%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM580+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 12:15:50 PM UTC 2026
% Result : Theorem 3.23s 1.09s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 115 ( 25 unt; 10 def)
% Number of atoms : 538 ( 63 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 607 ( 184 ~; 171 |; 199 &)
% ( 22 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 8 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 101 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(f43,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
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,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)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f88,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)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(negated_conjecture,[status(cth)],[f87]) ).
fof(f91,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f93,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(f94,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,[],[f88]) ).
fof(f107,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f108,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f114,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,[],[f93]) ).
fof(f115,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(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 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f116,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(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 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f115]) ).
fof(f131,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f165,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f183]) ).
fof(f199,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f200,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP4(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP5(X0) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f201,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f108,f200,f199]) ).
fof(f224,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP4(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f225,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP4(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP5(X0) ),
inference(rectify,[],[f224]) ).
fof(f226,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f227,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP4(X0) ),
inference(flattening,[],[f226]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP4(X0) ),
inference(rectify,[],[f227]) ).
fof(f229,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK20(X0),szNzAzT0)
& aElementOf0(sK20(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f201]) ).
fof(f232,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,[],[f114]) ).
fof(f233,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,[],[f232]) ).
fof(f234,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(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)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(nnf_transformation,[],[f116]) ).
fof(f235,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(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)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f234]) ).
fof(f236,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) ),
inference(rectify,[],[f235]) ).
fof(f242,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f131]) ).
fof(f326,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f327,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f332,plain,
! [X0] :
( ~ sP5(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f336,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f340,plain,
! [X0] :
( sP5(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f346,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f347,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f349,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f357,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f359,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f233]) ).
fof(f361,plain,
! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) ),
inference(cnf_transformation,[],[f233]) ).
fof(f362,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f233]) ).
fof(f371,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f236]) ).
fof(f377,plain,
xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f236]) ).
fof(f392,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f437,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f461,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f490,definition,
~ sP41(xK),
introduced(definition,[new_symbols(definition,[sP41])],[inequality_splitting_name_introduction]) ).
fof(f491,plain,
sP41(sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))),
inference(inequality_splitting,[],[f377,f490]) ).
fof(f503,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP4(X0) ),
inference(equality_resolution,[],[f336]) ).
fof(f532,plain,
! [X0] :
( sP5(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f340,f347]) ).
fof(f546,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP5(X0) ),
inference(forward_subsumption_resolution,[],[f532,f346]) ).
fof(f567,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(resolution,[],[f371,f437]) ).
fof(f578,definition,
( spl51_5
<=> aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f580,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl51_5 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f588,definition,
( spl51_7
<=> aSet0(sdtlpdtrp0(xN,xi)) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f590,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| spl51_7 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f591,plain,
( ~ spl51_7
| spl51_5 ),
inference(avatar_split_clause,[],[f567,f578,f588]) ).
fof(f595,plain,
( sP41(szszuzczcdt0(sbrdtbr0(xQ)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(xQ)
| ~ isFinite0(xQ) ),
inference(superposition,[],[f491,f461]) ).
fof(f596,plain,
( sP41(szszuzczcdt0(sbrdtbr0(xQ)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f595,f580]) ).
fof(f605,plain,
( sP41(szszuzczcdt0(sbrdtbr0(xQ)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ isFinite0(xQ)
| ~ spl51_5 ),
inference(forward_subsumption_resolution,[],[f596,f362]) ).
fof(f606,plain,
( sP41(szszuzczcdt0(xk))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ isFinite0(xQ)
| ~ spl51_5 ),
inference(forward_demodulation,[],[f605,f359]) ).
fof(f608,definition,
( spl51_10
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[spl51_10])],[avatar_definition]) ).
fof(f610,plain,
( ~ isFinite0(xQ)
| spl51_10 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f612,definition,
( spl51_11
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
introduced(definition,[new_symbols(definition,[spl51_11])],[avatar_definition]) ).
fof(f614,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ spl51_11 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f616,definition,
( spl51_12
<=> sP41(szszuzczcdt0(xk)) ),
introduced(definition,[new_symbols(definition,[spl51_12])],[avatar_definition]) ).
fof(f619,plain,
( ~ spl51_10
| spl51_11
| spl51_12
| ~ spl51_5 ),
inference(avatar_split_clause,[],[f606,f578,f616,f612,f608]) ).
fof(f791,definition,
( spl51_24
<=> sP4(xi) ),
introduced(definition,[new_symbols(definition,[spl51_24])],[avatar_definition]) ).
fof(f792,plain,
( sP4(xi)
| ~ spl51_24 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f793,plain,
( ~ sP4(xi)
| spl51_24 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f836,definition,
( spl51_26
<=> sP5(xi) ),
introduced(definition,[new_symbols(definition,[spl51_26])],[avatar_definition]) ).
fof(f837,plain,
( sP5(xi)
| ~ spl51_26 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f838,plain,
( ~ sP5(xi)
| spl51_26 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f1031,plain,
~ sP41(szszuzczcdt0(xk)),
inference(superposition,[],[f490,f326]) ).
fof(f1032,plain,
~ spl51_12,
inference(avatar_split_clause,[],[f1031,f616]) ).
fof(f1093,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f392,f359]) ).
fof(f1103,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f1093,f327]) ).
fof(f1104,plain,
( ~ aSet0(xQ)
| spl51_10 ),
inference(forward_subsumption_resolution,[],[f1103,f610]) ).
fof(f1105,plain,
( $false
| spl51_10 ),
inference(forward_subsumption_resolution,[],[f1104,f362]) ).
fof(f1106,plain,
spl51_10,
inference(avatar_contradiction_clause,[],[f1105]) ).
fof(f1217,plain,
sP5(xi),
inference(resolution,[],[f546,f357]) ).
fof(f1236,plain,
( $false
| spl51_26 ),
inference(forward_subsumption_resolution,[],[f1217,f838]) ).
fof(f1237,plain,
spl51_26,
inference(avatar_contradiction_clause,[],[f1236]) ).
fof(f1249,plain,
( sP4(xi)
| ~ spl51_26 ),
inference(resolution,[],[f837,f332]) ).
fof(f1250,plain,
( $false
| spl51_24
| ~ spl51_26 ),
inference(forward_subsumption_resolution,[],[f1249,f793]) ).
fof(f1251,plain,
( spl51_24
| ~ spl51_26 ),
inference(avatar_contradiction_clause,[],[f1250]) ).
fof(f1417,plain,
( ~ aElementOf0(xi,szNzAzT0)
| spl51_7 ),
inference(resolution,[],[f349,f590]) ).
fof(f1426,plain,
( $false
| spl51_7 ),
inference(forward_subsumption_resolution,[],[f1417,f357]) ).
fof(f1427,plain,
spl51_7,
inference(avatar_contradiction_clause,[],[f1426]) ).
fof(f2588,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ sP4(xi) ),
inference(resolution,[],[f361,f503]) ).
fof(f2601,plain,
( ~ sP4(xi)
| ~ spl51_11 ),
inference(forward_subsumption_resolution,[],[f2588,f614]) ).
fof(f2621,plain,
( $false
| ~ spl51_11
| ~ spl51_24 ),
inference(forward_subsumption_resolution,[],[f2601,f792]) ).
fof(f2622,plain,
( ~ spl51_11
| ~ spl51_24 ),
inference(avatar_contradiction_clause,[],[f2621]) ).
cnf(s5,plain,
( spl51_5
| ~ spl51_7 ),
inference(sat_conversion,[],[f591]) ).
cnf(s7,plain,
( ~ spl51_5
| ~ spl51_10
| spl51_11
| spl51_12 ),
inference(sat_conversion,[],[f619]) ).
cnf(s40,plain,
~ spl51_12,
inference(sat_conversion,[],[f1032]) ).
cnf(s49,plain,
spl51_10,
inference(sat_conversion,[],[f1106]) ).
cnf(s65,plain,
spl51_26,
inference(sat_conversion,[],[f1237]) ).
cnf(s69,plain,
( spl51_24
| ~ spl51_26 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s82,plain,
spl51_7,
inference(sat_conversion,[],[f1427]) ).
cnf(s233,plain,
( ~ spl51_11
| ~ spl51_24 ),
inference(sat_conversion,[],[f2622]) ).
cnf(s241,plain,
spl51_24,
inference(rat,[],[s69,s65]) ).
cnf(s242,plain,
~ spl51_11,
inference(rat,[],[s233,s241]) ).
cnf(s254,plain,
~ spl51_5,
inference(rat,[],[s7,s40,s242,s49]) ).
cnf(s257,plain,
$false,
inference(rat,[],[s5,s82,s254]) ).
fof(f2624,plain,
$false,
inference(avatar_sat_refutation,[],[s257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM580+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 20:38:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.23/1.09 % (3857344)Detected formulas, will run a generic FOF schedule.
% 3.23/1.09 % (3857354)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2376330337:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.23/1.09 % (3857355)dis-21_1_sil=8000:lcm=predicate:random_seed=3579718141: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)
% 3.23/1.09 % (3857353)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=216945368:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.23/1.09 % (3857352)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=763617389:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.23/1.09 % (3857349)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=2761921882:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.23/1.09 % (3857350)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=1163895700:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.23/1.09 % (3857351)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=1254188042:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.23/1.09 % (3857354)Instruction limit reached!
% 3.23/1.09 % (3857354)------------------------------
% 3.23/1.09 % (3857354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.09 % (3857354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.09 % (3857354)CaDiCaL version: 2.1.3
% 3.23/1.09 % (3857354)Termination reason: Instruction limit
% 3.23/1.09 % (3857354)Termination phase: Saturation
% 3.23/1.09 % (3857354)Time elapsed: 0.056 s
% 3.23/1.09 % (3857354)Peak memory usage: 90 MB
% 3.23/1.09 % (3857354)Instructions burned: 142 (million)
% 3.23/1.09 % (3857352)First to succeed.
% 3.23/1.09 % (3857352)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3857344"
% 3.23/1.09 % (3857355)Instruction limit reached!
% 3.23/1.09 % (3857355)------------------------------
% 3.23/1.09 % (3857355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.09 % (3857355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.09 % (3857355)CaDiCaL version: 2.1.3
% 3.23/1.09 % (3857355)Termination reason: Instruction limit
% 3.23/1.09 % (3857355)Termination phase: Saturation
% 3.23/1.09 % (3857355)Time elapsed: 0.072 s
% 3.23/1.09 % (3857355)Peak memory usage: 90 MB
% 3.23/1.09 % (3857355)Instructions burned: 129 (million)
% 3.23/1.09 % (3857353)Instruction limit reached!
% 3.23/1.09 % (3857353)------------------------------
% 3.23/1.09 % (3857353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.09 % (3857353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.09 % (3857353)CaDiCaL version: 2.1.3
% 3.23/1.09 % (3857353)Termination reason: Instruction limit
% 3.23/1.09 % (3857353)Termination phase: Saturation
% 3.23/1.09 % (3857353)Time elapsed: 0.073 s
% 3.23/1.09 % (3857353)Peak memory usage: 89 MB
% 3.23/1.09 % (3857353)Instructions burned: 119 (million)
% 3.23/1.09 % (3857363)lrs+10_1_sil=8000:sp=occurrence:random_seed=3810668343:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.23/1.09 % (3857364)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2497956919:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.23/1.09 % (3857365)lrs+1011_1_sil=32000:sp=occurrence:random_seed=898469237:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.23/1.09 % (3857364)Also succeeded, but the first one will report.
% 3.23/1.09 % (3857363)Instruction limit reached!
% 3.23/1.09 % (3857363)------------------------------
% 3.23/1.09 % (3857363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.09 % (3857363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.09 % (3857363)CaDiCaL version: 2.1.3
% 3.23/1.09 % (3857363)Termination reason: Instruction limit
% 3.23/1.09 % (3857363)Termination phase: Saturation
% 3.23/1.09 % (3857363)Time elapsed: 0.095 s
% 3.23/1.09 % (3857363)Peak memory usage: 92 MB
% 3.23/1.09 % (3857363)Instructions burned: 288 (million)
% 3.23/1.09 % (3857352)Refutation found. Thanks to Tanya!
% 3.23/1.09 % SZS status Theorem for theBenchmark
% 3.23/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.29 % (3857352)------------------------------
% 3.78/1.29 % (3857352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.29 % (3857352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.29 % (3857352)CaDiCaL version: 2.1.3
% 3.78/1.29 % (3857352)Termination reason: Refutation
% 3.78/1.29 % (3857352)Time elapsed: 0.063 s
% 3.78/1.29 % (3857352)Peak memory usage: 91 MB
% 3.78/1.29 % (3857352)Instructions burned: 102 (million)
% 3.78/1.29 % (3857352)------------------------------
% 3.78/1.29 % (3857352)------------------------------
% 3.78/1.29 % (3857344)Success in time 0.488 s
% 3.78/1.29 % Vampire exiting
%------------------------------------------------------------------------------