%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:24:42 PM UTC 2026
% Result : Theorem 0.13s 5.49s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 145 ( 18 unt; 23 def)
% Number of atoms : 607 ( 59 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 706 ( 244 ~; 250 |; 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 : 73 ( 0 sgn 64 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/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/sandbox/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] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ 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,sdtmndt0(xS,xx))
| aElementOf0(X0,xS) )
| ~ 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] :
( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElement0(X0) )
| ~ 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,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(X0,sdtmndt0(xS,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(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,
( aElement0(sK14)
| ~ aSet0(xS)
| ~ spl15_7 ),
inference(resolution,[],[f92,f203]) ).
fof(f284,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f92,f130]) ).
fof(f286,plain,
( aElement0(sK14)
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f283,f129]) ).
fof(f289,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f284,f129]) ).
fof(f290,plain,
spl15_17,
inference(avatar_split_clause,[],[f289,f244]) ).
fof(f435,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(f439,plain,
( ~ aElementOf0(sK14,sdtmndt0(xS,xx))
| spl15_8
| ~ spl15_12
| ~ spl15_19 ),
inference(resolution,[],[f435,f208]) ).
fof(f441,plain,
( xx = sK14
| ~ aElementOf0(sK14,xS)
| ~ aElement0(sK14)
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(resolution,[],[f439,f229]) ).
fof(f442,plain,
( xx = sK14
| ~ aElement0(sK14)
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f441,f203]) ).
fof(f443,plain,
( xx = sK14
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f442,f286]) ).
fof(f448,plain,
( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_19 ),
inference(superposition,[],[f208,f443]) ).
fof(f450,plain,
( $false
| ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_18
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f448,f250]) ).
fof(f451,plain,
( ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_18
| ~ spl15_19 ),
inference(avatar_contradiction_clause,[],[f450]) ).
fof(f492,plain,
( aElementOf0(sK13,sdtmndt0(xS,xx))
| xx = sK13
| ~ spl15_15
| ~ spl15_21 ),
inference(resolution,[],[f237,f276]) ).
fof(f508,definition,
( spl15_41
<=> xx = sK13 ),
introduced(definition,[new_symbols(definition,[spl15_41])],[avatar_definition]) ).
fof(f510,plain,
( xx = sK13
| ~ spl15_41 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f512,definition,
( spl15_42
<=> aElementOf0(sK13,sdtmndt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl15_42])],[avatar_definition]) ).
fof(f514,plain,
( aElementOf0(sK13,sdtmndt0(xS,xx))
| ~ spl15_42 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f515,plain,
( spl15_41
| spl15_42
| ~ spl15_15
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f492,f274,f236,f512,f508]) ).
fof(f726,plain,
( aElementOf0(sK13,xS)
| ~ spl15_11
| ~ spl15_42 ),
inference(resolution,[],[f514,f221]) ).
fof(f729,plain,
( $false
| ~ spl15_11
| spl15_22
| ~ spl15_42 ),
inference(forward_subsumption_resolution,[],[f726,f281]) ).
fof(f730,plain,
( ~ spl15_11
| spl15_22
| ~ spl15_42 ),
inference(avatar_contradiction_clause,[],[f729]) ).
fof(f733,plain,
( ~ aElementOf0(xx,xS)
| spl15_22
| ~ spl15_41 ),
inference(superposition,[],[f281,f510]) ).
fof(f734,plain,
( $false
| spl15_22
| ~ spl15_41 ),
inference(forward_subsumption_resolution,[],[f733,f130]) ).
fof(f735,plain,
( spl15_22
| ~ spl15_41 ),
inference(avatar_contradiction_clause,[],[f734]) ).
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(s32,plain,
spl15_17,
inference(sat_conversion,[],[f290]) ).
cnf(s42,plain,
( ~ spl15_7
| spl15_8
| ~ spl15_12
| ~ spl15_13
| ~ spl15_18
| ~ spl15_19 ),
inference(sat_conversion,[],[f451]) ).
cnf(s46,plain,
( ~ spl15_15
| ~ spl15_21
| spl15_41
| spl15_42 ),
inference(sat_conversion,[],[f515]) ).
cnf(s50,plain,
( ~ spl15_11
| spl15_22
| ~ spl15_42 ),
inference(sat_conversion,[],[f730]) ).
cnf(s51,plain,
( spl15_22
| ~ spl15_41 ),
inference(sat_conversion,[],[f735]) ).
cnf(s53,plain,
( ~ spl15_4
| spl15_18 ),
inference(rat,[],[s22,s32]) ).
cnf(s55,plain,
spl15_1,
inference(rat,[],[s42,s18,s19,s53,s23,s1,s3,s6,s7]) ).
cnf(s56,plain,
~ spl15_22,
inference(rat,[],[s30,s55]) ).
cnf(s57,plain,
spl15_21,
inference(rat,[],[s29,s55]) ).
cnf(s60,plain,
spl15_14,
inference(rat,[],[s26,s55]) ).
cnf(s62,plain,
spl15_9,
inference(rat,[],[s24,s55]) ).
cnf(s63,plain,
~ spl15_41,
inference(rat,[],[s51,s56]) ).
cnf(s67,plain,
spl15_15,
inference(rat,[],[s12,s60]) ).
cnf(s70,plain,
spl15_11,
inference(rat,[],[s9,s62]) ).
cnf(s73,plain,
spl15_42,
inference(rat,[],[s46,s57,s63,s67]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s50,s56,s73,s70]) ).
fof(f736,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/5.41 % Computer : n019.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sun Sep 27 20:23:30 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/5.44 Running first-order model finding
% 0.13/5.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.49 % (3381584)Will run a generic schedule for satisfiability detection.
% 0.13/5.49 % (3381592)dis+10_1_sil=32000:sp=arity:random_seed=3236475864:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/5.49 % (3381590)% WARNING: option uhcvi not known.
% 0.13/5.49 % (3381589)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1957992537_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/5.49 % (3381590)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3028341190:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/5.49 % (3381595)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1294560186:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/5.49 % (3381591)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=774891313:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/5.49 % (3381593)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=823789440:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/5.49 % (3381594)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2652174819:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/5.49 % (3381592) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3381584-3381592"...
% 0.13/5.49 % (3381592)...printing done.
% 0.13/5.49 % (3381592)Refutation found. Thanks to Tanya!
% 0.13/5.49 % SZS status Theorem for theBenchmark
% 0.13/5.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/5.49 % (3381592)------------------------------
% 0.13/5.49 % (3381592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/5.49 % (3381592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/5.49 % (3381592)CaDiCaL version: 2.1.3
% 0.13/5.49 % (3381592)Termination reason: Refutation
% 0.13/5.49 % (3381592)Time elapsed: 0.009 s
% 0.13/5.49 % (3381592)Peak memory usage: 12 MB
% 0.13/5.49 % (3381592)Instructions burned: 21 (million)
% 0.13/5.49 % (3381584)Success in time 0.038 s
% 0.13/5.49 % Vampire exiting
%------------------------------------------------------------------------------