%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:24:43 PM UTC 2026
% Result : Theorem 0.38s 0.49s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 114 ( 13 unt; 7 def)
% Number of atoms : 400 ( 47 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 451 ( 165 ~; 179 |; 76 &)
% ( 19 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 75 !; 3 ?)
% 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(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(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 ) ) )
=> 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(f35,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f35]) ).
fof(f44,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,[],[f26]) ).
fof(f45,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,[],[f44]) ).
fof(f56,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(f57,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,[],[f56]) ).
fof(f58,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,[],[f57]) ).
fof(f59,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))],[f58]) ).
fof(f72,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,[],[f45]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f80,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| X0 = X1
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f113,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f115,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f116,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xS,xx))
| aElement0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f119,plain,
! [X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f74]) ).
fof(f120,plain,
aSet0(sdtpldt0(xS,xx)),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx != X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f122,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f125,plain,
aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(cnf_transformation,[],[f74]) ).
fof(f126,plain,
xS != sdtmndt0(sdtpldt0(xS,xx),xx),
inference(cnf_transformation,[],[f74]) ).
fof(f127,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt0(xS,xx))
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| xx = X0 ),
inference(forward_subsumption_resolution,[],[f124,f117]) ).
fof(f143,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElement0(X0) ),
inference(resolution,[],[f75,f113]) ).
fof(f147,plain,
! [X0] :
( ~ aSubsetOf0(X0,xS)
| aSet0(X0) ),
inference(resolution,[],[f81,f113]) ).
fof(f261,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,X1)
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(resolution,[],[f80,f120]) ).
fof(f268,plain,
! [X0] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0) ),
inference(resolution,[],[f82,f125]) ).
fof(f269,plain,
! [X0] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,xS),xS)
| aSubsetOf0(xS,X0) ),
inference(resolution,[],[f82,f113]) ).
fof(f274,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),X0)
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0) ),
inference(resolution,[],[f83,f125]) ).
fof(f275,plain,
! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,xS),X0)
| aSubsetOf0(xS,X0) ),
inference(resolution,[],[f83,f113]) ).
fof(f339,plain,
! [X0] :
( ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,xS)
| xS = X0
| ~ aSet0(X0) ),
inference(resolution,[],[f86,f113]) ).
fof(f340,plain,
! [X0] :
( ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,xS)
| xS = X0 ),
inference(forward_subsumption_resolution,[],[f339,f147]) ).
fof(f375,definition,
( spl8_21
<=> aSubsetOf0(xS,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl8_21])],[avatar_definition]) ).
fof(f376,plain,
( aSubsetOf0(xS,sdtpldt0(xS,xx))
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f377,plain,
( ~ aSubsetOf0(xS,sdtpldt0(xS,xx))
| spl8_21 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f630,plain,
( ~ aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(resolution,[],[f274,f113]) ).
fof(f632,definition,
( spl8_28
<=> aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
introduced(definition,[new_symbols(definition,[spl8_28])],[avatar_definition]) ).
fof(f633,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| spl8_28 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f634,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ spl8_28 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f636,definition,
( spl8_29
<=> aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS) ),
introduced(definition,[new_symbols(definition,[spl8_29])],[avatar_definition]) ).
fof(f638,plain,
( ~ aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| spl8_29 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f639,plain,
( spl8_28
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f630,f636,f632]) ).
fof(f677,plain,
( aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
inference(resolution,[],[f268,f113]) ).
fof(f855,plain,
( aElementOf0(sK5(sdtpldt0(xS,xx),xS),xS)
| aSubsetOf0(xS,sdtpldt0(xS,xx)) ),
inference(resolution,[],[f269,f120]) ).
fof(f856,plain,
( aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS)
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[],[f269,f125]) ).
fof(f859,plain,
( aElementOf0(sK5(sdtpldt0(xS,xx),xS),xS)
| spl8_21 ),
inference(forward_subsumption_resolution,[],[f855,f377]) ).
fof(f869,plain,
( aElement0(sK5(sdtpldt0(xS,xx),xS))
| spl8_21 ),
inference(resolution,[],[f859,f143]) ).
fof(f877,definition,
( spl8_39
<=> aElement0(sK5(sdtpldt0(xS,xx),xS)) ),
introduced(definition,[new_symbols(definition,[spl8_39])],[avatar_definition]) ).
fof(f879,plain,
( aElement0(sK5(sdtpldt0(xS,xx),xS))
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f882,plain,
( spl8_39
| spl8_21 ),
inference(avatar_split_clause,[],[f869,f375,f877]) ).
fof(f884,plain,
( ~ aElementOf0(sK5(sdtpldt0(xS,xx),xS),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtpldt0(xS,xx)) ),
inference(resolution,[],[f275,f120]) ).
fof(f885,plain,
( ~ aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[],[f275,f125]) ).
fof(f888,plain,
( ~ aElementOf0(sK5(sdtpldt0(xS,xx),xS),sdtpldt0(xS,xx))
| spl8_21 ),
inference(forward_subsumption_resolution,[],[f884,f377]) ).
fof(f895,plain,
( aElementOf0(sK5(sdtpldt0(xS,xx),xS),sdtpldt0(xS,xx))
| ~ aElementOf0(sK5(sdtpldt0(xS,xx),xS),xS)
| ~ spl8_39 ),
inference(resolution,[],[f879,f119]) ).
fof(f896,plain,
( ~ aElementOf0(sK5(sdtpldt0(xS,xx),xS),xS)
| spl8_21
| ~ spl8_39 ),
inference(forward_subsumption_resolution,[],[f895,f888]) ).
fof(f898,plain,
( $false
| spl8_21
| ~ spl8_39 ),
inference(forward_subsumption_resolution,[],[f896,f859]) ).
fof(f899,plain,
( spl8_21
| ~ spl8_39 ),
inference(avatar_contradiction_clause,[],[f898]) ).
fof(f918,plain,
( ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl8_21 ),
inference(resolution,[],[f376,f261]) ).
fof(f1169,plain,
( aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtmndt0(sdtpldt0(xS,xx),xx))
| spl8_28 ),
inference(forward_subsumption_resolution,[],[f677,f633]) ).
fof(f1171,definition,
( spl8_45
<=> aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl8_45])],[avatar_definition]) ).
fof(f1173,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f1175,definition,
( spl8_46
<=> aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS) ),
introduced(definition,[new_symbols(definition,[spl8_46])],[avatar_definition]) ).
fof(f1177,plain,
( aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),xS)
| ~ spl8_46 ),
inference(avatar_component_clause,[],[f1175]) ).
fof(f1178,plain,
( spl8_45
| spl8_46 ),
inference(avatar_split_clause,[],[f856,f1175,f1171]) ).
fof(f1180,definition,
( spl8_47
<=> aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl8_47])],[avatar_definition]) ).
fof(f1182,plain,
( ~ aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| spl8_47 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f1183,plain,
( spl8_45
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f885,f1180,f1171]) ).
fof(f1197,plain,
( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl8_45 ),
inference(resolution,[],[f1173,f340]) ).
fof(f1259,plain,
( aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
| spl8_28 ),
inference(resolution,[],[f1169,f122]) ).
fof(f1260,plain,
( xx != sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| spl8_28 ),
inference(resolution,[],[f1169,f121]) ).
fof(f1410,plain,
( xx = sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| spl8_28 ),
inference(resolution,[],[f1259,f116]) ).
fof(f1418,plain,
( aElementOf0(sK5(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| spl8_28 ),
inference(forward_subsumption_resolution,[],[f1410,f1260]) ).
fof(f1419,plain,
( $false
| spl8_28
| spl8_29 ),
inference(forward_subsumption_resolution,[],[f1418,f638]) ).
fof(f1420,plain,
( spl8_28
| spl8_29 ),
inference(avatar_contradiction_clause,[],[f1419]) ).
fof(f1423,plain,
( xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl8_28
| ~ spl8_45 ),
inference(forward_subsumption_resolution,[],[f1197,f634]) ).
fof(f1435,plain,
( $false
| ~ spl8_28
| ~ spl8_45 ),
inference(forward_subsumption_resolution,[],[f1423,f126]) ).
fof(f1436,plain,
( ~ spl8_28
| ~ spl8_45 ),
inference(avatar_contradiction_clause,[],[f1435]) ).
fof(f1442,plain,
( aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtpldt0(xS,xx))
| ~ spl8_21
| ~ spl8_46 ),
inference(resolution,[],[f1177,f918]) ).
fof(f1582,plain,
( aElementOf0(sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS),sdtmndt0(sdtpldt0(xS,xx),xx))
| xx = sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ spl8_21
| ~ spl8_46 ),
inference(resolution,[],[f1442,f127]) ).
fof(f1591,plain,
( xx = sK5(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ spl8_21
| ~ spl8_46
| spl8_47 ),
inference(forward_subsumption_resolution,[],[f1582,f1182]) ).
fof(f1600,plain,
( aElementOf0(xx,xS)
| ~ spl8_21
| ~ spl8_46
| spl8_47 ),
inference(superposition,[],[f1177,f1591]) ).
fof(f1608,plain,
( $false
| ~ spl8_21
| ~ spl8_46
| spl8_47 ),
inference(forward_subsumption_resolution,[],[f1600,f115]) ).
fof(f1609,plain,
( ~ spl8_21
| ~ spl8_46
| spl8_47 ),
inference(avatar_contradiction_clause,[],[f1608]) ).
cnf(s28,plain,
( spl8_28
| ~ spl8_29 ),
inference(sat_conversion,[],[f639]) ).
cnf(s37,plain,
( spl8_21
| spl8_39 ),
inference(sat_conversion,[],[f882]) ).
cnf(s38,plain,
( spl8_21
| ~ spl8_39 ),
inference(sat_conversion,[],[f899]) ).
cnf(s49,plain,
( spl8_45
| spl8_46 ),
inference(sat_conversion,[],[f1178]) ).
cnf(s50,plain,
( spl8_45
| ~ spl8_47 ),
inference(sat_conversion,[],[f1183]) ).
cnf(s68,plain,
( spl8_28
| spl8_29 ),
inference(sat_conversion,[],[f1420]) ).
cnf(s72,plain,
( ~ spl8_28
| ~ spl8_45 ),
inference(sat_conversion,[],[f1436]) ).
cnf(s76,plain,
( ~ spl8_21
| ~ spl8_46
| spl8_47 ),
inference(sat_conversion,[],[f1609]) ).
cnf(s79,plain,
spl8_21,
inference(rat,[],[s37,s38]) ).
cnf(s83,plain,
spl8_28,
inference(rat,[],[s28,s68]) ).
cnf(s84,plain,
~ spl8_45,
inference(rat,[],[s72,s83]) ).
cnf(s88,plain,
~ spl8_47,
inference(rat,[],[s50,s84]) ).
cnf(s89,plain,
spl8_46,
inference(rat,[],[s49,s84]) ).
cnf(s93,plain,
$false,
inference(rat,[],[s76,s79,s88,s89]) ).
fof(f1610,plain,
$false,
inference(avatar_sat_refutation,[],[s93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM536+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:24:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.49 % (2699095)Will run a generic schedule for satisfiability detection.
% 0.38/0.49 % (2699104)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3012283614:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.49 % (2699100)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=413392287_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.49 % (2699102)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1347779804:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.49 % (2699103)dis+10_1_sil=32000:sp=arity:random_seed=3244825186:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.49 % (2699106)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1468884540:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.49 % (2699105)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2076116779:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.49 % (2699101)% WARNING: option uhcvi not known.
% 0.38/0.49 % TRYING [1]
% 0.38/0.49 % TRYING [2]
% 0.38/0.49 % TRYING [3]
% 0.38/0.49 % (2699101)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=96623012:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.49 % TRYING [4]
% 0.38/0.49 % TRYING [5]
% 0.38/0.49 % (2699104)Instruction limit reached!
% 0.38/0.49 % (2699104)------------------------------
% 0.38/0.49 % (2699104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.49 % (2699104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.49 % (2699104)CaDiCaL version: 2.1.3
% 0.38/0.49 % (2699104)Termination reason: Instruction limit
% 0.38/0.49 % (2699104)Termination phase: Saturation
% 0.38/0.49 % (2699104)Time elapsed: 0.039 s
% 0.38/0.49 % (2699104)Peak memory usage: 12 MB
% 0.38/0.49 % (2699104)Instructions burned: 118 (million)
% 0.38/0.49 % (2699105) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2699095-2699105"...
% 0.38/0.49 % TRYING [6]
% 0.38/0.49 % (2699114)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=526854794:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.38/0.49 % (2699105)...printing done.
% 0.38/0.49 % TRYING [1]
% 0.38/0.49 % TRYING [2]
% 0.38/0.49 % (2699105)Refutation found. Thanks to Tanya!
% 0.38/0.49 % SZS status Theorem for theBenchmark
% 0.38/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.49 % (2699105)------------------------------
% 0.38/0.49 % (2699105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.49 % (2699105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.49 % (2699105)CaDiCaL version: 2.1.3
% 0.38/0.49 % (2699105)Termination reason: Refutation
% 0.38/0.49 % (2699105)Time elapsed: 0.044 s
% 0.38/0.49 % (2699105)Peak memory usage: 13 MB
% 0.38/0.49 % (2699105)Instructions burned: 63 (million)
% 0.38/0.49 % (2699095)Success in time 0.081 s
% 0.38/0.49 % Vampire exiting
%------------------------------------------------------------------------------