%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:48 PM UTC 2026
% Result : Theorem 3.09s 1.07s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 19 unt; 6 def)
% Number of atoms : 321 ( 53 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 358 ( 116 ~; 110 |; 100 &)
% ( 8 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 60 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(f83,axiom,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
fof(f85,axiom,
( ( sdtlseqdt0(xj,xi)
& ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xi ) )
=> ( sdtlseqdt0(xj,xi)
=> ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786_02) ).
fof(f86,conjecture,
( sdtlseqdt0(xj,xi)
=> ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f87,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f90,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f91,plain,
( ( sdtlseqdt0(xj,xi)
& ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xi ) )
=> ( sdtlseqdt0(xj,xi)
=> ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ) ),
inference(rectify,[],[f85]) ).
fof(f104,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f90]) ).
fof(f105,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f104]) ).
fof(f109,plain,
( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) )
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xi ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f110,plain,
( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) )
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xi ) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
& aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& sdtlseqdt0(xj,xi) ),
inference(ennf_transformation,[],[f87]) ).
fof(f112,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
& aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& sdtlseqdt0(xj,xi) ),
inference(flattening,[],[f111]) ).
fof(f149,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f150,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f151,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f150]) ).
fof(f172,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f172]) ).
fof(f184,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f185,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP4(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP5(X0) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f186,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f105,f185,f184]) ).
fof(f211,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK18(X0),szNzAzT0)
& aElementOf0(sK18(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f186]) ).
fof(f212,plain,
( ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) )
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi ) ),
inference(rectify,[],[f110]) ).
fof(f213,plain,
( ~ aElementOf0(sK19,sdtlpdtrp0(xN,xj))
& aElementOf0(sK19,sdtlpdtrp0(xN,xi))
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& sdtlseqdt0(xj,xi) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f112]) ).
fof(f230,plain,
! [X0] :
( X0 = sz00
| ( aElementOf0(sK29(X0),szNzAzT0)
& szszuzczcdt0(sK29(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X1,sK29(X0))],[f151]) ).
fof(f314,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f211]) ).
fof(f321,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f322,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f325,plain,
! [X1] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi ),
inference(cnf_transformation,[],[f212]) ).
fof(f327,plain,
sdtlseqdt0(xj,xi),
inference(cnf_transformation,[],[f213]) ).
fof(f328,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f213]) ).
fof(f329,plain,
aElementOf0(sK19,sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f213]) ).
fof(f330,plain,
~ aElementOf0(sK19,sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f213]) ).
fof(f378,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f379,plain,
! [X0] :
( szszuzczcdt0(sK29(X0)) = X0
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f380,plain,
! [X0] :
( aElementOf0(sK29(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f407,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f426,definition,
~ sP38(xi),
introduced(definition,[new_symbols(definition,[sP38])],[inequality_splitting_name_introduction]) ).
fof(f427,plain,
! [X1] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| sP38(szszuzczcdt0(X1)) ),
inference(inequality_splitting,[],[f325,f426]) ).
fof(f460,plain,
! [X1] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| sP38(szszuzczcdt0(X1)) ),
inference(duplicate_literal_removal,[],[f427]) ).
fof(f462,plain,
! [X1] :
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| sP38(szszuzczcdt0(X1)) ),
inference(forward_subsumption_resolution,[],[f460,f328]) ).
fof(f475,plain,
! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| sP38(szszuzczcdt0(X1)) ),
inference(forward_subsumption_resolution,[],[f462,f327]) ).
fof(f483,plain,
( ~ sdtlseqdt0(xi,xj)
| xj = xi
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolution,[],[f327,f407]) ).
fof(f486,plain,
( ~ sdtlseqdt0(xi,xj)
| xj = xi
| ~ aElementOf0(xj,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f483,f321]) ).
fof(f488,plain,
( ~ sdtlseqdt0(xi,xj)
| xj = xi ),
inference(forward_subsumption_resolution,[],[f486,f322]) ).
fof(f490,definition,
( spl45_4
<=> xj = xi ),
introduced(definition,[new_symbols(definition,[spl45_4])],[avatar_definition]) ).
fof(f492,plain,
( xj = xi
| ~ spl45_4 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f494,definition,
( spl45_5
<=> sdtlseqdt0(xi,xj) ),
introduced(definition,[new_symbols(definition,[spl45_5])],[avatar_definition]) ).
fof(f496,plain,
( ~ sdtlseqdt0(xi,xj)
| spl45_5 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f497,plain,
( spl45_4
| ~ spl45_5 ),
inference(avatar_split_clause,[],[f488,f494,f490]) ).
fof(f518,plain,
! [X0] :
( sP38(szszuzczcdt0(sK29(X0)))
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f475,f380]) ).
fof(f571,plain,
! [X0] :
( sP38(X0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f518,f379]) ).
fof(f572,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sz00 = X0
| sP38(X0) ),
inference(duplicate_literal_removal,[],[f571]) ).
fof(f732,plain,
( sz00 = xi
| sP38(xi) ),
inference(resolution,[],[f321,f572]) ).
fof(f746,plain,
sz00 = xi,
inference(forward_subsumption_resolution,[],[f732,f426]) ).
fof(f755,plain,
sdtlseqdt0(sz00,xj),
inference(resolution,[],[f322,f378]) ).
fof(f770,definition,
( spl45_27
<=> sz00 = xj ),
introduced(definition,[new_symbols(definition,[spl45_27])],[avatar_definition]) ).
fof(f772,plain,
( sz00 = xj
| ~ spl45_27 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f886,plain,
aElementOf0(sK19,sdtlpdtrp0(xN,sz00)),
inference(superposition,[],[f329,f746]) ).
fof(f889,plain,
( ~ sdtlseqdt0(sz00,xj)
| spl45_5 ),
inference(superposition,[],[f496,f746]) ).
fof(f899,plain,
( $false
| spl45_5 ),
inference(forward_subsumption_resolution,[],[f889,f755]) ).
fof(f900,plain,
spl45_5,
inference(avatar_contradiction_clause,[],[f899]) ).
fof(f901,plain,
aElementOf0(sK19,xS),
inference(forward_demodulation,[],[f886,f314]) ).
fof(f905,plain,
( sz00 = xj
| ~ spl45_4 ),
inference(forward_demodulation,[],[f492,f746]) ).
fof(f908,plain,
( spl45_27
| ~ spl45_4 ),
inference(avatar_split_clause,[],[f905,f490,f770]) ).
fof(f1324,plain,
( ~ aElementOf0(sK19,sdtlpdtrp0(xN,sz00))
| ~ spl45_27 ),
inference(superposition,[],[f330,f772]) ).
fof(f1331,plain,
( ~ aElementOf0(sK19,xS)
| ~ spl45_27 ),
inference(forward_demodulation,[],[f1324,f314]) ).
fof(f1333,plain,
( $false
| ~ spl45_27 ),
inference(forward_subsumption_resolution,[],[f1331,f901]) ).
fof(f1334,plain,
~ spl45_27,
inference(avatar_contradiction_clause,[],[f1333]) ).
cnf(s3,plain,
( spl45_4
| ~ spl45_5 ),
inference(sat_conversion,[],[f497]) ).
cnf(s34,plain,
spl45_5,
inference(sat_conversion,[],[f900]) ).
cnf(s36,plain,
( ~ spl45_4
| spl45_27 ),
inference(sat_conversion,[],[f908]) ).
cnf(s73,plain,
~ spl45_27,
inference(sat_conversion,[],[f1334]) ).
cnf(s82,plain,
~ spl45_4,
inference(rat,[],[s36,s73]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s3,s34,s82]) ).
fof(f1337,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:40:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.09/1.07 % (3931866)Detected formulas, will run a generic FOF schedule.
% 3.09/1.07 % (3931871)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=353995849:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.09/1.07 % (3931872)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=1127495894:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.09/1.07 % (3931873)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=1342630886:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.09/1.07 % (3931877)dis-21_1_sil=8000:lcm=predicate:random_seed=1792739866: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)
% 3.09/1.07 % (3931874)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2159552469:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.09/1.07 % (3931876)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2706014397:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.09/1.07 % (3931875)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=100890423:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.09/1.07 % (3931874)First to succeed.
% 3.09/1.07 % (3931874)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3931866"
% 3.09/1.07 % (3931875)Also succeeded, but the first one will report.
% 3.09/1.07 % (3931877)Instruction limit reached!
% 3.09/1.07 % (3931877)------------------------------
% 3.09/1.07 % (3931877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.07 % (3931877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.07 % (3931877)CaDiCaL version: 2.1.3
% 3.09/1.07 % (3931877)Termination reason: Instruction limit
% 3.09/1.07 % (3931877)Termination phase: Saturation
% 3.09/1.07 % (3931877)Time elapsed: 0.078 s
% 3.09/1.07 % (3931877)Peak memory usage: 91 MB
% 3.09/1.07 % (3931877)Instructions burned: 130 (million)
% 3.09/1.07 % (3931876)Instruction limit reached!
% 3.09/1.07 % (3931876)------------------------------
% 3.09/1.07 % (3931876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.07 % (3931876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.07 % (3931876)CaDiCaL version: 2.1.3
% 3.09/1.07 % (3931876)Termination reason: Instruction limit
% 3.09/1.07 % (3931876)Termination phase: Saturation
% 3.09/1.07 % (3931876)Time elapsed: 0.103 s
% 3.09/1.07 % (3931876)Peak memory usage: 90 MB
% 3.09/1.07 % (3931876)Instructions burned: 139 (million)
% 3.09/1.07 % (3931885)lrs+10_1_sil=8000:sp=occurrence:random_seed=1434046356:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.09/1.07 % (3931886)lrs+10_1_sil=32000:urr=on:br=off:random_seed=830844341:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.09/1.07 % (3931874)Refutation found. Thanks to Tanya!
% 3.09/1.07 % SZS status Theorem for theBenchmark
% 3.09/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.27 % (3931874)------------------------------
% 3.56/1.27 % (3931874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.27 % (3931874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.27 % (3931874)CaDiCaL version: 2.1.3
% 3.56/1.27 % (3931874)Termination reason: Refutation
% 3.56/1.27 % (3931874)Time elapsed: 0.028 s
% 3.56/1.27 % (3931874)Peak memory usage: 90 MB
% 3.56/1.27 % (3931874)Instructions burned: 40 (million)
% 3.56/1.27 % (3931874)------------------------------
% 3.56/1.27 % (3931874)------------------------------
% 3.56/1.27 % (3931866)Success in time 0.452 s
% 3.56/1.27 % Vampire exiting
%------------------------------------------------------------------------------