%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM142+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 : n011.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 01:04:30 PM UTC 2026
% Result : Theorem 10.20s 27.60s
% Output : CNFRefutation 10.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 36 unt; 4 def)
% Number of atoms : 314 ( 114 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 239 ( 88 ~; 88 |; 52 &)
% ( 0 <=>; 11 =>; 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; 4 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 287 ( 0 sgn 233 !; 54 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-app') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-abs-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(f9,axiom,
! [X0,X1,X2] :
( X2 = vapp(X0,X1)
=> ~ visValue(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isValue2) ).
fof(f53,axiom,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X3,X0)
& vtcheck(X1,X2,varrow(X0,X4)) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-app') ).
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(f55,axiom,
! [X0,X1,X2,X3] :
( ( vtcheck(X2,ve1app,X3)
& vlookup(X0,X2) = vnoType )
=> vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-app-IH1') ).
fof(f56,axiom,
! [X0,X1,X2,X3] :
( ( vtcheck(X2,ve2app,X3)
& vlookup(X0,X2) = vnoType )
=> vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-app-IH2') ).
fof(f57,conjecture,
! [X0,X1,X2,X3] :
( ( vtcheck(X2,vapp(ve1app,ve2app),X3)
& vlookup(X0,X2) = vnoType )
=> vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-app') ).
fof(f58,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( vtcheck(X2,vapp(ve1app,ve2app),X3)
& vlookup(X0,X2) = vnoType )
=> vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
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(f69,plain,
! [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2
| vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) != vapp(X2,X3)
| ( X1 = X3
& X0 = X2 ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2
| vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) != vapp(X2,X3)
| ( X1 = X3
& X0 = X2 ) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f73,plain,
! [X0,X1,X2] :
( vapp(X0,X1) != X2
| ~ visValue(X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4] :
( ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| vtcheck(X1,vapp(X2,X3),X4) ),
inference(ennf_transformation,[],[f53]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4] :
( ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| vtcheck(X1,vapp(X2,X3),X4) ),
inference(flattening,[],[f139]) ).
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(f143,plain,
! [X0,X1,X2,X3] :
( ~ vtcheck(X2,ve1app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
inference(ennf_transformation,[],[f55]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ~ vtcheck(X2,ve1app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ~ vtcheck(X2,ve2app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
inference(ennf_transformation,[],[f56]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( ~ vtcheck(X2,ve2app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
? [X0,X1,X2,X3] :
( vtcheck(X2,vapp(ve1app,ve2app),X3)
& vlookup(X0,X2) = vnoType
& ~ vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
inference(ennf_transformation,[],[f58]) ).
fof(f148,plain,
? [X0,X1,X2,X3] :
( vtcheck(X2,vapp(ve1app,ve2app),X3)
& vlookup(X0,X2) = vnoType
& ~ vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
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,vapp(ve1app,ve2app),sK90)
& vnoType = vlookup(sK87,sK89)
& ~ vtcheck(vbind(sK87,sK88,sK89),vapp(ve1app,ve2app),sK90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90]),skolemize(X0,sK87),skolemize(X1,sK88),skolemize(X2,sK89),skolemize(X3,sK90)],[f148]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f70]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f222,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f223,plain,
! [X2,X3,X0,X1,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[],[f6]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(cnf_transformation,[],[f71]) ).
fof(f226,plain,
! [X2,X0,X1] :
( vapp(X0,X1) != X2
| ~ visValue(X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f350,plain,
! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| vtcheck(X1,vapp(X2,X3),X4) ),
inference(cnf_transformation,[],[f140]) ).
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(f360,plain,
! [X2,X3,X0,X1] :
( ~ vtcheck(X2,ve1app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f361,plain,
! [X2,X3,X0,X1] :
( ~ vtcheck(X2,ve2app,X3)
| vnoType != vlookup(X0,X2)
| vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
inference(cnf_transformation,[],[f146]) ).
fof(f362,plain,
vtcheck(sK89,vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f211]) ).
fof(f363,plain,
vnoType = vlookup(sK87,sK89),
inference(cnf_transformation,[],[f211]) ).
fof(f364,plain,
~ vtcheck(vbind(sK87,sK88,sK89),vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f211]) ).
fof(f371,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f224]) ).
fof(f373,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f226]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( vapp(X0,X1) != vapp(X2,X3) ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( vapp(X0,X1) != vapp(X2,X3) ) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : vapp(X0,X1) != vvar(X2),
inference(cnf_transformation,[],[f222]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[],[f223]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : visValue(vabs(X0,X1,X2)),
inference(cnf_transformation,[],[f371]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : ~ visValue(vapp(X0,X1)),
inference(cnf_transformation,[],[f373]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( vtcheck(X0,vapp(X1,X4),X3)
| ~ vtcheck(X0,X4,X2)
| ~ vtcheck(X0,X1,varrow(X2,X3)) ),
inference(cnf_transformation,[],[f350]) ).
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_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( vtcheck(vbind(X0,X3,X1),ve1app,X2)
| ~ vtcheck(X1,ve1app,X2)
| ( vlookup(X0,X1) != vnoType ) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( vtcheck(vbind(X0,X3,X1),ve2app,X2)
| ~ vtcheck(X1,ve2app,X2)
| ( vlookup(X0,X1) != vnoType ) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_189,negated_conjecture,
~ vtcheck(vbind(sK87,sK88,sK89),vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f364]) ).
tcf(c_190,negated_conjecture,
vlookup(sK87,sK89) = vnoType,
inference(cnf_transformation,[],[f363]) ).
tcf(c_191,negated_conjecture,
vtcheck(sK89,vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f362]) ).
tcf(c_13196,definition,
iPr_def_10 = vapp(ve1app,ve2app),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13197,definition,
iPr_def_11 = vlookup(sK87,sK89),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_13198,definition,
iPr_def_12 = vbind(sK87,sK88,sK89),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_13199,negated_conjecture,
vtcheck(sK89,iPr_def_10,sK90),
inference(demodulation,[status(thm)],[c_191,c_13196]) ).
tcf(c_13200,negated_conjecture,
iPr_def_11 = vnoType,
inference(demodulation,[status(thm)],[c_190,c_13197]) ).
tcf(c_13201,negated_conjecture,
~ vtcheck(iPr_def_12,iPr_def_10,sK90),
inference(demodulation,[status(thm)],[c_189,c_13198]) ).
tcf(c_16228,plain,
~ visValue(iPr_def_10),
inference(superposition,[status(thm)],[c_13196,c_60]) ).
tcf(c_16231,plain,
! [X0: $i] : vvar(X0) != iPr_def_10,
inference(superposition,[status(thm)],[c_13196,c_56]) ).
tcf(c_16236,plain,
! [X0: $i,X1: $i] :
( ( X0 = ve1app )
| ( vapp(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13196,c_53]) ).
tcf(c_16416,plain,
! [X0: $i,X1: $i] :
( ( X1 = ve2app )
| ( vapp(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13196,c_54]) ).
tcf(c_18904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( vtcheck(vbind(X0,X3,X1),ve1app,X2)
| ~ vtcheck(X1,ve1app,X2)
| ( vlookup(X0,X1) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_187,c_13200]) ).
tcf(c_18917,plain,
! [X0: $i,X1: $i] :
( vtcheck(vbind(sK87,X1,sK89),ve1app,X0)
| ~ vtcheck(sK89,ve1app,X0) ),
inference(superposition,[status(thm)],[c_13197,c_18904]) ).
tcf(c_18970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( vtcheck(vbind(X0,X3,X1),ve2app,X2)
| ~ vtcheck(X1,ve2app,X2)
| ( vlookup(X0,X1) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_188,c_13200]) ).
tcf(c_18983,plain,
! [X0: $i,X1: $i] :
( vtcheck(vbind(sK87,X1,sK89),ve2app,X0)
| ~ vtcheck(sK89,ve2app,X0) ),
inference(superposition,[status(thm)],[c_13197,c_18970]) ).
tcf(c_19167,plain,
! [X0: $i] :
( vtcheck(iPr_def_12,ve1app,X0)
| ~ vtcheck(sK89,ve1app,X0) ),
inference(superposition,[status(thm)],[c_13198,c_18917]) ).
tcf(c_19189,plain,
! [X0: $i] :
( vtcheck(iPr_def_12,ve2app,X0)
| ~ vtcheck(sK89,ve2app,X0) ),
inference(superposition,[status(thm)],[c_13198,c_18983]) ).
tcf(c_25453,plain,
( sP12(iPr_def_10,sK90,sK89)
| ( vvar(sK82(iPr_def_10,sK90,sK89)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK90,sK89),sK85(iPr_def_10,sK90,sK89),sK84(iPr_def_10,sK90,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13199,c_181]) ).
tcf(c_25466,plain,
( sP12(iPr_def_10,sK90,sK89)
| ( vabs(sK83(iPr_def_10,sK90,sK89),sK85(iPr_def_10,sK90,sK89),sK84(iPr_def_10,sK90,sK89)) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25453,c_16231]) ).
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(f351,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2)) ),
inference(cnf_transformation,[],[f209]) ).
fof(f352,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1)) ),
inference(cnf_transformation,[],[f209]) ).
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_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_25733,plain,
( ( vapp(sK79(iPr_def_10,sK90,sK89),sK80(iPr_def_10,sK90,sK89)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK90,sK89),sK85(iPr_def_10,sK90,sK89),sK84(iPr_def_10,sK90,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_25466,c_178]) ).
tcf(c_25758,plain,
( visValue(iPr_def_10)
| ( vapp(sK79(iPr_def_10,sK90,sK89),sK80(iPr_def_10,sK90,sK89)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_25733,c_58]) ).
tcf(c_25774,plain,
vapp(sK79(iPr_def_10,sK90,sK89),sK80(iPr_def_10,sK90,sK89)) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_25758,c_16228]) ).
tcf(c_26538,plain,
sK80(iPr_def_10,sK90,sK89) = ve2app,
inference(superposition,[status(thm)],[c_25774,c_16416]) ).
tcf(c_26544,plain,
sK79(iPr_def_10,sK90,sK89) = ve1app,
inference(superposition,[status(thm)],[c_25774,c_16236]) ).
tcf(c_26569,plain,
! [X0: $i,X1: $i,X2: $i] : vabs(X0,X1,X2) != iPr_def_10,
inference(superposition,[status(thm)],[c_25774,c_57]) ).
tcf(c_26609,plain,
sP12(iPr_def_10,sK90,sK89),
inference(backward_subsumption_resolution,[status(thm)],[c_25466,c_26569]) ).
tcf(c_26795,plain,
( vtcheck(sK89,ve2app,sK81(iPr_def_10,sK90,sK89))
| ~ sP12(iPr_def_10,sK90,sK89) ),
inference(superposition,[status(thm)],[c_26538,c_180]) ).
tcf(c_26796,plain,
vtcheck(sK89,ve2app,sK81(iPr_def_10,sK90,sK89)),
inference(forward_subsumption_resolution,[status(thm)],[c_26795,c_26609]) ).
tcf(c_26833,plain,
( vtcheck(sK89,ve1app,varrow(sK81(iPr_def_10,sK90,sK89),sK90))
| ~ sP12(iPr_def_10,sK90,sK89) ),
inference(superposition,[status(thm)],[c_26544,c_179]) ).
tcf(c_26834,plain,
vtcheck(sK89,ve1app,varrow(sK81(iPr_def_10,sK90,sK89),sK90)),
inference(forward_subsumption_resolution,[status(thm)],[c_26833,c_26609]) ).
tcf(c_27558,plain,
vtcheck(iPr_def_12,ve2app,sK81(iPr_def_10,sK90,sK89)),
inference(superposition,[status(thm)],[c_26796,c_19189]) ).
tcf(c_28924,plain,
vtcheck(iPr_def_12,ve1app,varrow(sK81(iPr_def_10,sK90,sK89),sK90)),
inference(superposition,[status(thm)],[c_26834,c_19167]) ).
tcf(c_28945,plain,
! [X0: $i] :
( vtcheck(iPr_def_12,vapp(ve1app,X0),sK90)
| ~ vtcheck(iPr_def_12,X0,sK81(iPr_def_10,sK90,sK89)) ),
inference(superposition,[status(thm)],[c_28924,c_177]) ).
tcf(c_33575,plain,
vtcheck(iPr_def_12,vapp(ve1app,ve2app),sK90),
inference(superposition,[status(thm)],[c_27558,c_28945]) ).
tcf(c_33576,plain,
vtcheck(iPr_def_12,iPr_def_10,sK90),
inference(light_normalisation,[status(thm)],[c_33575,c_13196]) ).
tcf(c_33577,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_33576,c_13201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM142+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.04/25.87 % CPULimit : 300
% 0.04/25.87 % WCLimit : 300
% 0.04/25.87 % DateTime : Fri Sep 25 07:55:28 UTC 2026
% 0.04/25.87 % CPUTime :
% 0.04/25.87 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/25.89 Running first-order theorem proving
% 0.04/25.89 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
% 0.04/25.90
% 0.04/25.90 % ======== iProver multi-core TPTP/SMT =========
% 0.04/25.90
% 0.16/25.90 % Detected problem language: tptp
% 0.16/25.90 % Proving...
% 10.20/27.60 % SZS status Started for theBenchmark.p
% 10.20/27.60 % SZS status Theorem for theBenchmark.p
% 10.20/27.60
% 10.20/27.60 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.20/27.60
% 10.20/27.60 % ------ iProver source info
% 10.20/27.60
% 10.20/27.60 % git: date: 2026-07-19 20:42:38 +0200
% 10.20/27.60 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.20/27.60 % git: non_committed_changes: false
% 10.20/27.60
% 10.20/27.60 % ------ Parsing...
% 10.20/27.60 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.20/27.60
% 10.20/27.60 % ------ 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 %
% 10.20/27.60
% 10.20/27.60 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.20/27.60
% 10.20/27.60 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.20/27.60 % ------ Proving...
% 10.20/27.60 % ------ Problem Properties
% 10.20/27.60
% 10.20/27.60 %
% 10.20/27.60 % clauses 142
% 10.20/27.60 % conjectures 3
% 10.20/27.60 % EPR 6
% 10.20/27.60 % Horn 116
% 10.20/27.60 % unary 29
% 10.20/27.60 % binary 86
% 10.20/27.60 % lits 305
% 10.20/27.60 % lits eq 138
% 10.20/27.60 % fd_pure 0
% 10.20/27.60 % fd_pseudo 0
% 10.20/27.60 % fd_cond 3
% 10.20/27.60 % fd_pseudo_cond 20
% 10.20/27.60 % AC symbols 0
% 10.20/27.60
% 10.20/27.60 % ------ Schedule dynamic 5 is on
% 10.20/27.60
% 10.20/27.60 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.20/27.60
% 10.20/27.60
% 10.20/27.60 % ------
% 10.20/27.60 % Current options:
% 10.20/27.60 % ------
% 10.20/27.60
% 10.20/27.60
% 10.20/27.60 %
% 10.20/27.60
% 10.20/27.60 % ------ Proving...
% 10.20/27.60 %
% 10.20/27.60
% 10.20/27.60 % SZS status Theorem for theBenchmark.p
% 10.20/27.60
% 10.20/27.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.20/27.60
% 10.20/27.60
%------------------------------------------------------------------------------