture,
~ visFreeVar(sK87,iPr_def_10),
inference(demodulation,[status(thm)],[c_190]) ).
tcf(c_13200,negated_conjecture,
~ vtcheck(iPr_def_11,iPr_def_10,sK91),
inference(demodulation,[status(thm)],[c_189,c_13197]) ).
tcf(c_13208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_16224,plain,
~ visValue(iPr_def_10),
inference(superposition,[status(thm)],[c_13196,c_59]) ).
tcf(c_17236,plain,
! [X0: $i,X1: $i,X2: $i] :
( visFreeVar(X0,X2)
| ~ visFreeVar(X1,vvar(X1))
| ( X2 != vvar(X1) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_13208]) ).
tcf(c_23562,plain,
( sP12(iPr_def_10,sK91,sK89)
| ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK91,sK89),sK85(iPr_def_10,sK91,sK89),sK84(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13198,c_181]) ).
tcf(c_23624,plain,
( sP12(iPr_def_10,sK91,sK89)
| ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( vabs(sK83(iPr_def_10,sK91,sK89),sK85(iPr_def_10,sK91,sK89),sK84(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13198,c_184]) ).
tcf(c_28381,plain,
! [X0: $i] :
( visFreeVar(X0,iPr_def_10)
| ~ visFreeVar(sK90,vvar(sK90))
| ( iPr_def_10 != vvar(sK90) )
| ( X0 != sK90 ) ),
inference(instantiation,[status(thm)],[c_17236]) ).
tcf(c_34423,plain,
visFreeVar(sK90,vvar(sK90)),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_38847,plain,
( visFreeVar(sK87,iPr_def_10)
| ~ visFreeVar(sK90,vvar(sK90))
| ( iPr_def_10 != vvar(sK90) )
| ( sK87 != sK90 ) ),
inference(instantiation,[status(thm)],[c_28381]) ).
tcf(c_141678,plain,
! [X0: $i] :
( ( X0 = sK90 )
| ( vvar(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13196,c_49]) ).
tcf(c_142142,plain,
! [X0: $i] :
( ( X0 = sK87 )
| ( vlookup(X0,sK89) = vlookup(X0,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_13197,c_80]) ).
tcf(c_146805,plain,
( sP12(iPr_def_10,sK91,sK89)
| ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( varrow(sK85(iPr_def_10,sK91,sK89),sK86(iPr_def_10,sK91,sK89)) = sK91 ) ),
inference(superposition,[status(thm)],[c_13198,c_182]) ).
tcf(c_146871,plain,
( sP12(iPr_def_10,sK91,sK89)
| ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( varrow(sK85(iPr_def_10,sK91,sK89),sK86(iPr_def_10,sK91,sK89)) = sK91 ) ),
inference(superposition,[status(thm)],[c_13198,c_185]) ).
fof(f164,definition,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 ) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(definition_folding,[],[f142,f164]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 ) ),
inference(nnf_transformation,[],[f164]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 ) ),
inference(rectify,[],[f207]) ).
fof(f209,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ( vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2))
& vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1))
& vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79,sK80,sK81]),skolemize(X3,sK79(X0,X1,X2)),skolemize(X4,sK80(X0,X1,X2)),skolemize(X5,sK81(X0,X1,X2))],[f208]) ).
fof(f353,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 )
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_23727,plain,
( ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK91,sK89),sK85(iPr_def_10,sK91,sK89),sK84(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_23562,c_178]) ).
tcf(c_23737,plain,
( ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK91,sK89),sK85(iPr_def_10,sK91,sK89),sK84(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_23624,c_178]) ).
tcf(c_39601,plain,
( visValue(iPr_def_10)
| ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_23727,c_58]) ).
tcf(c_39618,plain,
( ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39601,c_16224]) ).
tcf(c_52491,plain,
( visValue(iPr_def_10)
| ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_23737,c_58]) ).
tcf(c_52515,plain,
( ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52491,c_16224]) ).
tcf(c_146971,plain,
( ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( varrow(sK85(iPr_def_10,sK91,sK89),sK86(iPr_def_10,sK91,sK89)) = sK91 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_146805,c_178]) ).
tcf(c_147003,plain,
( ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( varrow(sK85(iPr_def_10,sK91,sK89),sK86(iPr_def_10,sK91,sK89)) = sK91 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_146871,c_178]) ).
tcf(c_154871,plain,
( ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_146971,c_39618]) ).
tcf(c_154909,plain,
! [X0: $i] :
( ( vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10 )
| ( vvar(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_154871,c_56]) ).
tcf(c_157643,plain,
( ( vlookup(sK82(iPr_def_10,sK91,sK89),sK89) = vsomeType(sK91) )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_147003,c_52515]) ).
tcf(c_162547,plain,
vvar(sK82(iPr_def_10,sK91,sK89)) = iPr_def_10,
inference(superposition,[status(thm)],[c_13196,c_154909]) ).
tcf(c_162569,plain,
sK82(iPr_def_10,sK91,sK89) = sK90,
inference(superposition,[status(thm)],[c_162547,c_141678]) ).
tcf(c_162587,plain,
! [X0: $i,X1: $i] : vapp(X0,X1) != iPr_def_10,
inference(superposition,[status(thm)],[c_162547,c_56]) ).
tcf(c_162616,plain,
vvar(sK90) = iPr_def_10,
inference(demodulation,[status(thm)],[c_162547,c_162569]) ).
tcf(c_162617,plain,
( ( vlookup(sK90,sK89) = vsomeType(sK91) )
| ( vapp(sK79(iPr_def_10,sK91,sK89),sK80(iPr_def_10,sK91,sK89)) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_157643,c_162569]) ).
tcf(c_162626,plain,
vlookup(sK90,sK89) = vsomeType(sK91),
inference(forward_subsumption_resolution,[status(thm)],[c_162617,c_162587]) ).
tcf(c_162725,plain,
( ( sK87 = sK90 )
| ( vlookup(sK90,iPr_def_11) = vsomeType(sK91) ) ),
inference(superposition,[status(thm)],[c_162626,c_142142]) ).
tcf(c_164430,plain,
vlookup(sK90,iPr_def_11) = vsomeType(sK91),
inference(global_subsumption_just,[status(thm)],[c_162725,c_13196,c_13199,c_34423,c_38847,c_162725]) ).
tcf(c_164435,plain,
! [X0: $i] :
( vtcheck(iPr_def_11,vvar(sK90),X0)
| ( vsomeType(X0) != vsomeType(sK91) ) ),
inference(superposition,[status(thm)],[c_164430,c_175]) ).
tcf(c_164437,plain,
! [X0: $i] :
( vtcheck(iPr_def_11,iPr_def_10,X0)
| ( vsomeType(X0) != vsomeType(sK91) ) ),
inference(light_normalisation,[status(thm)],[c_164435,c_162616]) ).
tcf(c_165766,plain,
vtcheck(iPr_def_11,iPr_def_10,sK91),
inference(equality_resolution,[status(thm)],[c_164437]) ).
tcf(c_165767,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_165766,c_13200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM127+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n006.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 07:54:05 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.40 Running first-order theorem proving
% 0.14/5.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.41
% 0.14/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.41
% 0.14/5.41 % Detected problem language: tptp
% 0.14/5.42 % Proving...
% 58.40/18.81 % SZS status Started for theBenchmark.p
% 58.40/18.81 % SZS status Theorem for theBenchmark.p
% 58.40/18.81
% 58.40/18.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 58.40/18.81
% 58.40/18.81 % ------ iProver source info
% 58.40/18.81
% 58.40/18.81 % git: date: 2026-07-19 20:42:38 +0200
% 58.40/18.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 58.40/18.81 % git: non_committed_changes: false
% 58.40/18.81
% 58.40/18.81 % ------ Parsing...
% 58.40/18.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 58.40/18.81
% 58.40/18.81 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 58.40/18.81
% 58.40/18.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 58.40/18.81
% 58.40/18.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 58.40/18.81 % ------ Proving...
% 58.40/18.81 % ------ Problem Properties
% 58.40/18.81
% 58.40/18.81 %
% 58.40/18.81 % clauses 141
% 58.40/18.81 % conjectures 3
% 58.40/18.81 % EPR 6
% 58.40/18.81 % Horn 114
% 58.40/18.81 % unary 28
% 58.40/18.81 % binary 86
% 58.40/18.81 % lits 304
% 58.40/18.81 % lits eq 135
% 58.40/18.81 % fd_pure 0
% 58.40/18.81 % fd_pseudo 0
% 58.40/18.81 % fd_cond 3
% 58.40/18.81 % fd_pseudo_cond 20
% 58.40/18.81 % AC symbols 0
% 58.40/18.81
% 58.40/18.81 % ------ Schedule dynamic 5 is on
% 58.40/18.81
% 58.40/18.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 58.40/18.81
% 58.40/18.81
% 58.40/18.81 % ------
% 58.40/18.81 % Current options:
% 58.40/18.81 % ------
% 58.40/18.81
% 58.40/18.81
% 58.40/18.81 %
% 58.40/18.81
% 58.40/18.81 % ------ Proving...
% 58.40/18.81 % Proof_search_loop: time out after: 3424 full_loop iterations
% 58.40/18.81
% 58.40/18.81 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 58.40/18.81
% 58.40/18.81
% 58.40/18.81 % ------
% 58.40/18.81 % Current options:
% 58.40/18.81 % ------
% 58.40/18.81
% 58.40/18.81
% 58.40/18.81 %
% 58.40/18.81
% 58.40/18.81 % ------ Proving...
% 58.40/18.81 %
% 58.40/18.81
% 58.40/18.81 % SZS status Theorem for theBenchmark.p
% 58.40/18.81
% 58.40/18.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 58.40/18.81
% 58.40/18.81
%------------------------------------------------------------------------------