%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM534+1 : 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 : n004.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 12:15:37 PM UTC 2026
% Result : Theorem 6.62s 1.95s
% Output : Refutation 8.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of formulae : 160 ( 24 unt; 13 def)
% Number of atoms : 717 ( 99 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 939 ( 382 ~; 416 |; 106 &)
% ( 27 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 8 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 195 ( 0 sgn 186 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aSet0(X1) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
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(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(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,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(flattening,[],[f20]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f35,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f34]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,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(f43,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(f44,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f39,f43,f42]) ).
fof(f45,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(f46,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(f47,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f41,f46,f45]) ).
fof(f52,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,[],[f30]) ).
fof(f53,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,[],[f52]) ).
fof(f54,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,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f54]) ).
fof(f56,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,[],[f43]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f42]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK6(X0,X1,X2))
| ( ~ aElementOf0(sK6(X0,X1,X2),X1)
& sK6(X0,X1,X2) != X2 )
| ~ aElementOf0(sK6(X0,X1,X2),X0) )
& ( ( aElement0(sK6(X0,X1,X2))
& ( aElementOf0(sK6(X0,X1,X2),X1)
| sK6(X0,X1,X2) = X2 ) )
| aElementOf0(sK6(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,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f60]) ).
fof(f62,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,[],[f46]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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,[],[f45]) ).
fof(f65,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,[],[f64]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X0) )
& ( ( aElement0(sK7(X0,X1,X2))
& aElementOf0(sK7(X0,X1,X2),X1)
& sK7(X0,X1,X2) != X2 )
| aElementOf0(sK7(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,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f75,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f81,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f83,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 = X4
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElement0(X4)
| X2 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f92,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f104,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f105,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f106,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f107,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f25]) ).
fof(f110,plain,
! [X0,X1] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f81]) ).
fof(f111,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f85]) ).
fof(f112,plain,
! [X0,X1] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f93]) ).
fof(f114,definition,
sF8 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f115,plain,
sdtmndt0(xS,xx) = sF8,
inference(reorient_equations,[],[f114]) ).
fof(f116,definition,
sF9 = sdtpldt0(sF8,xx),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f117,plain,
sdtpldt0(sF8,xx) = sF9,
inference(reorient_equations,[],[f116]) ).
fof(f118,plain,
xS != sF9,
inference(definition_folding,[],[f107,f117,f115]) ).
fof(f119,plain,
( sP0(sF9,sF8,xx)
| ~ sP1(xx,sF8) ),
inference(superposition,[],[f110,f117]) ).
fof(f121,definition,
( spl10_1
<=> sP1(xx,sF8) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f122,plain,
( sP1(xx,sF8)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( ~ sP1(xx,sF8)
| spl10_1 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl10_2
<=> sP0(sF9,sF8,xx) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f127,plain,
( sP0(sF9,sF8,xx)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f119,f125,f121]) ).
fof(f129,plain,
( sP2(sF8,xS,xx)
| ~ sP3(xx,xS) ),
inference(superposition,[],[f112,f115]) ).
fof(f131,definition,
( spl10_3
<=> sP3(xx,xS) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f133,plain,
( ~ sP3(xx,xS)
| spl10_3 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl10_4
<=> sP2(sF8,xS,xx) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f137,plain,
( sP2(sF8,xS,xx)
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( ~ spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f129,f135,f131]) ).
fof(f139,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f68,f106]) ).
fof(f140,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f139,f105]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,sdtpldt0(X2,X0))
| X0 = X1
| aElementOf0(X1,X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f83,f110]) ).
fof(f142,plain,
! [X0] :
( ~ aElementOf0(X0,sF9)
| xx = X0
| aElementOf0(X0,sF8)
| ~ sP1(xx,sF8) ),
inference(superposition,[],[f141,f117]) ).
fof(f143,plain,
( ~ aSet0(xS)
| ~ aElement0(xx)
| spl10_3 ),
inference(resolution,[],[f104,f133]) ).
fof(f144,plain,
( ~ aElement0(xx)
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f143,f105]) ).
fof(f145,plain,
( $false
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f144,f140]) ).
fof(f146,plain,
spl10_3,
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f147,plain,
( ~ aSet0(sF8)
| ~ aElement0(xx)
| spl10_1 ),
inference(resolution,[],[f92,f123]) ).
fof(f148,plain,
( ~ aSet0(sF8)
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f147,f140]) ).
fof(f150,plain,
( aSet0(sF8)
| ~ spl10_4 ),
inference(resolution,[],[f99,f137]) ).
fof(f151,plain,
( $false
| spl10_1
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f150,f148]) ).
fof(f152,plain,
( spl10_1
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f153,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF9)
| xx = X0
| aElementOf0(X0,sF8) )
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f142,f122]) ).
fof(f157,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| xx = X0
| aElementOf0(X0,sF8) )
| ~ spl10_4 ),
inference(resolution,[],[f98,f137]) ).
fof(f162,plain,
( aSet0(sF9)
| ~ spl10_2 ),
inference(resolution,[],[f87,f127]) ).
fof(f165,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF8)
| ~ aElement0(X0)
| aElementOf0(X0,sF9) )
| ~ spl10_2 ),
inference(resolution,[],[f86,f127]) ).
fof(f171,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF8)
| aElementOf0(X0,xS) )
| ~ spl10_4 ),
inference(resolution,[],[f96,f137]) ).
fof(f175,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(sK5(X1,X0))
| ~ aSet0(X0) ),
inference(resolution,[],[f75,f68]) ).
fof(f178,plain,
( ! [X0] :
( ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS))
| xx = sK5(X0,xS)
| aElementOf0(sK5(X0,xS),sF8) )
| ~ spl10_4 ),
inference(resolution,[],[f75,f157]) ).
fof(f181,plain,
( ! [X0] :
( ~ aSet0(sF9)
| aSubsetOf0(sF9,X0)
| ~ aSet0(X0)
| xx = sK5(X0,sF9)
| aElementOf0(sK5(X0,sF9),sF8) )
| ~ spl10_1 ),
inference(resolution,[],[f75,f153]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(sK5(X1,X0)) ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f183,plain,
( ! [X0] :
( aElementOf0(sK5(X0,sF9),sF8)
| ~ aSet0(X0)
| xx = sK5(X0,sF9)
| aSubsetOf0(sF9,X0) )
| ~ spl10_1
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f181,f162]) ).
fof(f186,plain,
( ! [X0] :
( aElementOf0(sK5(X0,xS),sF8)
| ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS))
| xx = sK5(X0,xS)
| aSubsetOf0(xS,X0) )
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f178,f105]) ).
fof(f189,plain,
( ! [X0] :
( aElementOf0(sK5(X0,sF9),xS)
| xx = sK5(X0,sF9)
| aSubsetOf0(sF9,X0)
| ~ aSet0(X0) )
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(resolution,[],[f183,f171]) ).
fof(f197,plain,
( ! [X0] :
( ~ aSet0(X0)
| ~ aElement0(sK5(X0,xS))
| xx = sK5(X0,xS)
| aSubsetOf0(xS,X0)
| ~ aElement0(sK5(X0,xS))
| aElementOf0(sK5(X0,xS),sF9) )
| ~ spl10_2
| ~ spl10_4 ),
inference(resolution,[],[f186,f165]) ).
fof(f199,plain,
( ! [X0] :
( aElementOf0(sK5(X0,xS),sF9)
| ~ aElement0(sK5(X0,xS))
| xx = sK5(X0,xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) )
| ~ spl10_2
| ~ spl10_4 ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f218,plain,
( ~ aSet0(sF9)
| aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| xx = sK5(xS,sF9)
| aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(resolution,[],[f76,f189]) ).
fof(f221,plain,
( ~ aSet0(sF9)
| aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| xx = sK5(xS,sF9)
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f227,plain,
( aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| xx = sK5(xS,sF9)
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f221,f162]) ).
fof(f232,plain,
( aSubsetOf0(sF9,xS)
| xx = sK5(xS,sF9)
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f227,f105]) ).
fof(f236,definition,
( spl10_5
<=> xx = sK5(xS,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f238,plain,
( xx = sK5(xS,sF9)
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl10_6
<=> aSubsetOf0(sF9,xS) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f241,plain,
( ~ aSubsetOf0(sF9,xS)
| spl10_6 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( aSubsetOf0(sF9,xS)
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( spl10_5
| spl10_6
| ~ spl10_1
| ~ spl10_2
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f232,f135,f125,f121,f240,f236]) ).
fof(f270,definition,
( spl10_11
<=> aElementOf0(xx,sF9) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f272,plain,
( aElementOf0(xx,sF9)
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f275,plain,
( ~ aSubsetOf0(xS,sF9)
| xS = sF9
| ~ aSet0(xS)
| ~ aSet0(sF9)
| ~ spl10_6 ),
inference(resolution,[],[f242,f79]) ).
fof(f276,plain,
( ~ aSubsetOf0(xS,sF9)
| xS = sF9
| ~ aSet0(sF9)
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f275,f74]) ).
fof(f278,plain,
( ~ aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f276,f118]) ).
fof(f280,plain,
( ~ aSubsetOf0(xS,sF9)
| ~ spl10_2
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f278,f162]) ).
fof(f326,plain,
( ~ aElement0(xx)
| aElementOf0(xx,sF9)
| ~ spl10_2 ),
inference(resolution,[],[f111,f127]) ).
fof(f327,plain,
( aElementOf0(xx,sF9)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f326,f140]) ).
fof(f328,plain,
( spl10_11
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f327,f125,f270]) ).
fof(f356,plain,
( ~ aElement0(sK5(sF9,xS))
| xx = sK5(sF9,xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ aSet0(xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ spl10_2
| ~ spl10_4 ),
inference(resolution,[],[f199,f76]) ).
fof(f361,plain,
( ~ aElement0(sK5(sF9,xS))
| xx = sK5(sF9,xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_4 ),
inference(duplicate_literal_removal,[],[f356]) ).
fof(f362,plain,
( xx = sK5(sF9,xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f361,f182]) ).
fof(f363,plain,
( xx = sK5(sF9,xS)
| ~ aSet0(sF9)
| ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f362,f280]) ).
fof(f364,plain,
( xx = sK5(sF9,xS)
| ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f363,f162]) ).
fof(f365,plain,
( xx = sK5(sF9,xS)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f364,f105]) ).
fof(f366,plain,
( ~ aElementOf0(xx,sF9)
| ~ aSet0(xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6 ),
inference(superposition,[],[f76,f365]) ).
fof(f368,plain,
( ~ aSet0(xS)
| aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f366,f272]) ).
fof(f369,plain,
( aSubsetOf0(xS,sF9)
| ~ aSet0(sF9)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f368,f105]) ).
fof(f370,plain,
( ~ aSet0(sF9)
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f369,f280]) ).
fof(f371,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f370,f162]) ).
fof(f372,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f384,plain,
( ~ aElementOf0(xx,xS)
| ~ aSet0(sF9)
| aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| ~ spl10_5 ),
inference(superposition,[],[f76,f238]) ).
fof(f386,plain,
( ~ aSet0(sF9)
| aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f384,f106]) ).
fof(f387,plain,
( aSubsetOf0(sF9,xS)
| ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f386,f162]) ).
fof(f388,plain,
( ~ aSet0(xS)
| ~ spl10_2
| ~ spl10_5
| spl10_6 ),
inference(forward_subsumption_resolution,[],[f387,f241]) ).
fof(f389,plain,
( $false
| ~ spl10_2
| ~ spl10_5
| spl10_6 ),
inference(forward_subsumption_resolution,[],[f388,f105]) ).
fof(f390,plain,
( ~ spl10_2
| ~ spl10_5
| spl10_6 ),
inference(avatar_contradiction_clause,[],[f389]) ).
cnf(s1,plain,
( ~ spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f128]) ).
cnf(s2,plain,
( ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f138]) ).
cnf(s3,plain,
spl10_3,
inference(sat_conversion,[],[f146]) ).
cnf(s4,plain,
( spl10_1
| ~ spl10_4 ),
inference(sat_conversion,[],[f152]) ).
cnf(s5,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_4
| spl10_5
| spl10_6 ),
inference(sat_conversion,[],[f243]) ).
cnf(s10,plain,
( ~ spl10_2
| spl10_11 ),
inference(sat_conversion,[],[f328]) ).
cnf(s12,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_6
| ~ spl10_11 ),
inference(sat_conversion,[],[f372]) ).
cnf(s14,plain,
( ~ spl10_2
| ~ spl10_5
| spl10_6 ),
inference(sat_conversion,[],[f390]) ).
cnf(s15,plain,
spl10_4,
inference(rat,[],[s2,s3]) ).
cnf(s16,plain,
spl10_1,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl10_2,
inference(rat,[],[s1,s16]) ).
cnf(s18,plain,
spl10_11,
inference(rat,[],[s10,s17]) ).
cnf(s20,plain,
~ spl10_6,
inference(rat,[],[s12,s17,s15,s18]) ).
cnf(s22,plain,
~ spl10_5,
inference(rat,[],[s14,s17,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s17,s16,s15,s20,s22]) ).
fof(f391,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:22:22 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 6.62/1.95 % (3851783)Detected formulas, will run a generic FOF schedule.
% 6.62/1.95 % (3851791)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3513581238:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.62/1.95 % (3851791)Refutation not found, incomplete strategy
% 6.62/1.95 % (3851791)------------------------------
% 6.62/1.95 % (3851791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851791)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851791)Termination reason: Refutation not found, incomplete strategy
% 6.62/1.95 % (3851791)Time elapsed: 0.002 s
% 6.62/1.95 % (3851791)Peak memory usage: 88 MB
% 6.62/1.95 % (3851791)Instructions burned: 2 (million)
% 6.62/1.95 % (3851788)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=3367705140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.62/1.95 % (3851790)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=2798731017:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.62/1.95 % (3851789)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=2706735864:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.62/1.95 % (3851792)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1060921523:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.62/1.95 % (3851793)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1190621821:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.62/1.95 % (3851794)dis-21_1_sil=8000:lcm=predicate:random_seed=993298284: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)
% 6.62/1.95 % (3851792)Instruction limit reached!
% 6.62/1.95 % (3851792)------------------------------
% 6.62/1.95 % (3851792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851792)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851792)Termination reason: Instruction limit
% 6.62/1.95 % (3851792)Termination phase: Saturation
% 6.62/1.95 % (3851792)Time elapsed: 0.071 s
% 6.62/1.95 % (3851792)Peak memory usage: 88 MB
% 6.62/1.95 % (3851792)Instructions burned: 119 (million)
% 6.62/1.95 % (3851794)Instruction limit reached!
% 6.62/1.95 % (3851794)------------------------------
% 6.62/1.95 % (3851794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851794)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851794)Termination reason: Instruction limit
% 6.62/1.95 % (3851794)Termination phase: Saturation
% 6.62/1.95 % (3851794)Time elapsed: 0.076 s
% 6.62/1.95 % (3851794)Peak memory usage: 89 MB
% 6.62/1.95 % (3851794)Instructions burned: 130 (million)
% 6.62/1.95 % (3851793)Instruction limit reached!
% 6.62/1.95 % (3851793)------------------------------
% 6.62/1.95 % (3851793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851793)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851793)Termination reason: Instruction limit
% 6.62/1.95 % (3851793)Termination phase: Saturation
% 6.62/1.95 % (3851793)Time elapsed: 0.096 s
% 6.62/1.95 % (3851793)Peak memory usage: 89 MB
% 6.62/1.95 % (3851793)Instructions burned: 139 (million)
% 6.62/1.95 % (3851791)------------------------------
% 6.62/1.95 % (3851791)------------------------------
% 6.62/1.95 % (3851802)lrs+10_1_sil=8000:sp=occurrence:random_seed=525898172:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.62/1.95 % (3851803)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2440041599:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.62/1.95 % (3851805)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1474376934:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.62/1.95 % (3851804)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2182829345:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.62/1.95 % (3851803)Instruction limit reached!
% 6.62/1.95 % (3851803)------------------------------
% 6.62/1.95 % (3851803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851803)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851803)Termination reason: Instruction limit
% 6.62/1.95 % (3851803)Termination phase: Saturation
% 6.62/1.95 % (3851803)Time elapsed: 0.074 s
% 6.62/1.95 % (3851803)Peak memory usage: 89 MB
% 6.62/1.95 % (3851803)Instructions burned: 157 (million)
% 6.62/1.95 % (3851805)Instruction limit reached!
% 6.62/1.95 % (3851805)------------------------------
% 6.62/1.95 % (3851805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851805)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851805)Termination reason: Instruction limit
% 6.62/1.95 % (3851805)Termination phase: Saturation
% 6.62/1.95 % (3851805)Time elapsed: 0.079 s
% 6.62/1.95 % (3851805)Peak memory usage: 90 MB
% 6.62/1.95 % (3851805)Instructions burned: 250 (million)
% 6.62/1.95 % (3851802)Instruction limit reached!
% 6.62/1.95 % (3851802)------------------------------
% 6.62/1.95 % (3851802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851802)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851802)Termination reason: Instruction limit
% 6.62/1.95 % (3851802)Termination phase: Saturation
% 6.62/1.95 % (3851802)Time elapsed: 0.175 s
% 6.62/1.95 % (3851802)Peak memory usage: 91 MB
% 6.62/1.95 % (3851802)Instructions burned: 287 (million)
% 6.62/1.95 % (3851811)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3312671768:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.62/1.95 % (3851810)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2177825305:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.62/1.95 % (3851810)Refutation not found, incomplete strategy
% 6.62/1.95 % (3851810)------------------------------
% 6.62/1.95 % (3851810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851810)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851810)Termination reason: Refutation not found, incomplete strategy
% 6.62/1.95 % (3851810)Time elapsed: 0.003 s
% 6.62/1.95 % (3851810)Peak memory usage: 88 MB
% 6.62/1.95 % (3851810)Instructions burned: 2 (million)
% 6.62/1.95 % (3851804)Instruction limit reached!
% 6.62/1.95 % (3851804)------------------------------
% 6.62/1.95 % (3851804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851804)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851804)Termination reason: Instruction limit
% 6.62/1.95 % (3851804)Termination phase: Saturation
% 6.62/1.95 % (3851804)Time elapsed: 0.220 s
% 6.62/1.95 % (3851804)Peak memory usage: 92 MB
% 6.62/1.95 % (3851804)Instructions burned: 327 (million)
% 6.62/1.95 % (3851812)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1256638214:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.62/1.95 % (3851815)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=124153255:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.62/1.95 % (3851788)First to succeed.
% 6.62/1.95 % (3851788)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3851783"
% 6.62/1.95 % (3851790)Also succeeded, but the first one will report.
% 6.62/1.95 % (3851812)Instruction limit reached!
% 6.62/1.95 % (3851812)------------------------------
% 6.62/1.95 % (3851812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851812)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851812)Termination reason: Instruction limit
% 6.62/1.95 % (3851812)Termination phase: Saturation
% 6.62/1.95 % (3851812)Time elapsed: 0.082 s
% 6.62/1.95 % (3851812)Peak memory usage: 90 MB
% 6.62/1.95 % (3851812)Instructions burned: 114 (million)
% 6.62/1.95 % (3851810)------------------------------
% 6.62/1.95 % (3851810)------------------------------
% 6.62/1.95 % (3851815)Instruction limit reached!
% 6.62/1.95 % (3851815)------------------------------
% 6.62/1.95 % (3851815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851815)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851815)Termination reason: Instruction limit
% 6.62/1.95 % (3851815)Termination phase: Saturation
% 6.62/1.95 % (3851815)Time elapsed: 0.068 s
% 6.62/1.95 % (3851815)Peak memory usage: 89 MB
% 6.62/1.95 % (3851815)Instructions burned: 127 (million)
% 6.62/1.95 % (3851818)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=453081294:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.62/1.95 % (3851811)Also succeeded, but the first one will report.
% 6.62/1.95 % (3851819)lrs+10_1_sil=8000:sp=occurrence:random_seed=221642404:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.62/1.95 % (3851820)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1165123457:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.62/1.95 % (3851820)Refutation not found, incomplete strategy
% 6.62/1.95 % (3851820)------------------------------
% 6.62/1.95 % (3851820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851820)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851820)Termination reason: Refutation not found, incomplete strategy
% 6.62/1.95 % (3851820)Time elapsed: 0.003 s
% 6.62/1.95 % (3851820)Peak memory usage: 88 MB
% 6.62/1.95 % (3851820)Instructions burned: 3 (million)
% 6.62/1.95 % (3851818)Instruction limit reached!
% 6.62/1.95 % (3851818)------------------------------
% 6.62/1.95 % (3851818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.62/1.95 % (3851818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.62/1.95 % (3851818)CaDiCaL version: 2.1.3
% 6.62/1.95 % (3851818)Termination reason: Instruction limit
% 6.62/1.95 % (3851818)Termination phase: Saturation
% 6.62/1.95 % (3851818)Time elapsed: 0.067 s
% 6.62/1.95 % (3851818)Peak memory usage: 89 MB
% 6.62/1.95 % (3851818)Instructions burned: 115 (million)
% 6.62/1.95 % (3851788)Refutation found. Thanks to Tanya!
% 6.62/1.95 % SZS status Theorem for theBenchmark
% 6.62/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 8.11/2.05 % (3851788)------------------------------
% 8.11/2.05 % (3851788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.11/2.05 % (3851788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.11/2.05 % (3851788)CaDiCaL version: 2.1.3
% 8.11/2.05 % (3851788)Termination reason: Refutation
% 8.11/2.05 % (3851788)Time elapsed: 0.637 s
% 8.11/2.05 % (3851788)Peak memory usage: 127 MB
% 8.11/2.05 % (3851788)Instructions burned: 952 (million)
% 8.11/2.05 % (3851788)------------------------------
% 8.11/2.05 % (3851788)------------------------------
% 8.11/2.05 % (3851783)Success in time 1.073 s
% 8.11/2.05 % Vampire exiting
%------------------------------------------------------------------------------