%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM137+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 09:40:22 AM UTC 2026
% Result : Theorem 0.18s 0.32s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 103 ( 17 unt; 6 def)
% Number of atoms : 306 ( 89 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 322 ( 119 ~; 128 |; 58 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 234 ( 0 sgn 180 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
=> ( X0 = X2
& X1 = X3 ) )
& ( ( X0 = X2
& X1 = X3 )
=> vapp(X0,X1) = vapp(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','EQ-app') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/COM001+0.ax','DIFF-abs-app') ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( X0 = X3
& X1 = vapp(X2,X4) )
=> ( ( ( visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
=> visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X2)
| visFreeVar(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).
fof(f53,axiom,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X2,varrow(X0,X4))
& vtcheck(X1,X3,X0) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','T-app') ).
fof(f54,axiom,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X3,X4,X5,X6] :
( X0 = vabs(X3,X5,X4)
& X1 = varrow(X5,X6)
& vtcheck(vbind(X3,X5,X2),X4,X6) )
| ? [X7,X4,X8] :
( X0 = vapp(X7,X4)
& vtcheck(X2,X7,varrow(X8,X1))
& vtcheck(X2,X4,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','T-inv') ).
fof(f56,axiom,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,ve1app)
& vtcheck(vbind(X0,X1,X2),ve1app,X3) )
=> vtcheck(X2,ve1app,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong-app-IH1') ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,ve2app)
& vtcheck(vbind(X0,X1,X2),ve2app,X3) )
=> vtcheck(X2,ve2app,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong-app-IH2') ).
fof(f58,conjecture,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) )
=> vtcheck(X2,vapp(ve1app,ve2app),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong-app') ).
fof(f59,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) )
=> vtcheck(X2,vapp(ve1app,ve2app),X3) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f66,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) ) ) ),
inference(rectify,[],[f54]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X2
& X1 = X3 )
| vapp(X0,X1) != vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
| X0 != X2
| X1 != X3 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X2
& X1 = X3 )
| vapp(X0,X1) != vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
| X0 != X2
| X1 != X3 ) ),
inference(flattening,[],[f70]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X2)
& ~ visFreeVar(X3,X4) ) )
& ( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X2)
& ~ visFreeVar(X3,X4) ) )
& ( visFreeVar(X3,X2)
| visFreeVar(X3,X4)
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(flattening,[],[f79]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0) ),
inference(flattening,[],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ vtcheck(X2,X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ vtcheck(X2,X0,X1) ),
inference(flattening,[],[f142]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( vtcheck(X2,ve1app,X3)
| visFreeVar(X0,ve1app)
| ~ vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
inference(ennf_transformation,[],[f56]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( vtcheck(X2,ve1app,X3)
| visFreeVar(X0,ve1app)
| ~ vtcheck(vbind(X0,X1,X2),ve1app,X3) ),
inference(flattening,[],[f146]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( vtcheck(X2,ve2app,X3)
| visFreeVar(X0,ve2app)
| ~ vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( vtcheck(X2,ve2app,X3)
| visFreeVar(X0,ve2app)
| ~ vtcheck(vbind(X0,X1,X2),ve2app,X3) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
? [X0,X1,X2,X3] :
( ~ vtcheck(X2,vapp(ve1app,ve2app),X3)
& ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
inference(ennf_transformation,[],[f59]) ).
fof(f151,plain,
? [X0,X1,X2,X3] :
( ~ vtcheck(X2,vapp(ve1app,ve2app),X3)
& ~ visFreeVar(X0,vapp(ve1app,ve2app))
& vtcheck(vbind(X0,X1,X2),vapp(ve1app,ve2app),X3) ),
inference(flattening,[],[f150]) ).
fof(f167,definition,
! [X0,X1,X2] :
( ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ sP12(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ? [X3] :
( X0 = vvar(X3)
& vlookup(X3,X2) = vsomeType(X1) )
| ? [X4,X5,X6,X7] :
( vabs(X4,X6,X5) = X0
& varrow(X6,X7) = X1
& vtcheck(vbind(X4,X6,X2),X5,X7) )
| sP12(X0,X1,X2)
| ~ vtcheck(X2,X0,X1) ),
inference(definition_folding,[],[f143,f167]) ).
fof(f210,plain,
! [X0,X1,X2] :
( ? [X8,X9,X10] :
( vapp(X8,X9) = X0
& vtcheck(X2,X8,varrow(X10,X1))
& vtcheck(X2,X9,X10) )
| ~ sP12(X0,X1,X2) ),
inference(nnf_transformation,[],[f167]) ).
fof(f211,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vapp(X3,X4) = X0
& vtcheck(X2,X3,varrow(X5,X1))
& vtcheck(X2,X4,X5) )
| ~ sP12(X0,X1,X2) ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ( vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0
& vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1))
& vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2)) )
| ~ sP12(X0,X1,X2) ),
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))],[f211]) ).
fof(f213,plain,
! [X0,X1,X2] :
( ( vvar(sK82(X0,X1,X2)) = X0
& vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2) )
| ( vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0
& varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
& vtcheck(vbind(sK83(X0,X1,X2),sK85(X0,X1,X2),X2),sK84(X0,X1,X2),sK86(X0,X1,X2)) )
| sP12(X0,X1,X2)
| ~ vtcheck(X2,X0,X1) ),
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))],[f168]) ).
fof(f214,plain,
( ~ vtcheck(sK89,vapp(ve1app,ve2app),sK90)
& ~ visFreeVar(sK87,vapp(ve1app,ve2app))
& 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)],[f151]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f71]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f225,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f226,plain,
! [X2,X3,X0,X1,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[],[f6]) ).
fof(f236,plain,
! [X2,X3,X0,X1,X4] :
( ~ visFreeVar(X3,X4)
| visFreeVar(X0,X1)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f237,plain,
! [X2,X3,X0,X1,X4] :
( ~ visFreeVar(X3,X2)
| visFreeVar(X0,X1)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f353,plain,
! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f354,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2)) ),
inference(cnf_transformation,[],[f212]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1)) ),
inference(cnf_transformation,[],[f212]) ).
fof(f356,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f212]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0
| sP12(X0,X1,X2)
| vvar(sK82(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f213]) ).
fof(f364,plain,
! [X2,X3,X0,X1] :
( ~ vtcheck(vbind(X0,X1,X2),ve1app,X3)
| visFreeVar(X0,ve1app)
| vtcheck(X2,ve1app,X3) ),
inference(cnf_transformation,[],[f147]) ).
fof(f365,plain,
! [X2,X3,X0,X1] :
( ~ vtcheck(vbind(X0,X1,X2),ve2app,X3)
| visFreeVar(X0,ve2app)
| vtcheck(X2,ve2app,X3) ),
inference(cnf_transformation,[],[f149]) ).
fof(f366,plain,
vtcheck(vbind(sK87,sK88,sK89),vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f214]) ).
fof(f367,plain,
~ visFreeVar(sK87,vapp(ve1app,ve2app)),
inference(cnf_transformation,[],[f214]) ).
fof(f368,plain,
~ vtcheck(sK89,vapp(ve1app,ve2app),sK90),
inference(cnf_transformation,[],[f214]) ).
fof(f681,definition,
( spl91_8
<=> sP12(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)) ),
introduced(definition,[new_symbols(definition,[spl91_8])],[avatar_definition]) ).
fof(f682,plain,
( ~ sP12(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| spl91_8 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f683,plain,
( sP12(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| ~ spl91_8 ),
inference(avatar_component_clause,[],[f681]) ).
fof(f690,plain,
( vapp(ve1app,ve2app) = vapp(sK79(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK80(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_8 ),
inference(resolution,[],[f683,f356]) ).
fof(f691,plain,
( vtcheck(vbind(sK87,sK88,sK89),sK80(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_8 ),
inference(resolution,[],[f683,f354]) ).
fof(f711,plain,
( ! [X0,X1] :
( vapp(X0,X1) != vapp(ve1app,ve2app)
| sK80(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)) = X1 )
| ~ spl91_8 ),
inference(superposition,[],[f222,f690]) ).
fof(f729,plain,
( ve2app = sK80(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| ~ spl91_8 ),
inference(equality_resolution,[],[f711]) ).
fof(f730,plain,
( vapp(ve1app,ve2app) = vabs(sK83(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK85(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK84(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| sP12(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| vapp(ve1app,ve2app) = vvar(sK82(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))) ),
inference(resolution,[],[f362,f366]) ).
fof(f742,plain,
( vtcheck(vbind(sK87,sK88,sK89),ve2app,sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_8 ),
inference(superposition,[],[f691,f729]) ).
fof(f786,plain,
( visFreeVar(sK87,ve2app)
| vtcheck(sK89,ve2app,sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_8 ),
inference(resolution,[],[f742,f365]) ).
fof(f794,definition,
( spl91_15
<=> vtcheck(sK89,ve2app,sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))) ),
introduced(definition,[new_symbols(definition,[spl91_15])],[avatar_definition]) ).
fof(f796,plain,
( vtcheck(sK89,ve2app,sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_15 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f798,definition,
( spl91_16
<=> visFreeVar(sK87,ve2app) ),
introduced(definition,[new_symbols(definition,[spl91_16])],[avatar_definition]) ).
fof(f800,plain,
( visFreeVar(sK87,ve2app)
| ~ spl91_16 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f801,plain,
( spl91_15
| spl91_16
| ~ spl91_8 ),
inference(avatar_split_clause,[],[f786,f681,f798,f794]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( sK87 != X0
| visFreeVar(X0,X1)
| vapp(X2,ve2app) != X1 )
| ~ spl91_16 ),
inference(resolution,[],[f800,f236]) ).
fof(f873,plain,
( ! [X0,X1] :
( vapp(X1,ve2app) != X0
| visFreeVar(sK87,X0) )
| ~ spl91_16 ),
inference(equality_resolution,[],[f844]) ).
fof(f875,plain,
( ! [X0] : visFreeVar(sK87,vapp(X0,ve2app))
| ~ spl91_16 ),
inference(equality_resolution,[],[f873]) ).
fof(f884,plain,
( $false
| ~ spl91_16 ),
inference(resolution,[],[f875,f367]) ).
fof(f894,plain,
~ spl91_16,
inference(avatar_contradiction_clause,[],[f884]) ).
fof(f895,plain,
( sP12(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| vapp(ve1app,ve2app) = vvar(sK82(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))) ),
inference(forward_subsumption_resolution,[],[f730,f226]) ).
fof(f899,plain,
( vapp(ve1app,ve2app) = vvar(sK82(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| spl91_8 ),
inference(forward_subsumption_resolution,[],[f895,f682]) ).
fof(f911,plain,
( $false
| spl91_8 ),
inference(forward_subsumption_resolution,[],[f899,f225]) ).
fof(f912,plain,
spl91_8,
inference(avatar_contradiction_clause,[],[f911]) ).
fof(f916,plain,
( vtcheck(vbind(sK87,sK88,sK89),sK79(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),varrow(sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK90))
| ~ spl91_8 ),
inference(resolution,[],[f683,f355]) ).
fof(f917,plain,
( vapp(ve1app,ve2app) = vapp(sK79(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK80(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| ~ spl91_8 ),
inference(resolution,[],[f683,f356]) ).
fof(f953,plain,
( ! [X0,X1] :
( vapp(X0,X1) != vapp(ve1app,ve2app)
| sK79(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)) = X0 )
| ~ spl91_8 ),
inference(superposition,[],[f223,f917]) ).
fof(f1024,plain,
( ve1app = sK79(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89))
| ~ spl91_8 ),
inference(equality_resolution,[],[f953]) ).
fof(f1151,plain,
( vtcheck(vbind(sK87,sK88,sK89),ve1app,varrow(sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK90))
| ~ spl91_8 ),
inference(superposition,[],[f916,f1024]) ).
fof(f1228,plain,
( visFreeVar(sK87,ve1app)
| vtcheck(sK89,ve1app,varrow(sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK90))
| ~ spl91_8 ),
inference(resolution,[],[f1151,f364]) ).
fof(f1239,definition,
( spl91_44
<=> vtcheck(sK89,ve1app,varrow(sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK90)) ),
introduced(definition,[new_symbols(definition,[spl91_44])],[avatar_definition]) ).
fof(f1241,plain,
( vtcheck(sK89,ve1app,varrow(sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)),sK90))
| ~ spl91_44 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1243,definition,
( spl91_45
<=> visFreeVar(sK87,ve1app) ),
introduced(definition,[new_symbols(definition,[spl91_45])],[avatar_definition]) ).
fof(f1245,plain,
( visFreeVar(sK87,ve1app)
| ~ spl91_45 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f1246,plain,
( spl91_44
| spl91_45
| ~ spl91_8 ),
inference(avatar_split_clause,[],[f1228,f681,f1243,f1239]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( sK87 != X0
| visFreeVar(X0,X1)
| vapp(ve1app,X2) != X1 )
| ~ spl91_45 ),
inference(resolution,[],[f1245,f237]) ).
fof(f1391,plain,
( ! [X0,X1] :
( vapp(ve1app,X1) != X0
| visFreeVar(sK87,X0) )
| ~ spl91_45 ),
inference(equality_resolution,[],[f1348]) ).
fof(f1396,plain,
( ! [X0] : visFreeVar(sK87,vapp(ve1app,X0))
| ~ spl91_45 ),
inference(equality_resolution,[],[f1391]) ).
fof(f1398,plain,
( $false
| ~ spl91_45 ),
inference(resolution,[],[f1396,f367]) ).
fof(f1408,plain,
~ spl91_45,
inference(avatar_contradiction_clause,[],[f1398]) ).
fof(f1419,plain,
( ! [X0] :
( ~ vtcheck(sK89,X0,sK81(vapp(ve1app,ve2app),sK90,vbind(sK87,sK88,sK89)))
| vtcheck(sK89,vapp(ve1app,X0),sK90) )
| ~ spl91_44 ),
inference(resolution,[],[f1241,f353]) ).
fof(f1450,plain,
( vtcheck(sK89,vapp(ve1app,ve2app),sK90)
| ~ spl91_15
| ~ spl91_44 ),
inference(resolution,[],[f1419,f796]) ).
fof(f1451,plain,
( $false
| ~ spl91_15
| ~ spl91_44 ),
inference(forward_subsumption_resolution,[],[f1450,f368]) ).
fof(f1452,plain,
( ~ spl91_15
| ~ spl91_44 ),
inference(avatar_contradiction_clause,[],[f1451]) ).
cnf(s14,plain,
( ~ spl91_8
| spl91_15
| spl91_16 ),
inference(sat_conversion,[],[f801]) ).
cnf(s19,plain,
~ spl91_16,
inference(sat_conversion,[],[f894]) ).
cnf(s21,plain,
spl91_8,
inference(sat_conversion,[],[f912]) ).
cnf(s51,plain,
( ~ spl91_8
| spl91_44
| spl91_45 ),
inference(sat_conversion,[],[f1246]) ).
cnf(s64,plain,
~ spl91_45,
inference(sat_conversion,[],[f1408]) ).
cnf(s65,plain,
( ~ spl91_15
| ~ spl91_44 ),
inference(sat_conversion,[],[f1452]) ).
cnf(s66,plain,
( ~ spl91_8
| spl91_44 ),
inference(rat,[],[s51,s64]) ).
cnf(s73,plain,
spl91_44,
inference(rat,[],[s66,s21]) ).
cnf(s77,plain,
~ spl91_15,
inference(rat,[],[s65,s73]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s14,s19,s77,s21]) ).
fof(f1453,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM137+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:55:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.32 % (250627)Will run a generic schedule for satisfiability detection.
% 0.18/0.32 % (250632)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3824962743_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.32 % (250633)% WARNING: option uhcvi not known.
% 0.18/0.32 % (250634)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2015926366:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.32 % (250633)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3180987231:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.32 % (250635)dis+10_1_sil=32000:sp=arity:random_seed=1012547472:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.32 % (250636)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3581497649:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.32 % (250637)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3192960838:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.32 % (250638)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1350260180:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.32 % TRYING [1]
% 0.18/0.32 % TRYING [2]
% 0.18/0.32 % TRYING [3]
% 0.18/0.32 % (250637) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-250627-250637"...
% 0.18/0.32 % (250637)...printing done.
% 0.18/0.32 % (250637)Refutation found. Thanks to Tanya!
% 0.18/0.32 % SZS status Theorem for theBenchmark
% 0.18/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.32 % (250637)------------------------------
% 0.18/0.32 % (250637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.32 % (250637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.32 % (250637)CaDiCaL version: 2.1.3
% 0.18/0.32 % (250637)Termination reason: Refutation
% 0.18/0.32 % (250637)Time elapsed: 0.047 s
% 0.18/0.32 % (250637)Peak memory usage: 13 MB
% 0.18/0.32 % (250637)Instructions burned: 76 (million)
% 0.18/0.32 % (250627)Success in time 0.092 s
% 0.18/0.32 % Vampire exiting
%------------------------------------------------------------------------------