%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM135+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:40:22 AM UTC 2026
% Result : Theorem 1.92s 0.51s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 142 ( 30 unt; 9 def)
% Number of atoms : 419 ( 237 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 451 ( 174 ~; 197 |; 54 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 9 con; 0-3 aty)
% Number of variables : 338 ( 0 sgn 280 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( vvar(X0) = vvar(X1)
=> X0 = X1 )
& ( X0 = X1
=> vvar(X0) = vvar(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-var') ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-abs') ).
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( ( X0 = X3
& X1 = vvar(X2) )
=> ( ( X2 = X3
=> visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).
fof(f21,axiom,
! [X0,X1,X2] :
( X0 = vsomeType(X2)
=> ( X1 = vgetSomeType(X0)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',getSomeType0) ).
fof(f23,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X3 = X1
& X4 = vbind(X2,X6,X0) )
=> ( X1 = X2
=> ( X5 = vlookup(X3,X4)
=> X5 = vsomeType(X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',lookup1) ).
fof(f29,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 = X0
& X3 = X6
& X4 = vvar(X1) )
=> ( X0 = X1
=> ( X5 = vsubst(X2,X3,X4)
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst0) ).
fof(f30,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( X2 = X1
& X3 = X0
& X4 = vvar(X6) )
=> ( X1 != X6
=> ( X5 = vsubst(X2,X3,X4)
=> X5 = vvar(X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst1) ).
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/Axioms/COM001+0.ax','T-inv') ).
fof(f56,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ visFreeVar(X0,X3)
& vtcheck(vbind(X0,X1,X2),X3,X4) )
=> vtcheck(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
fof(f58,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5) )
=> vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-var') ).
fof(f59,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5) )
=> vtcheck(X1,vsubst(X2,X3,vvar(X4)),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(f67,plain,
! [X0,X1] :
( ( X0 = X1
| vvar(X0) != vvar(X1) )
& ( vvar(X0) = vvar(X1)
| X0 != X1 ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( ( ( visFreeVar(X0,X1)
| X2 != X3 )
& ( X2 = X3
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vvar(X2) != X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( ( ( visFreeVar(X0,X1)
| X2 != X3 )
& ( X2 = X3
| ~ visFreeVar(X0,X1) ) )
| X0 != X3
| vvar(X2) != X1 ),
inference(flattening,[],[f75]) ).
fof(f86,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f21]) ).
fof(f87,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f86]) ).
fof(f90,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = vsomeType(X6)
| vlookup(X3,X4) != X5
| X1 != X2
| X1 != X3
| vbind(X2,X6,X0) != X4 ),
inference(ennf_transformation,[],[f23]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = vsomeType(X6)
| vlookup(X3,X4) != X5
| X1 != X2
| X1 != X3
| vbind(X2,X6,X0) != X4 ),
inference(flattening,[],[f90]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| X0 != X2
| X3 != X6
| vvar(X1) != X4 ),
inference(ennf_transformation,[],[f29]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| X0 != X2
| X3 != X6
| vvar(X1) != X4 ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = vvar(X6)
| vsubst(X2,X3,X4) != X5
| X1 = X6
| X1 != X2
| X0 != X3
| vvar(X6) != X4 ),
inference(ennf_transformation,[],[f30]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = vvar(X6)
| vsubst(X2,X3,X4) != X5
| X1 = X6
| X1 != X2
| X0 != X3
| vvar(X6) != X4 ),
inference(flattening,[],[f103]) ).
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,X4] :
( vtcheck(X2,X3,X4)
| visFreeVar(X0,X3)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(ennf_transformation,[],[f56]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| visFreeVar(X0,X3)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(flattening,[],[f146]) ).
fof(f150,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5) ),
inference(ennf_transformation,[],[f59]) ).
fof(f151,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5)
& vtcheck(X1,X3,X0)
& vtcheck(vbind(X2,X0,X1),vvar(X4),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(sK88,vsubst(sK89,sK90,vvar(sK91)),sK92)
& vtcheck(sK88,sK90,sK87)
& vtcheck(vbind(sK89,sK87,sK88),vvar(sK91),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(f216,plain,
! [X0,X1] :
( vvar(X0) != vvar(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f224,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f225,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| X0 != X3
| vvar(X2) != X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f250,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f252,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| X1 != X3
| vbind(X2,X6,X0) != X4 ),
inference(cnf_transformation,[],[f91]) ).
fof(f268,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| X0 != X2
| X3 != X6
| vvar(X1) != X4 ),
inference(cnf_transformation,[],[f102]) ).
fof(f269,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vvar(X6) = X5
| vsubst(X2,X3,X4) != X5
| X1 = X6
| X1 != X2
| X0 != X3
| vvar(X6) != X4 ),
inference(cnf_transformation,[],[f104]) ).
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(f359,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)
| vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2) ),
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(f364,plain,
! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3)
| vtcheck(X2,X3,X4) ),
inference(cnf_transformation,[],[f147]) ).
fof(f366,plain,
vtcheck(vbind(sK89,sK87,sK88),vvar(sK91),sK92),
inference(cnf_transformation,[],[f214]) ).
fof(f367,plain,
vtcheck(sK88,sK90,sK87),
inference(cnf_transformation,[],[f214]) ).
fof(f368,plain,
~ vtcheck(sK88,vsubst(sK89,sK90,vvar(sK91)),sK92),
inference(cnf_transformation,[],[f214]) ).
fof(f381,plain,
! [X2,X3,X1] :
( X2 = X3
| ~ visFreeVar(X3,X1)
| vvar(X2) != X1 ),
inference(equality_resolution,[],[f230]) ).
fof(f382,plain,
! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 ),
inference(equality_resolution,[],[f381]) ).
fof(f402,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f250]) ).
fof(f403,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f402]) ).
fof(f407,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| X1 != X3
| vbind(X2,X6,X0) != X4 ),
inference(equality_resolution,[],[f252]) ).
fof(f408,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X2 != X3
| vbind(X2,X6,X0) != X4 ),
inference(equality_resolution,[],[f407]) ).
fof(f409,plain,
! [X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X3,X6,X0) != X4 ),
inference(equality_resolution,[],[f408]) ).
fof(f410,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f409]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| X0 != X2
| X3 != X6
| vvar(X1) != X4 ),
inference(equality_resolution,[],[f268]) ).
fof(f420,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X1 != X2
| X3 != X6
| vvar(X1) != X4 ),
inference(equality_resolution,[],[f419]) ).
fof(f421,plain,
! [X2,X3,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X3 != X6
| vvar(X2) != X4 ),
inference(equality_resolution,[],[f420]) ).
fof(f422,plain,
! [X2,X6,X4] :
( vsubst(X2,X6,X4) = X6
| vvar(X2) != X4 ),
inference(equality_resolution,[],[f421]) ).
fof(f423,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f422]) ).
fof(f424,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = vvar(X6)
| X1 = X6
| X1 != X2
| X0 != X3
| vvar(X6) != X4 ),
inference(equality_resolution,[],[f269]) ).
fof(f425,plain,
! [X2,X3,X0,X6,X4] :
( vsubst(X2,X3,X4) = vvar(X6)
| X2 = X6
| X0 != X3
| vvar(X6) != X4 ),
inference(equality_resolution,[],[f424]) ).
fof(f426,plain,
! [X2,X3,X6,X4] :
( vsubst(X2,X3,X4) = vvar(X6)
| X2 = X6
| vvar(X6) != X4 ),
inference(equality_resolution,[],[f425]) ).
fof(f427,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f426]) ).
fof(f480,definition,
sF93 = vvar(sK91),
introduced(definition,[new_symbols(definition,[sF93])],[function_definition]) ).
fof(f481,plain,
vvar(sK91) = sF93,
inference(reorient_equations,[],[f480]) ).
fof(f482,definition,
sF94 = vsubst(sK89,sK90,sF93),
introduced(definition,[new_symbols(definition,[sF94])],[function_definition]) ).
fof(f483,plain,
vsubst(sK89,sK90,sF93) = sF94,
inference(reorient_equations,[],[f482]) ).
fof(f484,plain,
~ vtcheck(sK88,sF94,sK92),
inference(definition_folding,[],[f368,f483,f481]) ).
fof(f485,definition,
sF95 = vbind(sK89,sK87,sK88),
introduced(definition,[new_symbols(definition,[sF95])],[function_definition]) ).
fof(f486,plain,
vbind(sK89,sK87,sK88) = sF95,
inference(reorient_equations,[],[f485]) ).
fof(f487,plain,
vtcheck(sF95,sF93,sK92),
inference(definition_folding,[],[f366,f481,f486]) ).
fof(f492,plain,
! [X0,X1] : vapp(X0,X1) != sF93,
inference(superposition,[],[f225,f481]) ).
fof(f494,plain,
! [X2,X0,X1] : vabs(X0,X1,X2) != sF93,
inference(superposition,[],[f224,f481]) ).
fof(f496,plain,
! [X0] :
( ~ visFreeVar(X0,sF93)
| sK91 = X0 ),
inference(superposition,[],[f382,f481]) ).
fof(f497,plain,
! [X0] : vsubst(sK91,X0,sF93) = X0,
inference(superposition,[],[f423,f481]) ).
fof(f510,plain,
vsomeType(sK87) = vlookup(sK89,sF95),
inference(superposition,[],[f410,f486]) ).
fof(f545,plain,
! [X0,X1] :
( sF93 = vsubst(X0,X1,sF93)
| sK91 = X0 ),
inference(superposition,[],[f427,f481]) ).
fof(f546,plain,
( sF93 = sF94
| sK89 = sK91 ),
inference(superposition,[],[f545,f483]) ).
fof(f549,definition,
( spl96_1
<=> sK89 = sK91 ),
introduced(definition,[new_symbols(definition,[spl96_1])],[avatar_definition]) ).
fof(f551,plain,
( sK89 = sK91
| ~ spl96_1 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f553,definition,
( spl96_2
<=> sF93 = sF94 ),
introduced(definition,[new_symbols(definition,[spl96_2])],[avatar_definition]) ).
fof(f555,plain,
( sF93 = sF94
| ~ spl96_2 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f557,plain,
( spl96_1
| spl96_2 ),
inference(avatar_split_clause,[],[f546,f553,f549]) ).
fof(f559,plain,
( ~ vtcheck(sK88,sF93,sK92)
| ~ spl96_2 ),
inference(superposition,[],[f484,f555]) ).
fof(f613,plain,
! [X0,X1] :
( ~ vtcheck(sF95,X0,X1)
| visFreeVar(sK89,X0)
| vtcheck(sK88,X0,X1) ),
inference(superposition,[],[f364,f486]) ).
fof(f614,plain,
( visFreeVar(sK89,sF93)
| vtcheck(sK88,sF93,sK92) ),
inference(resolution,[],[f613,f487]) ).
fof(f617,plain,
( visFreeVar(sK89,sF93)
| ~ spl96_2 ),
inference(forward_subsumption_resolution,[],[f614,f559]) ).
fof(f621,plain,
( sK89 = sK91
| ~ spl96_2 ),
inference(resolution,[],[f617,f496]) ).
fof(f622,plain,
( spl96_1
| ~ spl96_2 ),
inference(avatar_split_clause,[],[f621,f553,f549]) ).
fof(f630,plain,
( ! [X0] : vsubst(sK89,X0,sF93) = X0
| ~ spl96_1 ),
inference(superposition,[],[f497,f551]) ).
fof(f632,plain,
( sF93 = vvar(sK89)
| ~ spl96_1 ),
inference(superposition,[],[f481,f551]) ).
fof(f635,plain,
( ! [X0] :
( vvar(X0) != sF93
| sK89 = X0 )
| ~ spl96_1 ),
inference(superposition,[],[f216,f632]) ).
fof(f672,plain,
( sK90 = sF94
| ~ spl96_1 ),
inference(superposition,[],[f483,f630]) ).
fof(f1038,definition,
( spl96_24
<=> sF93 = vvar(sK82(sF93,sK92,sF95)) ),
introduced(definition,[new_symbols(definition,[spl96_24])],[avatar_definition]) ).
fof(f1039,plain,
( sF93 != vvar(sK82(sF93,sK92,sF95))
| spl96_24 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1040,plain,
( sF93 = vvar(sK82(sF93,sK92,sF95))
| ~ spl96_24 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1042,definition,
( spl96_25
<=> sP12(sF93,sK92,sF95) ),
introduced(definition,[new_symbols(definition,[spl96_25])],[avatar_definition]) ).
fof(f1043,plain,
( ~ sP12(sF93,sK92,sF95)
| spl96_25 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1044,plain,
( sP12(sF93,sK92,sF95)
| ~ spl96_25 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1064,definition,
( spl96_27
<=> vsomeType(sK92) = vlookup(sK82(sF93,sK92,sF95),sF95) ),
introduced(definition,[new_symbols(definition,[spl96_27])],[avatar_definition]) ).
fof(f1065,plain,
( vsomeType(sK92) != vlookup(sK82(sF93,sK92,sF95),sF95)
| spl96_27 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1066,plain,
( vsomeType(sK92) = vlookup(sK82(sF93,sK92,sF95),sF95)
| ~ spl96_27 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1092,plain,
( sF93 = vabs(sK83(sF93,sK92,sF95),sK85(sF93,sK92,sF95),sK84(sF93,sK92,sF95))
| sP12(sF93,sK92,sF95)
| sF93 = vvar(sK82(sF93,sK92,sF95)) ),
inference(resolution,[],[f362,f487]) ).
fof(f1110,plain,
( sF93 = vabs(sK83(sF93,sK92,sF95),sK85(sF93,sK92,sF95),sK84(sF93,sK92,sF95))
| sP12(sF93,sK92,sF95)
| vsomeType(sK92) = vlookup(sK82(sF93,sK92,sF95),sF95) ),
inference(resolution,[],[f359,f487]) ).
fof(f1167,plain,
( sF93 != sF93
| sK89 = sK82(sF93,sK92,sF95)
| ~ spl96_1
| ~ spl96_24 ),
inference(superposition,[],[f635,f1040]) ).
fof(f1170,plain,
( sK89 = sK82(sF93,sK92,sF95)
| ~ spl96_1
| ~ spl96_24 ),
inference(trivial_inequality_removal,[],[f1167]) ).
fof(f1519,plain,
( vlookup(sK89,sF95) = vsomeType(sK92)
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(superposition,[],[f1066,f1170]) ).
fof(f1521,plain,
( vsomeType(sK87) = vsomeType(sK92)
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(forward_demodulation,[],[f1519,f510]) ).
fof(f1531,plain,
( sK92 = vgetSomeType(vsomeType(sK87))
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(superposition,[],[f403,f1521]) ).
fof(f1537,plain,
( sK87 = sK92
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(forward_demodulation,[],[f1531,f403]) ).
fof(f1544,plain,
( ~ vtcheck(sK88,sF94,sK87)
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(superposition,[],[f484,f1537]) ).
fof(f1554,plain,
( ~ vtcheck(sK88,sK90,sK87)
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(forward_demodulation,[],[f1544,f672]) ).
fof(f1555,plain,
( $false
| ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(forward_subsumption_resolution,[],[f1554,f367]) ).
fof(f1556,plain,
( ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(avatar_contradiction_clause,[],[f1555]) ).
fof(f1557,plain,
( sP12(sF93,sK92,sF95)
| sF93 = vvar(sK82(sF93,sK92,sF95)) ),
inference(forward_subsumption_resolution,[],[f1092,f494]) ).
fof(f1583,plain,
( sP12(sF93,sK92,sF95)
| spl96_24 ),
inference(forward_subsumption_resolution,[],[f1557,f1039]) ).
fof(f1584,plain,
( spl96_25
| spl96_24 ),
inference(avatar_split_clause,[],[f1583,f1038,f1042]) ).
fof(f1585,plain,
( sF93 = vapp(sK79(sF93,sK92,sF95),sK80(sF93,sK92,sF95))
| ~ spl96_25 ),
inference(resolution,[],[f1044,f356]) ).
fof(f1586,plain,
( $false
| ~ spl96_25 ),
inference(forward_subsumption_resolution,[],[f1585,f492]) ).
fof(f1587,plain,
~ spl96_25,
inference(avatar_contradiction_clause,[],[f1586]) ).
fof(f1592,plain,
( sP12(sF93,sK92,sF95)
| vsomeType(sK92) = vlookup(sK82(sF93,sK92,sF95),sF95) ),
inference(forward_subsumption_resolution,[],[f1110,f494]) ).
fof(f1595,plain,
( vsomeType(sK92) = vlookup(sK82(sF93,sK92,sF95),sF95)
| spl96_25 ),
inference(forward_subsumption_resolution,[],[f1592,f1043]) ).
fof(f1604,plain,
( $false
| spl96_25
| spl96_27 ),
inference(forward_subsumption_resolution,[],[f1595,f1065]) ).
fof(f1605,plain,
( spl96_25
| spl96_27 ),
inference(avatar_contradiction_clause,[],[f1604]) ).
cnf(s2,plain,
( spl96_1
| spl96_2 ),
inference(sat_conversion,[],[f557]) ).
cnf(s3,plain,
( spl96_1
| ~ spl96_2 ),
inference(sat_conversion,[],[f622]) ).
cnf(s46,plain,
( ~ spl96_1
| ~ spl96_24
| ~ spl96_27 ),
inference(sat_conversion,[],[f1556]) ).
cnf(s52,plain,
( spl96_24
| spl96_25 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s53,plain,
~ spl96_25,
inference(sat_conversion,[],[f1587]) ).
cnf(s56,plain,
( spl96_25
| spl96_27 ),
inference(sat_conversion,[],[f1605]) ).
cnf(s58,plain,
spl96_27,
inference(rat,[],[s56,s53]) ).
cnf(s59,plain,
spl96_24,
inference(rat,[],[s52,s53]) ).
cnf(s65,plain,
~ spl96_1,
inference(rat,[],[s46,s58,s59]) ).
cnf(s67,plain,
~ spl96_2,
inference(rat,[],[s3,s65]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s2,s67,s65]) ).
fof(f1608,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM135+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 22:00:48 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 Running first-order model finding
% 0.08/0.19 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.92/0.51 % (4077053)Will run a generic schedule for satisfiability detection.
% 1.92/0.51 % (4077063)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=26440109:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.92/0.51 % (4077059)% WARNING: option uhcvi not known.
% 1.92/0.51 % (4077058)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2993802744_2999 on theBenchmark for (2999ds/0Mi)
% 1.92/0.51 % (4077061)dis+10_1_sil=32000:sp=arity:random_seed=2767055355:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.92/0.51 % (4077059)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=401790118:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.92/0.51 % (4077060)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=64423769:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.92/0.51 % (4077062)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3923882992:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.92/0.51 % (4077064)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1733885358:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.92/0.51 % TRYING [1]
% 1.92/0.51 % TRYING [2]
% 1.92/0.51 % (4077063)Instruction limit reached!
% 1.92/0.51 % (4077063)------------------------------
% 1.92/0.51 % (4077063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077063)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077063)Termination reason: Instruction limit
% 1.92/0.51 % (4077063)Termination phase: Saturation
% 1.92/0.51 % (4077063)Time elapsed: 0.042 s
% 1.92/0.51 % (4077063)Peak memory usage: 13 MB
% 1.92/0.51 % (4077063)Instructions burned: 131 (million)
% 1.92/0.51 % TRYING [3]
% 1.92/0.51 % (4077072)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=226941116:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.92/0.51 % TRYING [1]
% 1.92/0.51 % TRYING [2]
% 1.92/0.51 % (4077062)Instruction limit reached!
% 1.92/0.51 % (4077062)------------------------------
% 1.92/0.51 % (4077062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077062)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077062)Termination reason: Instruction limit
% 1.92/0.51 % (4077062)Termination phase: Saturation
% 1.92/0.51 % (4077062)Time elapsed: 0.063 s
% 1.92/0.51 % (4077062)Peak memory usage: 13 MB
% 1.92/0.51 % (4077062)Instructions burned: 117 (million)
% 1.92/0.51 % (4077061)Instruction limit reached!
% 1.92/0.51 % (4077061)------------------------------
% 1.92/0.51 % (4077061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077061)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077061)Termination reason: Instruction limit
% 1.92/0.51 % (4077061)Termination phase: Saturation
% 1.92/0.51 % (4077061)Time elapsed: 0.064 s
% 1.92/0.51 % (4077061)Peak memory usage: 13 MB
% 1.92/0.51 % (4077061)Instructions burned: 104 (million)
% 1.92/0.51 % TRYING [3]
% 1.92/0.51 % (4077075)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1613401700:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.92/0.51 % (4077074)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=700458711:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.92/0.51 % (4077064)Instruction limit reached!
% 1.92/0.51 % (4077064)------------------------------
% 1.92/0.51 % (4077064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077064)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077064)Termination reason: Instruction limit
% 1.92/0.51 % (4077064)Termination phase: Saturation
% 1.92/0.51 % (4077064)Time elapsed: 0.091 s
% 1.92/0.51 % (4077064)Peak memory usage: 13 MB
% 1.92/0.51 % (4077064)Instructions burned: 160 (million)
% 1.92/0.51 % (4077078)ott-21_1_sil=16000:fs=off:random_seed=3762939457:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.92/0.51 % (4077074)Instruction limit reached!
% 1.92/0.51 % (4077074)------------------------------
% 1.92/0.51 % (4077074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077074)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077074)Termination reason: Instruction limit
% 1.92/0.51 % (4077074)Termination phase: Saturation
% 1.92/0.51 % (4077074)Time elapsed: 0.077 s
% 1.92/0.51 % (4077074)Peak memory usage: 13 MB
% 1.92/0.51 % (4077074)Instructions burned: 132 (million)
% 1.92/0.51 % (4077080)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=700214327:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.92/0.51 % (4077072)Instruction limit reached!
% 1.92/0.51 % (4077072)------------------------------
% 1.92/0.51 % (4077072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077072)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077072)Termination reason: Instruction limit
% 1.92/0.51 % (4077072)Termination phase: Finite model building SAT solving
% 1.92/0.51 % (4077072)Time elapsed: 0.142 s
% 1.92/0.51 % (4077072)Peak memory usage: 42 MB
% 1.92/0.51 % (4077072)Instructions burned: 715 (million)
% 1.92/0.51 % (4077082)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2589647499:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.92/0.51 % TRYING [1]
% 1.92/0.51 % (4077078)Instruction limit reached!
% 1.92/0.51 % (4077078)------------------------------
% 1.92/0.51 % (4077078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.51 % (4077078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.51 % (4077078)CaDiCaL version: 2.1.3
% 1.92/0.51 % (4077078)Termination reason: Instruction limit
% 1.92/0.51 % (4077078)Termination phase: Saturation
% 1.92/0.51 % (4077078)Time elapsed: 0.100 s
% 1.92/0.51 % (4077078)Peak memory usage: 13 MB
% 1.92/0.51 % (4077078)Instructions burned: 183 (million)
% 1.92/0.51 % TRYING [2]
% 1.92/0.51 % (4077084)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=393534825:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.92/0.51 % TRYING [3]
% 1.92/0.51 % TRYING [4]
% 1.92/0.51 % (4077084) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4077053-4077084"...
% 1.92/0.51 % (4077084)...printing done.
% 1.92/0.51 % (4077084)Refutation found. Thanks to Tanya!
% 1.92/0.51 % SZS status Theorem for theBenchmark
% 1.92/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 1.92/0.52 % (4077084)------------------------------
% 1.92/0.52 % (4077084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.92/0.52 % (4077084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/0.52 % (4077084)CaDiCaL version: 2.1.3
% 1.92/0.52 % (4077084)Termination reason: Refutation
% 1.92/0.52 % (4077084)Time elapsed: 0.045 s
% 1.92/0.52 % (4077084)Peak memory usage: 13 MB
% 1.92/0.52 % (4077084)Instructions burned: 69 (million)
% 1.92/0.52 % (4077053)Success in time 0.315 s
% 1.92/0.52 % Vampire exiting
%------------------------------------------------------------------------------