%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM631+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:16:04 PM UTC 2026
% Result : Theorem 11.14s 2.26s
% Output : Refutation 11.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 37 unt; 2 def)
% Number of atoms : 250 ( 88 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 252 ( 72 ~; 64 |; 96 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-2 aty)
% Number of variables : 53 ( 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f112,axiom,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5321) ).
fof(f113,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f116,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xP)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5632) ).
fof(f117,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f118,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f140,plain,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(rectify,[],[f104]) ).
fof(f142,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(rectify,[],[f116]) ).
fof(f143,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(flattening,[],[f118]) ).
fof(f162,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f266,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f267,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f268,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f267]) ).
fof(f272,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f277,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f278,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(ennf_transformation,[],[f140]) ).
fof(f281,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f113]) ).
fof(f284,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(ennf_transformation,[],[f142]) ).
fof(f453,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK67(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK67(X0,X1),X1)
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(X2,sK67(X0,X1))],[f268]) ).
fof(f466,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(nnf_transformation,[],[f278]) ).
fof(f467,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(flattening,[],[f466]) ).
fof(f471,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xP)
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(nnf_transformation,[],[f284]) ).
fof(f472,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xP)
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(flattening,[],[f471]) ).
fof(f512,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f822,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f828,plain,
! [X0,X1] :
( sbrdtbr0(X1) != xk
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f869,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f272]) ).
fof(f880,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f277]) ).
fof(f883,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f467]) ).
fof(f889,plain,
aSet0(xP),
inference(cnf_transformation,[],[f467]) ).
fof(f890,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f897,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f899,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f900,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f904,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xd,xn),
inference(cnf_transformation,[],[f112]) ).
fof(f905,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f281]) ).
fof(f917,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f472]) ).
fof(f924,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(cnf_transformation,[],[f143]) ).
fof(f986,definition,
sF73 = sdtlpdtrp0(xd,xn),
introduced(definition,[new_symbols(definition,[sF73])],[function_definition]) ).
fof(f987,plain,
sdtlpdtrp0(xd,xn) = sF73,
inference(reorient_equations,[],[f986]) ).
fof(f988,definition,
sF74 = sdtlpdtrp0(xc,xQ),
introduced(definition,[new_symbols(definition,[sF74])],[function_definition]) ).
fof(f989,plain,
sdtlpdtrp0(xc,xQ) = sF74,
inference(reorient_equations,[],[f988]) ).
fof(f990,plain,
sF73 != sF74,
inference(definition_folding,[],[f924,f989,f987]) ).
fof(f1021,plain,
szDzizrdt0(xd) = sF73,
inference(forward_demodulation,[],[f987,f904]) ).
fof(f1056,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[],[f822,f900]) ).
fof(f1057,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[],[f1056,f899]) ).
fof(f1059,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,xp)),
inference(superposition,[],[f917,f1057]) ).
fof(f1077,plain,
xP = sdtmndt0(xQ,xp),
inference(superposition,[],[f883,f880]) ).
fof(f1136,plain,
( xQ = sdtpldt0(sdtmndt0(xQ,xp),xp)
| ~ aSet0(xQ) ),
inference(resolution,[],[f512,f890]) ).
fof(f1264,plain,
xQ = sdtpldt0(sdtmndt0(xQ,xp),xp),
inference(forward_subsumption_resolution,[],[f1136,f869]) ).
fof(f1373,plain,
xQ = sdtpldt0(xP,xp),
inference(forward_demodulation,[],[f1264,f1077]) ).
fof(f1521,plain,
! [X0] :
( xk != xk
| ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f828,f897]) ).
fof(f1522,plain,
! [X0] :
( ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(trivial_inequality_removal,[],[f1521]) ).
fof(f1523,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1522,f889]) ).
fof(f1524,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1523,f905]) ).
fof(f1526,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(forward_subsumption_resolution,[],[f1524,f900]) ).
fof(f1527,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,sdtpldt0(xP,xp)),
inference(forward_demodulation,[],[f1526,f1059]) ).
fof(f1528,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ),
inference(forward_demodulation,[],[f1527,f1373]) ).
fof(f1529,plain,
sdtlpdtrp0(xd,xn) = sF74,
inference(forward_demodulation,[],[f1528,f989]) ).
fof(f1530,plain,
szDzizrdt0(xd) = sF74,
inference(forward_demodulation,[],[f1529,f904]) ).
fof(f1531,plain,
sF73 = sF74,
inference(forward_demodulation,[],[f1530,f1021]) ).
fof(f1532,plain,
$false,
inference(forward_subsumption_resolution,[],[f1531,f990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM631+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:50:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 11.14/2.26 % (536369)Detected formulas, will run a generic FOF schedule.
% 11.14/2.26 % (536451)dis-21_1_sil=8000:lcm=predicate:random_seed=3771456683: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)
% 11.14/2.26 % (536451)Instruction limit reached!
% 11.14/2.26 % (536451)------------------------------
% 11.14/2.26 % (536451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536451)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536451)Termination reason: Instruction limit
% 11.14/2.26 % (536451)Termination phase: Saturation
% 11.14/2.26 % (536451)Time elapsed: 0.038 s
% 11.14/2.26 % (536451)Peak memory usage: 90 MB
% 11.14/2.26 % (536451)Instructions burned: 133 (million)
% 11.14/2.26 % (536444)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=2278022479:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.14/2.26 % (536445)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=1221556438:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.14/2.26 % (536449)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2445468727:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.14/2.26 % (536450)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3231744671:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.14/2.26 % (536446)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=3693839428:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.14/2.26 % (536448)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=822044482:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.14/2.26 % (536449)Instruction limit reached!
% 11.14/2.26 % (536449)------------------------------
% 11.14/2.26 % (536449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536449)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536449)Termination reason: Instruction limit
% 11.14/2.26 % (536449)Termination phase: Saturation
% 11.14/2.26 % (536449)Time elapsed: 0.074 s
% 11.14/2.26 % (536449)Peak memory usage: 89 MB
% 11.14/2.26 % (536449)Instructions burned: 120 (million)
% 11.14/2.26 % (536448)Instruction limit reached!
% 11.14/2.26 % (536448)------------------------------
% 11.14/2.26 % (536448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536448)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536448)Termination reason: Instruction limit
% 11.14/2.26 % (536448)Termination phase: Saturation
% 11.14/2.26 % (536448)Time elapsed: 0.068 s
% 11.14/2.26 % (536448)Peak memory usage: 90 MB
% 11.14/2.26 % (536448)Instructions burned: 109 (million)
% 11.14/2.26 % (536450)Instruction limit reached!
% 11.14/2.26 % (536450)------------------------------
% 11.14/2.26 % (536450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536450)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536450)Termination reason: Instruction limit
% 11.14/2.26 % (536450)Termination phase: Saturation
% 11.14/2.26 % (536450)Time elapsed: 0.097 s
% 11.14/2.26 % (536450)Peak memory usage: 90 MB
% 11.14/2.26 % (536450)Instructions burned: 139 (million)
% 11.14/2.26 % (536485)lrs+10_1_sil=8000:sp=occurrence:random_seed=3969159443:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 11.14/2.26 % (536490)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3233916499:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.14/2.26 % (536491)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2715185775:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.14/2.26 % (536490)Refutation not found, incomplete strategy
% 11.14/2.26 % (536490)------------------------------
% 11.14/2.26 % (536490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536490)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536490)Termination reason: Refutation not found, incomplete strategy
% 11.14/2.26 % (536490)Time elapsed: 0.010 s
% 11.14/2.26 % (536490)Peak memory usage: 89 MB
% 11.14/2.26 % (536490)Instructions burned: 14 (million)
% 11.14/2.26 % (536492)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=119481986:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 11.14/2.26 % (536485)Instruction limit reached!
% 11.14/2.26 % (536485)------------------------------
% 11.14/2.26 % (536485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536485)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536485)Termination reason: Instruction limit
% 11.14/2.26 % (536485)Termination phase: Saturation
% 11.14/2.26 % (536485)Time elapsed: 0.219 s
% 11.14/2.26 % (536485)Peak memory usage: 92 MB
% 11.14/2.26 % (536485)Instructions burned: 286 (million)
% 11.14/2.26 % (536492)Instruction limit reached!
% 11.14/2.26 % (536492)------------------------------
% 11.14/2.26 % (536492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536492)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536492)Termination reason: Instruction limit
% 11.14/2.26 % (536492)Termination phase: Saturation
% 11.14/2.26 % (536492)Time elapsed: 0.229 s
% 11.14/2.26 % (536492)Peak memory usage: 92 MB
% 11.14/2.26 % (536492)Instructions burned: 248 (million)
% 11.14/2.26 % (536491)Instruction limit reached!
% 11.14/2.26 % (536491)------------------------------
% 11.14/2.26 % (536491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536491)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536491)Termination reason: Instruction limit
% 11.14/2.26 % (536491)Termination phase: Saturation
% 11.14/2.26 % (536491)Time elapsed: 0.324 s
% 11.14/2.26 % (536491)Peak memory usage: 92 MB
% 11.14/2.26 % (536491)Instructions burned: 325 (million)
% 11.14/2.26 % (536490)------------------------------
% 11.14/2.26 % (536490)------------------------------
% 11.14/2.26 % (536524)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1538426534:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 11.14/2.26 % (536530)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1107667718:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 11.14/2.26 % (536524)Instruction limit reached!
% 11.14/2.26 % (536524)------------------------------
% 11.14/2.26 % (536524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536524)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536524)Termination reason: Instruction limit
% 11.14/2.26 % (536524)Termination phase: Saturation
% 11.14/2.26 % (536524)Time elapsed: 0.168 s
% 11.14/2.26 % (536524)Peak memory usage: 90 MB
% 11.14/2.26 % (536524)Instructions burned: 295 (million)
% 11.14/2.26 % (536534)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3973578315:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 11.14/2.26 % (536535)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=533125853:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 11.14/2.26 % (536534)Instruction limit reached!
% 11.14/2.26 % (536534)------------------------------
% 11.14/2.26 % (536534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536534)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536534)Termination reason: Instruction limit
% 11.14/2.26 % (536534)Termination phase: Saturation
% 11.14/2.26 % (536534)Time elapsed: 0.123 s
% 11.14/2.26 % (536534)Peak memory usage: 91 MB
% 11.14/2.26 % (536534)Instructions burned: 113 (million)
% 11.14/2.26 % (536535)Instruction limit reached!
% 11.14/2.26 % (536535)------------------------------
% 11.14/2.26 % (536535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536535)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536535)Termination reason: Instruction limit
% 11.14/2.26 % (536535)Termination phase: Saturation
% 11.14/2.26 % (536535)Time elapsed: 0.118 s
% 11.14/2.26 % (536535)Peak memory usage: 89 MB
% 11.14/2.26 % (536535)Instructions burned: 127 (million)
% 11.14/2.26 % (536444)First to succeed.
% 11.14/2.26 % (536444)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-536369"
% 11.14/2.26 % (536542)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2834243950:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 11.14/2.26 % (536445)Also succeeded, but the first one will report.
% 11.14/2.26 % (536542)Instruction limit reached!
% 11.14/2.26 % (536542)------------------------------
% 11.14/2.26 % (536542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.14/2.26 % (536542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.14/2.26 % (536542)CaDiCaL version: 2.1.3
% 11.14/2.26 % (536542)Termination reason: Instruction limit
% 11.14/2.26 % (536542)Termination phase: Saturation
% 11.14/2.26 % (536542)Time elapsed: 0.117 s
% 11.14/2.26 % (536542)Peak memory usage: 89 MB
% 11.14/2.26 % (536542)Instructions burned: 114 (million)
% 11.14/2.26 % (536546)lrs+10_1_sil=8000:sp=occurrence:random_seed=2884213080:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 11.14/2.26 % (536550)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3738376333:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 11.14/2.26 % (536444)Refutation found. Thanks to Tanya!
% 11.14/2.26 % SZS status Theorem for theBenchmark
% 11.14/2.26 % SZS output start Proof for theBenchmark
% See solution above
% 11.66/2.46 % (536444)------------------------------
% 11.66/2.46 % (536444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.66/2.46 % (536444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.66/2.46 % (536444)CaDiCaL version: 2.1.3
% 11.66/2.46 % (536444)Termination reason: Refutation
% 11.66/2.46 % (536444)Time elapsed: 1.007 s
% 11.66/2.46 % (536444)Peak memory usage: 134 MB
% 11.66/2.46 % (536444)Instructions burned: 1117 (million)
% 11.66/2.46 % (536444)------------------------------
% 11.66/2.46 % (536444)------------------------------
% 11.66/2.46 % (536369)Success in time 1.619 s
% 11.66/2.46 % Vampire exiting
%------------------------------------------------------------------------------