%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM132+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 09:39:38 AM UTC 2026
% Result : Theorem 8.90s 2.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 22 unt; 3 def)
% Number of atoms : 230 ( 94 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 263 ( 106 ~; 111 |; 32 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 256 ( 242 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(f28,axiom,
! [X0,X1] :
( vgensym(X1) = X0
=> ~ visFreeVar(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f33,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( X0 = X4
& X1 = X5
& X2 = vabs(X7,X6,X9) )
=> ( ( X4 != X7
& visFreeVar(X7,X5)
& X8 = vgensym(vapp(vapp(X5,X9),vvar(X4))) )
=> ( X3 = vsubst(X0,X1,X2)
=> X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst4) ).
fof(f58,axiom,
! [X0,X1,X2,X3] :
( ~ visFreeVar(X2,X3)
=> valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-subst-abs') ).
fof(f59,axiom,
! [X0,X1,X2,X3] :
( ( vtcheck(X1,X0,X3)
& valphaEquivalent(X0,X2) )
=> vtcheck(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','alpha-equiv-typing') ).
fof(f64,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( X2 != X4
& ~ visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-2-gen') ).
fof(f65,axiom,
! [X0,X1,X2,X3] :
( X3 = vgensym(vapp(vapp(X0,X1),vvar(X2)))
=> X2 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-unequal-var-3') ).
fof(f66,axiom,
! [X0,X1,X2,X3] :
( X2 = vgensym(vapp(vapp(X0,X3),vvar(X1)))
=> ~ visFreeVar(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-free-2') ).
fof(f67,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 != X4
& visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-3') ).
fof(f68,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 != X4
& visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f88,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(f89,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,[],[f88]) ).
fof(f109,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9)))
| vsubst(X0,X1,X2) != X3
| X4 = X7
| ~ visFreeVar(X7,X5)
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| X0 != X4
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(ennf_transformation,[],[f33]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9)))
| vsubst(X0,X1,X2) != X3
| X4 = X7
| ~ visFreeVar(X7,X5)
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| X0 != X4
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(flattening,[],[f118]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3)))
| visFreeVar(X2,X3) ),
inference(ennf_transformation,[],[f58]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( vtcheck(X1,X2,X3)
| ~ vtcheck(X1,X0,X3)
| ~ valphaEquivalent(X0,X2) ),
inference(ennf_transformation,[],[f59]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( vtcheck(X1,X2,X3)
| ~ vtcheck(X1,X0,X3)
| ~ valphaEquivalent(X0,X2) ),
inference(flattening,[],[f157]) ).
fof(f167,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7) ),
inference(ennf_transformation,[],[f64]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| vgensym(vapp(vapp(X0,X1),vvar(X2))) != X3 ),
inference(ennf_transformation,[],[f65]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( ~ visFreeVar(X2,X3)
| vgensym(vapp(vapp(X0,X3),vvar(X1))) != X2 ),
inference(ennf_transformation,[],[f66]) ).
fof(f171,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& X2 != X4
& visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(ennf_transformation,[],[f68]) ).
fof(f172,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& X2 != X4
& visFreeVar(X4,X3)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6) ),
inference(flattening,[],[f171]) ).
fof(f235,plain,
( ~ vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93)
& sK89 != sK91
& visFreeVar(sK91,sK90)
& vtcheck(sK88,sK90,sK87)
& vtcheck(vbind(sK89,sK87,sK88),vabs(sK91,sK92,veabs),sK93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90,sK91,sK92,sK93]),skolemize(X0,sK87),skolemize(X1,sK88),skolemize(X2,sK89),skolemize(X3,sK90),skolemize(X4,sK91),skolemize(X5,sK92),skolemize(X6,sK93)],[f172]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| X0 != X3
| vapp(X2,X4) != X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f288,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f293,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3
| vsubst(X0,X1,X2) != X3
| X4 = X7
| ~ visFreeVar(X7,X5)
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| X0 != X4
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(cnf_transformation,[],[f119]) ).
fof(f387,plain,
! [X2,X3,X0,X1] :
( valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3)))
| visFreeVar(X2,X3) ),
inference(cnf_transformation,[],[f156]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( ~ vtcheck(X1,X0,X3)
| vtcheck(X1,X2,X3)
| ~ valphaEquivalent(X0,X2) ),
inference(cnf_transformation,[],[f158]) ).
fof(f393,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
| X2 = X4
| visFreeVar(X4,X3)
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
inference(cnf_transformation,[],[f168]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( X2 != X3
| vgensym(vapp(vapp(X0,X1),vvar(X2))) != X3 ),
inference(cnf_transformation,[],[f169]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(X2,X3)
| vgensym(vapp(vapp(X0,X3),vvar(X1))) != X2 ),
inference(cnf_transformation,[],[f170]) ).
fof(f396,plain,
vtcheck(vbind(sK89,sK87,sK88),vabs(sK91,sK92,veabs),sK93),
inference(cnf_transformation,[],[f235]) ).
fof(f397,plain,
vtcheck(sK88,sK90,sK87),
inference(cnf_transformation,[],[f235]) ).
fof(f398,plain,
visFreeVar(sK91,sK90),
inference(cnf_transformation,[],[f235]) ).
fof(f399,plain,
sK89 != sK91,
inference(cnf_transformation,[],[f235]) ).
fof(f400,plain,
~ vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93),
inference(cnf_transformation,[],[f235]) ).
fof(f422,plain,
! [X2,X3,X1,X4] :
( visFreeVar(X3,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1 ),
inference(equality_resolution,[],[f258]) ).
fof(f423,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f422]) ).
fof(f450,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f288]) ).
fof(f469,plain,
! [X2,X0,X1,X8,X6,X9,X7,X4,X5] :
( vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9)))
| X4 = X7
| ~ visFreeVar(X7,X5)
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| X0 != X4
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(equality_resolution,[],[f293]) ).
fof(f470,plain,
! [X2,X0,X1,X6,X9,X7,X4,X5] :
( vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9)))
| X4 = X7
| ~ visFreeVar(X7,X5)
| X0 != X4
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(equality_resolution,[],[f469]) ).
fof(f471,plain,
! [X2,X1,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X1,X2)
| X4 = X7
| ~ visFreeVar(X7,X5)
| X1 != X5
| vabs(X7,X6,X9) != X2 ),
inference(equality_resolution,[],[f470]) ).
fof(f472,plain,
! [X2,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,X2)
| X4 = X7
| ~ visFreeVar(X7,X5)
| vabs(X7,X6,X9) != X2 ),
inference(equality_resolution,[],[f471]) ).
fof(f473,plain,
! [X6,X9,X7,X4,X5] :
( ~ visFreeVar(X7,X5)
| X4 = X7
| vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9)) ),
inference(equality_resolution,[],[f472]) ).
fof(f512,plain,
! [X3,X0,X1] : vgensym(vapp(vapp(X0,X1),vvar(X3))) != X3,
inference(equality_resolution,[],[f394]) ).
fof(f513,plain,
! [X3,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X3),vvar(X1))),X3),
inference(equality_resolution,[],[f395]) ).
fof(f514,definition,
sF94 = vabs(sK91,sK92,veabs),
introduced(definition,[new_symbols(definition,[sF94])],[function_definition]) ).
fof(f515,plain,
vabs(sK91,sK92,veabs) = sF94,
inference(reorient_equations,[],[f514]) ).
fof(f516,definition,
sF95 = vsubst(sK89,sK90,sF94),
introduced(definition,[new_symbols(definition,[sF95])],[function_definition]) ).
fof(f517,plain,
vsubst(sK89,sK90,sF94) = sF95,
inference(reorient_equations,[],[f516]) ).
fof(f518,plain,
~ vtcheck(sK88,sF95,sK93),
inference(definition_folding,[],[f400,f517,f515]) ).
fof(f519,definition,
sF96 = vbind(sK89,sK87,sK88),
introduced(definition,[new_symbols(definition,[sF96])],[function_definition]) ).
fof(f520,plain,
vbind(sK89,sK87,sK88) = sF96,
inference(reorient_equations,[],[f519]) ).
fof(f521,plain,
vtcheck(sF96,sF94,sK93),
inference(definition_folding,[],[f396,f515,f520]) ).
fof(f523,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(sK88,vsubst(sK89,X4,vabs(X0,X1,X2)),X3)
| sK89 = X0
| visFreeVar(X0,X4)
| ~ vtcheck(sK88,X4,sK87)
| ~ vtcheck(sF96,vabs(X0,X1,X2),X3) ),
inference(superposition,[],[f393,f520]) ).
fof(f532,plain,
! [X0] :
( vtcheck(sF96,X0,sK93)
| ~ valphaEquivalent(sF94,X0) ),
inference(resolution,[],[f388,f521]) ).
fof(f536,plain,
! [X0] :
( valphaEquivalent(sF94,vabs(X0,sK92,vsubst(sK91,vvar(X0),veabs)))
| visFreeVar(X0,veabs) ),
inference(superposition,[],[f387,f515]) ).
fof(f614,plain,
! [X2,X0,X1] :
( vsubst(X0,sK90,vabs(vgensym(vapp(vapp(sK90,X1),vvar(X0))),X2,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(X0)))),X1))) = vsubst(X0,sK90,vabs(sK91,X2,X1))
| sK91 = X0 ),
inference(resolution,[],[f473,f398]) ).
fof(f674,plain,
! [X2,X0,X1] :
( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X0,X1)),X2)
| sK89 = vgensym(vapp(vapp(sK90,X1),vvar(sK89)))
| visFreeVar(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),sK90)
| ~ vtcheck(sK88,sK90,sK87)
| ~ vtcheck(sF96,vabs(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),X0,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(sK89)))),X1)),X2)
| sK89 = sK91 ),
inference(superposition,[],[f523,f614]) ).
fof(f675,plain,
! [X2,X0,X1] :
( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X0,X1)),X2)
| sK89 = vgensym(vapp(vapp(sK90,X1),vvar(sK89)))
| visFreeVar(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),sK90)
| ~ vtcheck(sF96,vabs(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),X0,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(sK89)))),X1)),X2)
| sK89 = sK91 ),
inference(forward_subsumption_resolution,[],[f674,f397]) ).
fof(f677,plain,
! [X2,X0,X1] :
( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X0,X1)),X2)
| sK89 = vgensym(vapp(vapp(sK90,X1),vvar(sK89)))
| visFreeVar(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),sK90)
| ~ vtcheck(sF96,vabs(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),X0,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(sK89)))),X1)),X2) ),
inference(forward_subsumption_resolution,[],[f675,f399]) ).
fof(f679,plain,
! [X2,X0,X1] :
( ~ vtcheck(sF96,vabs(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),X0,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(sK89)))),X1)),X2)
| visFreeVar(vgensym(vapp(vapp(sK90,X1),vvar(sK89))),sK90)
| vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X0,X1)),X2) ),
inference(forward_subsumption_resolution,[],[f677,f512]) ).
fof(f694,plain,
! [X0,X1] :
( ~ valphaEquivalent(sF94,vabs(vgensym(vapp(vapp(sK90,X0),vvar(sK89))),X1,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X0),vvar(sK89)))),X0)))
| vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X1,X0)),sK93)
| visFreeVar(vgensym(vapp(vapp(sK90,X0),vvar(sK89))),sK90) ),
inference(resolution,[],[f679,f532]) ).
fof(f718,plain,
! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0),
inference(resolution,[],[f423,f450]) ).
fof(f727,plain,
! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0),
inference(resolution,[],[f718,f423]) ).
fof(f1503,plain,
( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93)
| visFreeVar(vgensym(vapp(vapp(sK90,veabs),vvar(sK89))),sK90)
| visFreeVar(vgensym(vapp(vapp(sK90,veabs),vvar(sK89))),veabs) ),
inference(resolution,[],[f694,f536]) ).
fof(f1509,plain,
( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93)
| visFreeVar(vgensym(vapp(vapp(sK90,veabs),vvar(sK89))),veabs) ),
inference(forward_subsumption_resolution,[],[f1503,f727]) ).
fof(f1510,plain,
vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93),
inference(forward_subsumption_resolution,[],[f1509,f513]) ).
fof(f1511,plain,
vtcheck(sK88,vsubst(sK89,sK90,sF94),sK93),
inference(forward_demodulation,[],[f1510,f515]) ).
fof(f1512,plain,
vtcheck(sK88,sF95,sK93),
inference(forward_demodulation,[],[f1511,f517]) ).
fof(f1513,plain,
$false,
inference(forward_subsumption_resolution,[],[f1512,f518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM132+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:55:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 8.90/2.40 % (315576)Detected formulas, will run a generic FOF schedule.
% 8.90/2.40 % (315584)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2631859641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.90/2.40 % (315584)Refutation not found, incomplete strategy
% 8.90/2.40 % (315584)------------------------------
% 8.90/2.40 % (315584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315584)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315584)Termination reason: Refutation not found, incomplete strategy
% 8.90/2.40 % (315584)Time elapsed: 0.002 s
% 8.90/2.40 % (315584)Peak memory usage: 88 MB
% 8.90/2.40 % (315584)Instructions burned: 3 (million)
% 8.90/2.40 % (315585)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=823747245:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.90/2.40 % (315581)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=1724394416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.90/2.40 % (315587)dis-21_1_sil=8000:lcm=predicate:random_seed=890768770: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)
% 8.90/2.40 % (315582)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=2504306916:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.90/2.40 % (315583)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=3857936545:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.90/2.40 % (315586)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2179387974:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.90/2.40 % (315585)Instruction limit reached!
% 8.90/2.40 % (315585)------------------------------
% 8.90/2.40 % (315585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315585)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315585)Termination reason: Instruction limit
% 8.90/2.40 % (315585)Termination phase: Saturation
% 8.90/2.40 % (315585)Time elapsed: 0.072 s
% 8.90/2.40 % (315585)Peak memory usage: 88 MB
% 8.90/2.40 % (315585)Instructions burned: 119 (million)
% 8.90/2.40 % (315587)Instruction limit reached!
% 8.90/2.40 % (315587)------------------------------
% 8.90/2.40 % (315587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315587)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315587)Termination reason: Instruction limit
% 8.90/2.40 % (315587)Termination phase: Saturation
% 8.90/2.40 % (315587)Time elapsed: 0.077 s
% 8.90/2.40 % (315587)Peak memory usage: 89 MB
% 8.90/2.40 % (315587)Instructions burned: 130 (million)
% 8.90/2.40 % (315586)Instruction limit reached!
% 8.90/2.40 % (315586)------------------------------
% 8.90/2.40 % (315586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315586)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315586)Termination reason: Instruction limit
% 8.90/2.40 % (315586)Termination phase: Saturation
% 8.90/2.40 % (315586)Time elapsed: 0.092 s
% 8.90/2.40 % (315586)Peak memory usage: 90 MB
% 8.90/2.40 % (315586)Instructions burned: 139 (million)
% 8.90/2.40 % (315584)------------------------------
% 8.90/2.40 % (315584)------------------------------
% 8.90/2.40 % (315596)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1643209837:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.90/2.40 % (315595)lrs+10_1_sil=8000:sp=occurrence:random_seed=1566373065:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.90/2.40 % (315598)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=3249336899:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.90/2.40 % (315597)lrs+1011_1_sil=32000:sp=occurrence:random_seed=410291686:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.90/2.40 % (315598)Instruction limit reached!
% 8.90/2.40 % (315598)------------------------------
% 8.90/2.40 % (315598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315598)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315598)Termination reason: Instruction limit
% 8.90/2.40 % (315598)Termination phase: Saturation
% 8.90/2.40 % (315598)Time elapsed: 0.079 s
% 8.90/2.40 % (315598)Peak memory usage: 91 MB
% 8.90/2.40 % (315598)Instructions burned: 252 (million)
% 8.90/2.40 % (315596)Instruction limit reached!
% 8.90/2.40 % (315596)------------------------------
% 8.90/2.40 % (315596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315596)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315596)Termination reason: Instruction limit
% 8.90/2.40 % (315596)Termination phase: Saturation
% 8.90/2.40 % (315596)Time elapsed: 0.096 s
% 8.90/2.40 % (315596)Peak memory usage: 90 MB
% 8.90/2.40 % (315596)Instructions burned: 157 (million)
% 8.90/2.40 % (315595)Instruction limit reached!
% 8.90/2.40 % (315595)------------------------------
% 8.90/2.40 % (315595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315595)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315595)Termination reason: Instruction limit
% 8.90/2.40 % (315595)Termination phase: Saturation
% 8.90/2.40 % (315595)Time elapsed: 0.175 s
% 8.90/2.40 % (315595)Peak memory usage: 91 MB
% 8.90/2.40 % (315595)Instructions burned: 287 (million)
% 8.90/2.40 % (315603)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4019717997:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.90/2.40 % (315597)Instruction limit reached!
% 8.90/2.40 % (315597)------------------------------
% 8.90/2.40 % (315597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315597)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315597)Termination reason: Instruction limit
% 8.90/2.40 % (315597)Termination phase: Saturation
% 8.90/2.40 % (315597)Time elapsed: 0.183 s
% 8.90/2.40 % (315597)Peak memory usage: 92 MB
% 8.90/2.40 % (315597)Instructions burned: 326 (million)
% 8.90/2.40 % (315604)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2366539465:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.90/2.40 % (315603)Instruction limit reached!
% 8.90/2.40 % (315603)------------------------------
% 8.90/2.40 % (315603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315603)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315603)Termination reason: Instruction limit
% 8.90/2.40 % (315603)Termination phase: Saturation
% 8.90/2.40 % (315603)Time elapsed: 0.079 s
% 8.90/2.40 % (315603)Peak memory usage: 89 MB
% 8.90/2.40 % (315603)Instructions burned: 294 (million)
% 8.90/2.40 % (315605)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1611096809:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.90/2.40 % (315607)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4151018668:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.90/2.40 % (315609)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3904620362:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.90/2.40 % (315605)Instruction limit reached!
% 8.90/2.40 % (315605)------------------------------
% 8.90/2.40 % (315605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315605)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315605)Termination reason: Instruction limit
% 8.90/2.40 % (315605)Termination phase: Saturation
% 8.90/2.40 % (315605)Time elapsed: 0.074 s
% 8.90/2.40 % (315605)Peak memory usage: 89 MB
% 8.90/2.40 % (315605)Instructions burned: 114 (million)
% 8.90/2.40 % (315607)Instruction limit reached!
% 8.90/2.40 % (315607)------------------------------
% 8.90/2.40 % (315607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315607)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315607)Termination reason: Instruction limit
% 8.90/2.40 % (315607)Termination phase: Saturation
% 8.90/2.40 % (315607)Time elapsed: 0.068 s
% 8.90/2.40 % (315607)Peak memory usage: 88 MB
% 8.90/2.40 % (315607)Instructions burned: 127 (million)
% 8.90/2.40 % (315609)Instruction limit reached!
% 8.90/2.40 % (315609)------------------------------
% 8.90/2.40 % (315609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315609)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315609)Termination reason: Instruction limit
% 8.90/2.40 % (315609)Termination phase: Saturation
% 8.90/2.40 % (315609)Time elapsed: 0.030 s
% 8.90/2.40 % (315609)Peak memory usage: 89 MB
% 8.90/2.40 % (315609)Instructions burned: 117 (million)
% 8.90/2.40 % (315613)lrs+10_1_sil=8000:sp=occurrence:random_seed=3473413941:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.90/2.40 % (315615)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=131250254:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 8.90/2.40 % (315614)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3183065468:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.90/2.40 % (315614)Refutation not found, incomplete strategy
% 8.90/2.40 % (315614)------------------------------
% 8.90/2.40 % (315614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315614)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315614)Termination reason: Refutation not found, incomplete strategy
% 8.90/2.40 % (315614)Time elapsed: 0.005 s
% 8.90/2.40 % (315614)Peak memory usage: 88 MB
% 8.90/2.40 % (315614)Instructions burned: 6 (million)
% 8.90/2.40 % (315614)------------------------------
% 8.90/2.40 % (315614)------------------------------
% 8.90/2.40 % (315619)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2868064764:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 8.90/2.40 % (315619)Instruction limit reached!
% 8.90/2.40 % (315619)------------------------------
% 8.90/2.40 % (315619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315619)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315619)Termination reason: Instruction limit
% 8.90/2.40 % (315619)Termination phase: Saturation
% 8.90/2.40 % (315619)Time elapsed: 0.075 s
% 8.90/2.40 % (315619)Peak memory usage: 91 MB
% 8.90/2.40 % (315619)Instructions burned: 135 (million)
% 8.90/2.40 % (315613)Instruction limit reached!
% 8.90/2.40 % (315613)------------------------------
% 8.90/2.40 % (315613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/2.40 % (315613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/2.40 % (315613)CaDiCaL version: 2.1.3
% 8.90/2.40 % (315613)Termination reason: Instruction limit
% 8.90/2.40 % (315613)Termination phase: Saturation
% 8.90/2.40 % (315613)Time elapsed: 0.515 s
% 8.90/2.40 % (315613)Peak memory usage: 98 MB
% 8.90/2.40 % (315613)Instructions burned: 909 (million)
% 8.90/2.40 % (315621)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3470906123:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 8.90/2.40 % (315604)First to succeed.
% 8.90/2.40 % (315604)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-315576"
% 8.90/2.40 % (315622)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1952017569:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 8.90/2.40 % (315615)Also succeeded, but the first one will report.
% 8.90/2.40 % (315581)Also succeeded, but the first one will report.
% 8.90/2.40 % (315604)Refutation found. Thanks to Tanya!
% 8.90/2.40 % SZS status Theorem for theBenchmark
% 8.90/2.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/2.50 % (315604)------------------------------
% 0.19/2.50 % (315604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.50 % (315604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.50 % (315604)CaDiCaL version: 2.1.3
% 0.19/2.50 % (315604)Termination reason: Refutation
% 0.19/2.50 % (315604)Time elapsed: 0.913 s
% 0.19/2.50 % (315604)Peak memory usage: 133 MB
% 0.19/2.50 % (315604)Instructions burned: 1377 (million)
% 0.19/2.50 % (315604)------------------------------
% 0.19/2.50 % (315604)------------------------------
% 0.19/2.50 % (315576)Success in time 1.75 s
% 0.19/2.50 % Vampire exiting
%------------------------------------------------------------------------------