%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM536+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 2.57s 0.95s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 107 ( 18 unt; 5 def)
% Number of atoms : 355 ( 63 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 429 ( 181 ~; 207 |; 18 &)
% ( 17 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(f18,axiom,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
fof(f19,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
fof(f20,conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
xS != sdtmndt0(sdtpldt0(xS,xx),xx),
inference(flattening,[],[f21]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ aSet0(X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| X1 != X3
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| sdtpldt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| sdtpldt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| X1 = X3
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| sdtpldt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aSet0(X2)
| sdtpldt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sK3(X0,X1,X2) = X1
| ~ aElementOf0(sK3(X0,X1,X2),X0)
| ~ aElement0(sK3(X0,X1,X2))
| ~ aElementOf0(sK3(X0,X1,X2),X2)
| ~ aSet0(X2)
| sdtmndt0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
! [X2,X0,X1] :
( sK3(X0,X1,X2) != X1
| ~ aSet0(X0)
| ~ aElement0(X1)
| aElementOf0(sK3(X0,X1,X2),X2)
| ~ aSet0(X2)
| sdtmndt0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(sK3(X0,X1,X2),X0)
| aElementOf0(sK3(X0,X1,X2),X2)
| ~ aSet0(X2)
| sdtmndt0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aSet0(X2)
| sdtmndt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| ~ aSet0(X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f77,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f78,plain,
aElement0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f79,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f80,plain,
xS != sdtmndt0(sdtpldt0(xS,xx),xx),
inference(cnf_transformation,[],[f22]) ).
fof(f83,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f66]) ).
fof(f85,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X3,sdtpldt0(X0,X1))
| ~ aSet0(X0)
| X1 = X3
| aElementOf0(X3,X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f63]) ).
fof(f86,plain,
! [X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(X0,X1)) ),
inference(equality_resolution,[],[f62]) ).
fof(f87,plain,
! [X2,X3,X0] :
( ~ aElement0(X3)
| ~ aSet0(X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| sdtpldt0(X0,X3) != X2 ),
inference(equality_resolution,[],[f61]) ).
fof(f88,plain,
! [X3,X0] :
( ~ aElement0(X3)
| ~ aSet0(X0)
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(X0,X3)) ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f75]) ).
fof(f95,plain,
! [X3,X0] :
( aElementOf0(X3,sdtpldt0(X0,X3))
| ~ aSet0(X0)
| ~ aElement0(X3) ),
inference(duplicate_literal_removal,[],[f88]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aSet0(sdtpldt0(X0,X1))
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(sdtpldt0(X0,X1),X1),X1)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(resolution,[],[f76,f95]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(sdtmndt0(sdtpldt0(X0,X1),X1),X1) ),
inference(forward_subsumption_resolution,[],[f136,f83]) ).
fof(f154,plain,
! [X3,X0,X1] :
( aElementOf0(X3,sdtpldt0(X0,X1))
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X1) ),
inference(forward_subsumption_resolution,[],[f86,f45]) ).
fof(f186,plain,
! [X0] :
( ~ aSet0(X0)
| sdtpldt0(X0,xx) = sdtpldt0(sdtmndt0(sdtpldt0(X0,xx),xx),xx) ),
inference(resolution,[],[f140,f78]) ).
fof(f192,plain,
sdtpldt0(xS,xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS,xx),xx),xx),
inference(resolution,[],[f186,f77]) ).
fof(f436,plain,
( aSet0(sdtpldt0(xS,xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(superposition,[],[f83,f192]) ).
fof(f437,plain,
( aSet0(sdtpldt0(xS,xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(forward_subsumption_resolution,[],[f436,f78]) ).
fof(f443,definition,
( spl4_26
<=> aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition]) ).
fof(f445,plain,
( ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| spl4_26 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f447,definition,
( spl4_27
<=> aSet0(sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl4_27])],[avatar_definition]) ).
fof(f449,plain,
( aSet0(sdtpldt0(xS,xx))
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f450,plain,
( ~ spl4_26
| spl4_27 ),
inference(avatar_split_clause,[],[f437,f447,f443]) ).
fof(f468,plain,
( ~ aSet0(sdtpldt0(xS,xx))
| ~ aElement0(xx)
| spl4_26 ),
inference(resolution,[],[f445,f89]) ).
fof(f469,plain,
( ~ aSet0(sdtpldt0(xS,xx))
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f468,f78]) ).
fof(f470,plain,
( ~ aSet0(xS)
| ~ aElement0(xx)
| spl4_26 ),
inference(resolution,[],[f469,f83]) ).
fof(f471,plain,
( ~ aElement0(xx)
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f470,f77]) ).
fof(f472,plain,
( $false
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f471,f78]) ).
fof(f473,plain,
spl4_26,
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f1324,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aElementOf0(sK3(X0,xx,X1),X0)
| aElementOf0(sK3(X0,xx,X1),X1)
| ~ aSet0(X0)
| sdtmndt0(X0,xx) = X1 ),
inference(resolution,[],[f73,f78]) ).
fof(f2921,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK3(X0,X1,X2),X2)
| ~ aSet0(X0)
| sK3(X0,X1,X2) = X1
| ~ aElementOf0(sK3(X0,X1,X2),X0)
| ~ aElement0(X1)
| ~ aSet0(X2)
| sdtmndt0(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f71,f45]) ).
fof(f4857,plain,
! [X0] :
( ~ aSet0(X0)
| aElementOf0(sK3(X0,xx,xS),xS)
| aElementOf0(sK3(X0,xx,xS),X0)
| xS = sdtmndt0(X0,xx) ),
inference(resolution,[],[f1324,f77]) ).
fof(f13648,plain,
( aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_27 ),
inference(resolution,[],[f4857,f449]) ).
fof(f13769,plain,
( aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f13648,f80]) ).
fof(f13859,definition,
( spl4_799
<=> aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[spl4_799])],[avatar_definition]) ).
fof(f13860,plain,
( ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| spl4_799 ),
inference(avatar_component_clause,[],[f13859]) ).
fof(f13861,plain,
( aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ spl4_799 ),
inference(avatar_component_clause,[],[f13859]) ).
fof(f13863,definition,
( spl4_800
<=> aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS) ),
introduced(definition,[new_symbols(definition,[spl4_800])],[avatar_definition]) ).
fof(f13864,plain,
( ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| spl4_800 ),
inference(avatar_component_clause,[],[f13863]) ).
fof(f13865,plain,
( aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ spl4_800 ),
inference(avatar_component_clause,[],[f13863]) ).
fof(f13866,plain,
( spl4_799
| spl4_800
| ~ spl4_27 ),
inference(avatar_split_clause,[],[f13769,f447,f13863,f13859]) ).
fof(f13936,plain,
( ~ aSet0(sdtpldt0(xS,xx))
| xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_800 ),
inference(resolution,[],[f13865,f2921]) ).
fof(f13960,definition,
( spl4_806
<=> xx = sK3(sdtpldt0(xS,xx),xx,xS) ),
introduced(definition,[new_symbols(definition,[spl4_806])],[avatar_definition]) ).
fof(f13961,plain,
( xx != sK3(sdtpldt0(xS,xx),xx,xS)
| spl4_806 ),
inference(avatar_component_clause,[],[f13960]) ).
fof(f13962,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ spl4_806 ),
inference(avatar_component_clause,[],[f13960]) ).
fof(f13964,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f13936,f83]) ).
fof(f13965,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f13964,f78]) ).
fof(f13966,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f13965,f77]) ).
fof(f13967,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f13966,f80]) ).
fof(f13968,plain,
( ~ spl4_799
| spl4_806
| ~ spl4_800 ),
inference(avatar_split_clause,[],[f13967,f13863,f13960,f13859]) ).
fof(f14021,plain,
( xx != xx
| ~ aSet0(sdtpldt0(xS,xx))
| ~ aElement0(xx)
| aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(superposition,[],[f72,f13962]) ).
fof(f14023,plain,
( ~ aSet0(sdtpldt0(xS,xx))
| ~ aElement0(xx)
| aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(trivial_inequality_removal,[],[f14021]) ).
fof(f14024,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(forward_subsumption_resolution,[],[f14023,f83]) ).
fof(f14027,plain,
( aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(forward_subsumption_resolution,[],[f14024,f78]) ).
fof(f14028,plain,
( ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(forward_subsumption_resolution,[],[f14027,f79]) ).
fof(f14029,plain,
( xS = sdtmndt0(sdtpldt0(xS,xx),xx)
| ~ spl4_806 ),
inference(forward_subsumption_resolution,[],[f14028,f77]) ).
fof(f14030,plain,
( $false
| ~ spl4_806 ),
inference(forward_subsumption_resolution,[],[f14029,f80]) ).
fof(f14031,plain,
~ spl4_806,
inference(avatar_contradiction_clause,[],[f14030]) ).
fof(f14466,plain,
( ~ aSet0(xS)
| ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aElement0(xx)
| spl4_799 ),
inference(resolution,[],[f13860,f154]) ).
fof(f14467,plain,
( ~ aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aElement0(xx)
| spl4_799 ),
inference(forward_subsumption_resolution,[],[f14466,f77]) ).
fof(f14468,plain,
( ~ aElement0(xx)
| spl4_799
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f14467,f13865]) ).
fof(f14469,plain,
( $false
| spl4_799
| ~ spl4_800 ),
inference(forward_subsumption_resolution,[],[f14468,f78]) ).
fof(f14470,plain,
( spl4_799
| ~ spl4_800 ),
inference(avatar_contradiction_clause,[],[f14469]) ).
fof(f14474,plain,
( ~ aSet0(xS)
| xx = sK3(sdtpldt0(xS,xx),xx,xS)
| aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aElement0(xx)
| ~ spl4_799 ),
inference(resolution,[],[f13861,f85]) ).
fof(f14481,plain,
( xx = sK3(sdtpldt0(xS,xx),xx,xS)
| aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aElement0(xx)
| ~ spl4_799 ),
inference(forward_subsumption_resolution,[],[f14474,f77]) ).
fof(f14485,plain,
( aElementOf0(sK3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aElement0(xx)
| ~ spl4_799
| spl4_806 ),
inference(forward_subsumption_resolution,[],[f14481,f13961]) ).
fof(f14488,plain,
( ~ aElement0(xx)
| ~ spl4_799
| spl4_800
| spl4_806 ),
inference(forward_subsumption_resolution,[],[f14485,f13864]) ).
fof(f14489,plain,
( $false
| ~ spl4_799
| spl4_800
| spl4_806 ),
inference(forward_subsumption_resolution,[],[f14488,f78]) ).
fof(f14490,plain,
( ~ spl4_799
| spl4_800
| spl4_806 ),
inference(avatar_contradiction_clause,[],[f14489]) ).
cnf(s26,plain,
( ~ spl4_26
| spl4_27 ),
inference(sat_conversion,[],[f450]) ).
cnf(s31,plain,
spl4_26,
inference(sat_conversion,[],[f473]) ).
cnf(s898,plain,
( ~ spl4_27
| spl4_799
| spl4_800 ),
inference(sat_conversion,[],[f13866]) ).
cnf(s904,plain,
( ~ spl4_799
| ~ spl4_800
| spl4_806 ),
inference(sat_conversion,[],[f13968]) ).
cnf(s911,plain,
~ spl4_806,
inference(sat_conversion,[],[f14031]) ).
cnf(s950,plain,
( spl4_799
| ~ spl4_800 ),
inference(sat_conversion,[],[f14470]) ).
cnf(s952,plain,
( ~ spl4_799
| spl4_800
| spl4_806 ),
inference(sat_conversion,[],[f14490]) ).
cnf(s953,plain,
( ~ spl4_799
| ~ spl4_800 ),
inference(rat,[],[s904,s911]) ).
cnf(s959,plain,
spl4_27,
inference(rat,[],[s26,s31]) ).
cnf(s989,plain,
spl4_799,
inference(rat,[],[s898,s950,s959]) ).
cnf(s990,plain,
spl4_800,
inference(rat,[],[s952,s911,s989]) ).
cnf(s991,plain,
$false,
inference(rat,[],[s953,s990,s989]) ).
fof(f14491,plain,
$false,
inference(avatar_sat_refutation,[],[s991]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM536+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:25:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.57/0.95 % (3852472)Will run a generic schedule for satisfiability detection.
% 2.57/0.95 % (3852477)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1818497201_2999 on theBenchmark for (2999ds/0Mi)
% 2.57/0.95 % TRYING [1]
% 2.57/0.95 % TRYING [2]
% 2.57/0.95 % TRYING [3]
% 2.57/0.95 % (3852478)% WARNING: option uhcvi not known.
% 2.57/0.95 % TRYING [4]
% 2.57/0.95 % (3852479)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1578089482:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.57/0.95 % (3852480)dis+10_1_sil=32000:sp=arity:random_seed=3994160800:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.57/0.95 % (3852481)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3525115849:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.57/0.95 % (3852478)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1663777534:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.57/0.95 % (3852482)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=436342591:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.57/0.95 % (3852483)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3534439520:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.57/0.95 % TRYING [5]
% 2.57/0.95 % TRYING [6]
% 2.57/0.95 % TRYING [7]
% 2.57/0.95 % (3852480)Instruction limit reached!
% 2.57/0.95 % (3852480)------------------------------
% 2.57/0.95 % (3852480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852480)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852480)Termination reason: Instruction limit
% 2.57/0.95 % (3852480)Termination phase: Saturation
% 2.57/0.95 % (3852480)Time elapsed: 0.068 s
% 2.57/0.95 % (3852480)Peak memory usage: 12 MB
% 2.57/0.95 % (3852480)Instructions burned: 104 (million)
% 2.57/0.95 % (3852481)Instruction limit reached!
% 2.57/0.95 % (3852481)------------------------------
% 2.57/0.95 % (3852481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852481)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852481)Termination reason: Instruction limit
% 2.57/0.95 % (3852481)Termination phase: Saturation
% 2.57/0.95 % (3852481)Time elapsed: 0.071 s
% 2.57/0.95 % (3852481)Peak memory usage: 12 MB
% 2.57/0.95 % (3852481)Instructions burned: 117 (million)
% 2.57/0.95 % (3852482)Instruction limit reached!
% 2.57/0.95 % (3852482)------------------------------
% 2.57/0.95 % (3852482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852482)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852482)Termination reason: Instruction limit
% 2.57/0.95 % (3852482)Termination phase: Saturation
% 2.57/0.95 % (3852482)Time elapsed: 0.083 s
% 2.57/0.95 % (3852482)Peak memory usage: 13 MB
% 2.57/0.95 % (3852482)Instructions burned: 131 (million)
% 2.57/0.95 % (3852491)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3057639258:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.57/0.95 % (3852492)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3664551821:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.57/0.95 % TRYING [1]
% 2.57/0.95 % TRYING [2]
% 2.57/0.95 % TRYING [3]
% 2.57/0.95 % TRYING [4]
% 2.57/0.95 % (3852493)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3222931516:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.57/0.95 % (3852483)Instruction limit reached!
% 2.57/0.95 % (3852483)------------------------------
% 2.57/0.95 % (3852483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852483)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852483)Termination reason: Instruction limit
% 2.57/0.95 % (3852483)Termination phase: Saturation
% 2.57/0.95 % (3852483)Time elapsed: 0.110 s
% 2.57/0.95 % (3852483)Peak memory usage: 14 MB
% 2.57/0.95 % (3852483)Instructions burned: 159 (million)
% 2.57/0.95 % TRYING [8]
% 2.57/0.95 % (3852497)ott-21_1_sil=16000:fs=off:random_seed=2077515547:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.57/0.95 % TRYING [5]
% 2.57/0.95 % (3852492)Instruction limit reached!
% 2.57/0.95 % (3852492)------------------------------
% 2.57/0.95 % (3852492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852492)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852492)Termination reason: Instruction limit
% 2.57/0.95 % (3852492)Termination phase: Saturation
% 2.57/0.95 % (3852492)Time elapsed: 0.087 s
% 2.57/0.95 % (3852492)Peak memory usage: 13 MB
% 2.57/0.95 % (3852492)Instructions burned: 133 (million)
% 2.57/0.95 % (3852499)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2392451283:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.57/0.95 % (3852497)Instruction limit reached!
% 2.57/0.95 % (3852497)------------------------------
% 2.57/0.95 % (3852497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852497)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852497)Termination reason: Instruction limit
% 2.57/0.95 % (3852497)Termination phase: Saturation
% 2.57/0.95 % (3852497)Time elapsed: 0.100 s
% 2.57/0.95 % (3852497)Peak memory usage: 13 MB
% 2.57/0.95 % (3852497)Instructions burned: 180 (million)
% 2.57/0.95 % (3852501)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=485451671:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.57/0.95 % TRYING [1]
% 2.57/0.95 % TRYING [2]
% 2.57/0.95 % TRYING [3]
% 2.57/0.95 % TRYING [9]
% 2.57/0.95 % TRYING [4]
% 2.57/0.95 % TRYING [6]
% 2.57/0.95 % TRYING [5]
% 2.57/0.95 % TRYING [6]
% 2.57/0.95 % (3852491)Instruction limit reached!
% 2.57/0.95 % (3852491)------------------------------
% 2.57/0.95 % (3852491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.95 % (3852491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.95 % (3852491)CaDiCaL version: 2.1.3
% 2.57/0.95 % (3852491)Termination reason: Instruction limit
% 2.57/0.95 % (3852491)Termination phase: Finite model building SAT solving
% 2.57/0.95 % (3852491)Time elapsed: 0.369 s
% 2.57/0.95 % (3852491)Peak memory usage: 20 MB
% 2.57/0.95 % (3852491)Instructions burned: 714 (million)
% 2.57/0.95 % (3852503)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2629001809:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 2.57/0.95 % (3852493) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3852472-3852493"...
% 2.57/0.95 % (3852493)...printing done.
% 2.57/0.95 % (3852493)Refutation found. Thanks to Tanya!
% 2.57/0.95 % SZS status Theorem for theBenchmark
% 2.57/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/0.96 % (3852493)------------------------------
% 2.57/0.96 % (3852493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.57/0.96 % (3852493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/0.96 % (3852493)CaDiCaL version: 2.1.3
% 2.57/0.96 % (3852493)Termination reason: Refutation
% 2.57/0.96 % (3852493)Time elapsed: 0.391 s
% 2.57/0.96 % (3852493)Peak memory usage: 19 MB
% 2.57/0.96 % (3852493)Instructions burned: 646 (million)
% 2.57/0.96 % (3852472)Success in time 0.543 s
% 2.57/0.96 % Vampire exiting
%------------------------------------------------------------------------------