%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM587+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 : n016.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 12:15:52 PM UTC 2026
% Result : Theorem 4.85s 1.66s
% Output : Refutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 114 ( 36 unt; 12 def)
% Number of atoms : 1042 ( 184 equ)
% Maximal formula atoms : 47 ( 9 avg)
% Number of connectives : 1288 ( 360 ~; 336 |; 509 &)
% ( 39 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 12 con; 0-2 aty)
% Number of variables : 224 ( 0 sgn 197 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f69,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
fof(f76,axiom,
( aFunction0(xc)
& ! [X0] :
( ( aElementOf0(X0,szDzozmdt0(xc))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xK )
=> aElementOf0(X0,szDzozmdt0(xc)) ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X1] :
( aElementOf0(X1,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X0,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f86,axiom,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,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)) ) )
& ! [X1] :
( ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( aSet0(X1)
& ! [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 ) )
& ( ( ( ( aSet0(X1)
& ! [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,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [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) )
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& ( aElementOf0(X2,X1)
| X2 = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
fof(f87,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4200) ).
fof(f89,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))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4237) ).
fof(f90,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& ? [X0] :
( aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4263) ).
fof(f91,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f92,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f91]) ).
fof(f100,plain,
( aFunction0(xc)
& ! [X0] :
( ( aElementOf0(X0,szDzozmdt0(xc))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK ) )
& ( ( ( ( aSet0(X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xK )
=> aElementOf0(X0,szDzozmdt0(xc)) ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X5,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rectify,[],[f76]) ).
fof(f105,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk ) )
& ( ( ( ( aSet0(X3)
& ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& sbrdtbr0(X3) = xk )
=> aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aSet0(X6)
& ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) ) )
=> ( ( ( ! [X9] :
( aElementOf0(X9,X6)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& xk = sbrdtbr0(X6) )
| aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( aElementOf0(X10,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f106,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))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx ),
inference(rectify,[],[f89]) ).
fof(f107,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 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X3 ) ) )
& ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,X4) ) ),
inference(rectify,[],[f90]) ).
fof(f108,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f92]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f209,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(ennf_transformation,[],[f100]) ).
fof(f210,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(flattening,[],[f209]) ).
fof(f222,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f105]) ).
fof(f223,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f222]) ).
fof(f224,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))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx ),
inference(ennf_transformation,[],[f106]) ).
fof(f225,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X3 ) ) )
& ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,X4) ) ),
inference(ennf_transformation,[],[f107]) ).
fof(f233,definition,
! [X0,X6] :
( ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP4(X0,X6) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f234,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| sP4(X0,X6) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f223,f233]) ).
fof(f290,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(nnf_transformation,[],[f210]) ).
fof(f291,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ? [X5] :
( aElementOf0(X5,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X5) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rectify,[],[f290]) ).
fof(f292,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK24(X0),xS)
& aElementOf0(sK24(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ( aElementOf0(sK25(X3),szDzozmdt0(xc))
& sdtlpdtrp0(xc,sK25(X3)) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X2,sK24(X0)),skolemize(X5,sK25(X3))],[f291]) ).
fof(f315,plain,
! [X0,X6] :
( ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP4(X0,X6) ),
inference(nnf_transformation,[],[f233]) ).
fof(f316,plain,
! [X0,X6] :
( ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP4(X0,X6) ),
inference(flattening,[],[f315]) ).
fof(f317,plain,
! [X0,X1] :
( ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X2,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))
& 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)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) ) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f316]) ).
fof(f318,plain,
! [X0,X1] :
( ( ( ( ~ aElementOf0(sK37(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK37(X0,X1),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))
& 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)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) ) )
| ~ sP4(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(X2,sK37(X0,X1))],[f317]) ).
fof(f319,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2 )
& ( ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( ( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X11)
| ( ~ aElementOf0(X11,X6)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X11 ) )
& ( ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) )
| ~ aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| sP4(X0,X6) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(nnf_transformation,[],[f234]) ).
fof(f320,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2 )
& ( ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( ( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X11)
| ( ~ aElementOf0(X11,X6)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X11 ) )
& ( ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) )
| ~ aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| sP4(X0,X6) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f319]) ).
fof(f321,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2 )
& ( ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& ! [X8] :
( ( aElementOf0(X8,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ( ~ aElementOf0(X8,X6)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& ( ( aElement0(X8)
& ( aElementOf0(X8,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 ) )
| ~ aElementOf0(X8,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| sP4(X0,X6) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(rectify,[],[f320]) ).
fof(f322,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X2 )
& ( ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 )
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ( ~ aElementOf0(sK38(X0,X3),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK38(X0,X3),X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& ! [X8] :
( ( aElementOf0(X8,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ( ~ aElementOf0(X8,X6)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& ( ( aElement0(X8)
& ( aElementOf0(X8,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 ) )
| ~ aElementOf0(X8,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| sP4(X0,X6) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(X5,sK38(X0,X3))],[f321]) ).
fof(f324,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))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx ),
inference(nnf_transformation,[],[f224]) ).
fof(f325,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))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = xx ),
inference(flattening,[],[f324]) ).
fof(f326,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,X4) ) ),
inference(nnf_transformation,[],[f225]) ).
fof(f327,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,X4) ) ),
inference(flattening,[],[f326]) ).
fof(f328,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X3 ) )
| ~ aElementOf0(X3,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(sK40,szDzozmdt0(xc))
& sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,sK40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X4,sK40)],[f327]) ).
fof(f454,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f474,plain,
! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cnf_transformation,[],[f292]) ).
fof(f487,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f292]) ).
fof(f601,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| sbrdtbr0(X1) != xk
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f318]) ).
fof(f604,plain,
! [X0,X6] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X6)
| sP4(X0,X6)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f629,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f87]) ).
fof(f633,plain,
xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ),
inference(cnf_transformation,[],[f325]) ).
fof(f635,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f325]) ).
fof(f636,plain,
aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f325]) ).
fof(f638,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f325]) ).
fof(f646,plain,
sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,sK40),
inference(cnf_transformation,[],[f328]) ).
fof(f647,plain,
aElementOf0(sK40,szDzozmdt0(xc)),
inference(cnf_transformation,[],[f328]) ).
fof(f662,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f108]) ).
fof(f776,definition,
( spl61_1
<=> xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) ),
introduced(definition,[new_symbols(definition,[spl61_1])],[avatar_definition]) ).
fof(f778,plain,
( xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ)
| ~ spl61_1 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f779,plain,
spl61_1,
inference(avatar_split_clause,[],[f633,f776]) ).
fof(f812,definition,
( spl61_4
<=> aElementOf0(xx,xT) ),
introduced(definition,[new_symbols(definition,[spl61_4])],[avatar_definition]) ).
fof(f814,plain,
( ~ aElementOf0(xx,xT)
| spl61_4 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f815,plain,
~ spl61_4,
inference(avatar_split_clause,[],[f662,f812]) ).
fof(f833,definition,
( spl61_5
<=> ! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
introduced(definition,[new_symbols(definition,[spl61_5])],[avatar_definition]) ).
fof(f834,plain,
( ! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) )
| ~ spl61_5 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f835,plain,
spl61_5,
inference(avatar_split_clause,[],[f474,f833]) ).
fof(f848,plain,
( ! [X0] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc))
| ~ aFunction0(xc) )
| ~ spl61_5 ),
inference(resolution,[],[f834,f454]) ).
fof(f899,plain,
( ! [X0] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
| ~ spl61_5 ),
inference(forward_subsumption_resolution,[],[f848,f487]) ).
fof(f1001,definition,
( spl61_10
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl61_10])],[avatar_definition]) ).
fof(f1003,plain,
( aElementOf0(xi,szNzAzT0)
| ~ spl61_10 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1004,plain,
spl61_10,
inference(avatar_split_clause,[],[f629,f1001]) ).
fof(f1086,definition,
( spl61_11
<=> sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,sK40) ),
introduced(definition,[new_symbols(definition,[spl61_11])],[avatar_definition]) ).
fof(f1088,plain,
( sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = sdtlpdtrp0(xc,sK40)
| ~ spl61_11 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1089,plain,
spl61_11,
inference(avatar_split_clause,[],[f646,f1086]) ).
fof(f1134,definition,
( spl61_13
<=> ! [X0] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[spl61_13])],[avatar_definition]) ).
fof(f1135,plain,
( ! [X0] :
( aElementOf0(sdtlpdtrp0(xc,X0),xT)
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
| ~ spl61_13 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1136,plain,
( spl61_13
| ~ spl61_5 ),
inference(avatar_split_clause,[],[f899,f833,f1134]) ).
fof(f1532,definition,
( spl61_20
<=> aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl61_20])],[avatar_definition]) ).
fof(f1534,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl61_20 ),
inference(avatar_component_clause,[],[f1532]) ).
fof(f1535,plain,
spl61_20,
inference(avatar_split_clause,[],[f636,f1532]) ).
fof(f1536,plain,
( xk != sbrdtbr0(xQ)
| ~ sP4(xi,xQ)
| ~ spl61_20 ),
inference(resolution,[],[f1534,f601]) ).
fof(f1570,plain,
( ~ sP4(xi,xQ)
| ~ spl61_20 ),
inference(forward_subsumption_resolution,[],[f1536,f635]) ).
fof(f1888,definition,
( spl61_30
<=> aElementOf0(sK40,szDzozmdt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl61_30])],[avatar_definition]) ).
fof(f1890,plain,
( aElementOf0(sK40,szDzozmdt0(xc))
| ~ spl61_30 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f1891,plain,
spl61_30,
inference(avatar_split_clause,[],[f647,f1888]) ).
fof(f1916,definition,
( spl61_31
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl61_31])],[avatar_definition]) ).
fof(f1918,plain,
( aSet0(xQ)
| ~ spl61_31 ),
inference(avatar_component_clause,[],[f1916]) ).
fof(f1919,plain,
spl61_31,
inference(avatar_split_clause,[],[f638,f1916]) ).
fof(f2374,definition,
( spl61_37
<=> ! [X6,X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X6)
| sP4(X0,X6)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl61_37])],[avatar_definition]) ).
fof(f2375,plain,
( ! [X0,X6] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X6)
| sP4(X0,X6)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl61_37 ),
inference(avatar_component_clause,[],[f2374]) ).
fof(f2376,plain,
spl61_37,
inference(avatar_split_clause,[],[f604,f2374]) ).
fof(f2399,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sK40)
| ~ aSet0(xQ)
| sP4(xi,xQ)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl61_11
| ~ spl61_37 ),
inference(superposition,[],[f1088,f2375]) ).
fof(f2421,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sK40)
| sP4(xi,xQ)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl61_11
| ~ spl61_31
| ~ spl61_37 ),
inference(forward_subsumption_resolution,[],[f2399,f1918]) ).
fof(f2438,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sK40)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl61_11
| ~ spl61_20
| ~ spl61_31
| ~ spl61_37 ),
inference(forward_subsumption_resolution,[],[f2421,f1570]) ).
fof(f2443,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),xQ) = sdtlpdtrp0(xc,sK40)
| ~ spl61_10
| ~ spl61_11
| ~ spl61_20
| ~ spl61_31
| ~ spl61_37 ),
inference(forward_subsumption_resolution,[],[f2438,f1003]) ).
fof(f2445,plain,
( xx = sdtlpdtrp0(xc,sK40)
| ~ spl61_1
| ~ spl61_10
| ~ spl61_11
| ~ spl61_20
| ~ spl61_31
| ~ spl61_37 ),
inference(forward_demodulation,[],[f2443,f778]) ).
fof(f2448,definition,
( spl61_38
<=> xx = sdtlpdtrp0(xc,sK40) ),
introduced(definition,[new_symbols(definition,[spl61_38])],[avatar_definition]) ).
fof(f2450,plain,
( xx = sdtlpdtrp0(xc,sK40)
| ~ spl61_38 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f2451,plain,
( spl61_38
| ~ spl61_1
| ~ spl61_10
| ~ spl61_11
| ~ spl61_20
| ~ spl61_31
| ~ spl61_37 ),
inference(avatar_split_clause,[],[f2445,f2374,f1916,f1532,f1086,f1001,f776,f2448]) ).
fof(f2454,plain,
( aElementOf0(xx,xT)
| ~ aElementOf0(sK40,szDzozmdt0(xc))
| ~ spl61_13
| ~ spl61_38 ),
inference(superposition,[],[f1135,f2450]) ).
fof(f2467,plain,
( ~ aElementOf0(sK40,szDzozmdt0(xc))
| spl61_4
| ~ spl61_13
| ~ spl61_38 ),
inference(forward_subsumption_resolution,[],[f2454,f814]) ).
fof(f2474,plain,
( $false
| spl61_4
| ~ spl61_13
| ~ spl61_30
| ~ spl61_38 ),
inference(forward_subsumption_resolution,[],[f2467,f1890]) ).
fof(f2475,plain,
( spl61_4
| ~ spl61_13
| ~ spl61_30
| ~ spl61_38 ),
inference(avatar_contradiction_clause,[],[f2474]) ).
cnf(s1,plain,
spl61_1,
inference(sat_conversion,[],[f779]) ).
cnf(s4,plain,
~ spl61_4,
inference(sat_conversion,[],[f815]) ).
cnf(s5,plain,
spl61_5,
inference(sat_conversion,[],[f835]) ).
cnf(s10,plain,
spl61_10,
inference(sat_conversion,[],[f1004]) ).
cnf(s11,plain,
spl61_11,
inference(sat_conversion,[],[f1089]) ).
cnf(s13,plain,
( ~ spl61_5
| spl61_13 ),
inference(sat_conversion,[],[f1136]) ).
cnf(s20,plain,
spl61_20,
inference(sat_conversion,[],[f1535]) ).
cnf(s30,plain,
spl61_30,
inference(sat_conversion,[],[f1891]) ).
cnf(s31,plain,
spl61_31,
inference(sat_conversion,[],[f1919]) ).
cnf(s37,plain,
spl61_37,
inference(sat_conversion,[],[f2376]) ).
cnf(s38,plain,
( ~ spl61_1
| ~ spl61_10
| ~ spl61_11
| ~ spl61_20
| ~ spl61_31
| ~ spl61_37
| spl61_38 ),
inference(sat_conversion,[],[f2451]) ).
cnf(s39,plain,
( spl61_4
| ~ spl61_13
| ~ spl61_30
| ~ spl61_38 ),
inference(sat_conversion,[],[f2475]) ).
cnf(s45,plain,
spl61_13,
inference(rat,[],[s13,s5]) ).
cnf(s46,plain,
~ spl61_38,
inference(rat,[],[s39,s45,s30,s4]) ).
cnf(s48,plain,
~ spl61_1,
inference(rat,[],[s38,s10,s37,s31,s20,s11,s46]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s1,s48]) ).
fof(f2486,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM587+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:43:02 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.85/1.66 % (2970061)Detected formulas, will run a generic FOF schedule.
% 4.85/1.66 % (2970068)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=3906200096:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.85/1.66 % (2970069)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=522568742:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.85/1.66 % (2970070)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3817537452:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.85/1.66 % (2970066)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=1238132196:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.85/1.66 % (2970067)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=866106566:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.85/1.66 % (2970072)dis-21_1_sil=8000:lcm=predicate:random_seed=2807015220: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)
% 4.85/1.66 % (2970071)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3268169434:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.85/1.66 % (2970069)Instruction limit reached!
% 4.85/1.66 % (2970069)------------------------------
% 4.85/1.66 % (2970069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970069)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970069)Termination reason: Instruction limit
% 4.85/1.66 % (2970069)Termination phase: Saturation
% 4.85/1.66 % (2970069)Time elapsed: 0.071 s
% 4.85/1.66 % (2970069)Peak memory usage: 90 MB
% 4.85/1.66 % (2970069)Instructions burned: 110 (million)
% 4.85/1.66 % (2970072)Instruction limit reached!
% 4.85/1.66 % (2970072)------------------------------
% 4.85/1.66 % (2970072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970072)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970072)Termination reason: Instruction limit
% 4.85/1.66 % (2970072)Termination phase: Saturation
% 4.85/1.66 % (2970072)Time elapsed: 0.071 s
% 4.85/1.66 % (2970072)Peak memory usage: 90 MB
% 4.85/1.66 % (2970072)Instructions burned: 129 (million)
% 4.85/1.66 % (2970070)Instruction limit reached!
% 4.85/1.66 % (2970070)------------------------------
% 4.85/1.66 % (2970070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970070)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970070)Termination reason: Instruction limit
% 4.85/1.66 % (2970070)Termination phase: Saturation
% 4.85/1.66 % (2970070)Time elapsed: 0.077 s
% 4.85/1.66 % (2970070)Peak memory usage: 89 MB
% 4.85/1.66 % (2970070)Instructions burned: 124 (million)
% 4.85/1.66 % (2970071)Instruction limit reached!
% 4.85/1.66 % (2970071)------------------------------
% 4.85/1.66 % (2970071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970071)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970071)Termination reason: Instruction limit
% 4.85/1.66 % (2970071)Termination phase: Saturation
% 4.85/1.66 % (2970071)Time elapsed: 0.100 s
% 4.85/1.66 % (2970071)Peak memory usage: 90 MB
% 4.85/1.66 % (2970071)Instructions burned: 139 (million)
% 4.85/1.66 % (2970080)lrs+10_1_sil=8000:sp=occurrence:random_seed=4210128539:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.85/1.66 % (2970081)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1218468422:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.85/1.66 % (2970081)Refutation not found, incomplete strategy
% 4.85/1.66 % (2970081)------------------------------
% 4.85/1.66 % (2970081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970081)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970081)Termination reason: Refutation not found, incomplete strategy
% 4.85/1.66 % (2970081)Time elapsed: 0.004 s
% 4.85/1.66 % (2970081)Peak memory usage: 89 MB
% 4.85/1.66 % (2970081)Instructions burned: 5 (million)
% 4.85/1.66 % (2970082)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1342164988:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.85/1.66 % (2970083)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=2139358540:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.85/1.66 % (2970082)Instruction limit reached!
% 4.85/1.66 % (2970082)------------------------------
% 4.85/1.66 % (2970082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970082)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970082)Termination reason: Instruction limit
% 4.85/1.66 % (2970082)Termination phase: Saturation
% 4.85/1.66 % (2970082)Time elapsed: 0.151 s
% 4.85/1.66 % (2970082)Peak memory usage: 90 MB
% 4.85/1.66 % (2970082)Instructions burned: 327 (million)
% 4.85/1.66 % (2970080)Instruction limit reached!
% 4.85/1.66 % (2970080)------------------------------
% 4.85/1.66 % (2970080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970080)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970080)Termination reason: Instruction limit
% 4.85/1.66 % (2970080)Termination phase: Saturation
% 4.85/1.66 % (2970080)Time elapsed: 0.174 s
% 4.85/1.66 % (2970080)Peak memory usage: 92 MB
% 4.85/1.66 % (2970080)Instructions burned: 285 (million)
% 4.85/1.66 % (2970083)Instruction limit reached!
% 4.85/1.66 % (2970083)------------------------------
% 4.85/1.66 % (2970083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970083)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970083)Termination reason: Instruction limit
% 4.85/1.66 % (2970083)Termination phase: Saturation
% 4.85/1.66 % (2970083)Time elapsed: 0.149 s
% 4.85/1.66 % (2970083)Peak memory usage: 92 MB
% 4.85/1.66 % (2970083)Instructions burned: 251 (million)
% 4.85/1.66 % (2970081)------------------------------
% 4.85/1.66 % (2970081)------------------------------
% 4.85/1.66 % (2970068)First to succeed.
% 4.85/1.66 % (2970088)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2026430075:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.85/1.66 % (2970068)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2970061"
% 4.85/1.66 % (2970089)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1477424239:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.85/1.66 % (2970090)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1514026637:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.85/1.66 % (2970091)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2891639744:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.85/1.66 % (2970090)Instruction limit reached!
% 4.85/1.66 % (2970090)------------------------------
% 4.85/1.66 % (2970090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970090)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970090)Termination reason: Instruction limit
% 4.85/1.66 % (2970090)Termination phase: Saturation
% 4.85/1.66 % (2970090)Time elapsed: 0.074 s
% 4.85/1.66 % (2970090)Peak memory usage: 91 MB
% 4.85/1.66 % (2970090)Instructions burned: 113 (million)
% 4.85/1.66 % (2970091)Instruction limit reached!
% 4.85/1.66 % (2970091)------------------------------
% 4.85/1.66 % (2970091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.66 % (2970091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.66 % (2970091)CaDiCaL version: 2.1.3
% 4.85/1.66 % (2970091)Termination reason: Instruction limit
% 4.85/1.66 % (2970091)Termination phase: Saturation
% 4.85/1.66 % (2970091)Time elapsed: 0.068 s
% 4.85/1.66 % (2970091)Peak memory usage: 89 MB
% 4.85/1.66 % (2970091)Instructions burned: 127 (million)
% 4.85/1.66 % (2970068)Refutation found. Thanks to Tanya!
% 4.85/1.66 % SZS status Theorem for theBenchmark
% 4.85/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 6.09/1.75 % (2970068)------------------------------
% 6.09/1.75 % (2970068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.09/1.75 % (2970068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.09/1.75 % (2970068)CaDiCaL version: 2.1.3
% 6.09/1.75 % (2970068)Termination reason: Refutation
% 6.09/1.75 % (2970068)Time elapsed: 0.530 s
% 6.09/1.75 % (2970068)Peak memory usage: 136 MB
% 6.09/1.75 % (2970068)Instructions burned: 1458 (million)
% 6.09/1.75 % (2970068)------------------------------
% 6.09/1.75 % (2970068)------------------------------
% 6.09/1.75 % (2970061)Success in time 0.794 s
% 6.09/1.75 % Vampire exiting
%------------------------------------------------------------------------------