%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM123+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:39:36 AM UTC 2026
% Result : Theorem 6.88s 2.02s
% Output : Refutation 8.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 121 ( 25 unt; 7 def)
% Number of atoms : 367 ( 144 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 382 ( 136 ~; 162 |; 68 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 290 ( 0 sgn 232 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
=> ( X0 = X3
& X1 = X4
& X2 = X5 ) )
& ( ( X0 = X3
& X1 = X4
& X2 = X5 )
=> vabs(X0,X1,X2) = vabs(X3,X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( X1 = X4
& X2 = vabs(X3,X0,X5) )
=> ( ( ( X3 != X4
& visFreeVar(X4,X5) )
=> visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
=> ( X3 != X4
& visFreeVar(X4,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 != X0
& vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
=> vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
fof(f52,axiom,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X1,X3,X0),X2,X4)
=> vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-abs') ).
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/sandbox2/benchmark/theBenchmark.p','T-inv') ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( ~ visFreeVar(X0,veabs)
& vtcheck(X2,veabs,X3) )
=> vtcheck(vbind(X0,X1,X2),veabs,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-IH') ).
fof(f58,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( X0 != X3
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& vtcheck(X2,vabs(X3,X4,veabs),X5) )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1') ).
fof(f59,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( X0 != X3
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& vtcheck(X2,vabs(X3,X4,veabs),X5) )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
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(f68,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X0 = X3
& X1 = X4
& X2 = X5 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X0 != X3
| X1 != X4
| X2 != X5 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X0 = X3
& X1 = X4
& X2 = X5 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X0 != X3
| X1 != X4
| X2 != X5 ) ),
inference(flattening,[],[f68]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( visFreeVar(X1,X2)
| X3 = X4
| ~ visFreeVar(X4,X5) )
& ( ( X3 != X4
& visFreeVar(X4,X5) )
| ~ visFreeVar(X1,X2) ) )
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(ennf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( visFreeVar(X1,X2)
| X3 = X4
| ~ visFreeVar(X4,X5) )
& ( ( X3 != X4
& visFreeVar(X4,X5) )
| ~ visFreeVar(X1,X2) ) )
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(flattening,[],[f77]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ),
inference(ennf_transformation,[],[f27]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ),
inference(flattening,[],[f98]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ),
inference(ennf_transformation,[],[f52]) ).
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(f148,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| visFreeVar(X0,veabs)
| ~ vtcheck(X2,veabs,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| visFreeVar(X0,veabs)
| ~ vtcheck(X2,veabs,X3) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& X0 != X3
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& vtcheck(X2,vabs(X3,X4,veabs),X5) ),
inference(ennf_transformation,[],[f59]) ).
fof(f151,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& X0 != X3
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& vtcheck(X2,vabs(X3,X4,veabs),X5) ),
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(vbind(sK87,sK88,sK89),vabs(sK90,sK91,veabs),sK92)
& sK87 != sK90
& ~ visFreeVar(sK87,vabs(sK90,sK91,veabs))
& vtcheck(sK89,vabs(sK90,sK91,veabs),sK92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90,sK91,sK92]),skolemize(X0,sK87),skolemize(X1,sK88),skolemize(X2,sK89),skolemize(X3,sK90),skolemize(X4,sK91),skolemize(X5,sK92)],[f151]) ).
fof(f218,plain,
! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,X2) != vabs(X3,X4,X5)
| X2 = X5 ),
inference(cnf_transformation,[],[f69]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,X2) != vabs(X3,X4,X5)
| X1 = X4 ),
inference(cnf_transformation,[],[f69]) ).
fof(f220,plain,
! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,X2) != vabs(X3,X4,X5)
| X0 = X3 ),
inference(cnf_transformation,[],[f69]) ).
fof(f224,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f226,plain,
! [X2,X3,X0,X1,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
inference(cnf_transformation,[],[f6]) ).
fof(f234,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X1,X2)
| X3 = X4
| ~ visFreeVar(X4,X5)
| X1 != X4
| vabs(X3,X0,X5) != X2 ),
inference(cnf_transformation,[],[f78]) ).
fof(f266,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2
| vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6) ),
inference(cnf_transformation,[],[f99]) ).
fof(f352,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ),
inference(cnf_transformation,[],[f139]) ).
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(f360,plain,
! [X2,X0,X1] :
( vtcheck(vbind(sK83(X0,X1,X2),sK85(X0,X1,X2),X2),sK84(X0,X1,X2),sK86(X0,X1,X2))
| vvar(sK82(X0,X1,X2)) = X0
| sP12(X0,X1,X2)
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f361,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
| sP12(X0,X1,X2)
| vvar(sK82(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f213]) ).
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(f365,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| visFreeVar(X0,veabs)
| ~ vtcheck(X2,veabs,X3) ),
inference(cnf_transformation,[],[f149]) ).
fof(f366,plain,
vtcheck(sK89,vabs(sK90,sK91,veabs),sK92),
inference(cnf_transformation,[],[f214]) ).
fof(f367,plain,
~ visFreeVar(sK87,vabs(sK90,sK91,veabs)),
inference(cnf_transformation,[],[f214]) ).
fof(f368,plain,
sK87 != sK90,
inference(cnf_transformation,[],[f214]) ).
fof(f369,plain,
~ vtcheck(vbind(sK87,sK88,sK89),vabs(sK90,sK91,veabs),sK92),
inference(cnf_transformation,[],[f214]) ).
fof(f384,plain,
! [X2,X3,X0,X4,X5] :
( visFreeVar(X4,X2)
| X3 = X4
| ~ visFreeVar(X4,X5)
| vabs(X3,X0,X5) != X2 ),
inference(equality_resolution,[],[f234]) ).
fof(f385,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| X3 = X4
| ~ visFreeVar(X4,X5) ),
inference(equality_resolution,[],[f384]) ).
fof(f481,definition,
sF93 = vbind(sK87,sK88,sK89),
introduced(definition,[new_symbols(definition,[sF93])],[function_definition]) ).
fof(f482,plain,
vbind(sK87,sK88,sK89) = sF93,
inference(reorient_equations,[],[f481]) ).
fof(f483,definition,
sF94 = vabs(sK90,sK91,veabs),
introduced(definition,[new_symbols(definition,[sF94])],[function_definition]) ).
fof(f484,plain,
vabs(sK90,sK91,veabs) = sF94,
inference(reorient_equations,[],[f483]) ).
fof(f485,plain,
~ vtcheck(sF93,sF94,sK92),
inference(definition_folding,[],[f369,f484,f482]) ).
fof(f486,plain,
~ visFreeVar(sK87,sF94),
inference(definition_folding,[],[f367,f484]) ).
fof(f487,plain,
vtcheck(sK89,sF94,sK92),
inference(definition_folding,[],[f366,f484]) ).
fof(f491,definition,
( spl95_1
<=> visFreeVar(sK87,veabs) ),
introduced(definition,[new_symbols(definition,[spl95_1])],[avatar_definition]) ).
fof(f492,plain,
( ~ visFreeVar(sK87,veabs)
| spl95_1 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f493,plain,
( visFreeVar(sK87,veabs)
| ~ spl95_1 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f502,plain,
! [X0,X1] :
( ~ vtcheck(vbind(sK90,sK91,X0),veabs,X1)
| vtcheck(X0,sF94,varrow(sK91,X1)) ),
inference(superposition,[],[f352,f484]) ).
fof(f513,plain,
! [X2,X0,X1] :
( vabs(X0,X1,X2) != sF94
| veabs = X2 ),
inference(superposition,[],[f218,f484]) ).
fof(f516,plain,
! [X2,X0,X1] :
( vabs(X0,X1,X2) != sF94
| sK91 = X1 ),
inference(superposition,[],[f219,f484]) ).
fof(f519,plain,
! [X2,X0,X1] :
( vabs(X0,X1,X2) != sF94
| sK90 = X0 ),
inference(superposition,[],[f220,f484]) ).
fof(f523,plain,
( sF94 = vabs(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK84(sF94,sK92,sK89))
| sP12(sF94,sK92,sK89)
| sF94 = vvar(sK82(sF94,sK92,sK89)) ),
inference(resolution,[],[f362,f487]) ).
fof(f528,definition,
( spl95_5
<=> sF94 = vvar(sK82(sF94,sK92,sK89)) ),
introduced(definition,[new_symbols(definition,[spl95_5])],[avatar_definition]) ).
fof(f530,plain,
( sF94 = vvar(sK82(sF94,sK92,sK89))
| ~ spl95_5 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f532,definition,
( spl95_6
<=> sP12(sF94,sK92,sK89) ),
introduced(definition,[new_symbols(definition,[spl95_6])],[avatar_definition]) ).
fof(f533,plain,
( ~ sP12(sF94,sK92,sK89)
| spl95_6 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f534,plain,
( sP12(sF94,sK92,sK89)
| ~ spl95_6 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f536,definition,
( spl95_7
<=> sF94 = vabs(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK84(sF94,sK92,sK89)) ),
introduced(definition,[new_symbols(definition,[spl95_7])],[avatar_definition]) ).
fof(f538,plain,
( sF94 = vabs(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK84(sF94,sK92,sK89))
| ~ spl95_7 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f539,plain,
( spl95_5
| spl95_6
| spl95_7 ),
inference(avatar_split_clause,[],[f523,f536,f532,f528]) ).
fof(f541,plain,
( ! [X2,X0,X1] : vabs(X0,X1,X2) != sF94
| ~ spl95_5 ),
inference(superposition,[],[f224,f530]) ).
fof(f542,plain,
! [X0] : vvar(X0) != sF94,
inference(superposition,[],[f224,f484]) ).
fof(f543,plain,
( sF94 != sF94
| ~ spl95_5 ),
inference(superposition,[],[f541,f484]) ).
fof(f544,plain,
( $false
| ~ spl95_5 ),
inference(trivial_inequality_removal,[],[f543]) ).
fof(f545,plain,
~ spl95_5,
inference(avatar_contradiction_clause,[],[f544]) ).
fof(f548,plain,
! [X0] :
( ~ visFreeVar(X0,veabs)
| sK90 = X0
| visFreeVar(X0,sF94) ),
inference(superposition,[],[f385,f484]) ).
fof(f555,plain,
( sF94 = vapp(sK79(sF94,sK92,sK89),sK80(sF94,sK92,sK89))
| ~ spl95_6 ),
inference(resolution,[],[f356,f534]) ).
fof(f566,plain,
( sK92 = varrow(sK85(sF94,sK92,sK89),sK86(sF94,sK92,sK89))
| sP12(sF94,sK92,sK89)
| sF94 = vvar(sK82(sF94,sK92,sK89)) ),
inference(resolution,[],[f361,f487]) ).
fof(f576,plain,
( ! [X2,X0,X1] : vabs(X0,X1,X2) != sF94
| ~ spl95_6 ),
inference(superposition,[],[f226,f555]) ).
fof(f577,plain,
( sF94 != sF94
| ~ spl95_6 ),
inference(superposition,[],[f576,f484]) ).
fof(f578,plain,
( $false
| ~ spl95_6 ),
inference(trivial_inequality_removal,[],[f577]) ).
fof(f579,plain,
~ spl95_6,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f580,plain,
( sK92 = varrow(sK85(sF94,sK92,sK89),sK86(sF94,sK92,sK89))
| sF94 = vvar(sK82(sF94,sK92,sK89))
| spl95_6 ),
inference(forward_subsumption_resolution,[],[f566,f533]) ).
fof(f581,plain,
( sK92 = varrow(sK85(sF94,sK92,sK89),sK86(sF94,sK92,sK89))
| spl95_6 ),
inference(forward_subsumption_resolution,[],[f580,f542]) ).
fof(f596,plain,
( sF94 != sF94
| veabs = sK84(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(superposition,[],[f513,f538]) ).
fof(f597,plain,
( sF94 != sF94
| sK91 = sK85(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(superposition,[],[f516,f538]) ).
fof(f598,plain,
( sF94 != sF94
| sK90 = sK83(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(superposition,[],[f519,f538]) ).
fof(f600,plain,
( sK90 = sK83(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(trivial_inequality_removal,[],[f598]) ).
fof(f601,plain,
( sK91 = sK85(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(trivial_inequality_removal,[],[f597]) ).
fof(f602,plain,
( veabs = sK84(sF94,sK92,sK89)
| ~ spl95_7 ),
inference(trivial_inequality_removal,[],[f596]) ).
fof(f626,plain,
( sK92 = varrow(sK91,sK86(sF94,sK92,sK89))
| spl95_6
| ~ spl95_7 ),
inference(superposition,[],[f581,f601]) ).
fof(f653,plain,
( vtcheck(vbind(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK89),veabs,sK86(sF94,sK92,sK89))
| sF94 = vvar(sK82(sF94,sK92,sK89))
| sP12(sF94,sK92,sK89)
| ~ vtcheck(sK89,sF94,sK92)
| ~ spl95_7 ),
inference(superposition,[],[f360,f602]) ).
fof(f654,plain,
( vtcheck(vbind(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK89),veabs,sK86(sF94,sK92,sK89))
| sP12(sF94,sK92,sK89)
| ~ vtcheck(sK89,sF94,sK92)
| ~ spl95_7 ),
inference(forward_subsumption_resolution,[],[f653,f542]) ).
fof(f658,plain,
( vtcheck(vbind(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK89),veabs,sK86(sF94,sK92,sK89))
| ~ vtcheck(sK89,sF94,sK92)
| spl95_6
| ~ spl95_7 ),
inference(forward_subsumption_resolution,[],[f654,f533]) ).
fof(f662,plain,
( vtcheck(vbind(sK83(sF94,sK92,sK89),sK85(sF94,sK92,sK89),sK89),veabs,sK86(sF94,sK92,sK89))
| spl95_6
| ~ spl95_7 ),
inference(forward_subsumption_resolution,[],[f658,f487]) ).
fof(f666,plain,
( vtcheck(vbind(sK83(sF94,sK92,sK89),sK91,sK89),veabs,sK86(sF94,sK92,sK89))
| spl95_6
| ~ spl95_7 ),
inference(forward_demodulation,[],[f662,f601]) ).
fof(f670,plain,
( vtcheck(vbind(sK90,sK91,sK89),veabs,sK86(sF94,sK92,sK89))
| spl95_6
| ~ spl95_7 ),
inference(forward_demodulation,[],[f666,f600]) ).
fof(f739,plain,
( sK87 = sK90
| visFreeVar(sK87,sF94)
| ~ spl95_1 ),
inference(resolution,[],[f493,f548]) ).
fof(f740,plain,
( visFreeVar(sK87,sF94)
| ~ spl95_1 ),
inference(forward_subsumption_resolution,[],[f739,f368]) ).
fof(f741,plain,
( $false
| ~ spl95_1 ),
inference(forward_subsumption_resolution,[],[f740,f486]) ).
fof(f742,plain,
~ spl95_1,
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f760,plain,
! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X2,vbind(X1,X3,X4)),veabs,X5)
| X0 = X1
| visFreeVar(X1,veabs)
| ~ vtcheck(vbind(X0,X2,X4),veabs,X5) ),
inference(resolution,[],[f266,f365]) ).
fof(f777,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X3,X1),sF94,varrow(sK91,X2))
| visFreeVar(X0,veabs)
| ~ vtcheck(vbind(sK90,sK91,X1),veabs,X2)
| sK90 = X0 ),
inference(resolution,[],[f760,f502]) ).
fof(f803,plain,
! [X0] :
( vtcheck(sF93,sF94,varrow(sK91,X0))
| visFreeVar(sK87,veabs)
| ~ vtcheck(vbind(sK90,sK91,sK89),veabs,X0)
| sK87 = sK90 ),
inference(superposition,[],[f777,f482]) ).
fof(f805,plain,
( ! [X0] :
( vtcheck(sF93,sF94,varrow(sK91,X0))
| ~ vtcheck(vbind(sK90,sK91,sK89),veabs,X0)
| sK87 = sK90 )
| spl95_1 ),
inference(forward_subsumption_resolution,[],[f803,f492]) ).
fof(f810,plain,
( ! [X0] :
( ~ vtcheck(vbind(sK90,sK91,sK89),veabs,X0)
| vtcheck(sF93,sF94,varrow(sK91,X0)) )
| spl95_1 ),
inference(forward_subsumption_resolution,[],[f805,f368]) ).
fof(f812,plain,
( vtcheck(sF93,sF94,varrow(sK91,sK86(sF94,sK92,sK89)))
| spl95_1
| spl95_6
| ~ spl95_7 ),
inference(resolution,[],[f810,f670]) ).
fof(f814,plain,
( vtcheck(sF93,sF94,sK92)
| spl95_1
| spl95_6
| ~ spl95_7 ),
inference(forward_demodulation,[],[f812,f626]) ).
fof(f815,plain,
( $false
| spl95_1
| spl95_6
| ~ spl95_7 ),
inference(forward_subsumption_resolution,[],[f814,f485]) ).
fof(f816,plain,
( spl95_1
| spl95_6
| ~ spl95_7 ),
inference(avatar_contradiction_clause,[],[f815]) ).
cnf(s3,plain,
( spl95_5
| spl95_6
| spl95_7 ),
inference(sat_conversion,[],[f539]) ).
cnf(s4,plain,
~ spl95_5,
inference(sat_conversion,[],[f545]) ).
cnf(s5,plain,
~ spl95_6,
inference(sat_conversion,[],[f579]) ).
cnf(s10,plain,
~ spl95_1,
inference(sat_conversion,[],[f742]) ).
cnf(s11,plain,
( spl95_1
| spl95_6
| ~ spl95_7 ),
inference(sat_conversion,[],[f816]) ).
cnf(s13,plain,
~ spl95_7,
inference(rat,[],[s11,s10,s5]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s13,s5,s4]) ).
fof(f817,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM123+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n007.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 21:52:55 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.88/2.02 % (2893186)Detected formulas, will run a generic FOF schedule.
% 6.88/2.02 % (2893193)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4170272267:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.88/2.02 % (2893199)dis-21_1_sil=8000:lcm=predicate:random_seed=605793472:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.88/2.02 % (2893195)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3314597544:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.88/2.02 % (2893198)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1792087228:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.88/2.02 % (2893197)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1499061628:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.88/2.02 % (2893196)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=503224078:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.88/2.02 % (2893194)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2173078440:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.88/2.02 % (2893196)Refutation not found, incomplete strategy
% 6.88/2.02 % (2893196)------------------------------
% 6.88/2.02 % (2893196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893196)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893196)Termination reason: Refutation not found, incomplete strategy
% 6.88/2.02 % (2893196)Time elapsed: 0.004 s
% 6.88/2.02 % (2893196)Peak memory usage: 88 MB
% 6.88/2.02 % (2893196)Instructions burned: 2 (million)
% 6.88/2.02 % (2893199)Instruction limit reached!
% 6.88/2.02 % (2893199)------------------------------
% 6.88/2.02 % (2893199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893199)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893199)Termination reason: Instruction limit
% 6.88/2.02 % (2893199)Termination phase: Saturation
% 6.88/2.02 % (2893199)Time elapsed: 0.101 s
% 6.88/2.02 % (2893199)Peak memory usage: 90 MB
% 6.88/2.02 % (2893199)Instructions burned: 129 (million)
% 6.88/2.02 % (2893197)Instruction limit reached!
% 6.88/2.02 % (2893197)------------------------------
% 6.88/2.02 % (2893197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893197)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893197)Termination reason: Instruction limit
% 6.88/2.02 % (2893197)Termination phase: Saturation
% 6.88/2.02 % (2893197)Time elapsed: 0.082 s
% 6.88/2.02 % (2893197)Peak memory usage: 87 MB
% 6.88/2.02 % (2893197)Instructions burned: 119 (million)
% 6.88/2.02 % (2893198)Instruction limit reached!
% 6.88/2.02 % (2893198)------------------------------
% 6.88/2.02 % (2893198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893198)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893198)Termination reason: Instruction limit
% 6.88/2.02 % (2893198)Termination phase: Saturation
% 6.88/2.02 % (2893198)Time elapsed: 0.136 s
% 6.88/2.02 % (2893198)Peak memory usage: 89 MB
% 6.88/2.02 % (2893198)Instructions burned: 139 (million)
% 6.88/2.02 % (2893207)lrs+10_1_sil=8000:sp=occurrence:random_seed=1889300897:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.88/2.02 % (2893208)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3573683568:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 6.88/2.02 % (2893196)------------------------------
% 6.88/2.02 % (2893196)------------------------------
% 6.88/2.02 % (2893209)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4129564300:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.88/2.02 % (2893207)Instruction limit reached!
% 6.88/2.02 % (2893207)------------------------------
% 6.88/2.02 % (2893207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893207)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893207)Termination reason: Instruction limit
% 6.88/2.02 % (2893207)Termination phase: Saturation
% 6.88/2.02 % (2893207)Time elapsed: 0.208 s
% 6.88/2.02 % (2893207)Peak memory usage: 89 MB
% 6.88/2.02 % (2893207)Instructions burned: 285 (million)
% 6.88/2.02 % (2893208)Instruction limit reached!
% 6.88/2.02 % (2893208)------------------------------
% 6.88/2.02 % (2893208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893208)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893208)Termination reason: Instruction limit
% 6.88/2.02 % (2893208)Termination phase: Saturation
% 6.88/2.02 % (2893208)Time elapsed: 0.144 s
% 6.88/2.02 % (2893208)Peak memory usage: 91 MB
% 6.88/2.02 % (2893208)Instructions burned: 157 (million)
% 6.88/2.02 % (2893193)First to succeed.
% 6.88/2.02 % (2893193)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2893186"
% 6.88/2.02 % (2893212)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1147503749:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 6.88/2.02 % (2893209)Instruction limit reached!
% 6.88/2.02 % (2893209)------------------------------
% 6.88/2.02 % (2893209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893209)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893209)Termination reason: Instruction limit
% 6.88/2.02 % (2893209)Termination phase: Saturation
% 6.88/2.02 % (2893209)Time elapsed: 0.247 s
% 6.88/2.02 % (2893209)Peak memory usage: 91 MB
% 6.88/2.02 % (2893209)Instructions burned: 326 (million)
% 6.88/2.02 % (2893214)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2550077013:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 6.88/2.02 % (2893216)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2443655986:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 6.88/2.02 % (2893214)Refutation not found, incomplete strategy
% 6.88/2.02 % (2893214)------------------------------
% 6.88/2.02 % (2893214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.02 % (2893214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.02 % (2893214)CaDiCaL version: 2.1.3
% 6.88/2.02 % (2893214)Termination reason: Refutation not found, incomplete strategy
% 6.88/2.02 % (2893214)Time elapsed: 0.012 s
% 6.88/2.02 % (2893214)Peak memory usage: 88 MB
% 6.88/2.02 % (2893214)Instructions burned: 10 (million)
% 6.88/2.02 % (2893193)Refutation found. Thanks to Tanya!
% 6.88/2.02 % SZS status Theorem for theBenchmark
% 6.88/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 8.71/2.36 % (2893193)------------------------------
% 8.71/2.36 % (2893193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/2.36 % (2893193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/2.36 % (2893193)CaDiCaL version: 2.1.3
% 8.71/2.36 % (2893193)Termination reason: Refutation
% 8.71/2.36 % (2893193)Time elapsed: 0.655 s
% 8.71/2.36 % (2893193)Peak memory usage: 131 MB
% 8.71/2.36 % (2893193)Instructions burned: 1072 (million)
% 8.71/2.36 % (2893193)------------------------------
% 8.71/2.36 % (2893193)------------------------------
% 8.71/2.36 % (2893186)Success in time 1.082 s
% 8.71/2.36 % Vampire exiting
%------------------------------------------------------------------------------