%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM583+3 : 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 : n010.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 12:24:54 PM UTC 2026
% Result : Theorem 0.42s 0.47s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 2 def)
% Number of atoms : 244 ( 29 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 272 ( 71 ~; 61 |; 113 &)
% ( 10 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f86,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
fof(f88,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4037) ).
fof(f89,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f102,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,xQ)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(rectify,[],[f86]) ).
fof(f104,plain,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X2,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
inference(rectify,[],[f90]) ).
fof(f216,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(ennf_transformation,[],[f102]) ).
fof(f218,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(ennf_transformation,[],[f88]) ).
fof(f219,plain,
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(ennf_transformation,[],[f104]) ).
fof(f220,plain,
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f219]) ).
fof(f318,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(nnf_transformation,[],[f216]) ).
fof(f319,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(flattening,[],[f318]) ).
fof(f322,plain,
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(nnf_transformation,[],[f220]) ).
fof(f323,plain,
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f322]) ).
fof(f324,plain,
( ? [X0] :
( ~ aElementOf0(X0,xS)
& aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) ),
inference(rectify,[],[f323]) ).
fof(f325,plain,
( ~ aElementOf0(sK41,xS)
& aElementOf0(sK41,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X0,sK41)],[f324]) ).
fof(f559,plain,
! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) ),
inference(cnf_transformation,[],[f319]) ).
fof(f562,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f319]) ).
fof(f577,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f218]) ).
fof(f579,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f325]) ).
fof(f580,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) ),
inference(cnf_transformation,[],[f325]) ).
fof(f586,plain,
aElementOf0(sK41,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f325]) ).
fof(f587,plain,
~ aElementOf0(sK41,xS),
inference(cnf_transformation,[],[f325]) ).
fof(f971,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41
| aElementOf0(sK41,xQ) ),
inference(resolution,[],[f580,f586]) ).
fof(f1101,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(resolution,[],[f577,f579]) ).
fof(f1155,definition,
( spl42_41
<=> aElementOf0(sK41,xQ) ),
introduced(definition,[new_symbols(definition,[spl42_41])],[avatar_definition]) ).
fof(f1157,plain,
( aElementOf0(sK41,xQ)
| ~ spl42_41 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f1159,definition,
( spl42_42
<=> szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41 ),
introduced(definition,[new_symbols(definition,[spl42_42])],[avatar_definition]) ).
fof(f1161,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK41
| ~ spl42_42 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1162,plain,
( spl42_41
| spl42_42 ),
inference(avatar_split_clause,[],[f971,f1159,f1155]) ).
fof(f1341,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[],[f562,f559]) ).
fof(f1362,plain,
( aElementOf0(sK41,xS)
| ~ spl42_42 ),
inference(superposition,[],[f1101,f1161]) ).
fof(f1372,plain,
( $false
| ~ spl42_42 ),
inference(forward_subsumption_resolution,[],[f1362,f587]) ).
fof(f1373,plain,
~ spl42_42,
inference(avatar_contradiction_clause,[],[f1372]) ).
fof(f1387,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) ),
inference(resolution,[],[f1341,f577]) ).
fof(f1391,plain,
( aElementOf0(sK41,xS)
| ~ spl42_41 ),
inference(resolution,[],[f1387,f1157]) ).
fof(f1392,plain,
( $false
| ~ spl42_41 ),
inference(forward_subsumption_resolution,[],[f1391,f587]) ).
fof(f1393,plain,
~ spl42_41,
inference(avatar_contradiction_clause,[],[f1392]) ).
cnf(s693,plain,
( spl42_41
| spl42_42 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s839,plain,
~ spl42_42,
inference(sat_conversion,[],[f1373]) ).
cnf(s872,plain,
~ spl42_41,
inference(sat_conversion,[],[f1393]) ).
cnf(s874,plain,
$false,
inference(rat,[],[s693,s839,s872]) ).
fof(f1394,plain,
$false,
inference(avatar_sat_refutation,[],[s874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 20:37:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.39 Running first-order model finding
% 0.08/0.39 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
% 0.42/0.47 % (1288863)Will run a generic schedule for satisfiability detection.
% 0.42/0.47 % (1288868)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2421363681_2999 on theBenchmark for (2999ds/0Mi)
% 0.42/0.47 % (1288869)% WARNING: option uhcvi not known.
% 0.42/0.47 % (1288870)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4140606183:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.42/0.47 % (1288871)dis+10_1_sil=32000:sp=arity:random_seed=618250875:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.42/0.47 % (1288872)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2257419735:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.42/0.47 % (1288873)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2971104315:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.47 % (1288874)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2713808903:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.42/0.47 % (1288869)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3365986977:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.42/0.47 % TRYING [1]
% 0.42/0.47 % TRYING [2]
% 0.42/0.47 % TRYING [3]
% 0.42/0.47 % (1288870) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1288863-1288870"...
% 0.42/0.47 % TRYING [4]
% 0.42/0.47 % (1288870)...printing done.
% 0.42/0.47 % (1288870)Refutation found. Thanks to Tanya!
% 0.42/0.47 % SZS status Theorem for theBenchmark
% 0.42/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.42/0.47 % (1288870)------------------------------
% 0.42/0.47 % (1288870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.47 % (1288870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.47 % (1288870)CaDiCaL version: 2.1.3
% 0.42/0.47 % (1288870)Termination reason: Refutation
% 0.42/0.47 % (1288870)Time elapsed: 0.032 s
% 0.42/0.47 % (1288870)Peak memory usage: 13 MB
% 0.42/0.47 % (1288870)Instructions burned: 44 (million)
% 0.42/0.47 % (1288863)Success in time 0.069 s
% 0.42/0.47 % Vampire exiting
%------------------------------------------------------------------------------