%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM628+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 : n014.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 12:16:03 PM UTC 2026
% Result : Theorem 8.20s 3.14s
% Output : Refutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 150 ( 41 unt; 10 def)
% Number of atoms : 902 ( 173 equ)
% Maximal formula atoms : 47 ( 6 avg)
% Number of connectives : 1075 ( 323 ~; 289 |; 382 &)
% ( 26 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 2 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 18 con; 0-2 aty)
% Number of variables : 248 ( 0 sgn 227 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(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(f90,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( ( aSet0(X2)
& ( ( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& sbrdtbr0(X2) = xk )
| aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4618) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
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(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
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/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
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/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f112,axiom,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5321) ).
fof(f113,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f114,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f115,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f125,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(f128,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(f137,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(f138,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(flattening,[],[f115]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f151,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f152,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f151]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f243,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,[],[f125]) ).
fof(f244,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,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f252,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,[],[f128]) ).
fof(f253,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,[],[f252]) ).
fof(f259,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1
| ~ aSet0(X2)
| ( ( ( ? [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X3,X2) )
& ~ aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X2) != xk )
& ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f260,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = X1
| ~ aSet0(X2)
| ( ( ( ? [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X3,X2) )
& ~ aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X2) != xk )
& ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f259]) ).
fof(f261,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f262,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(f263,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,[],[f262]) ).
fof(f267,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f272,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f273,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,[],[f137]) ).
fof(f276,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f113]) ).
fof(f288,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f289,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f290,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f244,f289,f288]) ).
fof(f295,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 ) )
| ~ sP13(X0) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f296,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))))
& sP13(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP14(X0,X6) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f297,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)
| sP14(X0,X6) )
| ~ sP15(X0) ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f298,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 ) )
| ~ sP16(X0) ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f299,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 ) )
| ~ sP17(X0) ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f300,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))))
& sP17(X0)
& sP16(X0)
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& sP15(X0) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f253,f299,f298,f297,f296,f295]) ).
fof(f314,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f145]) ).
fof(f315,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f314]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f315]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK26(X0,X1),X0)
& aElementOf0(sK26(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(X2,sK26(X0,X1))],[f316]) ).
fof(f385,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f289]) ).
fof(f386,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(rectify,[],[f385]) ).
fof(f390,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK54(X0),szNzAzT0)
& aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X1,sK54(X0))],[f290]) ).
fof(f409,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)
| sP14(X0,X6) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f297]) ).
fof(f410,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)
| sP14(X0,X6) )
| ~ sP15(X0) ),
inference(flattening,[],[f409]) ).
fof(f411,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)
| sP14(X0,X1) )
| ~ sP15(X0) ),
inference(rectify,[],[f410]) ).
fof(f412,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))))
& sP13(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) ) )
| ~ sP14(X0,X6) ),
inference(nnf_transformation,[],[f296]) ).
fof(f413,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))))
& sP13(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ sP14(X0,X1) ),
inference(rectify,[],[f412]) ).
fof(f414,plain,
! [X0,X1] :
( ( ( ( ~ aElementOf0(sK58(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK58(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))))
& sP13(X0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ sP14(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(X2,sK58(X0,X1))],[f413]) ).
fof(f444,plain,
! [X0] :
( ( aElementOf0(sK65(X0),xT)
& ! [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = sK65(X0)
| ~ aSet0(X2)
| ( ( ( ~ aElementOf0(sK66(X0,X2),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK66(X0,X2),X2)
& ~ aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X2) != xk )
& ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65,sK66]),skolemize(X1,sK65(X0)),skolemize(X3,sK66(X0,X2))],[f260]) ).
fof(f445,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK67(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK67(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,[sK67]),skolemize(X2,sK67(X0,X1))],[f263]) ).
fof(f458,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,[],[f273]) ).
fof(f459,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,[],[f458]) ).
fof(f469,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f317]) ).
fof(f475,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f500,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f662,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f664,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f666,plain,
! [X0] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f386]) ).
fof(f673,plain,
! [X0] :
( sP9(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f390]) ).
fof(f679,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f680,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f725,plain,
! [X0,X1] :
( sP14(X0,X1)
| ~ aSet0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f411]) ).
fof(f737,plain,
! [X0,X1] :
( sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
fof(f744,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP15(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f806,plain,
! [X2,X0] :
( sbrdtbr0(X2) != xk
| ~ aSet0(X2)
| ~ aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2) = sK65(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f444]) ).
fof(f810,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f816,plain,
! [X0,X1] :
( sbrdtbr0(X1) != xk
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f445]) ).
fof(f857,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f267]) ).
fof(f868,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f272]) ).
fof(f871,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f459]) ).
fof(f877,plain,
aSet0(xP),
inference(cnf_transformation,[],[f459]) ).
fof(f878,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f885,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f887,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f888,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f892,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xd,xn),
inference(cnf_transformation,[],[f112]) ).
fof(f893,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f276]) ).
fof(f895,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(cnf_transformation,[],[f138]) ).
fof(f955,definition,
sF73 = sdtlpdtrp0(xd,xn),
introduced(definition,[new_symbols(definition,[sF73])],[function_definition]) ).
fof(f956,plain,
sdtlpdtrp0(xd,xn) = sF73,
inference(reorient_equations,[],[f955]) ).
fof(f957,definition,
sF74 = sdtlpdtrp0(xc,xQ),
introduced(definition,[new_symbols(definition,[sF74])],[function_definition]) ).
fof(f958,plain,
sdtlpdtrp0(xc,xQ) = sF74,
inference(reorient_equations,[],[f957]) ).
fof(f959,plain,
sF73 != sF74,
inference(definition_folding,[],[f895,f958,f956]) ).
fof(f963,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f673,f680]) ).
fof(f992,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(forward_subsumption_resolution,[],[f963,f679]) ).
fof(f998,plain,
szDzizrdt0(xd) = sF73,
inference(superposition,[],[f956,f892]) ).
fof(f999,plain,
sP9(xn),
inference(resolution,[],[f992,f888]) ).
fof(f1001,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[],[f810,f888]) ).
fof(f1003,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[],[f1001,f887]) ).
fof(f1067,plain,
sP15(xn),
inference(resolution,[],[f744,f888]) ).
fof(f1069,plain,
xP = sdtmndt0(xQ,xp),
inference(superposition,[],[f871,f868]) ).
fof(f1140,plain,
( xQ = sdtpldt0(sdtmndt0(xQ,xp),xp)
| ~ aSet0(xQ) ),
inference(resolution,[],[f500,f878]) ).
fof(f1141,plain,
xQ = sdtpldt0(sdtmndt0(xQ,xp),xp),
inference(forward_subsumption_resolution,[],[f1140,f857]) ).
fof(f1165,plain,
xQ = sdtpldt0(xP,xp),
inference(forward_demodulation,[],[f1141,f1069]) ).
fof(f1192,plain,
! [X0] :
( xk != xk
| ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sK65(X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f806,f885]) ).
fof(f1193,plain,
! [X0] :
( ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sK65(X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(trivial_inequality_removal,[],[f1192]) ).
fof(f1194,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sK65(X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1193,f877]) ).
fof(f1204,plain,
( sK65(xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1194,f893]) ).
fof(f1205,plain,
sK65(xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(forward_subsumption_resolution,[],[f1204,f888]) ).
fof(f1210,plain,
! [X0] :
( xk != xk
| ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f816,f885]) ).
fof(f1211,plain,
! [X0] :
( ~ aSet0(xP)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(trivial_inequality_removal,[],[f1210]) ).
fof(f1212,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),xP)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1211,f877]) ).
fof(f1213,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1212,f893]) ).
fof(f1214,plain,
sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(forward_subsumption_resolution,[],[f1213,f888]) ).
fof(f1215,plain,
sdtlpdtrp0(xd,xn) = sK65(xn),
inference(forward_demodulation,[],[f1214,f1205]) ).
fof(f1216,plain,
szDzizrdt0(xd) = sK65(xn),
inference(forward_demodulation,[],[f1215,f892]) ).
fof(f1217,plain,
sF73 = sK65(xn),
inference(forward_demodulation,[],[f1216,f998]) ).
fof(f4122,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aSet0(X0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ sP9(X1) ),
inference(resolution,[],[f475,f662]) ).
fof(f4165,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ sP9(X1) ),
inference(forward_subsumption_resolution,[],[f4122,f469]) ).
fof(f4190,plain,
! [X0,X1] :
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ sP9(X1) ),
inference(forward_subsumption_resolution,[],[f4165,f664]) ).
fof(f4214,plain,
! [X0,X1] :
( aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ sP9(X1) ),
inference(forward_subsumption_resolution,[],[f4190,f666]) ).
fof(f5459,plain,
! [X0] :
( xk != xk
| ~ aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP14(X0,xP) ),
inference(superposition,[],[f737,f885]) ).
fof(f5461,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP14(X0,xP) ),
inference(trivial_inequality_removal,[],[f5459]) ).
fof(f5462,plain,
! [X0] :
( ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP14(X0,xP)
| ~ sP9(X0) ),
inference(resolution,[],[f5461,f4214]) ).
fof(f5475,definition,
( spl75_209
<=> sP14(xn,xP) ),
introduced(definition,[new_symbols(definition,[spl75_209])],[avatar_definition]) ).
fof(f5476,plain,
( sP14(xn,xP)
| ~ spl75_209 ),
inference(avatar_component_clause,[],[f5475]) ).
fof(f5477,plain,
( ~ sP14(xn,xP)
| spl75_209 ),
inference(avatar_component_clause,[],[f5475]) ).
fof(f7151,plain,
( ~ aSet0(xP)
| sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ sP15(xn)
| spl75_209 ),
inference(resolution,[],[f5477,f725]) ).
fof(f7152,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ sP15(xn)
| spl75_209 ),
inference(forward_subsumption_resolution,[],[f7151,f877]) ).
fof(f7153,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| spl75_209 ),
inference(forward_subsumption_resolution,[],[f7152,f1067]) ).
fof(f7154,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,sdtpldt0(xP,xp))
| spl75_209 ),
inference(forward_demodulation,[],[f7153,f1003]) ).
fof(f7155,plain,
( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| spl75_209 ),
inference(forward_demodulation,[],[f7154,f1165]) ).
fof(f7156,plain,
( sdtlpdtrp0(xc,xQ) = sK65(xn)
| spl75_209 ),
inference(forward_demodulation,[],[f7155,f1205]) ).
fof(f7157,plain,
( sdtlpdtrp0(xc,xQ) = sF73
| spl75_209 ),
inference(forward_demodulation,[],[f7156,f1217]) ).
fof(f7158,plain,
( sF73 = sF74
| spl75_209 ),
inference(superposition,[],[f7157,f958]) ).
fof(f7167,plain,
( $false
| spl75_209 ),
inference(forward_subsumption_resolution,[],[f7158,f959]) ).
fof(f7168,plain,
spl75_209,
inference(avatar_contradiction_clause,[],[f7167]) ).
fof(f7945,plain,
( ~ sP14(xn,xP)
| ~ sP9(xn) ),
inference(resolution,[],[f5462,f893]) ).
fof(f7948,plain,
( ~ sP9(xn)
| ~ spl75_209 ),
inference(forward_subsumption_resolution,[],[f7945,f5476]) ).
fof(f7949,plain,
( $false
| ~ spl75_209 ),
inference(forward_subsumption_resolution,[],[f7948,f999]) ).
fof(f7950,plain,
~ spl75_209,
inference(avatar_contradiction_clause,[],[f7949]) ).
cnf(s306,plain,
spl75_209,
inference(sat_conversion,[],[f7168]) ).
cnf(s344,plain,
~ spl75_209,
inference(sat_conversion,[],[f7950]) ).
cnf(s355,plain,
$false,
inference(rat,[],[s306,s344]) ).
fof(f7951,plain,
$false,
inference(avatar_sat_refutation,[],[s355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM628+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n014.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 20:50:17 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 15.60/3.08 % (1146262)Detected formulas, will run a generic FOF schedule.
% 15.60/3.08 % (1146268)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=4180990382:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 15.60/3.08 % (1146273)dis-21_1_sil=8000:lcm=predicate:random_seed=472727230: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)
% 15.60/3.08 % (1146269)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=3769466806:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 15.60/3.08 % (1146271)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3928611314:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 15.60/3.08 % (1146267)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=3286472129:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 15.60/3.08 % (1146270)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1138691215:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 15.60/3.08 % (1146272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2605773670:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 15.60/3.08 % (1146273)Instruction limit reached!
% 15.60/3.08 % (1146273)------------------------------
% 15.60/3.08 % (1146273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.60/3.08 % (1146273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.60/3.08 % (1146273)CaDiCaL version: 2.1.3
% 15.60/3.08 % (1146273)Termination reason: Instruction limit
% 15.60/3.08 % (1146273)Termination phase: Saturation
% 15.60/3.08 % (1146273)Time elapsed: 0.067 s
% 15.60/3.08 % (1146273)Peak memory usage: 90 MB
% 15.60/3.08 % (1146273)Instructions burned: 130 (million)
% 15.60/3.08 % (1146270)Instruction limit reached!
% 15.60/3.08 % (1146270)------------------------------
% 15.60/3.08 % (1146270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.60/3.08 % (1146270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.60/3.08 % (1146270)CaDiCaL version: 2.1.3
% 15.60/3.08 % (1146270)Termination reason: Instruction limit
% 15.60/3.08 % (1146270)Termination phase: Saturation
% 15.60/3.08 % (1146270)Time elapsed: 0.068 s
% 15.60/3.08 % (1146270)Peak memory usage: 90 MB
% 15.60/3.08 % (1146270)Instructions burned: 110 (million)
% 15.60/3.08 % (1146271)Instruction limit reached!
% 15.60/3.08 % (1146271)------------------------------
% 15.60/3.08 % (1146271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.60/3.08 % (1146271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.60/3.08 % (1146271)CaDiCaL version: 2.1.3
% 15.60/3.08 % (1146271)Termination reason: Instruction limit
% 15.60/3.08 % (1146271)Termination phase: Saturation
% 15.60/3.08 % (1146271)Time elapsed: 0.074 s
% 15.60/3.08 % (1146271)Peak memory usage: 89 MB
% 15.60/3.08 % (1146271)Instructions burned: 119 (million)
% 15.60/3.08 % (1146272)Instruction limit reached!
% 15.60/3.08 % (1146272)------------------------------
% 15.60/3.08 % (1146272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.60/3.08 % (1146272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.60/3.08 % (1146272)CaDiCaL version: 2.1.3
% 15.60/3.08 % (1146272)Termination reason: Instruction limit
% 15.60/3.08 % (1146272)Termination phase: Saturation
% 15.60/3.08 % (1146272)Time elapsed: 0.099 s
% 15.60/3.08 % (1146272)Peak memory usage: 90 MB
% 15.60/3.08 % (1146272)Instructions burned: 140 (million)
% 15.60/3.08 % (1146281)lrs+10_1_sil=8000:sp=occurrence:random_seed=3702144367:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 15.60/3.08 % (1146283)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2458315114:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 15.60/3.08 % (1146282)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2701867562:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 15.60/3.08 % (1146282)Refutation not found, incomplete strategy
% 15.60/3.08 % (1146282)------------------------------
% 15.60/3.08 % (1146282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.60/3.08 % (1146282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146282)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146282)Termination reason: Refutation not found, incomplete strategy
% 8.20/3.14 % (1146282)Time elapsed: 0.008 s
% 8.20/3.14 % (1146282)Peak memory usage: 89 MB
% 8.20/3.14 % (1146282)Instructions burned: 11 (million)
% 8.20/3.14 % (1146284)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=1260429141:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.20/3.14 % (1146284)Instruction limit reached!
% 8.20/3.14 % (1146284)------------------------------
% 8.20/3.14 % (1146284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146284)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146284)Termination reason: Instruction limit
% 8.20/3.14 % (1146284)Termination phase: Saturation
% 8.20/3.14 % (1146284)Time elapsed: 0.148 s
% 8.20/3.14 % (1146284)Peak memory usage: 92 MB
% 8.20/3.14 % (1146284)Instructions burned: 249 (million)
% 8.20/3.14 % (1146281)Instruction limit reached!
% 8.20/3.14 % (1146281)------------------------------
% 8.20/3.14 % (1146281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146281)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146281)Termination reason: Instruction limit
% 8.20/3.14 % (1146281)Termination phase: Saturation
% 8.20/3.14 % (1146281)Time elapsed: 0.173 s
% 8.20/3.14 % (1146281)Peak memory usage: 92 MB
% 8.20/3.14 % (1146281)Instructions burned: 286 (million)
% 8.20/3.14 % (1146283)Instruction limit reached!
% 8.20/3.14 % (1146283)------------------------------
% 8.20/3.14 % (1146283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146283)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146283)Termination reason: Instruction limit
% 8.20/3.14 % (1146283)Termination phase: Saturation
% 8.20/3.14 % (1146283)Time elapsed: 0.228 s
% 8.20/3.14 % (1146283)Peak memory usage: 92 MB
% 8.20/3.14 % (1146283)Instructions burned: 325 (million)
% 8.20/3.14 % (1146282)------------------------------
% 8.20/3.14 % (1146282)------------------------------
% 8.20/3.14 % (1146289)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1658524241:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 8.20/3.14 % (1146290)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=116018155:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.20/3.14 % (1146291)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2410028577:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.20/3.14 % (1146292)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2132856636:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.20/3.14 % (1146291)Instruction limit reached!
% 8.20/3.14 % (1146291)------------------------------
% 8.20/3.14 % (1146291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146291)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146291)Termination reason: Instruction limit
% 8.20/3.14 % (1146291)Termination phase: Saturation
% 8.20/3.14 % (1146291)Time elapsed: 0.073 s
% 8.20/3.14 % (1146291)Peak memory usage: 91 MB
% 8.20/3.14 % (1146291)Instructions burned: 115 (million)
% 8.20/3.14 % (1146292)Instruction limit reached!
% 8.20/3.14 % (1146292)------------------------------
% 8.20/3.14 % (1146292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146292)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146292)Termination reason: Instruction limit
% 8.20/3.14 % (1146292)Termination phase: Saturation
% 8.20/3.14 % (1146292)Time elapsed: 0.068 s
% 8.20/3.14 % (1146292)Peak memory usage: 89 MB
% 8.20/3.14 % (1146292)Instructions burned: 128 (million)
% 8.20/3.14 % (1146289)Instruction limit reached!
% 8.20/3.14 % (1146289)------------------------------
% 8.20/3.14 % (1146289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146289)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146289)Termination reason: Instruction limit
% 8.20/3.14 % (1146289)Termination phase: Saturation
% 8.20/3.14 % (1146289)Time elapsed: 0.175 s
% 8.20/3.14 % (1146289)Peak memory usage: 90 MB
% 8.20/3.14 % (1146289)Instructions burned: 294 (million)
% 8.20/3.14 % (1146297)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=800368811:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.20/3.14 % (1146298)lrs+10_1_sil=8000:sp=occurrence:random_seed=3686622089:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.20/3.14 % (1146299)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=126933708:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.20/3.14 % (1146297)Instruction limit reached!
% 8.20/3.14 % (1146297)------------------------------
% 8.20/3.14 % (1146297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146297)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146297)Termination reason: Instruction limit
% 8.20/3.14 % (1146297)Termination phase: Saturation
% 8.20/3.14 % (1146297)Time elapsed: 0.072 s
% 8.20/3.14 % (1146297)Peak memory usage: 89 MB
% 8.20/3.14 % (1146297)Instructions burned: 115 (million)
% 8.20/3.14 % (1146303)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=658737299:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 8.20/3.14 % (1146299)Instruction limit reached!
% 8.20/3.14 % (1146299)------------------------------
% 8.20/3.14 % (1146299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146299)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146299)Termination reason: Instruction limit
% 8.20/3.14 % (1146299)Termination phase: Saturation
% 8.20/3.14 % (1146299)Time elapsed: 0.277 s
% 8.20/3.14 % (1146299)Peak memory usage: 93 MB
% 8.20/3.14 % (1146299)Instructions burned: 437 (million)
% 8.20/3.14 % (1146305)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2949147161:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 8.20/3.14 % (1146298)Instruction limit reached!
% 8.20/3.14 % (1146298)------------------------------
% 8.20/3.14 % (1146298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146298)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146298)Termination reason: Instruction limit
% 8.20/3.14 % (1146298)Termination phase: Saturation
% 8.20/3.14 % (1146298)Time elapsed: 0.529 s
% 8.20/3.14 % (1146298)Peak memory usage: 98 MB
% 8.20/3.14 % (1146298)Instructions burned: 908 (million)
% 8.20/3.14 % (1146305)Instruction limit reached!
% 8.20/3.14 % (1146305)------------------------------
% 8.20/3.14 % (1146305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146305)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146305)Termination reason: Instruction limit
% 8.20/3.14 % (1146305)Termination phase: Saturation
% 8.20/3.14 % (1146305)Time elapsed: 0.079 s
% 8.20/3.14 % (1146305)Peak memory usage: 91 MB
% 8.20/3.14 % (1146305)Instructions burned: 135 (million)
% 8.20/3.14 % (1146307)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=268765100:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 8.20/3.14 % (1146308)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4082129878:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 8.20/3.14 % (1146290)First to succeed.
% 8.20/3.14 % (1146290)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1146262"
% 8.20/3.14 % (1146307)Instruction limit reached!
% 8.20/3.14 % (1146307)------------------------------
% 8.20/3.14 % (1146307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/3.14 % (1146307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/3.14 % (1146307)CaDiCaL version: 2.1.3
% 8.20/3.14 % (1146307)Termination reason: Instruction limit
% 8.20/3.14 % (1146307)Termination phase: Saturation
% 8.20/3.14 % (1146307)Time elapsed: 0.322 s
% 8.20/3.14 % (1146307)Peak memory usage: 94 MB
% 8.20/3.14 % (1146307)Instructions burned: 593 (million)
% 8.20/3.14 % (1146311)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=620376112:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2979 on theBenchmark for (2979ds/125Mi)
% 8.20/3.14 % (1146290)Refutation found. Thanks to Tanya!
% 8.20/3.14 % SZS status Theorem for theBenchmark
% 8.20/3.14 % SZS output start Proof for theBenchmark
% See solution above
% 16.52/3.33 % (1146290)------------------------------
% 16.52/3.33 % (1146290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.52/3.33 % (1146290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.52/3.33 % (1146290)CaDiCaL version: 2.1.3
% 16.52/3.33 % (1146290)Termination reason: Refutation
% 16.52/3.33 % (1146290)Time elapsed: 1.253 s
% 16.52/3.33 % (1146290)Peak memory usage: 140 MB
% 16.52/3.33 % (1146290)Instructions burned: 1879 (million)
% 16.52/3.33 % (1146290)------------------------------
% 16.52/3.33 % (1146290)------------------------------
% 16.52/3.33 % (1146262)Success in time 2.255 s
% 16.52/3.33 % Vampire exiting
%------------------------------------------------------------------------------