%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:24:42 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 95 ( 14 unt; 4 def)
% Number of atoms : 391 ( 56 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 479 ( 183 ~; 193 |; 75 &)
% ( 16 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 73 !; 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(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(f25,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(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(f42,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,[],[f25]) ).
fof(f43,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,[],[f42]) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f56,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,[],[f55]) ).
fof(f57,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))],[f56]) ).
fof(f70,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,[],[f43]) ).
fof(f71,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,[],[f70]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f80,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f84,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f110,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f111,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f113,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| aElementOf0(X1,xS) ),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(xS,xx))
| aElement0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
| ~ aElement0(X1)
| ~ aElementOf0(X1,xS)
| xx = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0] :
( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| xx != X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(cnf_transformation,[],[f72]) ).
fof(f122,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f72]) ).
fof(f129,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(equality_resolution,[],[f119]) ).
fof(f132,definition,
( spl8_1
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f136,definition,
( spl8_2
<=> aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f138,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f129,f136,f132]) ).
fof(f143,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(forward_subsumption_resolution,[],[f120,f114]) ).
fof(f148,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f73,f111]) ).
fof(f152,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[],[f148,f110]) ).
fof(f153,plain,
spl8_1,
inference(avatar_split_clause,[],[f152,f132]) ).
fof(f249,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(sK5(X1,X0))
| ~ aSet0(X0) ),
inference(resolution,[],[f80,f73]) ).
fof(f251,plain,
! [X0] :
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| xx = sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aElementOf0(sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx)) ),
inference(resolution,[],[f80,f117]) ).
fof(f255,plain,
! [X0,X1] :
( aElement0(sK5(X1,X0))
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literal_removal,[],[f249]) ).
fof(f259,plain,
! [X0] :
( aElementOf0(sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aSet0(X0)
| xx = sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0) ),
inference(forward_subsumption_resolution,[],[f251,f121]) ).
fof(f263,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx)) ),
inference(resolution,[],[f81,f143]) ).
fof(f265,plain,
! [X0] :
( ~ aElementOf0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx))
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f263,f121]) ).
fof(f276,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1
| ~ aSet0(X1) ),
inference(forward_subsumption_resolution,[],[f84,f79]) ).
fof(f319,plain,
! [X0] :
( ~ aElementOf0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xS)
| ~ aSet0(X0)
| ~ aElement0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),X0) ),
inference(resolution,[],[f265,f115]) ).
fof(f458,plain,
! [X0] :
( aElementOf0(sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| xx = sK5(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f259,f113]) ).
fof(f1070,plain,
( xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f458,f81]) ).
fof(f1072,plain,
( xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(duplicate_literal_removal,[],[f1070]) ).
fof(f1074,plain,
( xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(forward_subsumption_resolution,[],[f1072,f110]) ).
fof(f1075,plain,
( xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(forward_subsumption_resolution,[],[f1074,f121]) ).
fof(f1077,definition,
( spl8_31
<=> aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
introduced(definition,[new_symbols(definition,[spl8_31])],[avatar_definition]) ).
fof(f1078,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| spl8_31 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f1079,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f1081,definition,
( spl8_32
<=> xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl8_32])],[avatar_definition]) ).
fof(f1083,plain,
( xx = sK5(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1084,plain,
( spl8_31
| spl8_32 ),
inference(avatar_split_clause,[],[f1075,f1081,f1077]) ).
fof(f1089,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_31 ),
inference(resolution,[],[f1079,f276]) ).
fof(f1094,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1089,f122]) ).
fof(f1096,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1094,f121]) ).
fof(f1418,plain,
( ~ aSet0(xS)
| ~ aElement0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[],[f319,f80]) ).
fof(f1420,plain,
( ~ aSet0(xS)
| ~ aElement0(sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(duplicate_literal_removal,[],[f1418]) ).
fof(f1424,plain,
( ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(forward_subsumption_resolution,[],[f1420,f255]) ).
fof(f1427,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(forward_subsumption_resolution,[],[f1424,f110]) ).
fof(f1428,plain,
( xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1427,f1096]) ).
fof(f1429,plain,
( xx = sK5(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1428,f121]) ).
fof(f1432,plain,
( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_31 ),
inference(superposition,[],[f81,f1429]) ).
fof(f1434,plain,
( ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_2
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1432,f138]) ).
fof(f1435,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_2
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1434,f110]) ).
fof(f1436,plain,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ spl8_2
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1435,f1096]) ).
fof(f1437,plain,
( $false
| ~ spl8_2
| ~ spl8_31 ),
inference(forward_subsumption_resolution,[],[f1436,f121]) ).
fof(f1438,plain,
( ~ spl8_2
| ~ spl8_31 ),
inference(avatar_contradiction_clause,[],[f1437]) ).
fof(f1462,plain,
( ~ aElementOf0(xx,xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ spl8_32 ),
inference(superposition,[],[f81,f1083]) ).
fof(f1464,plain,
( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ spl8_32 ),
inference(forward_subsumption_resolution,[],[f1462,f111]) ).
fof(f1465,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ spl8_32 ),
inference(forward_subsumption_resolution,[],[f1464,f121]) ).
fof(f1466,plain,
( ~ aSet0(xS)
| spl8_31
| ~ spl8_32 ),
inference(forward_subsumption_resolution,[],[f1465,f1078]) ).
fof(f1467,plain,
( $false
| spl8_31
| ~ spl8_32 ),
inference(forward_subsumption_resolution,[],[f1466,f110]) ).
fof(f1468,plain,
( spl8_31
| ~ spl8_32 ),
inference(avatar_contradiction_clause,[],[f1467]) ).
cnf(s1,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f139]) ).
cnf(s3,plain,
spl8_1,
inference(sat_conversion,[],[f153]) ).
cnf(s29,plain,
( spl8_31
| spl8_32 ),
inference(sat_conversion,[],[f1084]) ).
cnf(s36,plain,
( ~ spl8_2
| ~ spl8_31 ),
inference(sat_conversion,[],[f1438]) ).
cnf(s38,plain,
( spl8_31
| ~ spl8_32 ),
inference(sat_conversion,[],[f1468]) ).
cnf(s49,plain,
spl8_2,
inference(rat,[],[s1,s3]) ).
cnf(s50,plain,
~ spl8_31,
inference(rat,[],[s36,s49]) ).
cnf(s51,plain,
~ spl8_32,
inference(rat,[],[s38,s50]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s29,s51,s50]) ).
fof(f1469,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.12/0.38 % Computer : n019.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 20:22:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.47 % (3380784)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3380792)dis+10_1_sil=32000:sp=arity:random_seed=4084621447:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3380790)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3380789)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2257425366_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3380791)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2887157446:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3380790)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3941400896:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3380793)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4266306244:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3380795)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2548545278:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (3380794)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1495684025:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (3380792) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3380784-3380792"...
% 0.17/0.47 % (3380792)...printing done.
% 0.17/0.47 % (3380792)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3380792)------------------------------
% 0.17/0.47 % (3380792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3380792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3380792)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3380792)Termination reason: Refutation
% 0.17/0.47 % (3380792)Time elapsed: 0.021 s
% 0.17/0.47 % (3380792)Peak memory usage: 13 MB
% 0.17/0.47 % (3380792)Instructions burned: 56 (million)
% 0.17/0.47 % (3380784)Success in time 0.049 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------