%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM534+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 : n018.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 1.26s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 11 unt; 2 def)
% Number of atoms : 362 ( 83 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 449 ( 149 ~; 170 |; 102 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 104 ( 101 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f15,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
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 ) ) ) )
=> 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 ) ) ) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,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 ) ) ) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(rectify,[],[f20]) ).
fof(f24,plain,
( 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 ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f25,plain,
( 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 ) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f32,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f33,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f27,f32,f31]) ).
fof(f37,plain,
( 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 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [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)) ) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f38,plain,
( 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 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xS,xx))
| xx = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [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)) ) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( xS != sdtpldt0(sdtmndt0(xS,xx),xx)
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [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)) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( ( aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,xS)
| xx = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xS)
& xx != X1 )
| ~ aElementOf0(X1,sdtmndt0(xS,xx)) ) ) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtpldt0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtpldt0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ( sP0(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) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ( sP0(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) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( sP0(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) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK4(X0,X1,X2))
| ( ~ aElementOf0(sK4(X0,X1,X2),X1)
& sK4(X0,X1,X2) != X2 )
| ~ aElementOf0(sK4(X0,X1,X2),X0) )
& ( ( aElement0(sK4(X0,X1,X2))
& ( aElementOf0(sK4(X0,X1,X2),X1)
| sK4(X0,X1,X2) = X2 ) )
| aElementOf0(sK4(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) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f44]) ).
fof(f52,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f53,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f55,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,xS)
| xx = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f39]) ).
fof(f66,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X0) = X2
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X2,X0,X1] :
( aElementOf0(sK4(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP0(X0,X1,X2)
| sK4(X0,X1,X2) = X2
| aElementOf0(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ~ aElement0(sK4(X0,X1,X2))
| sK4(X0,X1,X2) != X2
| ~ aElementOf0(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f75,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ~ aElement0(sK4(X0,X1,X2))
| ~ aElementOf0(sK4(X0,X1,X2),X1)
| ~ aElementOf0(sK4(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f76,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f105,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f77,f53]) ).
fof(f108,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f105,f52]) ).
fof(f124,plain,
! [X0] :
( xS != X0
| ~ sP0(X0,sdtmndt0(xS,xx),xx)
| ~ sP1(xx,sdtmndt0(xS,xx)) ),
inference(superposition,[],[f64,f66]) ).
fof(f133,plain,
( ~ sP0(xS,sdtmndt0(xS,xx),xx)
| ~ sP1(xx,sdtmndt0(xS,xx)) ),
inference(equality_resolution,[],[f124]) ).
fof(f221,plain,
! [X2,X0,X1] :
( sK4(X0,X1,X2) != X2
| ~ aSet0(X0)
| sP0(X0,X1,X2)
| ~ aElementOf0(sK4(X0,X1,X2),X0) ),
inference(forward_subsumption_resolution,[],[f74,f77]) ).
fof(f224,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK4(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP0(X0,X1,X2)
| ~ aElementOf0(sK4(X0,X1,X2),X0) ),
inference(forward_subsumption_resolution,[],[f75,f77]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aSet0(X0)
| sP0(X0,sdtmndt0(xS,xx),X1)
| ~ aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),X0)
| ~ aElement0(sK4(X0,sdtmndt0(xS,xx),X1))
| ~ aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),xS)
| xx = sK4(X0,sdtmndt0(xS,xx),X1) ),
inference(resolution,[],[f224,f57]) ).
fof(f243,plain,
! [X0,X1] :
( ~ aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),xS)
| sP0(X0,sdtmndt0(xS,xx),X1)
| ~ aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),X0)
| ~ aSet0(X0)
| xx = sK4(X0,sdtmndt0(xS,xx),X1) ),
inference(forward_subsumption_resolution,[],[f239,f77]) ).
fof(f253,plain,
! [X0,X1] :
( aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),xS)
| sP0(X0,sdtmndt0(xS,xx),X1)
| sK4(X0,sdtmndt0(xS,xx),X1) = X1
| aElementOf0(sK4(X0,sdtmndt0(xS,xx),X1),X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f72,f55]) ).
fof(f332,plain,
! [X0] :
( ~ aElementOf0(sK4(xS,sdtmndt0(xS,xx),X0),xS)
| sP0(xS,sdtmndt0(xS,xx),X0)
| ~ aSet0(xS)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(factoring,[],[f243]) ).
fof(f336,plain,
! [X0] :
( ~ aElementOf0(sK4(xS,sdtmndt0(xS,xx),X0),xS)
| sP0(xS,sdtmndt0(xS,xx),X0)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(forward_subsumption_resolution,[],[f332,f52]) ).
fof(f339,plain,
! [X0] :
( sP0(xS,sdtmndt0(xS,xx),X0)
| sK4(xS,sdtmndt0(xS,xx),X0) = X0
| aElementOf0(sK4(xS,sdtmndt0(xS,xx),X0),xS)
| ~ aSet0(xS)
| sP0(xS,sdtmndt0(xS,xx),X0)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(resolution,[],[f253,f336]) ).
fof(f344,plain,
! [X0] :
( sP0(xS,sdtmndt0(xS,xx),X0)
| sK4(xS,sdtmndt0(xS,xx),X0) = X0
| aElementOf0(sK4(xS,sdtmndt0(xS,xx),X0),xS)
| ~ aSet0(xS)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(duplicate_literal_removal,[],[f339]) ).
fof(f347,plain,
! [X0] :
( sP0(xS,sdtmndt0(xS,xx),X0)
| sK4(xS,sdtmndt0(xS,xx),X0) = X0
| aElementOf0(sK4(xS,sdtmndt0(xS,xx),X0),xS)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(forward_subsumption_resolution,[],[f344,f52]) ).
fof(f349,plain,
! [X0] :
( sK4(xS,sdtmndt0(xS,xx),X0) = X0
| sP0(xS,sdtmndt0(xS,xx),X0)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(forward_subsumption_resolution,[],[f347,f336]) ).
fof(f357,plain,
! [X0] :
( xx != X0
| sP0(xS,sdtmndt0(xS,xx),X0)
| xx = sK4(xS,sdtmndt0(xS,xx),X0) ),
inference(equality_factoring,[],[f349]) ).
fof(f400,plain,
( xx = sK4(xS,sdtmndt0(xS,xx),xx)
| sP0(xS,sdtmndt0(xS,xx),xx) ),
inference(equality_resolution,[],[f357]) ).
fof(f414,plain,
( xx != xx
| ~ aSet0(xS)
| sP0(xS,sdtmndt0(xS,xx),xx)
| ~ aElementOf0(xx,xS)
| sP0(xS,sdtmndt0(xS,xx),xx) ),
inference(superposition,[],[f221,f400]) ).
fof(f417,plain,
( xx != xx
| ~ aSet0(xS)
| sP0(xS,sdtmndt0(xS,xx),xx)
| ~ aElementOf0(xx,xS) ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f418,plain,
( ~ aSet0(xS)
| sP0(xS,sdtmndt0(xS,xx),xx)
| ~ aElementOf0(xx,xS) ),
inference(trivial_inequality_removal,[],[f417]) ).
fof(f421,plain,
( sP0(xS,sdtmndt0(xS,xx),xx)
| ~ aElementOf0(xx,xS) ),
inference(forward_subsumption_resolution,[],[f418,f52]) ).
fof(f422,plain,
sP0(xS,sdtmndt0(xS,xx),xx),
inference(forward_subsumption_resolution,[],[f421,f53]) ).
fof(f423,plain,
~ sP1(xx,sdtmndt0(xS,xx)),
inference(resolution,[],[f422,f133]) ).
fof(f450,plain,
( ~ aSet0(sdtmndt0(xS,xx))
| ~ aElement0(xx) ),
inference(resolution,[],[f423,f76]) ).
fof(f452,plain,
~ aElement0(xx),
inference(forward_subsumption_resolution,[],[f450,f58]) ).
fof(f453,plain,
$false,
inference(forward_subsumption_resolution,[],[f452,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:24:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.65/1.26 % (2698272)Detected formulas, will run a generic FOF schedule.
% 2.65/1.26 % (2698278)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=3896139231:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.26 % (2698282)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3793753045:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.26 % (2698281)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1692547646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.26 % (2698283)dis-21_1_sil=8000:lcm=predicate:random_seed=3664575296: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)
% 2.65/1.26 % (2698277)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=3504837076:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.26 % (2698280)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2624331694:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.26 % (2698279)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=1908103246:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.26 % (2698281)First to succeed.
% 2.65/1.26 % (2698281)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2698272"
% 2.65/1.26 % (2698282)Also succeeded, but the first one will report.
% 2.65/1.26 % (2698280)Instruction limit reached!
% 2.65/1.26 % (2698280)------------------------------
% 2.65/1.26 % (2698280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.26 % (2698280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.26 % (2698280)CaDiCaL version: 2.1.3
% 2.65/1.26 % (2698280)Termination reason: Instruction limit
% 2.65/1.26 % (2698280)Termination phase: Saturation
% 2.65/1.26 % (2698280)Time elapsed: 0.069 s
% 2.65/1.26 % (2698280)Peak memory usage: 89 MB
% 2.65/1.26 % (2698280)Instructions burned: 110 (million)
% 2.65/1.26 % (2698283)Instruction limit reached!
% 2.65/1.26 % (2698283)------------------------------
% 2.65/1.26 % (2698283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.26 % (2698283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.26 % (2698283)CaDiCaL version: 2.1.3
% 2.65/1.26 % (2698283)Termination reason: Instruction limit
% 2.65/1.26 % (2698283)Termination phase: Saturation
% 2.65/1.26 % (2698283)Time elapsed: 0.085 s
% 2.65/1.26 % (2698283)Peak memory usage: 90 MB
% 2.65/1.26 % (2698283)Instructions burned: 130 (million)
% 2.65/1.26 % (2698291)lrs+10_1_sil=8000:sp=occurrence:random_seed=3192407073:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.65/1.26 % (2698292)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3865668522:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.65/1.26 % (2698291)Also succeeded, but the first one will report.
% 2.65/1.26 % (2698281)Refutation found. Thanks to Tanya!
% 2.65/1.26 % SZS status Theorem for theBenchmark
% 2.65/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.36 % (2698281)------------------------------
% 3.39/1.36 % (2698281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.36 % (2698281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.36 % (2698281)CaDiCaL version: 2.1.3
% 3.39/1.36 % (2698281)Termination reason: Refutation
% 3.39/1.36 % (2698281)Time elapsed: 0.013 s
% 3.39/1.36 % (2698281)Peak memory usage: 88 MB
% 3.39/1.36 % (2698281)Instructions burned: 18 (million)
% 3.39/1.36 % (2698281)------------------------------
% 3.39/1.36 % (2698281)------------------------------
% 3.39/1.36 % (2698272)Success in time 0.411 s
% 3.39/1.36 % Vampire exiting
%------------------------------------------------------------------------------