%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM536+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 12:15:38 PM UTC 2026
% Result : Theorem 2.75s 1.29s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 10 unt; 2 def)
% Number of atoms : 357 ( 83 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 443 ( 146 ~; 162 |; 107 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 101 ( 98 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f18,axiom,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679) ).
fof(f19,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/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 ) ) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
file('/export/starexec/sandbox/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 ) ) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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 ) ) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
inference(rectify,[],[f21]) ).
fof(f25,plain,
( 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 ) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
( 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 ) ) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f32,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f31]) ).
fof(f36,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f37,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f38,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f32,f37,f36]) ).
fof(f39,plain,
( 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 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [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)) ) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f40,plain,
( 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 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [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)) ) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
( xS != sdtmndt0(sdtpldt0(xS,xx),xx)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [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)) ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xS)
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xS)
| xx = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xS,xx)) ) ) ),
inference(rectify,[],[f40]) ).
fof(f48,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ( sP2(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| X2 = X3
| ~ aElementOf0(X3,X0) )
& ( ( aElement0(X3)
& aElementOf0(X3,X1)
& X2 != X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK5(X0,X1,X2))
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| sK5(X0,X1,X2) = X2
| ~ aElementOf0(sK5(X0,X1,X2),X0) )
& ( ( aElement0(sK5(X0,X1,X2))
& aElementOf0(sK5(X0,X1,X2),X1)
& sK5(X0,X1,X2) != X2 )
| aElementOf0(sK5(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f52]) ).
fof(f54,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f55,plain,
aElement0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f56,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f57,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f41]) ).
fof(f60,plain,
! [X1] :
( aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f41]) ).
fof(f61,plain,
aSet0(sdtpldt0(xS,xx)),
inference(cnf_transformation,[],[f41]) ).
fof(f67,plain,
xS != sdtmndt0(sdtpldt0(xS,xx),xx),
inference(cnf_transformation,[],[f41]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f83,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f89,plain,
! [X2,X0,X1] :
( sK5(X0,X1,X2) != X2
| ~ aSet0(X0)
| sP2(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f90,plain,
! [X2,X0,X1] :
( aElementOf0(sK5(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP2(X0,X1,X2)
| aElementOf0(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,X1,X2))
| ~ aElementOf0(sK5(X0,X1,X2),X1)
| sK5(X0,X1,X2) = X2
| ~ aElementOf0(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f160,plain,
! [X0] :
( xS != X0
| ~ sP2(X0,sdtpldt0(xS,xx),xx)
| ~ sP3(xx,sdtpldt0(xS,xx)) ),
inference(superposition,[],[f67,f83]) ).
fof(f175,plain,
( ~ sP2(xS,sdtpldt0(xS,xx),xx)
| ~ sP3(xx,sdtpldt0(xS,xx)) ),
inference(equality_resolution,[],[f160]) ).
fof(f201,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),xS)
| sP2(X0,sdtpldt0(xS,xx),X1)
| aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),X0)
| xx = sK5(X0,sdtpldt0(xS,xx),X1)
| ~ aSet0(X0) ),
inference(resolution,[],[f90,f57]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK5(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP2(X0,X1,X2)
| sK5(X0,X1,X2) = X2
| ~ aElementOf0(sK5(X0,X1,X2),X0) ),
inference(forward_subsumption_resolution,[],[f92,f68]) ).
fof(f293,plain,
! [X0,X1] :
( ~ aSet0(X0)
| sP2(X0,sdtpldt0(xS,xx),X1)
| sK5(X0,sdtpldt0(xS,xx),X1) = X1
| ~ aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),X0)
| ~ aElement0(sK5(X0,sdtpldt0(xS,xx),X1))
| ~ aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),xS) ),
inference(resolution,[],[f272,f60]) ).
fof(f302,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),xS)
| sP2(X0,sdtpldt0(xS,xx),X1)
| sK5(X0,sdtpldt0(xS,xx),X1) = X1
| ~ aElementOf0(sK5(X0,sdtpldt0(xS,xx),X1),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f293,f68]) ).
fof(f311,plain,
! [X0] :
( ~ aElementOf0(sK5(xS,sdtpldt0(xS,xx),X0),xS)
| sP2(xS,sdtpldt0(xS,xx),X0)
| sK5(xS,sdtpldt0(xS,xx),X0) = X0
| ~ aSet0(xS) ),
inference(factoring,[],[f302]) ).
fof(f316,plain,
! [X0] :
( ~ aElementOf0(sK5(xS,sdtpldt0(xS,xx),X0),xS)
| sP2(xS,sdtpldt0(xS,xx),X0)
| sK5(xS,sdtpldt0(xS,xx),X0) = X0 ),
inference(forward_subsumption_resolution,[],[f311,f54]) ).
fof(f330,plain,
! [X0] :
( sP2(xS,sdtpldt0(xS,xx),X0)
| sK5(xS,sdtpldt0(xS,xx),X0) = X0
| sP2(xS,sdtpldt0(xS,xx),X0)
| aElementOf0(sK5(xS,sdtpldt0(xS,xx),X0),xS)
| xx = sK5(xS,sdtpldt0(xS,xx),X0)
| ~ aSet0(xS) ),
inference(resolution,[],[f316,f201]) ).
fof(f336,plain,
! [X0] :
( sP2(xS,sdtpldt0(xS,xx),X0)
| sK5(xS,sdtpldt0(xS,xx),X0) = X0
| aElementOf0(sK5(xS,sdtpldt0(xS,xx),X0),xS)
| xx = sK5(xS,sdtpldt0(xS,xx),X0)
| ~ aSet0(xS) ),
inference(duplicate_literal_removal,[],[f330]) ).
fof(f339,plain,
! [X0] :
( sP2(xS,sdtpldt0(xS,xx),X0)
| sK5(xS,sdtpldt0(xS,xx),X0) = X0
| xx = sK5(xS,sdtpldt0(xS,xx),X0)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[],[f336,f316]) ).
fof(f342,plain,
! [X0] :
( sK5(xS,sdtpldt0(xS,xx),X0) = X0
| sP2(xS,sdtpldt0(xS,xx),X0)
| xx = sK5(xS,sdtpldt0(xS,xx),X0) ),
inference(forward_subsumption_resolution,[],[f339,f54]) ).
fof(f846,plain,
! [X0] :
( xx != X0
| sP2(xS,sdtpldt0(xS,xx),X0)
| xx = sK5(xS,sdtpldt0(xS,xx),X0) ),
inference(equality_factoring,[],[f342]) ).
fof(f1047,plain,
( xx = sK5(xS,sdtpldt0(xS,xx),xx)
| sP2(xS,sdtpldt0(xS,xx),xx) ),
inference(equality_resolution,[],[f846]) ).
fof(f1085,plain,
( xx != xx
| ~ aSet0(xS)
| sP2(xS,sdtpldt0(xS,xx),xx)
| aElementOf0(xx,xS)
| sP2(xS,sdtpldt0(xS,xx),xx) ),
inference(superposition,[],[f89,f1047]) ).
fof(f1094,plain,
( xx != xx
| ~ aSet0(xS)
| sP2(xS,sdtpldt0(xS,xx),xx)
| aElementOf0(xx,xS) ),
inference(duplicate_literal_removal,[],[f1085]) ).
fof(f1095,plain,
( ~ aSet0(xS)
| sP2(xS,sdtpldt0(xS,xx),xx)
| aElementOf0(xx,xS) ),
inference(trivial_inequality_removal,[],[f1094]) ).
fof(f1097,plain,
( sP2(xS,sdtpldt0(xS,xx),xx)
| aElementOf0(xx,xS) ),
inference(forward_subsumption_resolution,[],[f1095,f54]) ).
fof(f1099,plain,
sP2(xS,sdtpldt0(xS,xx),xx),
inference(forward_subsumption_resolution,[],[f1097,f56]) ).
fof(f1100,plain,
~ sP3(xx,sdtpldt0(xS,xx)),
inference(resolution,[],[f1099,f175]) ).
fof(f1133,plain,
( ~ aSet0(sdtpldt0(xS,xx))
| ~ aElement0(xx) ),
inference(resolution,[],[f1100,f93]) ).
fof(f1137,plain,
~ aElement0(xx),
inference(forward_subsumption_resolution,[],[f1133,f61]) ).
fof(f1138,plain,
$false,
inference(forward_subsumption_resolution,[],[f1137,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM536+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:23:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/1.29 % (3381183)Detected formulas, will run a generic FOF schedule.
% 2.75/1.29 % (3381190)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=601078565:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.29 % (3381194)dis-21_1_sil=8000:lcm=predicate:random_seed=2840051811: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)
% 2.75/1.29 % (3381191)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1913159768:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.29 % (3381192)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=299493297:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.29 % (3381188)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=4012521216:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.29 % (3381189)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=1242540266:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.29 % (3381193)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3835143542:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.29 % (3381192)First to succeed.
% 2.75/1.29 % (3381192)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3381183"
% 2.75/1.29 % (3381193)Also succeeded, but the first one will report.
% 2.75/1.29 % (3381191)Instruction limit reached!
% 2.75/1.29 % (3381191)------------------------------
% 2.75/1.29 % (3381191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3381191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3381191)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3381191)Termination reason: Instruction limit
% 2.75/1.29 % (3381191)Termination phase: Saturation
% 2.75/1.29 % (3381191)Time elapsed: 0.070 s
% 2.75/1.29 % (3381191)Peak memory usage: 89 MB
% 2.75/1.29 % (3381191)Instructions burned: 110 (million)
% 2.75/1.29 % (3381194)Instruction limit reached!
% 2.75/1.29 % (3381194)------------------------------
% 2.75/1.29 % (3381194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.29 % (3381194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.29 % (3381194)CaDiCaL version: 2.1.3
% 2.75/1.29 % (3381194)Termination reason: Instruction limit
% 2.75/1.29 % (3381194)Termination phase: Saturation
% 2.75/1.29 % (3381194)Time elapsed: 0.083 s
% 2.75/1.29 % (3381194)Peak memory usage: 89 MB
% 2.75/1.29 % (3381194)Instructions burned: 130 (million)
% 2.75/1.29 % (3381203)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3509764495:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.75/1.29 % (3381202)lrs+10_1_sil=8000:sp=occurrence:random_seed=3866658775:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.75/1.29 % (3381192)Refutation found. Thanks to Tanya!
% 2.75/1.29 % SZS status Theorem for theBenchmark
% 2.75/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.39 % (3381192)------------------------------
% 3.67/1.39 % (3381192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.39 % (3381192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.39 % (3381192)CaDiCaL version: 2.1.3
% 3.67/1.39 % (3381192)Termination reason: Refutation
% 3.67/1.39 % (3381192)Time elapsed: 0.030 s
% 3.67/1.39 % (3381192)Peak memory usage: 88 MB
% 3.67/1.39 % (3381192)Instructions burned: 44 (million)
% 3.67/1.39 % (3381192)------------------------------
% 3.67/1.39 % (3381192)------------------------------
% 3.67/1.39 % (3381183)Success in time 0.457 s
% 3.67/1.39 % Vampire exiting
%------------------------------------------------------------------------------