%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM630+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 : n026.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 12:16:04 PM UTC 2026
% Result : Theorem 2.56s 1.35s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 10 unt; 5 def)
% Number of atoms : 565 ( 114 equ)
% Maximal formula atoms : 47 ( 11 avg)
% Number of connectives : 676 ( 162 ~; 139 |; 296 &)
% ( 29 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-2 aty)
% Number of variables : 144 ( 136 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f104,axiom,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f114,axiom,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(xD)
& ! [X0] :
( aElementOf0(X0,xD)
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xn))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
fof(f115,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xD) )
& aSubsetOf0(xP,xD)
& aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5599) ).
fof(f116,conjecture,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xP)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f117,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xP)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(negated_conjecture,[status(cth)],[f116]) ).
fof(f118,plain,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) ) ) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(rectify,[],[f117]) ).
fof(f124,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(f128,plain,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(rectify,[],[f104]) ).
fof(f129,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(rectify,[],[f114]) ).
fof(f130,plain,
( szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( 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(pure_predicate_removal,[],[f124]) ).
fof(f133,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) ) )
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(ennf_transformation,[],[f118]) ).
fof(f134,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) ) )
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(flattening,[],[f133]) ).
fof(f155,plain,
( szDzozmdt0(xC) = szNzAzT0
& ! [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,[],[f130]) ).
fof(f156,plain,
( szDzozmdt0(xC) = szNzAzT0
& ! [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,[],[f155]) ).
fof(f169,plain,
( ! [X0] :
( aElementOf0(X0,xD)
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,xD)
& aElementOf0(xP,slbdtsldtrb0(xD,xk)) ),
inference(ennf_transformation,[],[f115]) ).
fof(f173,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(ennf_transformation,[],[f128]) ).
fof(f174,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(ennf_transformation,[],[f129]) ).
fof(f178,definition,
! [X0] :
( ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f179,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))))
& sP2(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP3(X0,X6) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f180,definition,
! [X0] :
( ! [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)
| sP3(X0,X6) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f181,definition,
! [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 ) )
| ~ sP5(X0) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f182,definition,
! [X0] :
( ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
| ~ sP6(X0) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f183,plain,
( szDzozmdt0(xC) = szNzAzT0
& ! [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))))
& sP6(X0)
& sP5(X0)
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& sP4(X0) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f156,f182,f181,f180,f179,f178]) ).
fof(f188,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xP)
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f189,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xP)
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(flattening,[],[f188]) ).
fof(f190,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xP)
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xP)
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn)) ) ),
inference(rectify,[],[f189]) ).
fof(f205,plain,
! [X0] :
( ! [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)
| sP3(X0,X6) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f180]) ).
fof(f206,plain,
! [X0] :
( ! [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)
| sP3(X0,X6) )
| ~ sP4(X0) ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,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)))) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X1)
| sP3(X0,X1) )
| ~ sP4(X0) ),
inference(rectify,[],[f206]) ).
fof(f208,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))))
& sP2(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP3(X0,X6) ),
inference(nnf_transformation,[],[f179]) ).
fof(f209,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))))
& sP2(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f208]) ).
fof(f210,plain,
! [X0,X1] :
( ( ( ( ~ aElementOf0(sK13(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK13(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))))
& sP2(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ sP3(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f209]) ).
fof(f232,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(nnf_transformation,[],[f173]) ).
fof(f233,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(flattening,[],[f232]) ).
fof(f234,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( ( aElementOf0(X1,xD)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 )
| ~ aElementOf0(X1,xD) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(nnf_transformation,[],[f174]) ).
fof(f235,plain,
( ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& aSet0(xD)
& ! [X1] :
( ( aElementOf0(X1,xD)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| szmzizndt0(sdtlpdtrp0(xN,xn)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& szmzizndt0(sdtlpdtrp0(xN,xn)) != X1 )
| ~ aElementOf0(X1,xD) ) )
& xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))) ),
inference(flattening,[],[f234]) ).
fof(f242,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f190]) ).
fof(f285,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f296,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f210]) ).
fof(f304,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP4(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f367,plain,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(cnf_transformation,[],[f169]) ).
fof(f384,plain,
aSet0(xP),
inference(cnf_transformation,[],[f233]) ).
fof(f385,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f235]) ).
fof(f394,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f441,plain,
sP4(xn),
inference(unit_resulting_resolution,[],[f304,f394]) ).
fof(f685,plain,
sP3(xn,xP),
inference(unit_resulting_resolution,[],[f285,f441,f384,f242]) ).
fof(f689,plain,
~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)),
inference(unit_resulting_resolution,[],[f296,f685]) ).
fof(f694,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(forward_demodulation,[],[f689,f385]) ).
fof(f697,plain,
$false,
inference(forward_subsumption_resolution,[],[f694,f367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM630+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:53:43 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.56/1.35 % (3193426)Detected formulas, will run a generic FOF schedule.
% 2.56/1.35 % (3193437)dis-21_1_sil=8000:lcm=predicate:random_seed=3053169983: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)
% 2.56/1.35 % (3193432)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=121685551:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.35 % (3193437)Instruction limit reached!
% 2.56/1.35 % (3193437)------------------------------
% 2.56/1.35 % (3193437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3193437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3193437)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3193437)Termination reason: Instruction limit
% 2.56/1.35 % (3193437)Termination phase: Saturation
% 2.56/1.35 % (3193437)Time elapsed: 0.039 s
% 2.56/1.35 % (3193437)Peak memory usage: 90 MB
% 2.56/1.35 % (3193437)Instructions burned: 132 (million)
% 2.56/1.35 % (3193433)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=740111043:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.35 % (3193431)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=2958563198:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.35 % (3193435)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4060966060:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.35 % (3193434)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1241549417:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.35 % (3193436)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2246324542:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.35 % (3193436)Instruction limit reached!
% 2.56/1.35 % (3193436)------------------------------
% 2.56/1.35 % (3193436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3193436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3193436)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3193436)Termination reason: Instruction limit
% 2.56/1.35 % (3193436)Termination phase: Saturation
% 2.56/1.35 % (3193436)Time elapsed: 0.054 s
% 2.56/1.35 % (3193436)Peak memory usage: 90 MB
% 2.56/1.35 % (3193436)Instructions burned: 141 (million)
% 2.56/1.35 % (3193434)Instruction limit reached!
% 2.56/1.35 % (3193434)------------------------------
% 2.56/1.35 % (3193434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3193434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3193434)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3193434)Termination reason: Instruction limit
% 2.56/1.35 % (3193434)Termination phase: Saturation
% 2.56/1.35 % (3193434)Time elapsed: 0.065 s
% 2.56/1.35 % (3193434)Peak memory usage: 90 MB
% 2.56/1.35 % (3193434)Instructions burned: 110 (million)
% 2.56/1.35 % (3193435)Instruction limit reached!
% 2.56/1.35 % (3193435)------------------------------
% 2.56/1.35 % (3193435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3193435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3193435)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3193435)Termination reason: Instruction limit
% 2.56/1.35 % (3193435)Termination phase: Saturation
% 2.56/1.35 % (3193435)Time elapsed: 0.074 s
% 2.56/1.35 % (3193435)Peak memory usage: 89 MB
% 2.56/1.35 % (3193435)Instructions burned: 120 (million)
% 2.56/1.35 % (3193442)lrs+10_1_sil=8000:sp=occurrence:random_seed=466878807:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.56/1.35 % (3193446)lrs+10_1_sil=32000:urr=on:br=off:random_seed=227897506:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.56/1.35 % (3193446)First to succeed.
% 2.56/1.35 % (3193446)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3193426"
% 2.56/1.35 % (3193448)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=1238789578:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.56/1.35 % (3193447)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3256320798:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.56/1.35 % (3193442)Instruction limit reached!
% 2.56/1.35 % (3193442)------------------------------
% 2.56/1.35 % (3193442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3193442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3193442)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3193442)Termination reason: Instruction limit
% 2.56/1.35 % (3193442)Termination phase: Saturation
% 2.56/1.35 % (3193442)Time elapsed: 0.182 s
% 2.56/1.35 % (3193442)Peak memory usage: 93 MB
% 2.56/1.35 % (3193442)Instructions burned: 286 (million)
% 2.56/1.35 % (3193446)Refutation found. Thanks to Tanya!
% 2.56/1.35 % SZS status Theorem for theBenchmark
% 2.56/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.57 % (3193446)------------------------------
% 4.00/1.57 % (3193446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.57 % (3193446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.57 % (3193446)CaDiCaL version: 2.1.3
% 4.00/1.57 % (3193446)Termination reason: Refutation
% 4.00/1.57 % (3193446)Time elapsed: 0.014 s
% 4.00/1.57 % (3193446)Peak memory usage: 89 MB
% 4.00/1.57 % (3193446)Instructions burned: 39 (million)
% 4.00/1.57 % (3193446)------------------------------
% 4.00/1.57 % (3193446)------------------------------
% 4.00/1.57 % (3193426)Success in time 0.48 s
% 4.00/1.57 % Vampire exiting
%------------------------------------------------------------------------------