%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n019.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 09:39:39 AM UTC 2026
% Result : Theorem 6.99s 1.77s
% Output : Refutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 121 ( 26 unt; 9 def)
% Number of atoms : 341 ( 96 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 362 ( 142 ~; 144 |; 58 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-3 aty)
% Number of variables : 247 ( 0 sgn 193 !; 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/theBenchmark.p','EQ-app') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] : vabs(X0,X1,X2) != vapp(X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','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/theBenchmark.p',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/theBenchmark.p','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/theBenchmark.p','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(X0,X1)
| ~ visFreeVar(X3,X4)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f237,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| 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] :
( vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2))
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f212]) ).
fof(f355,plain,
! [X2,X0,X1] :
( vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1))
| ~ sP12(X0,X1,X2) ),
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(f390,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f237]) ).
fof(f391,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f390]) ).
fof(f392,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f236]) ).
fof(f393,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f392]) ).
fof(f480,definition,
sF91 = vapp(ve1app,ve2app),
introduced(definition,[new_symbols(definition,[sF91])],[function_definition]) ).
fof(f481,plain,
vapp(ve1app,ve2app) = sF91,
inference(reorient_equations,[],[f480]) ).
fof(f482,plain,
~ vtcheck(sK89,sF91,sK90),
inference(definition_folding,[],[f368,f481]) ).
fof(f483,plain,
~ visFreeVar(sK87,sF91),
inference(definition_folding,[],[f367,f481]) ).
fof(f484,definition,
sF92 = vbind(sK87,sK88,sK89),
introduced(definition,[new_symbols(definition,[sF92])],[function_definition]) ).
fof(f485,plain,
vbind(sK87,sK88,sK89) = sF92,
inference(reorient_equations,[],[f484]) ).
fof(f486,plain,
vtcheck(sF92,sF91,sK90),
inference(definition_folding,[],[f366,f481,f485]) ).
fof(f488,plain,
! [X0] :
( ~ visFreeVar(X0,ve2app)
| visFreeVar(X0,sF91) ),
inference(superposition,[],[f393,f481]) ).
fof(f489,plain,
! [X0] :
( ~ visFreeVar(X0,ve1app)
| visFreeVar(X0,sF91) ),
inference(superposition,[],[f391,f481]) ).
fof(f493,plain,
! [X0] : vvar(X0) != sF91,
inference(superposition,[],[f225,f481]) ).
fof(f494,plain,
! [X0] :
( ~ vtcheck(sF92,ve1app,X0)
| visFreeVar(sK87,ve1app)
| vtcheck(sK89,ve1app,X0) ),
inference(superposition,[],[f364,f485]) ).
fof(f496,definition,
( spl93_1
<=> visFreeVar(sK87,ve1app) ),
introduced(definition,[new_symbols(definition,[spl93_1])],[avatar_definition]) ).
fof(f498,plain,
( visFreeVar(sK87,ve1app)
| ~ spl93_1 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f500,definition,
( spl93_2
<=> ! [X0] :
( ~ vtcheck(sF92,ve1app,X0)
| vtcheck(sK89,ve1app,X0) ) ),
introduced(definition,[new_symbols(definition,[spl93_2])],[avatar_definition]) ).
fof(f501,plain,
( ! [X0] :
( ~ vtcheck(sF92,ve1app,X0)
| vtcheck(sK89,ve1app,X0) )
| ~ spl93_2 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f502,plain,
( spl93_1
| spl93_2 ),
inference(avatar_split_clause,[],[f494,f500,f496]) ).
fof(f503,plain,
! [X0] :
( ~ vtcheck(sF92,ve2app,X0)
| visFreeVar(sK87,ve2app)
| vtcheck(sK89,ve2app,X0) ),
inference(superposition,[],[f365,f485]) ).
fof(f505,definition,
( spl93_3
<=> visFreeVar(sK87,ve2app) ),
introduced(definition,[new_symbols(definition,[spl93_3])],[avatar_definition]) ).
fof(f507,plain,
( visFreeVar(sK87,ve2app)
| ~ spl93_3 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f509,definition,
( spl93_4
<=> ! [X0] :
( ~ vtcheck(sF92,ve2app,X0)
| vtcheck(sK89,ve2app,X0) ) ),
introduced(definition,[new_symbols(definition,[spl93_4])],[avatar_definition]) ).
fof(f510,plain,
( ! [X0] :
( ~ vtcheck(sF92,ve2app,X0)
| vtcheck(sK89,ve2app,X0) )
| ~ spl93_4 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( spl93_3
| spl93_4 ),
inference(avatar_split_clause,[],[f503,f509,f505]) ).
fof(f512,plain,
( visFreeVar(sK87,sF91)
| ~ spl93_3 ),
inference(resolution,[],[f507,f488]) ).
fof(f513,plain,
( $false
| ~ spl93_3 ),
inference(forward_subsumption_resolution,[],[f512,f483]) ).
fof(f514,plain,
~ spl93_3,
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f515,plain,
( sF91 = vabs(sK83(sF91,sK90,sF92),sK85(sF91,sK90,sF92),sK84(sF91,sK90,sF92))
| sP12(sF91,sK90,sF92)
| sF91 = vvar(sK82(sF91,sK90,sF92)) ),
inference(resolution,[],[f362,f486]) ).
fof(f516,plain,
( sF91 = vabs(sK83(sF91,sK90,sF92),sK85(sF91,sK90,sF92),sK84(sF91,sK90,sF92))
| sP12(sF91,sK90,sF92) ),
inference(forward_subsumption_resolution,[],[f515,f493]) ).
fof(f518,definition,
( spl93_5
<=> sP12(sF91,sK90,sF92) ),
introduced(definition,[new_symbols(definition,[spl93_5])],[avatar_definition]) ).
fof(f520,plain,
( sP12(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f522,definition,
( spl93_6
<=> sF91 = vabs(sK83(sF91,sK90,sF92),sK85(sF91,sK90,sF92),sK84(sF91,sK90,sF92)) ),
introduced(definition,[new_symbols(definition,[spl93_6])],[avatar_definition]) ).
fof(f524,plain,
( sF91 = vabs(sK83(sF91,sK90,sF92),sK85(sF91,sK90,sF92),sK84(sF91,sK90,sF92))
| ~ spl93_6 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f525,plain,
( spl93_5
| spl93_6 ),
inference(avatar_split_clause,[],[f516,f522,f518]) ).
fof(f536,plain,
! [X0,X1] :
( vapp(X0,X1) != sF91
| ve1app = X0 ),
inference(superposition,[],[f223,f481]) ).
fof(f579,plain,
( ! [X0,X1] : vapp(X0,X1) != sF91
| ~ spl93_6 ),
inference(superposition,[],[f226,f524]) ).
fof(f580,plain,
( sF91 != sF91
| ~ spl93_6 ),
inference(superposition,[],[f579,f481]) ).
fof(f581,plain,
( $false
| ~ spl93_6 ),
inference(trivial_inequality_removal,[],[f580]) ).
fof(f582,plain,
~ spl93_6,
inference(avatar_contradiction_clause,[],[f581]) ).
fof(f583,plain,
( sF91 = vapp(sK79(sF91,sK90,sF92),sK80(sF91,sK90,sF92))
| ~ spl93_5 ),
inference(resolution,[],[f520,f356]) ).
fof(f585,plain,
( ! [X0,X1] :
( vapp(X0,X1) != sF91
| sK80(sF91,sK90,sF92) = X1 )
| ~ spl93_5 ),
inference(superposition,[],[f222,f583]) ).
fof(f593,plain,
( sF91 != sF91
| ve1app = sK79(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(superposition,[],[f536,f583]) ).
fof(f594,plain,
( ve1app = sK79(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(trivial_inequality_removal,[],[f593]) ).
fof(f600,plain,
( vtcheck(sF92,ve1app,varrow(sK81(sF91,sK90,sF92),sK90))
| ~ sP12(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(superposition,[],[f355,f594]) ).
fof(f601,plain,
( vtcheck(sF92,ve1app,varrow(sK81(sF91,sK90,sF92),sK90))
| ~ spl93_5 ),
inference(forward_subsumption_resolution,[],[f600,f520]) ).
fof(f627,plain,
( visFreeVar(sK87,sF91)
| ~ spl93_1 ),
inference(resolution,[],[f498,f489]) ).
fof(f628,plain,
( $false
| ~ spl93_1 ),
inference(forward_subsumption_resolution,[],[f627,f483]) ).
fof(f629,plain,
~ spl93_1,
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f630,plain,
( vtcheck(sK89,ve1app,varrow(sK81(sF91,sK90,sF92),sK90))
| ~ spl93_2
| ~ spl93_5 ),
inference(resolution,[],[f501,f601]) ).
fof(f631,plain,
( ! [X0] :
( ~ vtcheck(sK89,X0,sK81(sF91,sK90,sF92))
| vtcheck(sK89,vapp(ve1app,X0),sK90) )
| ~ spl93_2
| ~ spl93_5 ),
inference(resolution,[],[f630,f353]) ).
fof(f655,plain,
( sF91 != sF91
| ve2app = sK80(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(superposition,[],[f585,f481]) ).
fof(f656,plain,
( ve2app = sK80(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(trivial_inequality_removal,[],[f655]) ).
fof(f660,plain,
( vtcheck(sF92,ve2app,sK81(sF91,sK90,sF92))
| ~ sP12(sF91,sK90,sF92)
| ~ spl93_5 ),
inference(superposition,[],[f354,f656]) ).
fof(f661,plain,
( vtcheck(sF92,ve2app,sK81(sF91,sK90,sF92))
| ~ spl93_5 ),
inference(forward_subsumption_resolution,[],[f660,f520]) ).
fof(f664,plain,
( vtcheck(sK89,ve2app,sK81(sF91,sK90,sF92))
| ~ spl93_4
| ~ spl93_5 ),
inference(resolution,[],[f661,f510]) ).
fof(f686,plain,
( vtcheck(sK89,vapp(ve1app,ve2app),sK90)
| ~ spl93_2
| ~ spl93_4
| ~ spl93_5 ),
inference(resolution,[],[f664,f631]) ).
fof(f707,plain,
( vtcheck(sK89,sF91,sK90)
| ~ spl93_2
| ~ spl93_4
| ~ spl93_5 ),
inference(forward_demodulation,[],[f686,f481]) ).
fof(f708,plain,
( $false
| ~ spl93_2
| ~ spl93_4
| ~ spl93_5 ),
inference(forward_subsumption_resolution,[],[f707,f482]) ).
fof(f709,plain,
( ~ spl93_2
| ~ spl93_4
| ~ spl93_5 ),
inference(avatar_contradiction_clause,[],[f708]) ).
cnf(s1,plain,
( spl93_1
| spl93_2 ),
inference(sat_conversion,[],[f502]) ).
cnf(s2,plain,
( spl93_3
| spl93_4 ),
inference(sat_conversion,[],[f511]) ).
cnf(s3,plain,
~ spl93_3,
inference(sat_conversion,[],[f514]) ).
cnf(s4,plain,
( spl93_5
| spl93_6 ),
inference(sat_conversion,[],[f525]) ).
cnf(s7,plain,
~ spl93_6,
inference(sat_conversion,[],[f582]) ).
cnf(s10,plain,
~ spl93_1,
inference(sat_conversion,[],[f629]) ).
cnf(s15,plain,
( ~ spl93_2
| ~ spl93_4
| ~ spl93_5 ),
inference(sat_conversion,[],[f709]) ).
cnf(s16,plain,
spl93_5,
inference(rat,[],[s4,s7]) ).
cnf(s17,plain,
spl93_4,
inference(rat,[],[s2,s3]) ).
cnf(s18,plain,
~ spl93_2,
inference(rat,[],[s15,s16,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s10]) ).
fof(f710,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM137+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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 21:55:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.99/1.77 % (316026)Detected formulas, will run a generic FOF schedule.
% 6.99/1.77 % (316035)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=5776799:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.99/1.77 % (316035)Refutation not found, incomplete strategy
% 6.99/1.77 % (316035)------------------------------
% 6.99/1.77 % (316035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316035)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316035)Termination reason: Refutation not found, incomplete strategy
% 6.99/1.77 % (316035)Time elapsed: 0.002 s
% 6.99/1.77 % (316035)Peak memory usage: 88 MB
% 6.99/1.77 % (316035)Instructions burned: 3 (million)
% 6.99/1.77 % (316032)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=1958996014:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.99/1.77 % (316031)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=693640463:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.99/1.77 % (316033)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=2199499616:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.99/1.77 % (316034)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2714927933:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.99/1.77 % (316034)Refutation not found, incomplete strategy
% 6.99/1.77 % (316034)------------------------------
% 6.99/1.77 % (316034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316034)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316034)Termination reason: Refutation not found, incomplete strategy
% 6.99/1.77 % (316034)Time elapsed: 0.002 s
% 6.99/1.77 % (316034)Peak memory usage: 88 MB
% 6.99/1.77 % (316034)Instructions burned: 2 (million)
% 6.99/1.77 % (316036)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2181563306:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.99/1.77 % (316037)dis-21_1_sil=8000:lcm=predicate:random_seed=4187456118: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)
% 6.99/1.77 % (316037)Instruction limit reached!
% 6.99/1.77 % (316037)------------------------------
% 6.99/1.77 % (316037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316037)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316037)Termination reason: Instruction limit
% 6.99/1.77 % (316037)Termination phase: Saturation
% 6.99/1.77 % (316037)Time elapsed: 0.071 s
% 6.99/1.77 % (316037)Peak memory usage: 89 MB
% 6.99/1.77 % (316037)Instructions burned: 130 (million)
% 6.99/1.77 % (316036)Instruction limit reached!
% 6.99/1.77 % (316036)------------------------------
% 6.99/1.77 % (316036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316036)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316036)Termination reason: Instruction limit
% 6.99/1.77 % (316036)Termination phase: Saturation
% 6.99/1.77 % (316036)Time elapsed: 0.088 s
% 6.99/1.77 % (316036)Peak memory usage: 90 MB
% 6.99/1.77 % (316036)Instructions burned: 140 (million)
% 6.99/1.77 % (316035)------------------------------
% 6.99/1.77 % (316035)------------------------------
% 6.99/1.77 % (316047)lrs+1011_1_sil=32000:sp=occurrence:random_seed=459675101:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.99/1.77 % (316045)lrs+10_1_sil=8000:sp=occurrence:random_seed=94538850:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.99/1.77 % (316045)Refutation not found, incomplete strategy
% 6.99/1.77 % (316045)------------------------------
% 6.99/1.77 % (316045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316045)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316045)Termination reason: Refutation not found, incomplete strategy
% 6.99/1.77 % (316045)Time elapsed: 0.002 s
% 6.99/1.77 % (316045)Peak memory usage: 88 MB
% 6.99/1.77 % (316045)Instructions burned: 2 (million)
% 6.99/1.77 % (316034)------------------------------
% 6.99/1.77 % (316034)------------------------------
% 6.99/1.77 % (316046)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1439776261:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.99/1.77 % (316047)Instruction limit reached!
% 6.99/1.77 % (316047)------------------------------
% 6.99/1.77 % (316047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316047)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316047)Termination reason: Instruction limit
% 6.99/1.77 % (316047)Termination phase: Saturation
% 6.99/1.77 % (316047)Time elapsed: 0.112 s
% 6.99/1.77 % (316047)Peak memory usage: 91 MB
% 6.99/1.77 % (316047)Instructions burned: 328 (million)
% 6.99/1.77 % (316046)Instruction limit reached!
% 6.99/1.77 % (316046)------------------------------
% 6.99/1.77 % (316046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316046)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316046)Termination reason: Instruction limit
% 6.99/1.77 % (316046)Termination phase: Saturation
% 6.99/1.77 % (316046)Time elapsed: 0.082 s
% 6.99/1.77 % (316046)Peak memory usage: 91 MB
% 6.99/1.77 % (316046)Instructions burned: 159 (million)
% 6.99/1.77 % (316050)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=4134351788:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.99/1.77 % (316052)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=89512395:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.99/1.77 % (316052)Refutation not found, incomplete strategy
% 6.99/1.77 % (316052)------------------------------
% 6.99/1.77 % (316052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316052)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316052)Termination reason: Refutation not found, incomplete strategy
% 6.99/1.77 % (316052)Time elapsed: 0.004 s
% 6.99/1.77 % (316052)Peak memory usage: 88 MB
% 6.99/1.77 % (316052)Instructions burned: 10 (million)
% 6.99/1.77 % (316045)------------------------------
% 6.99/1.77 % (316045)------------------------------
% 6.99/1.77 % (316053)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2417285017:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.99/1.77 % (316050)Instruction limit reached!
% 6.99/1.77 % (316050)------------------------------
% 6.99/1.77 % (316050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316050)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316050)Termination reason: Instruction limit
% 6.99/1.77 % (316050)Termination phase: Saturation
% 6.99/1.77 % (316050)Time elapsed: 0.150 s
% 6.99/1.77 % (316050)Peak memory usage: 91 MB
% 6.99/1.77 % (316050)Instructions burned: 248 (million)
% 6.99/1.77 % (316052)------------------------------
% 6.99/1.77 % (316052)------------------------------
% 6.99/1.77 % (316056)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2786642048:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.99/1.77 % (316031)First to succeed.
% 6.99/1.77 % (316032)Also succeeded, but the first one will report.
% 6.99/1.77 % (316031)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-316026"
% 6.99/1.77 % (316056)Instruction limit reached!
% 6.99/1.77 % (316056)------------------------------
% 6.99/1.77 % (316056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316056)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316056)Termination reason: Instruction limit
% 6.99/1.77 % (316056)Termination phase: Saturation
% 6.99/1.77 % (316056)Time elapsed: 0.068 s
% 6.99/1.77 % (316056)Peak memory usage: 89 MB
% 6.99/1.77 % (316056)Instructions burned: 114 (million)
% 6.99/1.77 % (316058)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3173101361:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.99/1.77 % (316059)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3662961791:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.99/1.77 % (316058)Instruction limit reached!
% 6.99/1.77 % (316058)------------------------------
% 6.99/1.77 % (316058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316058)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316058)Termination reason: Instruction limit
% 6.99/1.77 % (316058)Termination phase: Saturation
% 6.99/1.77 % (316058)Time elapsed: 0.065 s
% 6.99/1.77 % (316058)Peak memory usage: 89 MB
% 6.99/1.77 % (316058)Instructions burned: 127 (million)
% 6.99/1.77 % (316059)Instruction limit reached!
% 6.99/1.77 % (316059)------------------------------
% 6.99/1.77 % (316059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316059)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316059)Termination reason: Instruction limit
% 6.99/1.77 % (316059)Termination phase: Saturation
% 6.99/1.77 % (316059)Time elapsed: 0.035 s
% 6.99/1.77 % (316059)Peak memory usage: 89 MB
% 6.99/1.77 % (316059)Instructions burned: 117 (million)
% 6.99/1.77 % (316061)lrs+10_1_sil=8000:sp=occurrence:random_seed=634000256:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.99/1.77 % (316064)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3964374410:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.99/1.77 % (316064)Refutation not found, incomplete strategy
% 6.99/1.77 % (316064)------------------------------
% 6.99/1.77 % (316064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.99/1.77 % (316064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.77 % (316064)CaDiCaL version: 2.1.3
% 6.99/1.77 % (316064)Termination reason: Refutation not found, incomplete strategy
% 6.99/1.77 % (316064)Time elapsed: 0.001 s
% 6.99/1.77 % (316064)Peak memory usage: 88 MB
% 6.99/1.77 % (316064)Instructions burned: 2 (million)
% 6.99/1.77 % (316031)Refutation found. Thanks to Tanya!
% 6.99/1.77 % SZS status Theorem for theBenchmark
% 6.99/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 8.42/1.93 % (316031)------------------------------
% 8.42/1.93 % (316031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.42/1.93 % (316031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.93 % (316031)CaDiCaL version: 2.1.3
% 8.42/1.93 % (316031)Termination reason: Refutation
% 8.42/1.93 % (316031)Time elapsed: 0.674 s
% 8.42/1.93 % (316031)Peak memory usage: 129 MB
% 8.42/1.93 % (316031)Instructions burned: 1013 (million)
% 8.42/1.93 % (316031)------------------------------
% 8.42/1.93 % (316031)------------------------------
% 8.42/1.93 % (316026)Success in time 1.11 s
% 8.42/1.93 % Vampire exiting
%------------------------------------------------------------------------------