%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM579+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 6.57s 1.98s
% Output : Refutation 8.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 30
% Syntax : Number of formulae : 171 ( 43 unt; 18 def)
% Number of atoms : 801 ( 105 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 914 ( 284 ~; 270 |; 282 &)
% ( 29 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 11 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 15 con; 0-2 aty)
% Number of variables : 180 ( 0 sgn 159 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(f85,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& 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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& X2 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ( ( aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& ( aElementOf0(X2,X1)
| X2 = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ) )
=> ( ( ( ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X2,xS) )
| aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
& sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) = xK )
| aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f86,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& 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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& X2 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ( ( aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& ( aElementOf0(X2,X1)
| X2 = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ) )
=> ( ( ( ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X2,xS) )
| aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
& sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) = xK )
| aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
fof(f96,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(f98,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& 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 ) )
& ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5) ) )
=> ( ( aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X6)
& ( aElementOf0(X6,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 ) ) ) )
=> ( ( ( ! [X7] :
( aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X7,xS) )
| aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
& sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) = xK )
| aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f134,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f148,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f150,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f150]) ).
fof(f198,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f203,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,[],[f96]) ).
fof(f204,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,[],[f203]) ).
fof(f205,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(f206,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f207,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f206]) ).
fof(f210,plain,
? [X0] :
( ? [X1] :
( ( ( ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
| xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X6)
& ( aElementOf0(X6,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(X1)
& 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 ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f211,plain,
? [X0] :
( ? [X1] :
( ( ( ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
| xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X6)
& ( aElementOf0(X6,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(X1)
& 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 ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f210]) ).
fof(f223,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 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f224,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))))
& sP8(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))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f225,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(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,[],[f204,f224,f223]) ).
fof(f230,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,[],[f105]) ).
fof(f231,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,[],[f230]) ).
fof(f232,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,[],[f231]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK11(X0,X1),X0)
& aElementOf0(sK11(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f232]) ).
fof(f248,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f306,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f225]) ).
fof(f309,plain,
? [X0] :
( ? [X1] :
( ( ( ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
| xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( ( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X6)
| ( ~ aElementOf0(X6,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X6 ) )
& ( ( aElement0(X6)
& ( aElementOf0(X6,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 ) )
| ~ aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(X1)
& 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 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
& aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f211]) ).
fof(f310,plain,
? [X0] :
( ? [X1] :
( ( ( ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
| xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( ( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X6)
| ( ~ aElementOf0(X6,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X6 ) )
& ( ( aElement0(X6)
& ( aElementOf0(X6,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 ) )
| ~ aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(X1)
& 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 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f309]) ).
fof(f311,plain,
? [X0] :
( ? [X1] :
( ( ( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS) )
| xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X1)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aSet0(X1)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6 )
& ( ( aElement0(X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X6 )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X7] :
( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X7,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X1) = xk
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f310]) ).
fof(f312,plain,
( ( ( ~ aElementOf0(sK43,xS)
& aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ~ aSubsetOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),xS) )
| xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) )
& ~ aElementOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),slbdtsldtrb0(xS,xK))
& aSet0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,sK42)
& szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,sK42)
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK41)) )
& aSet0(sK42)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,sK41)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X6 )
& ( ( aElement0(X6)
& aElementOf0(X6,sdtlpdtrp0(xN,sK41))
& szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6 )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& ! [X7] :
( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X7,sK42) )
& aSubsetOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& xk = sbrdtbr0(sK42)
& aElementOf0(sK42,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))),xk))
& aElementOf0(sK41,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42,sK43]),skolemize(X0,sK41),skolemize(X1,sK42),skolemize(X2,sK43)],[f311]) ).
fof(f313,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f320,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f360,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f367,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f378,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f382,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f462,plain,
aSet0(xS),
inference(cnf_transformation,[],[f198]) ).
fof(f511,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f512,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f528,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f306]) ).
fof(f534,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f535,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f542,plain,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f312]) ).
fof(f544,plain,
xk = sbrdtbr0(sK42),
inference(cnf_transformation,[],[f312]) ).
fof(f546,plain,
! [X7] :
( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X7,sK42) ),
inference(cnf_transformation,[],[f312]) ).
fof(f547,plain,
! [X6] :
( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f548,plain,
! [X6] :
( aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f553,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f312]) ).
fof(f554,plain,
aSet0(sK42),
inference(cnf_transformation,[],[f312]) ).
fof(f557,plain,
! [X3] :
( aElementOf0(X3,sK42)
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| ~ aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f564,plain,
( aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f565,plain,
( ~ aElementOf0(sK43,xS)
| xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f610,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))),
inference(equality_resolution,[],[f547]) ).
fof(f611,definition,
sF44 = sdtlpdtrp0(xN,sK41),
introduced(definition,[new_symbols(definition,[sF44])],[function_definition]) ).
fof(f612,plain,
sdtlpdtrp0(xN,sK41) = sF44,
inference(reorient_equations,[],[f611]) ).
fof(f613,definition,
sF45 = szmzizndt0(sF44),
introduced(definition,[new_symbols(definition,[sF45])],[function_definition]) ).
fof(f614,plain,
szmzizndt0(sF44) = sF45,
inference(reorient_equations,[],[f613]) ).
fof(f615,definition,
sF46 = sdtpldt0(sK42,sF45),
introduced(definition,[new_symbols(definition,[sF46])],[function_definition]) ).
fof(f616,plain,
sdtpldt0(sK42,sF45) = sF46,
inference(reorient_equations,[],[f615]) ).
fof(f617,definition,
sF47 = sbrdtbr0(sF46),
introduced(definition,[new_symbols(definition,[sF47])],[function_definition]) ).
fof(f618,plain,
sbrdtbr0(sF46) = sF47,
inference(reorient_equations,[],[f617]) ).
fof(f619,plain,
( ~ aElementOf0(sK43,xS)
| xK != sF47 ),
inference(definition_folding,[],[f565,f618,f616,f614,f612]) ).
fof(f620,plain,
( aElementOf0(sK43,sF46)
| xK != sF47 ),
inference(definition_folding,[],[f564,f618,f616,f614,f612,f616,f614,f612]) ).
fof(f629,plain,
! [X3] :
( ~ aElementOf0(X3,sF46)
| sF45 = X3
| aElementOf0(X3,sK42) ),
inference(definition_folding,[],[f557,f616,f614,f612,f614,f612]) ).
fof(f632,plain,
aElementOf0(sF45,sF44),
inference(definition_folding,[],[f553,f612,f614,f612]) ).
fof(f634,definition,
sF49 = sdtmndt0(sF44,sF45),
introduced(definition,[new_symbols(definition,[sF49])],[function_definition]) ).
fof(f635,plain,
sdtmndt0(sF44,sF45) = sF49,
inference(reorient_equations,[],[f634]) ).
fof(f639,plain,
! [X6] :
( ~ aElementOf0(X6,sF49)
| aElementOf0(X6,sF44) ),
inference(definition_folding,[],[f548,f635,f614,f612,f612,f612]) ).
fof(f640,plain,
~ aElementOf0(sF45,sF49),
inference(definition_folding,[],[f610,f635,f614,f612,f612,f614,f612]) ).
fof(f641,plain,
! [X7] :
( ~ aElementOf0(X7,sK42)
| aElementOf0(X7,sF49) ),
inference(definition_folding,[],[f546,f635,f614,f612,f612]) ).
fof(f643,definition,
sF50 = sbrdtbr0(sK42),
introduced(definition,[new_symbols(definition,[sF50])],[function_definition]) ).
fof(f644,plain,
sbrdtbr0(sK42) = sF50,
inference(reorient_equations,[],[f643]) ).
fof(f645,plain,
xk = sF50,
inference(definition_folding,[],[f544,f644]) ).
fof(f651,definition,
( spl52_1
<=> aElement0(sF45) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f652,plain,
( aElement0(sF45)
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f653,plain,
( ~ aElement0(sF45)
| spl52_1 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f660,definition,
( spl52_3
<=> xK = sF47 ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
fof(f662,plain,
( xK != sF47
| spl52_3 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f669,definition,
( spl52_5
<=> aElementOf0(sK43,sF46) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
fof(f671,plain,
( aElementOf0(sK43,sF46)
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f672,plain,
( ~ spl52_3
| spl52_5 ),
inference(avatar_split_clause,[],[f620,f669,f660]) ).
fof(f674,definition,
( spl52_6
<=> aElementOf0(sK43,xS) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
fof(f676,plain,
( ~ aElementOf0(sK43,xS)
| spl52_6 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f677,plain,
( ~ spl52_3
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f619,f674,f660]) ).
fof(f697,plain,
xk = sbrdtbr0(sK42),
inference(forward_demodulation,[],[f644,f645]) ).
fof(f729,plain,
! [X0] :
( sbrdtbr0(sdtpldt0(sK42,X0)) = szszuzczcdt0(sbrdtbr0(sK42))
| ~ aElement0(X0)
| ~ aSet0(sK42)
| ~ isFinite0(sK42)
| aElementOf0(X0,sF49) ),
inference(resolution,[],[f382,f641]) ).
fof(f782,definition,
( spl52_21
<=> aSet0(sF44) ),
introduced(definition,[new_symbols(definition,[spl52_21])],[avatar_definition]) ).
fof(f784,plain,
( ~ aSet0(sF44)
| spl52_21 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f793,plain,
! [X0] :
( sbrdtbr0(sdtpldt0(sK42,X0)) = szszuzczcdt0(sbrdtbr0(sK42))
| ~ aElement0(X0)
| ~ isFinite0(sK42)
| aElementOf0(X0,sF49) ),
inference(forward_subsumption_resolution,[],[f729,f554]) ).
fof(f806,plain,
! [X0] :
( szszuzczcdt0(xk) = sbrdtbr0(sdtpldt0(sK42,X0))
| ~ aElement0(X0)
| ~ isFinite0(sK42)
| aElementOf0(X0,sF49) ),
inference(forward_demodulation,[],[f793,f697]) ).
fof(f816,plain,
! [X0] :
( xK = sbrdtbr0(sdtpldt0(sK42,X0))
| ~ aElement0(X0)
| ~ isFinite0(sK42)
| aElementOf0(X0,sF49) ),
inference(forward_demodulation,[],[f806,f511]) ).
fof(f819,definition,
( spl52_28
<=> isFinite0(sK42) ),
introduced(definition,[new_symbols(definition,[spl52_28])],[avatar_definition]) ).
fof(f821,plain,
( ~ isFinite0(sK42)
| spl52_28 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f823,definition,
( spl52_29
<=> ! [X0] :
( xK = sbrdtbr0(sdtpldt0(sK42,X0))
| aElementOf0(X0,sF49)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl52_29])],[avatar_definition]) ).
fof(f824,plain,
( ! [X0] :
( aElementOf0(X0,sF49)
| xK = sbrdtbr0(sdtpldt0(sK42,X0))
| ~ aElement0(X0) )
| ~ spl52_29 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f825,plain,
( ~ spl52_28
| spl52_29 ),
inference(avatar_split_clause,[],[f816,f823,f819]) ).
fof(f855,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(superposition,[],[f535,f528]) ).
fof(f856,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f855,f367]) ).
fof(f860,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f856,f360]) ).
fof(f861,plain,
( aSubsetOf0(sF44,xS)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(superposition,[],[f860,f612]) ).
fof(f864,plain,
aSubsetOf0(sF44,xS),
inference(forward_subsumption_resolution,[],[f861,f542]) ).
fof(f870,plain,
( aElement0(sF45)
| ~ aSet0(sF44) ),
inference(resolution,[],[f313,f632]) ).
fof(f872,plain,
( ~ aSet0(sF44)
| spl52_1 ),
inference(forward_subsumption_resolution,[],[f870,f653]) ).
fof(f881,plain,
( ~ spl52_21
| spl52_1 ),
inference(avatar_split_clause,[],[f872,f651,f782]) ).
fof(f1031,plain,
( aSet0(sF44)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(superposition,[],[f534,f612]) ).
fof(f1033,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| spl52_21 ),
inference(forward_subsumption_resolution,[],[f1031,f784]) ).
fof(f1034,plain,
( $false
| spl52_21 ),
inference(forward_subsumption_resolution,[],[f1033,f542]) ).
fof(f1035,plain,
spl52_21,
inference(avatar_contradiction_clause,[],[f1034]) ).
fof(f1054,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(sK42)
| ~ aSet0(sK42) ),
inference(superposition,[],[f378,f697]) ).
fof(f1056,plain,
( isFinite0(sK42)
| ~ aSet0(sK42) ),
inference(forward_subsumption_resolution,[],[f1054,f512]) ).
fof(f1058,plain,
( ~ aSet0(sK42)
| spl52_28 ),
inference(forward_subsumption_resolution,[],[f1056,f821]) ).
fof(f1060,plain,
( $false
| spl52_28 ),
inference(forward_subsumption_resolution,[],[f1058,f554]) ).
fof(f1061,plain,
spl52_28,
inference(avatar_contradiction_clause,[],[f1060]) ).
fof(f1073,plain,
( xK = sbrdtbr0(sdtpldt0(sK42,sF45))
| ~ aElement0(sF45)
| ~ spl52_29 ),
inference(resolution,[],[f824,f640]) ).
fof(f1074,plain,
( xK = sbrdtbr0(sdtpldt0(sK42,sF45))
| ~ spl52_1
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1073,f652]) ).
fof(f1075,plain,
( xK = sbrdtbr0(sF46)
| ~ spl52_1
| ~ spl52_29 ),
inference(forward_demodulation,[],[f1074,f616]) ).
fof(f1076,plain,
( xK = sF47
| ~ spl52_1
| ~ spl52_29 ),
inference(forward_demodulation,[],[f1075,f618]) ).
fof(f1077,plain,
( $false
| ~ spl52_1
| spl52_3
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1076,f662]) ).
fof(f1078,plain,
( ~ spl52_1
| spl52_3
| ~ spl52_29 ),
inference(avatar_contradiction_clause,[],[f1077]) ).
fof(f1079,plain,
( sK43 = sF45
| aElementOf0(sK43,sK42)
| ~ spl52_5 ),
inference(resolution,[],[f671,f629]) ).
fof(f1084,definition,
( spl52_61
<=> aElementOf0(sK43,sK42) ),
introduced(definition,[new_symbols(definition,[spl52_61])],[avatar_definition]) ).
fof(f1086,plain,
( aElementOf0(sK43,sK42)
| ~ spl52_61 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1088,definition,
( spl52_62
<=> sK43 = sF45 ),
introduced(definition,[new_symbols(definition,[spl52_62])],[avatar_definition]) ).
fof(f1090,plain,
( sK43 = sF45
| ~ spl52_62 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f1091,plain,
( spl52_61
| spl52_62
| ~ spl52_5 ),
inference(avatar_split_clause,[],[f1079,f669,f1088,f1084]) ).
fof(f1093,plain,
( aElementOf0(sK43,sF49)
| ~ spl52_61 ),
inference(resolution,[],[f1086,f641]) ).
fof(f1111,plain,
( aElementOf0(sK43,sF44)
| ~ spl52_61 ),
inference(resolution,[],[f1093,f639]) ).
fof(f1156,definition,
( spl52_69
<=> ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sF44) ) ),
introduced(definition,[new_symbols(definition,[spl52_69])],[avatar_definition]) ).
fof(f1157,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF44)
| aElementOf0(X0,xS) )
| ~ spl52_69 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1173,plain,
! [X0] :
( ~ aElementOf0(X0,sF44)
| aElementOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f320,f864]) ).
fof(f1176,plain,
! [X0] :
( ~ aElementOf0(X0,sF44)
| aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f1173,f462]) ).
fof(f1178,plain,
spl52_69,
inference(avatar_split_clause,[],[f1176,f1156]) ).
fof(f1182,plain,
( aElementOf0(sK43,xS)
| ~ spl52_61
| ~ spl52_69 ),
inference(resolution,[],[f1157,f1111]) ).
fof(f1183,plain,
( aElementOf0(sF45,xS)
| ~ spl52_69 ),
inference(resolution,[],[f1157,f632]) ).
fof(f1184,plain,
( $false
| spl52_6
| ~ spl52_61
| ~ spl52_69 ),
inference(forward_subsumption_resolution,[],[f1182,f676]) ).
fof(f1185,plain,
( spl52_6
| ~ spl52_61
| ~ spl52_69 ),
inference(avatar_contradiction_clause,[],[f1184]) ).
fof(f1188,plain,
( ~ aElementOf0(sF45,xS)
| spl52_6
| ~ spl52_62 ),
inference(superposition,[],[f676,f1090]) ).
fof(f1190,plain,
( $false
| spl52_6
| ~ spl52_62
| ~ spl52_69 ),
inference(forward_subsumption_resolution,[],[f1188,f1183]) ).
fof(f1191,plain,
( spl52_6
| ~ spl52_62
| ~ spl52_69 ),
inference(avatar_contradiction_clause,[],[f1190]) ).
cnf(s3,plain,
( ~ spl52_3
| spl52_5 ),
inference(sat_conversion,[],[f672]) ).
cnf(s4,plain,
( ~ spl52_3
| ~ spl52_6 ),
inference(sat_conversion,[],[f677]) ).
cnf(s16,plain,
( ~ spl52_28
| spl52_29 ),
inference(sat_conversion,[],[f825]) ).
cnf(s21,plain,
( spl52_1
| ~ spl52_21 ),
inference(sat_conversion,[],[f881]) ).
cnf(s33,plain,
spl52_21,
inference(sat_conversion,[],[f1035]) ).
cnf(s34,plain,
spl52_28,
inference(sat_conversion,[],[f1061]) ).
cnf(s36,plain,
( ~ spl52_1
| spl52_3
| ~ spl52_29 ),
inference(sat_conversion,[],[f1078]) ).
cnf(s37,plain,
( ~ spl52_5
| spl52_61
| spl52_62 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s42,plain,
spl52_69,
inference(sat_conversion,[],[f1178]) ).
cnf(s43,plain,
( spl52_6
| ~ spl52_61
| ~ spl52_69 ),
inference(sat_conversion,[],[f1185]) ).
cnf(s44,plain,
( spl52_6
| ~ spl52_62
| ~ spl52_69 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s45,plain,
spl52_1,
inference(rat,[],[s21,s33]) ).
cnf(s47,plain,
spl52_29,
inference(rat,[],[s16,s34]) ).
cnf(s48,plain,
spl52_3,
inference(rat,[],[s36,s45,s47]) ).
cnf(s53,plain,
~ spl52_6,
inference(rat,[],[s4,s48]) ).
cnf(s54,plain,
~ spl52_62,
inference(rat,[],[s44,s42,s53]) ).
cnf(s55,plain,
~ spl52_61,
inference(rat,[],[s43,s42,s53]) ).
cnf(s56,plain,
~ spl52_5,
inference(rat,[],[s37,s54,s55]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s3,s56,s48]) ).
fof(f1192,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM579+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:35:15 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.57/1.98 % (2377418)Detected formulas, will run a generic FOF schedule.
% 6.57/1.98 % (2377427)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3262188233:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.57/1.98 % (2377427)Instruction limit reached!
% 6.57/1.98 % (2377427)------------------------------
% 6.57/1.98 % (2377427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377427)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377427)Termination reason: Instruction limit
% 6.57/1.98 % (2377427)Termination phase: Saturation
% 6.57/1.98 % (2377427)Time elapsed: 0.041 s
% 6.57/1.98 % (2377427)Peak memory usage: 89 MB
% 6.57/1.98 % (2377427)Instructions burned: 122 (million)
% 6.57/1.98 % (2377426)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1490636291:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.57/1.98 % (2377429)dis-21_1_sil=8000:lcm=predicate:random_seed=2279978728: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)
% 6.57/1.98 % (2377423)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=3198635905:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.57/1.98 % (2377424)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=2642413581:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.57/1.98 % (2377425)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=2602013367:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.57/1.98 % (2377428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1226734796:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.57/1.98 % (2377426)Instruction limit reached!
% 6.57/1.98 % (2377426)------------------------------
% 6.57/1.98 % (2377426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377426)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377426)Termination reason: Instruction limit
% 6.57/1.98 % (2377426)Termination phase: Saturation
% 6.57/1.98 % (2377426)Time elapsed: 0.069 s
% 6.57/1.98 % (2377426)Peak memory usage: 89 MB
% 6.57/1.98 % (2377426)Instructions burned: 111 (million)
% 6.57/1.98 % (2377429)Instruction limit reached!
% 6.57/1.98 % (2377429)------------------------------
% 6.57/1.98 % (2377429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377429)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377429)Termination reason: Instruction limit
% 6.57/1.98 % (2377429)Termination phase: Saturation
% 6.57/1.98 % (2377429)Time elapsed: 0.074 s
% 6.57/1.98 % (2377429)Peak memory usage: 90 MB
% 6.57/1.98 % (2377429)Instructions burned: 130 (million)
% 6.57/1.98 % (2377428)Instruction limit reached!
% 6.57/1.98 % (2377428)------------------------------
% 6.57/1.98 % (2377428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377428)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377428)Termination reason: Instruction limit
% 6.57/1.98 % (2377428)Termination phase: Saturation
% 6.57/1.98 % (2377428)Time elapsed: 0.103 s
% 6.57/1.98 % (2377428)Peak memory usage: 90 MB
% 6.57/1.98 % (2377428)Instructions burned: 140 (million)
% 6.57/1.98 % (2377437)lrs+10_1_sil=8000:sp=occurrence:random_seed=502611127:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.57/1.98 % (2377437)Instruction limit reached!
% 6.57/1.98 % (2377437)------------------------------
% 6.57/1.98 % (2377437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377437)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377437)Termination reason: Instruction limit
% 6.57/1.98 % (2377437)Termination phase: Saturation
% 6.57/1.98 % (2377437)Time elapsed: 0.099 s
% 6.57/1.98 % (2377437)Peak memory usage: 92 MB
% 6.57/1.98 % (2377437)Instructions burned: 286 (million)
% 6.57/1.98 % (2377439)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4040212258:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.57/1.98 % (2377438)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2085957037:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.57/1.98 % (2377440)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=1722287790:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.57/1.98 % (2377438)Instruction limit reached!
% 6.57/1.98 % (2377438)------------------------------
% 6.57/1.98 % (2377438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377438)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377438)Termination reason: Instruction limit
% 6.57/1.98 % (2377438)Termination phase: Saturation
% 6.57/1.98 % (2377438)Time elapsed: 0.094 s
% 6.57/1.98 % (2377438)Peak memory usage: 91 MB
% 6.57/1.98 % (2377438)Instructions burned: 159 (million)
% 6.57/1.98 % (2377442)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4155060996:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.57/1.98 % (2377440)Instruction limit reached!
% 6.57/1.98 % (2377440)------------------------------
% 6.57/1.98 % (2377440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377440)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377440)Termination reason: Instruction limit
% 6.57/1.98 % (2377440)Termination phase: Saturation
% 6.57/1.98 % (2377440)Time elapsed: 0.151 s
% 6.57/1.98 % (2377440)Peak memory usage: 92 MB
% 6.57/1.98 % (2377440)Instructions burned: 249 (million)
% 6.57/1.98 % (2377442)Instruction limit reached!
% 6.57/1.98 % (2377442)------------------------------
% 6.57/1.98 % (2377442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377442)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377442)Termination reason: Instruction limit
% 6.57/1.98 % (2377442)Termination phase: Saturation
% 6.57/1.98 % (2377442)Time elapsed: 0.097 s
% 6.57/1.98 % (2377442)Peak memory usage: 90 MB
% 6.57/1.98 % (2377442)Instructions burned: 296 (million)
% 6.57/1.98 % (2377439)Instruction limit reached!
% 6.57/1.98 % (2377439)------------------------------
% 6.57/1.98 % (2377439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377439)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377439)Termination reason: Instruction limit
% 6.57/1.98 % (2377439)Termination phase: Saturation
% 6.57/1.98 % (2377439)Time elapsed: 0.228 s
% 6.57/1.98 % (2377439)Peak memory usage: 92 MB
% 6.57/1.98 % (2377439)Instructions burned: 325 (million)
% 6.57/1.98 % (2377446)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1845206746:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.57/1.98 % (2377449)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2961919730:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.57/1.98 % (2377448)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1388948610:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.57/1.98 % (2377449)Instruction limit reached!
% 6.57/1.98 % (2377449)------------------------------
% 6.57/1.98 % (2377449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377449)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377449)Termination reason: Instruction limit
% 6.57/1.98 % (2377449)Termination phase: Saturation
% 6.57/1.98 % (2377449)Time elapsed: 0.037 s
% 6.57/1.98 % (2377449)Peak memory usage: 89 MB
% 6.57/1.98 % (2377449)Instructions burned: 129 (million)
% 6.57/1.98 % (2377450)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=992702904:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.57/1.98 % (2377448)Instruction limit reached!
% 6.57/1.98 % (2377448)------------------------------
% 6.57/1.98 % (2377448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377448)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377448)Termination reason: Instruction limit
% 6.57/1.98 % (2377448)Termination phase: Saturation
% 6.57/1.98 % (2377448)Time elapsed: 0.075 s
% 6.57/1.98 % (2377448)Peak memory usage: 91 MB
% 6.57/1.98 % (2377448)Instructions burned: 114 (million)
% 6.57/1.98 % (2377450)Instruction limit reached!
% 6.57/1.98 % (2377450)------------------------------
% 6.57/1.98 % (2377450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.57/1.98 % (2377450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.57/1.98 % (2377450)CaDiCaL version: 2.1.3
% 6.57/1.98 % (2377450)Termination reason: Instruction limit
% 6.57/1.98 % (2377450)Termination phase: Saturation
% 6.57/1.98 % (2377450)Time elapsed: 0.067 s
% 6.57/1.98 % (2377450)Peak memory usage: 89 MB
% 6.57/1.98 % (2377450)Instructions burned: 115 (million)
% 6.57/1.98 % (2377423)First to succeed.
% 6.57/1.98 % (2377423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2377418"
% 6.57/1.98 % (2377454)lrs+10_1_sil=8000:sp=occurrence:random_seed=3512782536:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.57/1.98 % (2377456)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3720009313:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.57/1.98 % (2377457)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3625531201:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.57/1.98 % (2377423)Refutation found. Thanks to Tanya!
% 6.57/1.98 % SZS status Theorem for theBenchmark
% 6.57/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 8.58/2.17 % (2377423)------------------------------
% 8.58/2.17 % (2377423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.58/2.17 % (2377423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.58/2.17 % (2377423)CaDiCaL version: 2.1.3
% 8.58/2.17 % (2377423)Termination reason: Refutation
% 8.58/2.17 % (2377423)Time elapsed: 0.703 s
% 8.58/2.17 % (2377423)Peak memory usage: 131 MB
% 8.58/2.17 % (2377423)Instructions burned: 1056 (million)
% 8.58/2.17 % (2377423)------------------------------
% 8.58/2.17 % (2377423)------------------------------
% 8.58/2.17 % (2377418)Success in time 1.133 s
% 8.58/2.17 % Vampire exiting
%------------------------------------------------------------------------------