%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM537+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 : n009.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 2.65s 1.27s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 32
% Syntax : Number of formulae : 178 ( 15 unt; 27 def)
% Number of atoms : 741 ( 60 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 883 ( 320 ~; 328 |; 165 &)
% ( 48 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 28 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f18,axiom,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
fof(f19,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
fof(f20,conjecture,
( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
~ ( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f26,plain,
~ ( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) ) )
=> ( ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X5,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f44,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f45,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) ) ),
inference(flattening,[],[f44]) ).
fof(f52,definition,
( ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f53,definition,
( ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f54,definition,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) )
| ~ sP6 ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f55,definition,
( ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) )
| ~ sP7 ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f56,definition,
( ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP5
& aSet0(sdtpldt0(xS,xx))
& sP4 )
| ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f57,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP7
& aSet0(sdtpldt0(xS,xx))
& sP6 )
| sP8 ),
inference(definition_folding,[],[f45,f56,f55,f54,f53,f52]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f31]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f64]) ).
fof(f78,plain,
( ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP5
& aSet0(sdtpldt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(nnf_transformation,[],[f56]) ).
fof(f79,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP5
& aSet0(sdtpldt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
( ( ~ aElementOf0(sK13,xS)
& aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP5
& aSet0(sdtpldt0(xS,xx))
& sP4 )
| ~ sP8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f79]) ).
fof(f81,plain,
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(nnf_transformation,[],[f55]) ).
fof(f82,plain,
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& xx != X0 )
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP7 ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xS)
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) )
| ~ sP6 ),
inference(nnf_transformation,[],[f54]) ).
fof(f85,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xS)
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) )
| ~ sP6 ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X4)
| ~ aElementOf0(X4,sdtpldt0(xS,xx))
| xx = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 )
| ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(nnf_transformation,[],[f53]) ).
fof(f87,plain,
( ! [X4] :
( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X4)
| ~ aElementOf0(X4,sdtpldt0(xS,xx))
| xx = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 )
| ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& xx != X0 )
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ sP5 ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
( ! [X3] :
( ( aElementOf0(X3,sdtpldt0(xS,xx))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,xS)
& xx != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f52]) ).
fof(f90,plain,
( ! [X3] :
( ( aElementOf0(X3,sdtpldt0(xS,xx))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,xS)
& xx != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
| ~ sP4 ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xS)
& xx != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xS)
| xx = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) )
| ~ sP4 ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X0,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP7
& aSet0(sdtpldt0(xS,xx))
& sP6 )
| sP8 ),
inference(rectify,[],[f57]) ).
fof(f93,plain,
( ( ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(sK14,xS)
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& sP7
& aSet0(sdtpldt0(xS,xx))
& sP6 )
| sP8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f99,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f101,plain,
! [X0,X1] :
( aElementOf0(sK10(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aElementOf0(sK10(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f132,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f134,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f135,plain,
( sP4
| ~ sP8 ),
inference(cnf_transformation,[],[f80]) ).
fof(f137,plain,
( sP5
| ~ sP8 ),
inference(cnf_transformation,[],[f80]) ).
fof(f140,plain,
( aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP8 ),
inference(cnf_transformation,[],[f80]) ).
fof(f141,plain,
( ~ aElementOf0(sK13,xS)
| ~ sP8 ),
inference(cnf_transformation,[],[f80]) ).
fof(f145,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0
| ~ sP7 ),
inference(cnf_transformation,[],[f83]) ).
fof(f147,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP6 ),
inference(cnf_transformation,[],[f85]) ).
fof(f149,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS)
| ~ sP6 ),
inference(cnf_transformation,[],[f85]) ).
fof(f150,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP5 ),
inference(cnf_transformation,[],[f88]) ).
fof(f151,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP5 ),
inference(cnf_transformation,[],[f88]) ).
fof(f154,plain,
! [X0] :
( aElementOf0(X0,xS)
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP4 ),
inference(cnf_transformation,[],[f91]) ).
fof(f158,plain,
( sP6
| sP8 ),
inference(cnf_transformation,[],[f93]) ).
fof(f159,plain,
( aSet0(sdtpldt0(xS,xx))
| sP8 ),
inference(cnf_transformation,[],[f93]) ).
fof(f160,plain,
( sP7
| sP8 ),
inference(cnf_transformation,[],[f93]) ).
fof(f163,plain,
( aElementOf0(sK14,xS)
| sP8 ),
inference(cnf_transformation,[],[f93]) ).
fof(f164,plain,
( ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP8 ),
inference(cnf_transformation,[],[f93]) ).
fof(f173,plain,
( ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP5 ),
inference(equality_resolution,[],[f150]) ).
fof(f176,definition,
( spl15_1
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f180,definition,
( spl15_2
<=> sP6 ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f183,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f158,f180,f176]) ).
fof(f185,definition,
( spl15_3
<=> aSet0(sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f187,plain,
( aSet0(sdtpldt0(xS,xx))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f159,f185,f176]) ).
fof(f190,definition,
( spl15_4
<=> sP7 ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f193,plain,
( spl15_1
| spl15_4 ),
inference(avatar_split_clause,[],[f160,f190,f176]) ).
fof(f205,definition,
( spl15_7
<=> aElementOf0(sK14,xS) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f207,plain,
( aElementOf0(sK14,xS)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl15_1
| spl15_7 ),
inference(avatar_split_clause,[],[f163,f205,f176]) ).
fof(f210,definition,
( spl15_8
<=> aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f212,plain,
( ~ aElementOf0(sK14,sdtmndt0(sdtpldt0(xS,xx),xx))
| spl15_8 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f213,plain,
( spl15_1
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f164,f210,f176]) ).
fof(f215,definition,
( spl15_9
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f219,definition,
( spl15_10
<=> ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0 ) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f220,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0 )
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( ~ spl15_9
| spl15_10 ),
inference(avatar_split_clause,[],[f154,f219,f215]) ).
fof(f223,definition,
( spl15_11
<=> ! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f224,plain,
( ! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f236,definition,
( spl15_14
<=> ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f237,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl15_15
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
fof(f244,definition,
( spl15_16
<=> aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
fof(f246,plain,
( ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| spl15_16 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,plain,
( ~ spl15_15
| ~ spl15_16 ),
inference(avatar_split_clause,[],[f173,f244,f240]) ).
fof(f249,definition,
( spl15_17
<=> ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
fof(f250,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ spl15_15
| spl15_17 ),
inference(avatar_split_clause,[],[f151,f249,f240]) ).
fof(f257,definition,
( spl15_19
<=> ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
fof(f258,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0) )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,plain,
( ~ spl15_2
| spl15_11 ),
inference(avatar_split_clause,[],[f147,f223,f180]) ).
fof(f263,plain,
( ~ spl15_2
| spl15_14 ),
inference(avatar_split_clause,[],[f149,f236,f180]) ).
fof(f267,plain,
( ~ spl15_4
| spl15_19 ),
inference(avatar_split_clause,[],[f145,f257,f190]) ).
fof(f268,plain,
( ~ spl15_1
| spl15_9 ),
inference(avatar_split_clause,[],[f135,f215,f176]) ).
fof(f270,plain,
( ~ spl15_1
| spl15_15 ),
inference(avatar_split_clause,[],[f137,f240,f176]) ).
fof(f278,definition,
( spl15_21
<=> aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl15_21])],[avatar_definition]) ).
fof(f280,plain,
( aElementOf0(sK13,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f281,plain,
( ~ spl15_1
| spl15_21 ),
inference(avatar_split_clause,[],[f140,f278,f176]) ).
fof(f283,definition,
( spl15_22
<=> aElementOf0(sK13,xS) ),
introduced(definition,[new_symbols(definition,[spl15_22])],[avatar_definition]) ).
fof(f285,plain,
( ~ aElementOf0(sK13,xS)
| spl15_22 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,plain,
( ~ spl15_1
| ~ spl15_22 ),
inference(avatar_split_clause,[],[f141,f283,f176]) ).
fof(f314,plain,
( ! [X0] :
( ~ aElementOf0(sK10(sdtpldt0(xS,xx),X0),xS)
| ~ aElement0(sK10(sdtpldt0(xS,xx),X0))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) )
| ~ spl15_14 ),
inference(resolution,[],[f237,f102]) ).
fof(f315,plain,
( ! [X0] :
( ~ aElementOf0(sK10(sdtpldt0(xS,xx),X0),xS)
| ~ aElement0(sK10(sdtpldt0(xS,xx),X0))
| ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl15_3
| ~ spl15_14 ),
inference(forward_subsumption_resolution,[],[f314,f187]) ).
fof(f319,plain,
( ~ aElement0(sK10(sdtpldt0(xS,xx),xS))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| ~ spl15_3
| ~ spl15_14 ),
inference(resolution,[],[f315,f101]) ).
fof(f321,plain,
( ~ aElement0(sK10(sdtpldt0(xS,xx),xS))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| ~ spl15_3
| ~ spl15_14 ),
inference(duplicate_literal_removal,[],[f319]) ).
fof(f323,plain,
( ~ aElement0(sK10(sdtpldt0(xS,xx),xS))
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| ~ spl15_3
| ~ spl15_14 ),
inference(forward_subsumption_resolution,[],[f321,f132]) ).
fof(f324,plain,
( ~ aElement0(sK10(sdtpldt0(xS,xx),xS))
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ spl15_3
| ~ spl15_14 ),
inference(forward_subsumption_resolution,[],[f323,f187]) ).
fof(f326,definition,
( spl15_23
<=> aSubsetOf0(xS,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl15_23])],[avatar_definition]) ).
fof(f328,plain,
( aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f330,definition,
( spl15_24
<=> aElement0(sK10(sdtpldt0(xS,xx),xS)) ),
introduced(definition,[new_symbols(definition,[spl15_24])],[avatar_definition]) ).
fof(f332,plain,
( ~ aElement0(sK10(sdtpldt0(xS,xx),xS))
| spl15_24 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f333,plain,
( spl15_23
| ~ spl15_24
| ~ spl15_3
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f324,f236,f185,f330,f326]) ).
fof(f338,plain,
( ! [X0] :
( ~ aElementOf0(sK10(sdtpldt0(xS,xx),xS),X0)
| ~ aSet0(X0) )
| spl15_24 ),
inference(resolution,[],[f332,f94]) ).
fof(f340,plain,
( ~ aSet0(xS)
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| spl15_24 ),
inference(resolution,[],[f338,f101]) ).
fof(f343,plain,
( ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| spl15_24 ),
inference(duplicate_literal_removal,[],[f340]) ).
fof(f344,plain,
( aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx))
| spl15_24 ),
inference(forward_subsumption_resolution,[],[f343,f132]) ).
fof(f345,plain,
( aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ spl15_3
| spl15_24 ),
inference(forward_subsumption_resolution,[],[f344,f187]) ).
fof(f346,plain,
( spl15_23
| ~ spl15_3
| spl15_24 ),
inference(avatar_split_clause,[],[f345,f330,f185,f326]) ).
fof(f362,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aSet0(sdtpldt0(xS,xx)) )
| ~ spl15_23 ),
inference(resolution,[],[f328,f99]) ).
fof(f363,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,xS) )
| ~ spl15_3
| ~ spl15_23 ),
inference(forward_subsumption_resolution,[],[f362,f187]) ).
fof(f382,plain,
( ~ aElementOf0(sK13,sdtpldt0(xS,xx))
| xx = sK13
| ~ spl15_10
| spl15_22 ),
inference(resolution,[],[f285,f220]) ).
fof(f384,definition,
( spl15_29
<=> xx = sK13 ),
introduced(definition,[new_symbols(definition,[spl15_29])],[avatar_definition]) ).
fof(f386,plain,
( xx = sK13
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f388,definition,
( spl15_30
<=> aElementOf0(sK13,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl15_30])],[avatar_definition]) ).
fof(f391,plain,
( spl15_29
| ~ spl15_30
| ~ spl15_10
| spl15_22 ),
inference(avatar_split_clause,[],[f382,f283,f219,f388,f384]) ).
fof(f396,plain,
( aElementOf0(sK13,sdtpldt0(xS,xx))
| ~ spl15_17
| ~ spl15_21 ),
inference(resolution,[],[f280,f250]) ).
fof(f397,plain,
( spl15_30
| ~ spl15_17
| ~ spl15_21 ),
inference(avatar_split_clause,[],[f396,f278,f249,f388]) ).
fof(f409,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx = X0
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl15_11
| ~ spl15_19 ),
inference(forward_subsumption_resolution,[],[f258,f224]) ).
fof(f415,plain,
( xx = sK14
| ~ aElementOf0(sK14,sdtpldt0(xS,xx))
| spl15_8
| ~ spl15_11
| ~ spl15_19 ),
inference(resolution,[],[f409,f212]) ).
fof(f417,definition,
( spl15_31
<=> aElementOf0(sK14,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl15_31])],[avatar_definition]) ).
fof(f419,plain,
( ~ aElementOf0(sK14,sdtpldt0(xS,xx))
| spl15_31 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f421,definition,
( spl15_32
<=> xx = sK14 ),
introduced(definition,[new_symbols(definition,[spl15_32])],[avatar_definition]) ).
fof(f423,plain,
( xx = sK14
| ~ spl15_32 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f424,plain,
( ~ spl15_31
| spl15_32
| spl15_8
| ~ spl15_11
| ~ spl15_19 ),
inference(avatar_split_clause,[],[f415,f257,f223,f210,f421,f417]) ).
fof(f426,plain,
( ~ aElementOf0(sK14,xS)
| ~ spl15_3
| ~ spl15_23
| spl15_31 ),
inference(resolution,[],[f419,f363]) ).
fof(f429,plain,
( $false
| ~ spl15_3
| ~ spl15_7
| ~ spl15_23
| spl15_31 ),
inference(forward_subsumption_resolution,[],[f426,f207]) ).
fof(f430,plain,
( ~ spl15_3
| ~ spl15_7
| ~ spl15_23
| spl15_31 ),
inference(avatar_contradiction_clause,[],[f429]) ).
fof(f432,plain,
( aElementOf0(xx,xS)
| ~ spl15_7
| ~ spl15_32 ),
inference(superposition,[],[f207,f423]) ).
fof(f433,plain,
( $false
| ~ spl15_7
| ~ spl15_32 ),
inference(forward_subsumption_resolution,[],[f432,f134]) ).
fof(f434,plain,
( ~ spl15_7
| ~ spl15_32 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f498,plain,
( aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ spl15_21
| ~ spl15_29 ),
inference(superposition,[],[f280,f386]) ).
fof(f500,plain,
( $false
| spl15_16
| ~ spl15_21
| ~ spl15_29 ),
inference(forward_subsumption_resolution,[],[f498,f246]) ).
fof(f501,plain,
( spl15_16
| ~ spl15_21
| ~ spl15_29 ),
inference(avatar_contradiction_clause,[],[f500]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f183]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f188]) ).
cnf(s3,plain,
( spl15_1
| spl15_4 ),
inference(sat_conversion,[],[f193]) ).
cnf(s6,plain,
( spl15_1
| spl15_7 ),
inference(sat_conversion,[],[f208]) ).
cnf(s7,plain,
( spl15_1
| ~ spl15_8 ),
inference(sat_conversion,[],[f213]) ).
cnf(s8,plain,
( ~ spl15_9
| spl15_10 ),
inference(sat_conversion,[],[f221]) ).
cnf(s12,plain,
( ~ spl15_15
| ~ spl15_16 ),
inference(sat_conversion,[],[f247]) ).
cnf(s13,plain,
( ~ spl15_15
| spl15_17 ),
inference(sat_conversion,[],[f251]) ).
cnf(s17,plain,
( ~ spl15_2
| spl15_11 ),
inference(sat_conversion,[],[f261]) ).
cnf(s19,plain,
( ~ spl15_2
| spl15_14 ),
inference(sat_conversion,[],[f263]) ).
cnf(s23,plain,
( ~ spl15_4
| spl15_19 ),
inference(sat_conversion,[],[f267]) ).
cnf(s24,plain,
( ~ spl15_1
| spl15_9 ),
inference(sat_conversion,[],[f268]) ).
cnf(s26,plain,
( ~ spl15_1
| spl15_15 ),
inference(sat_conversion,[],[f270]) ).
cnf(s29,plain,
( ~ spl15_1
| spl15_21 ),
inference(sat_conversion,[],[f281]) ).
cnf(s30,plain,
( ~ spl15_1
| ~ spl15_22 ),
inference(sat_conversion,[],[f286]) ).
cnf(s32,plain,
( ~ spl15_3
| ~ spl15_14
| spl15_23
| ~ spl15_24 ),
inference(sat_conversion,[],[f333]) ).
cnf(s33,plain,
( ~ spl15_3
| spl15_23
| spl15_24 ),
inference(sat_conversion,[],[f346]) ).
cnf(s36,plain,
( ~ spl15_10
| spl15_22
| spl15_29
| ~ spl15_30 ),
inference(sat_conversion,[],[f391]) ).
cnf(s38,plain,
( ~ spl15_17
| ~ spl15_21
| spl15_30 ),
inference(sat_conversion,[],[f397]) ).
cnf(s39,plain,
( spl15_8
| ~ spl15_11
| ~ spl15_19
| ~ spl15_31
| spl15_32 ),
inference(sat_conversion,[],[f424]) ).
cnf(s40,plain,
( ~ spl15_3
| ~ spl15_7
| ~ spl15_23
| spl15_31 ),
inference(sat_conversion,[],[f430]) ).
cnf(s41,plain,
( ~ spl15_7
| ~ spl15_32 ),
inference(sat_conversion,[],[f434]) ).
cnf(s44,plain,
( spl15_16
| ~ spl15_21
| ~ spl15_29 ),
inference(sat_conversion,[],[f501]) ).
cnf(s47,plain,
spl15_1,
inference(rat,[],[s32,s33,s40,s39,s17,s19,s23,s41,s1,s2,s3,s6,s7]) ).
cnf(s48,plain,
~ spl15_22,
inference(rat,[],[s30,s47]) ).
cnf(s49,plain,
spl15_21,
inference(rat,[],[s29,s47]) ).
cnf(s52,plain,
spl15_15,
inference(rat,[],[s26,s47]) ).
cnf(s54,plain,
spl15_9,
inference(rat,[],[s24,s47]) ).
cnf(s58,plain,
spl15_17,
inference(rat,[],[s13,s52]) ).
cnf(s59,plain,
~ spl15_16,
inference(rat,[],[s12,s52]) ).
cnf(s63,plain,
spl15_10,
inference(rat,[],[s8,s54]) ).
cnf(s65,plain,
spl15_30,
inference(rat,[],[s38,s49,s58]) ).
cnf(s66,plain,
~ spl15_29,
inference(rat,[],[s44,s49,s59]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s36,s48,s66,s63,s65]) ).
fof(f502,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:23:16 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
% 2.65/1.27 % (2369454)Detected formulas, will run a generic FOF schedule.
% 2.65/1.27 % (2369462)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1871457099:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.27 % (2369462)Refutation not found, incomplete strategy
% 2.65/1.27 % (2369462)------------------------------
% 2.65/1.27 % (2369462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (2369462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (2369462)CaDiCaL version: 2.1.3
% 2.65/1.27 % (2369462)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.27 % (2369462)Time elapsed: 0.004 s
% 2.65/1.27 % (2369462)Peak memory usage: 88 MB
% 2.65/1.27 % (2369462)Instructions burned: 9 (million)
% 2.65/1.27 % (2369465)dis-21_1_sil=8000:lcm=predicate:random_seed=991890324: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)
% 2.65/1.27 % (2369464)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1274766326:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.27 % (2369463)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3583659996:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.27 % (2369459)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=1020710970:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.27 % (2369461)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=3255066734:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.27 % (2369460)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=3501619993:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.27 % (2369464)First to succeed.
% 2.65/1.27 % (2369464)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2369454"
% 2.65/1.27 % (2369463)Also succeeded, but the first one will report.
% 2.65/1.27 % (2369465)Instruction limit reached!
% 2.65/1.27 % (2369465)------------------------------
% 2.65/1.27 % (2369465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (2369465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (2369465)CaDiCaL version: 2.1.3
% 2.65/1.27 % (2369465)Termination reason: Instruction limit
% 2.65/1.27 % (2369465)Termination phase: Saturation
% 2.65/1.27 % (2369465)Time elapsed: 0.075 s
% 2.65/1.27 % (2369465)Peak memory usage: 90 MB
% 2.65/1.27 % (2369465)Instructions burned: 130 (million)
% 2.65/1.27 % (2369462)------------------------------
% 2.65/1.27 % (2369462)------------------------------
% 2.65/1.27 % (2369474)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1173334137:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.65/1.27 % (2369473)lrs+10_1_sil=8000:sp=occurrence:random_seed=874697390:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.65/1.27 % (2369474)Also succeeded, but the first one will report.
% 2.65/1.27 % (2369473)Also succeeded, but the first one will report.
% 2.65/1.27 % (2369464)Refutation found. Thanks to Tanya!
% 2.65/1.27 % SZS status Theorem for theBenchmark
% 2.65/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.47 % (2369464)------------------------------
% 3.55/1.47 % (2369464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (2369464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (2369464)CaDiCaL version: 2.1.3
% 3.55/1.47 % (2369464)Termination reason: Refutation
% 3.55/1.47 % (2369464)Time elapsed: 0.016 s
% 3.55/1.47 % (2369464)Peak memory usage: 90 MB
% 3.55/1.47 % (2369464)Instructions burned: 16 (million)
% 3.55/1.47 % (2369464)------------------------------
% 3.55/1.47 % (2369464)------------------------------
% 3.55/1.47 % (2369454)Success in time 0.418 s
% 3.55/1.47 % Vampire exiting
%------------------------------------------------------------------------------