%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM583+3 : 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 : 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 12:15:51 PM UTC 2026
% Result : Theorem 3.80s 1.52s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 271 ( 39 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 309 ( 73 ~; 64 |; 142 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 52 !; 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/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(f87,axiom,
( 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)) ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(f88,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox/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/sandbox/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(f91,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(f93,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 ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(rectify,[],[f87]) ).
fof(f96,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(f102,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,[],[f91]) ).
fof(f103,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,[],[f102]) ).
fof(f104,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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 ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(ennf_transformation,[],[f93]) ).
fof(f128,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,[],[f96]) ).
fof(f137,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(ennf_transformation,[],[f88]) ).
fof(f150,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,[],[f103]) ).
fof(f151,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,[],[f150]) ).
fof(f152,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,[],[f151]) ).
fof(f153,plain,
( ~ aElementOf0(sK4,xS)
& aElementOf0(sK4,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,[sK4]),skolemize(X0,sK4)],[f152]) ).
fof(f154,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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)))) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(nnf_transformation,[],[f104]) ).
fof(f155,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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)))) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(flattening,[],[f154]) ).
fof(f166,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,[],[f128]) ).
fof(f167,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,[],[f166]) ).
fof(f191,plain,
aElementOf0(sK4,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f153]) ).
fof(f192,plain,
~ aElementOf0(sK4,xS),
inference(cnf_transformation,[],[f153]) ).
fof(f194,plain,
! [X1] :
( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1
| aElementOf0(X1,xQ) ),
inference(cnf_transformation,[],[f155]) ).
fof(f232,plain,
! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) ),
inference(cnf_transformation,[],[f167]) ).
fof(f235,plain,
! [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f167]) ).
fof(f240,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f167]) ).
fof(f269,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f137]) ).
fof(f364,plain,
~ aElementOf0(sK4,sdtlpdtrp0(xN,xi)),
inference(unit_resulting_resolution,[],[f269,f192]) ).
fof(f365,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(unit_resulting_resolution,[],[f269,f240]) ).
fof(f615,plain,
~ aElementOf0(sK4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(unit_resulting_resolution,[],[f235,f364]) ).
fof(f1002,plain,
~ aElementOf0(sK4,xQ),
inference(unit_resulting_resolution,[],[f232,f615]) ).
fof(f1014,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = sK4,
inference(unit_resulting_resolution,[],[f194,f191,f1002]) ).
fof(f1119,plain,
aElementOf0(sK4,xS),
inference(superposition,[],[f365,f1014]) ).
fof(f1184,plain,
$false,
inference(forward_subsumption_resolution,[],[f1119,f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 20:39:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.80/1.52 % (3858576)Detected formulas, will run a generic FOF schedule.
% 3.80/1.52 % (3858583)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=4214930197:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.80/1.52 % (3858584)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2378537250:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.80/1.52 % (3858587)dis-21_1_sil=8000:lcm=predicate:random_seed=3122217849: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)
% 3.80/1.52 % (3858585)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3945603646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.80/1.52 % (3858581)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=3383615623:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.80/1.52 % (3858582)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=3589663149:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.80/1.52 % (3858586)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1414434344:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.80/1.52 % (3858584)Instruction limit reached!
% 3.80/1.52 % (3858584)------------------------------
% 3.80/1.52 % (3858584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3858584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3858584)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3858584)Termination reason: Instruction limit
% 3.80/1.52 % (3858584)Termination phase: Saturation
% 3.80/1.52 % (3858584)Time elapsed: 0.070 s
% 3.80/1.52 % (3858584)Peak memory usage: 90 MB
% 3.80/1.52 % (3858584)Instructions burned: 110 (million)
% 3.80/1.52 % (3858587)Instruction limit reached!
% 3.80/1.52 % (3858587)------------------------------
% 3.80/1.52 % (3858587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3858587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3858587)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3858587)Termination reason: Instruction limit
% 3.80/1.52 % (3858587)Termination phase: Saturation
% 3.80/1.52 % (3858587)Time elapsed: 0.073 s
% 3.80/1.52 % (3858587)Peak memory usage: 89 MB
% 3.80/1.52 % (3858587)Instructions burned: 130 (million)
% 3.80/1.52 % (3858585)Instruction limit reached!
% 3.80/1.52 % (3858585)------------------------------
% 3.80/1.52 % (3858585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3858585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3858585)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3858585)Termination reason: Instruction limit
% 3.80/1.52 % (3858585)Termination phase: Saturation
% 3.80/1.52 % (3858585)Time elapsed: 0.074 s
% 3.80/1.52 % (3858585)Peak memory usage: 88 MB
% 3.80/1.52 % (3858585)Instructions burned: 121 (million)
% 3.80/1.52 % (3858586)Instruction limit reached!
% 3.80/1.52 % (3858586)------------------------------
% 3.80/1.52 % (3858586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3858586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3858586)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3858586)Termination reason: Instruction limit
% 3.80/1.52 % (3858586)Termination phase: Saturation
% 3.80/1.52 % (3858586)Time elapsed: 0.103 s
% 3.80/1.52 % (3858586)Peak memory usage: 90 MB
% 3.80/1.52 % (3858586)Instructions burned: 139 (million)
% 3.80/1.52 % (3858595)lrs+10_1_sil=8000:sp=occurrence:random_seed=319256941:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.80/1.52 % (3858597)lrs+1011_1_sil=32000:sp=occurrence:random_seed=291596077:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.80/1.52 % (3858596)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3502617197:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.80/1.52 % (3858596)First to succeed.
% 3.80/1.52 % (3858598)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=2570388752:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.80/1.52 % (3858596)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3858576"
% 3.80/1.52 % (3858597)Also succeeded, but the first one will report.
% 3.80/1.52 % (3858595)Instruction limit reached!
% 3.80/1.52 % (3858595)------------------------------
% 3.80/1.52 % (3858595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3858595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3858595)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3858595)Termination reason: Instruction limit
% 3.80/1.52 % (3858595)Termination phase: Saturation
% 3.80/1.52 % (3858595)Time elapsed: 0.176 s
% 3.80/1.52 % (3858595)Peak memory usage: 92 MB
% 3.80/1.52 % (3858595)Instructions burned: 286 (million)
% 3.80/1.52 % (3858598)Also succeeded, but the first one will report.
% 3.80/1.52 % (3858596)Refutation found. Thanks to Tanya!
% 3.80/1.52 % SZS status Theorem for theBenchmark
% 3.80/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.45/1.72 % (3858596)------------------------------
% 5.45/1.72 % (3858596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.72 % (3858596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.72 % (3858596)CaDiCaL version: 2.1.3
% 5.45/1.72 % (3858596)Termination reason: Refutation
% 5.45/1.72 % (3858596)Time elapsed: 0.036 s
% 5.45/1.72 % (3858596)Peak memory usage: 90 MB
% 5.45/1.72 % (3858596)Instructions burned: 53 (million)
% 5.45/1.72 % (3858596)------------------------------
% 5.45/1.72 % (3858596)------------------------------
% 5.45/1.73 % (3858576)Success in time 0.687 s
% 5.45/1.73 % Vampire exiting
%------------------------------------------------------------------------------