%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM535+2 : 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 : 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 12:15:38 PM UTC 2026
% Result : Theorem 2.11s 1.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 145 ( 15 unt; 23 def)
% Number of atoms : 611 ( 59 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 712 ( 246 ~; 254 |; 150 &)
% ( 42 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 24 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(f19,conjecture,
( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| X0 = xx ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
~ ( ( ( aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 ) ) )
=> ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) ) )
=> ( ! [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X5,xS) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f42,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 ) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f43,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 ) ) ) ),
inference(flattening,[],[f42]) ).
fof(f50,definition,
( ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 ) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f51,definition,
( ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) ) )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f52,definition,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx ) )
| ~ sP6 ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f53,definition,
( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) ) )
| ~ sP7 ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f54,definition,
( ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP5
& aSet0(sdtmndt0(xS,xx))
& sP4 )
| ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f55,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP7
& aSet0(sdtmndt0(xS,xx))
& sP6 )
| sP8 ),
inference(definition_folding,[],[f43,f54,f53,f52,f51,f50]) ).
fof(f76,plain,
( ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP5
& aSet0(sdtmndt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(nnf_transformation,[],[f54]) ).
fof(f77,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP5
& aSet0(sdtmndt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
( ( ~ aElementOf0(sK13,xS)
& aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP5
& aSet0(sdtmndt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f77]) ).
fof(f79,plain,
( ! [X1] :
( ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(nnf_transformation,[],[f53]) ).
fof(f80,plain,
( ! [X1] :
( ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) )
| ~ sP6 ),
inference(nnf_transformation,[],[f52]) ).
fof(f83,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& X0 != xx )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) )
| ~ sP6 ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
& xx != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) )
| ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(nnf_transformation,[],[f51]) ).
fof(f85,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
& xx != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,sdtmndt0(xS,xx))
| xx = X4 ) )
| ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(xS,xx))
| ~ aElement0(X3)
| ~ aElementOf0(X3,xS)
| xx = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
| ~ aElementOf0(X3,sdtmndt0(xS,xx)) ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f50]) ).
fof(f88,plain,
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(xS,xx))
| ~ aElement0(X3)
| ~ aElementOf0(X3,xS)
| xx = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,xS)
& xx != X3 )
| ~ aElementOf0(X3,sdtmndt0(xS,xx)) ) )
| ~ sP4 ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xS)
& xx != X0 )
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) )
| ~ sP4 ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(X0,xS) )
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP7
& aSet0(sdtmndt0(xS,xx))
& sP6 )
| sP8 ),
inference(rectify,[],[f55]) ).
fof(f91,plain,
( ( ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK14,xS)
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& sP7
& aSet0(sdtmndt0(xS,xx))
& sP6 )
| sP8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f129,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f130,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f131,plain,
( sP4
| ~ sP8 ),
inference(cnf_transformation,[],[f78]) ).
fof(f133,plain,
( sP5
| ~ sP8 ),
inference(cnf_transformation,[],[f78]) ).
fof(f136,plain,
( aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP8 ),
inference(cnf_transformation,[],[f78]) ).
fof(f137,plain,
( ~ aElementOf0(sK13,xS)
| ~ sP8 ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| xx != X0
| ~ sP7 ),
inference(cnf_transformation,[],[f81]) ).
fof(f141,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP7 ),
inference(cnf_transformation,[],[f81]) ).
fof(f144,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP6 ),
inference(cnf_transformation,[],[f83]) ).
fof(f145,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| xx = X0
| ~ sP6 ),
inference(cnf_transformation,[],[f83]) ).
fof(f146,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP5 ),
inference(cnf_transformation,[],[f86]) ).
fof(f151,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ sP4 ),
inference(cnf_transformation,[],[f89]) ).
fof(f154,plain,
( sP6
| sP8 ),
inference(cnf_transformation,[],[f91]) ).
fof(f156,plain,
( sP7
| sP8 ),
inference(cnf_transformation,[],[f91]) ).
fof(f159,plain,
( aElementOf0(sK14,xS)
| sP8 ),
inference(cnf_transformation,[],[f91]) ).
fof(f160,plain,
( ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP8 ),
inference(cnf_transformation,[],[f91]) ).
fof(f167,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx)
| ~ sP7 ),
inference(equality_resolution,[],[f140]) ).
fof(f172,definition,
( spl15_1
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f176,definition,
( spl15_2
<=> sP6 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f179,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f154,f176,f172]) ).
fof(f186,definition,
( spl15_4
<=> sP7 ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f189,plain,
( spl15_1
| spl15_4 ),
inference(avatar_split_clause,[],[f156,f186,f172]) ).
fof(f201,definition,
( spl15_7
<=> aElementOf0(sK14,xS) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f203,plain,
( aElementOf0(sK14,xS)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl15_1
| spl15_7 ),
inference(avatar_split_clause,[],[f159,f201,f172]) ).
fof(f206,definition,
( spl15_8
<=> aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f208,plain,
( ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx))
| spl15_8 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f209,plain,
( spl15_1
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f160,f206,f172]) ).
fof(f211,definition,
( spl15_9
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f220,definition,
( spl15_11
<=> ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f221,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( ~ spl15_9
| spl15_11 ),
inference(avatar_split_clause,[],[f151,f220,f211]) ).
fof(f224,definition,
( spl15_12
<=> ! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f225,plain,
( ! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f228,definition,
( spl15_13
<=> ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
fof(f229,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl15_14
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f236,definition,
( spl15_15
<=> ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = X0 ) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
fof(f237,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = X0 )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ spl15_14
| spl15_15 ),
inference(avatar_split_clause,[],[f146,f236,f232]) ).
fof(f244,definition,
( spl15_17
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f246,plain,
( ~ aElement0(xx)
| spl15_17 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl15_18
<=> aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
fof(f250,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f253,definition,
( spl15_19
<=> ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
fof(f254,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0) )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f258,plain,
( ~ spl15_2
| spl15_12 ),
inference(avatar_split_clause,[],[f144,f224,f176]) ).
fof(f259,plain,
( ~ spl15_2
| spl15_13 ),
inference(avatar_split_clause,[],[f145,f228,f176]) ).
fof(f262,plain,
( ~ spl15_4
| ~ spl15_17
| spl15_18 ),
inference(avatar_split_clause,[],[f167,f248,f244,f186]) ).
fof(f263,plain,
( ~ spl15_4
| spl15_19 ),
inference(avatar_split_clause,[],[f141,f253,f186]) ).
fof(f264,plain,
( ~ spl15_1
| spl15_9 ),
inference(avatar_split_clause,[],[f131,f211,f172]) ).
fof(f266,plain,
( ~ spl15_1
| spl15_14 ),
inference(avatar_split_clause,[],[f133,f232,f172]) ).
fof(f274,definition,
( spl15_21
<=> aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_21])],[avatar_definition]) ).
fof(f276,plain,
( aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f277,plain,
( ~ spl15_1
| spl15_21 ),
inference(avatar_split_clause,[],[f136,f274,f172]) ).
fof(f279,definition,
( spl15_22
<=> aElementOf0(sK13,xS) ),
introduced(definition,[new_symbols(definition,[spl15_22])],[avatar_definition]) ).
fof(f281,plain,
( ~ aElementOf0(sK13,xS)
| spl15_22 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,plain,
( ~ spl15_1
| ~ spl15_22 ),
inference(avatar_split_clause,[],[f137,f279,f172]) ).
fof(f283,plain,
( ! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSet0(X0) )
| spl15_17 ),
inference(resolution,[],[f92,f246]) ).
fof(f284,plain,
( ~ aSet0(xS)
| spl15_17 ),
inference(resolution,[],[f283,f130]) ).
fof(f285,plain,
( $false
| spl15_17 ),
inference(forward_subsumption_resolution,[],[f284,f129]) ).
fof(f286,plain,
spl15_17,
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f344,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ spl15_12
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f254,f225]) ).
fof(f348,plain,
( ~ aElementOf0(sK14,sdtmndt0(xS,xx))
| spl15_8
| ~ spl15_12
| ~ spl15_19 ),
inference(resolution,[],[f344,f208]) ).
fof(f350,plain,
( xx = sK14
| ~ aElementOf0(sK14,xS)
| ~ aElement0(sK14)
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(resolution,[],[f348,f229]) ).
fof(f351,plain,
( xx = sK14
| ~ aElement0(sK14)
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f350,f203]) ).
fof(f353,definition,
( spl15_25
<=> aElement0(sK14) ),
introduced(definition,[new_symbols(definition,[spl15_25])],[avatar_definition]) ).
fof(f355,plain,
( ~ aElement0(sK14)
| spl15_25 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f357,definition,
( spl15_26
<=> xx = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_26])],[avatar_definition]) ).
fof(f359,plain,
( xx = sK14
| ~ spl15_26 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f360,plain,
( ~ spl15_25
| spl15_26
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(avatar_split_clause,[],[f351,f253,f228,f224,f206,f201,f357,f353]) ).
fof(f367,plain,
( ! [X0] :
( ~ aElementOf0(sK14,X0)
| ~ aSet0(X0) )
| spl15_25 ),
inference(resolution,[],[f355,f92]) ).
fof(f378,plain,
( ~ aSet0(xS)
| ~ spl15_7
| spl15_25 ),
inference(resolution,[],[f367,f203]) ).
fof(f380,plain,
( $false
| ~ spl15_7
| spl15_25 ),
inference(forward_subsumption_resolution,[],[f378,f129]) ).
fof(f381,plain,
( ~ spl15_7
| spl15_25 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f385,plain,
( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| spl15_8
| ~ spl15_26 ),
inference(superposition,[],[f208,f359]) ).
fof(f387,plain,
( $false
| spl15_8
| ~ spl15_18
| ~ spl15_26 ),
inference(forward_subsumption_resolution,[],[f385,f250]) ).
fof(f388,plain,
( spl15_8
| ~ spl15_18
| ~ spl15_26 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f389,plain,
( ~ aElementOf0(sK13,sdtmndt0(xS,xx))
| ~ spl15_11
| spl15_22 ),
inference(resolution,[],[f281,f221]) ).
fof(f525,plain,
( ~ aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK13
| ~ spl15_11
| ~ spl15_15
| spl15_22 ),
inference(resolution,[],[f389,f237]) ).
fof(f527,plain,
( xx = sK13
| ~ spl15_11
| ~ spl15_15
| ~ spl15_21
| spl15_22 ),
inference(forward_subsumption_resolution,[],[f525,f276]) ).
fof(f547,plain,
( ~ aElementOf0(xx,xS)
| ~ spl15_11
| ~ spl15_15
| ~ spl15_21
| spl15_22 ),
inference(superposition,[],[f281,f527]) ).
fof(f548,plain,
( $false
| ~ spl15_11
| ~ spl15_15
| ~ spl15_21
| spl15_22 ),
inference(forward_subsumption_resolution,[],[f547,f130]) ).
fof(f549,plain,
( ~ spl15_11
| ~ spl15_15
| ~ spl15_21
| spl15_22 ),
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f179]) ).
cnf(s3,plain,
( spl15_1
| spl15_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s6,plain,
( spl15_1
| spl15_7 ),
inference(sat_conversion,[],[f204]) ).
cnf(s7,plain,
( spl15_1
| ~ spl15_8 ),
inference(sat_conversion,[],[f209]) ).
cnf(s9,plain,
( ~ spl15_9
| spl15_11 ),
inference(sat_conversion,[],[f222]) ).
cnf(s12,plain,
( ~ spl15_14
| spl15_15 ),
inference(sat_conversion,[],[f238]) ).
cnf(s18,plain,
( ~ spl15_2
| spl15_12 ),
inference(sat_conversion,[],[f258]) ).
cnf(s19,plain,
( ~ spl15_2
| spl15_13 ),
inference(sat_conversion,[],[f259]) ).
cnf(s22,plain,
( ~ spl15_4
| ~ spl15_17
| spl15_18 ),
inference(sat_conversion,[],[f262]) ).
cnf(s23,plain,
( ~ spl15_4
| spl15_19 ),
inference(sat_conversion,[],[f263]) ).
cnf(s24,plain,
( ~ spl15_1
| spl15_9 ),
inference(sat_conversion,[],[f264]) ).
cnf(s26,plain,
( ~ spl15_1
| spl15_14 ),
inference(sat_conversion,[],[f266]) ).
cnf(s29,plain,
( ~ spl15_1
| spl15_21 ),
inference(sat_conversion,[],[f277]) ).
cnf(s30,plain,
( ~ spl15_1
| ~ spl15_22 ),
inference(sat_conversion,[],[f282]) ).
cnf(s31,plain,
spl15_17,
inference(sat_conversion,[],[f286]) ).
cnf(s33,plain,
( ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19
| ~ spl15_25
| spl15_26 ),
inference(sat_conversion,[],[f360]) ).
cnf(s34,plain,
( ~ spl15_7
| spl15_25 ),
inference(sat_conversion,[],[f381]) ).
cnf(s35,plain,
( spl15_8
| ~ spl15_18
| ~ spl15_26 ),
inference(sat_conversion,[],[f388]) ).
cnf(s48,plain,
( ~ spl15_11
| ~ spl15_15
| ~ spl15_21
| spl15_22 ),
inference(sat_conversion,[],[f549]) ).
cnf(s51,plain,
( ~ spl15_4
| spl15_18 ),
inference(rat,[],[s22,s31]) ).
cnf(s53,plain,
spl15_1,
inference(rat,[],[s33,s35,s18,s19,s51,s23,s34,s1,s3,s6,s7]) ).
cnf(s54,plain,
~ spl15_22,
inference(rat,[],[s30,s53]) ).
cnf(s55,plain,
spl15_21,
inference(rat,[],[s29,s53]) ).
cnf(s58,plain,
spl15_14,
inference(rat,[],[s26,s53]) ).
cnf(s60,plain,
spl15_9,
inference(rat,[],[s24,s53]) ).
cnf(s64,plain,
spl15_15,
inference(rat,[],[s12,s58]) ).
cnf(s67,plain,
spl15_11,
inference(rat,[],[s9,s60]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s48,s54,s55,s64,s67]) ).
fof(f550,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:22:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.11/1.31 % (524901)Detected formulas, will run a generic FOF schedule.
% 2.11/1.31 % (524906)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=1303214104:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.11/1.31 % (524907)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=3698371318:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.11/1.31 % (524911)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1640193175:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.11/1.31 % (524912)dis-21_1_sil=8000:lcm=predicate:random_seed=2408932326: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)
% 2.11/1.31 % (524910)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=128029804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.11/1.31 % (524909)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3826546623:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.11/1.31 % (524908)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=2877289272:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.11/1.31 % (524909)Refutation not found, incomplete strategy
% 2.11/1.31 % (524909)------------------------------
% 2.11/1.31 % (524909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (524909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (524909)CaDiCaL version: 2.1.3
% 2.11/1.31 % (524909)Termination reason: Refutation not found, incomplete strategy
% 2.11/1.31 % (524909)Time elapsed: 0.007 s
% 2.11/1.31 % (524909)Peak memory usage: 88 MB
% 2.11/1.31 % (524909)Instructions burned: 9 (million)
% 2.11/1.31 % (524911)First to succeed.
% 2.11/1.31 % (524911)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-524901"
% 2.11/1.31 % (524910)Also succeeded, but the first one will report.
% 2.11/1.31 % (524912)Instruction limit reached!
% 2.11/1.31 % (524912)------------------------------
% 2.11/1.31 % (524912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.11/1.31 % (524912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/1.31 % (524912)CaDiCaL version: 2.1.3
% 2.11/1.31 % (524912)Termination reason: Instruction limit
% 2.11/1.31 % (524912)Termination phase: Saturation
% 2.11/1.31 % (524912)Time elapsed: 0.075 s
% 2.11/1.31 % (524912)Peak memory usage: 90 MB
% 2.11/1.31 % (524912)Instructions burned: 131 (million)
% 2.11/1.31 % (524920)lrs+10_1_sil=8000:sp=occurrence:random_seed=3167121159:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.11/1.31 % (524909)------------------------------
% 2.11/1.31 % (524909)------------------------------
% 2.11/1.31 % (524920)Also succeeded, but the first one will report.
% 2.11/1.31 % (524911)Refutation found. Thanks to Tanya!
% 2.11/1.31 % SZS status Theorem for theBenchmark
% 2.11/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (524911)------------------------------
% 0.18/1.51 % (524911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (524911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (524911)CaDiCaL version: 2.1.3
% 0.18/1.51 % (524911)Termination reason: Refutation
% 0.18/1.51 % (524911)Time elapsed: 0.014 s
% 0.18/1.51 % (524911)Peak memory usage: 89 MB
% 0.18/1.51 % (524911)Instructions burned: 17 (million)
% 0.18/1.51 % (524911)------------------------------
% 0.18/1.51 % (524911)------------------------------
% 0.18/1.51 % (524901)Success in time 0.449 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------