%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM600+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:56 PM UTC 2026
% Result : Theorem 2.74s 1.27s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 16 unt; 10 def)
% Number of atoms : 659 ( 137 equ)
% Maximal formula atoms : 47 ( 7 avg)
% Number of connectives : 792 ( 218 ~; 193 |; 309 &)
% ( 29 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 3 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-3 aty)
% Number of variables : 173 ( 0 sgn 147 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f66,axiom,
! [X0,X1] :
( ( aFunction0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPtt) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(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/sandbox/benchmark/theBenchmark.p',m__4151) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
fof(f97,conjecture,
! [X0] :
( ( ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
& aElementOf0(X0,xO) )
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
| aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& sdtlpdtrp0(xe,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f98,negated_conjecture,
~ ! [X0] :
( ( ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
& aElementOf0(X0,xO) )
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& ( sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
| aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& sdtlpdtrp0(xe,X1) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f101,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f104,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(f110,plain,
~ ! [X0] :
( ( ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
& aElementOf0(X0,xO) )
=> ? [X2] :
( aElementOf0(X2,szNzAzT0)
& ( szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
| aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& sdtlpdtrp0(xe,X2) = X0 ) ),
inference(rectify,[],[f98]) ).
fof(f123,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f101]) ).
fof(f124,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f123]) ).
fof(f132,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,[],[f104]) ).
fof(f133,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,[],[f132]) ).
fof(f142,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f143,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f142]) ).
fof(f145,plain,
? [X0] :
( ! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ( szDzizrdt0(xd) != sdtlpdtrp0(xd,X2)
& ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sdtlpdtrp0(xe,X2) != X0 )
& ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
& aElementOf0(X0,xO) ),
inference(ennf_transformation,[],[f110]) ).
fof(f146,plain,
? [X0] :
( ! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ( szDzizrdt0(xd) != sdtlpdtrp0(xd,X2)
& ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sdtlpdtrp0(xe,X2) != X0 )
& ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
& aElementOf0(X0,xO) ),
inference(flattening,[],[f145]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f222,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f223,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f222]) ).
fof(f231,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f232,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP4(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP5(X0) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f233,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f124,f232,f231]) ).
fof(f238,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 ) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f239,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))))
& sP9(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP10(X0,X6) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f240,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)
| sP10(X0,X6) )
| ~ sP11(X0) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f241,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 ) )
| ~ sP12(X0) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f242,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 ) )
| ~ sP13(X0) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f243,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))))
& sP13(X0)
& sP12(X0)
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& sP11(X0) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f133,f242,f241,f240,f239,f238]) ).
fof(f280,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP5(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK35(X0),szNzAzT0)
& aElementOf0(sK35(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(X1,sK35(X0))],[f233]) ).
fof(f335,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK48(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK48(X0,X1),X1)
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(X2,sK48(X0,X1))],[f143]) ).
fof(f339,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f340,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(flattening,[],[f339]) ).
fof(f345,plain,
? [X0] :
( ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ( sdtlpdtrp0(xd,X1) != szDzizrdt0(xd)
& ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sdtlpdtrp0(xe,X1) != X0 )
& ? [X2] :
( aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X0 )
& aElementOf0(X0,xO) ),
inference(rectify,[],[f146]) ).
fof(f346,plain,
( ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ( sdtlpdtrp0(xd,X1) != szDzizrdt0(xd)
& ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
| sdtlpdtrp0(xe,X1) != sK51 )
& aElementOf0(sK52,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sK51 = sdtlpdtrp0(xe,sK52)
& aElementOf0(sK51,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51,sK52]),skolemize(X0,sK51),skolemize(X2,sK52)],[f345]) ).
fof(f381,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1 )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f223]) ).
fof(f382,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1 )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f381]) ).
fof(f383,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X4) != X1 )
& ( ( aElementOf0(X4,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f382]) ).
fof(f384,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aElementOf0(sK66(X0,X1,X2),szDzozmdt0(X0))
| sdtlpdtrp0(X0,sK66(X0,X1,X2)) != X1
| ~ aElementOf0(sK66(X0,X1,X2),X2) )
& ( ( aElementOf0(sK66(X0,X1,X2),szDzozmdt0(X0))
& sdtlpdtrp0(X0,sK66(X0,X1,X2)) = X1 )
| aElementOf0(sK66(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X4) != X1 )
& ( ( aElementOf0(X4,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(X3,sK66(X0,X1,X2))],[f383]) ).
fof(f386,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f458,plain,
szNzAzT0 = szDzozmdt0(xN),
inference(cnf_transformation,[],[f280]) ).
fof(f533,plain,
szNzAzT0 = szDzozmdt0(xC),
inference(cnf_transformation,[],[f243]) ).
fof(f600,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f335]) ).
fof(f601,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f335]) ).
fof(f612,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f340]) ).
fof(f625,plain,
sK51 = sdtlpdtrp0(xe,sK52),
inference(cnf_transformation,[],[f346]) ).
fof(f626,plain,
aElementOf0(sK52,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f346]) ).
fof(f627,plain,
! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X1) != sK51 ),
inference(cnf_transformation,[],[f346]) ).
fof(f686,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f729,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,szDzozmdt0(X0))
| ~ aElementOf0(X4,X2)
| sdtlbdtrb0(X0,X1) != X2
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f384]) ).
fof(f796,definition,
~ sP97(sK51),
introduced(definition,[new_symbols(definition,[sP97])],[inequality_splitting_name_introduction]) ).
fof(f797,plain,
! [X1] :
( ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X1,szNzAzT0)
| sP97(sdtlpdtrp0(xe,X1)) ),
inference(inequality_splitting,[],[f627,f796]) ).
fof(f836,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| aElementOf0(X4,szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f729]) ).
fof(f986,definition,
( spl112_6
<=> aElementOf0(sK52,szDzozmdt0(xC)) ),
introduced(definition,[new_symbols(definition,[spl112_6])],[avatar_definition]) ).
fof(f987,plain,
( aElementOf0(sK52,szDzozmdt0(xC))
| ~ spl112_6 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f988,plain,
( ~ aElementOf0(sK52,szDzozmdt0(xC))
| spl112_6 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f998,plain,
( aElementOf0(sK52,szDzozmdt0(xd))
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd)) ),
inference(resolution,[],[f626,f836]) ).
fof(f1018,plain,
( aElementOf0(sK52,szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd)) ),
inference(forward_subsumption_resolution,[],[f998,f601]) ).
fof(f1021,plain,
( aElementOf0(sK52,szNzAzT0)
| ~ aElement0(szDzizrdt0(xd)) ),
inference(forward_demodulation,[],[f1018,f600]) ).
fof(f1023,definition,
( spl112_11
<=> aElement0(szDzizrdt0(xd)) ),
introduced(definition,[new_symbols(definition,[spl112_11])],[avatar_definition]) ).
fof(f1025,plain,
( ~ aElement0(szDzizrdt0(xd))
| spl112_11 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1031,plain,
( aElementOf0(sK52,szDzozmdt0(xC))
| ~ aElement0(szDzizrdt0(xd)) ),
inference(forward_demodulation,[],[f1021,f533]) ).
fof(f1032,plain,
( ~ aElement0(szDzizrdt0(xd))
| spl112_6 ),
inference(forward_subsumption_resolution,[],[f1031,f988]) ).
fof(f1033,plain,
( ~ spl112_11
| spl112_6 ),
inference(avatar_split_clause,[],[f1032,f986,f1023]) ).
fof(f1079,plain,
( ~ aElementOf0(sK52,szNzAzT0)
| sP97(sdtlpdtrp0(xe,sK52)) ),
inference(resolution,[],[f797,f626]) ).
fof(f1106,plain,
( ~ aElementOf0(sK52,szDzozmdt0(xC))
| sP97(sdtlpdtrp0(xe,sK52)) ),
inference(forward_demodulation,[],[f1079,f533]) ).
fof(f1202,plain,
szDzozmdt0(xN) = szDzozmdt0(xC),
inference(superposition,[],[f458,f533]) ).
fof(f1436,plain,
( aElement0(szDzizrdt0(xd))
| ~ aSet0(xT) ),
inference(resolution,[],[f612,f686]) ).
fof(f1442,plain,
( ~ aSet0(xT)
| spl112_11 ),
inference(forward_subsumption_resolution,[],[f1436,f1025]) ).
fof(f1443,plain,
( $false
| spl112_11 ),
inference(forward_subsumption_resolution,[],[f1442,f386]) ).
fof(f1444,plain,
spl112_11,
inference(avatar_contradiction_clause,[],[f1443]) ).
fof(f1446,plain,
( aElementOf0(sK52,szDzozmdt0(xN))
| ~ spl112_6 ),
inference(forward_demodulation,[],[f987,f1202]) ).
fof(f1449,plain,
( ~ aElementOf0(sK52,szDzozmdt0(xN))
| sP97(sdtlpdtrp0(xe,sK52)) ),
inference(forward_demodulation,[],[f1106,f1202]) ).
fof(f1452,plain,
( sP97(sdtlpdtrp0(xe,sK52))
| ~ spl112_6 ),
inference(forward_subsumption_resolution,[],[f1449,f1446]) ).
fof(f1454,plain,
( sP97(sK51)
| ~ spl112_6 ),
inference(forward_demodulation,[],[f1452,f625]) ).
fof(f1457,plain,
( $false
| ~ spl112_6 ),
inference(forward_subsumption_resolution,[],[f1454,f796]) ).
fof(f1458,plain,
~ spl112_6,
inference(avatar_contradiction_clause,[],[f1457]) ).
cnf(s11,plain,
( spl112_6
| ~ spl112_11 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s37,plain,
spl112_11,
inference(sat_conversion,[],[f1444]) ).
cnf(s39,plain,
~ spl112_6,
inference(sat_conversion,[],[f1458]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s11,s37,s39]) ).
fof(f1459,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM600+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:41:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.74/1.27 % (2379067)Detected formulas, will run a generic FOF schedule.
% 2.74/1.27 % (2379074)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=3336316813:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.27 % (2379075)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1746138083:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.27 % (2379073)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=47756749:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.27 % (2379072)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=3626325887:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.27 % (2379077)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=760535796:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.27 % (2379076)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2226718795:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.27 % (2379078)dis-21_1_sil=8000:lcm=predicate:random_seed=1435231231: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)
% 2.74/1.27 % (2379075)First to succeed.
% 2.74/1.27 % (2379075)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2379067"
% 2.74/1.27 % (2379076)Also succeeded, but the first one will report.
% 2.74/1.27 % (2379077)Also succeeded, but the first one will report.
% 2.74/1.27 % (2379078)Instruction limit reached!
% 2.74/1.27 % (2379078)------------------------------
% 2.74/1.27 % (2379078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.27 % (2379078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.27 % (2379078)CaDiCaL version: 2.1.3
% 2.74/1.27 % (2379078)Termination reason: Instruction limit
% 2.74/1.27 % (2379078)Termination phase: Saturation
% 2.74/1.27 % (2379078)Time elapsed: 0.068 s
% 2.74/1.27 % (2379078)Peak memory usage: 90 MB
% 2.74/1.27 % (2379078)Instructions burned: 130 (million)
% 2.74/1.27 % (2379086)lrs+10_1_sil=8000:sp=occurrence:random_seed=1047997292:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.74/1.27 % (2379086)Also succeeded, but the first one will report.
% 2.74/1.27 % (2379075)Refutation found. Thanks to Tanya!
% 2.74/1.27 % SZS status Theorem for theBenchmark
% 2.74/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.43 % (2379075)------------------------------
% 3.56/1.43 % (2379075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.43 % (2379075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.43 % (2379075)CaDiCaL version: 2.1.3
% 3.56/1.43 % (2379075)Termination reason: Refutation
% 3.56/1.43 % (2379075)Time elapsed: 0.032 s
% 3.56/1.43 % (2379075)Peak memory usage: 90 MB
% 3.56/1.43 % (2379075)Instructions burned: 53 (million)
% 3.56/1.43 % (2379075)------------------------------
% 3.56/1.43 % (2379075)------------------------------
% 3.56/1.43 % (2379067)Success in time 0.426 s
% 3.56/1.43 % Vampire exiting
%------------------------------------------------------------------------------