TSTP Solution File: NUM630+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM630+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:50:18 EDT 2024
% Result : Theorem 103.92s 14.76s
% Output : CNFRefutation 103.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 105 ( 12 unt; 0 def)
% Number of atoms : 837 ( 125 equ)
% Maximal formula atoms : 47 ( 7 avg)
% Number of connectives : 1033 ( 301 ~; 272 |; 375 &)
% ( 30 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-2 aty)
% Number of variables : 244 ( 0 sgn 194 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f86,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( ( ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) )
& aSet0(X1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| aElementOf0(X2,X1) )
& aElement0(X2) ) )
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X1] :
( ( ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X1) ) ) )
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f109,axiom,
xk = sbrdtbr0(xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(f111,axiom,
( xp = sdtlpdtrp0(xe,xn)
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& szDzizrdt0(xd) = sdtlpdtrp0(xd,xn)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f116,conjecture,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
| aElementOf0(X0,xP) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f117,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
| aElementOf0(X0,xP) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(negated_conjecture,[],[f116]) ).
fof(f127,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(rectify,[],[f81]) ).
fof(f130,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( ( ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) )
& aSet0(X1) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( aElementOf0(X6,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( ( xk = sbrdtbr0(X7)
& ( aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X7) ) ) )
=> aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(X7) ) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( aElementOf0(X11,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) ) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(rectify,[],[f86]) ).
fof(f139,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& aSet0(xP) ),
inference(rectify,[],[f104]) ).
fof(f141,plain,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
=> sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
inference(rectify,[],[f117]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f154,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f155,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f154]) ).
fof(f246,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(ennf_transformation,[],[f127]) ).
fof(f247,plain,
( ! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(flattening,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f255,plain,
( ! [X0] :
( ( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(X1) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& ( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(ennf_transformation,[],[f130]) ).
fof(f256,plain,
( ! [X0] :
( ( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(X1) )
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& ( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(flattening,[],[f255]) ).
fof(f276,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(ennf_transformation,[],[f139]) ).
fof(f279,plain,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,xP) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f282,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(ennf_transformation,[],[f141]) ).
fof(f283,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(flattening,[],[f282]) ).
fof(f295,plain,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f296,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f297,plain,
( ! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(definition_folding,[],[f247,f296,f295]) ).
fof(f302,plain,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f303,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP14(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f304,plain,
! [X0] :
( ! [X7] :
( ( aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| xk != sbrdtbr0(X7)
| ( ~ aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ? [X8] :
( ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X8,X7) )
| ~ aSet0(X7) ) ) )
& ( ( xk = sbrdtbr0(X7)
& aSubsetOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X7) )
& aSet0(X7) )
| ~ aElementOf0(X7,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f305,plain,
! [X0] :
( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| sP14(X0,X1)
| ~ aSet0(X1) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f306,plain,
! [X0] :
( ! [X10] :
( aElementOf0(X10,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X10
& aElementOf0(X10,sdtlpdtrp0(xN,X0))
& aElement0(X10) ) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f307,plain,
( ! [X0] :
( ( sP16(X0)
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& sP15(X0)
& sP17(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X11] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X11)
| ~ aElementOf0(X11,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(definition_folding,[],[f256,f306,f305,f304,f303,f302]) ).
fof(f322,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f323,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f322]) ).
fof(f324,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f323]) ).
fof(f325,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK26(X0,X1),X0)
& aElementOf0(sK26(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK26(X0,X1),X0)
& aElementOf0(sK26(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f324,f325]) ).
fof(f418,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f296]) ).
fof(f419,plain,
! [X0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP9(X0) ),
inference(rectify,[],[f418]) ).
fof(f423,plain,
! [X0] :
( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
=> ( ~ aElementOf0(sK54(X0),szNzAzT0)
& aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f424,plain,
( ! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( ~ aElementOf0(sK54(X0),szNzAzT0)
& aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0)) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0) )
& xS = sdtlpdtrp0(xN,sz00)
& szNzAzT0 = szDzozmdt0(xN)
& aFunction0(xN) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f297,f423]) ).
fof(f442,plain,
! [X0] :
( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( ( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X5
& ~ aElementOf0(X5,X1) )
| ~ aElement0(X5) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) )
| ~ aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| sP14(X0,X1)
| ~ aSet0(X1) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f305]) ).
fof(f443,plain,
! [X0] :
( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( ( aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X5
& ~ aElementOf0(X5,X1) )
| ~ aElement0(X5) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X5
| aElementOf0(X5,X1) )
& aElement0(X5) )
| ~ aElementOf0(X5,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X6] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| sP14(X0,X1)
| ~ aSet0(X1) )
| ~ sP16(X0) ),
inference(flattening,[],[f442]) ).
fof(f444,plain,
! [X0] :
( ! [X1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
& ~ aElementOf0(X2,X1) )
| ~ aElement0(X2) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| aElementOf0(X2,X1) )
& aElement0(X2) )
| ~ aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| sP14(X0,X1)
| ~ aSet0(X1) )
| ~ sP16(X0) ),
inference(rectify,[],[f443]) ).
fof(f449,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X4,X1) ) ) )
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP14(X0,X1) ),
inference(nnf_transformation,[],[f303]) ).
fof(f450,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X2,X1) ) ) )
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP14(X0,X1) ),
inference(rectify,[],[f449]) ).
fof(f451,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK58(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK58(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f452,plain,
! [X0,X1] :
( ( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& ( sbrdtbr0(X1) != xk
| ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(sK58(X0,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(sK58(X0,X1),X1) ) )
& sP13(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
| ~ sP14(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f450,f451]) ).
fof(f456,plain,
( ! [X0] :
( ( sP16(X0)
& slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk) = szDzozmdt0(sdtlpdtrp0(xC,X0))
& sP15(X0)
& sP17(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aFunction0(sdtlpdtrp0(xC,X0)) )
| ~ aElementOf0(X0,szNzAzT0) )
& szNzAzT0 = szDzozmdt0(xC)
& aFunction0(xC) ),
inference(rectify,[],[f307]) ).
fof(f510,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( ( aElementOf0(X0,xP)
| szmzizndt0(xQ) = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(nnf_transformation,[],[f276]) ).
fof(f511,plain,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( ( aElementOf0(X0,xP)
| szmzizndt0(xQ) = X0
| ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) )
& ( ( szmzizndt0(xQ) != X0
& aElementOf0(X0,xQ)
& aElement0(X0) )
| ~ aElementOf0(X0,xP) ) )
& ! [X1] :
( sdtlseqdt0(szmzizndt0(xQ),X1)
| ~ aElementOf0(X1,xQ) )
& aSet0(xP) ),
inference(flattening,[],[f510]) ).
fof(f516,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X1
& ~ aElementOf0(X1,xP) )
| ~ aElement0(X1) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(nnf_transformation,[],[f283]) ).
fof(f517,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X1
& ~ aElementOf0(X1,xP) )
| ~ aElement0(X1) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X1
| aElementOf0(X1,xP) )
& aElement0(X1) )
| ~ aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ) ),
inference(flattening,[],[f516]) ).
fof(f518,plain,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
& ~ aElementOf0(X0,xP) )
| ~ aElement0(X0) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
| aElementOf0(X0,xP) )
& aElement0(X0) )
| ~ aElementOf0(X0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xn)) ) ),
inference(rectify,[],[f517]) ).
fof(f526,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f533,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f725,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f419]) ).
fof(f734,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f424]) ).
fof(f736,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f424]) ).
fof(f739,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f740,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f782,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| sP14(X0,X1)
| ~ aSet0(X1)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f444]) ).
fof(f796,plain,
! [X0,X1] :
( sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f452]) ).
fof(f807,plain,
! [X0] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f456]) ).
fof(f811,plain,
! [X0] :
( sP16(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f456]) ).
fof(f929,plain,
aSet0(xP),
inference(cnf_transformation,[],[f511]) ).
fof(f943,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f948,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f952,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f279]) ).
fof(f969,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f518]) ).
cnf(c_59,plain,
( ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| aSet0(X0) ),
inference(cnf_transformation,[],[f526]) ).
cnf(c_63,plain,
( ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1) ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_250,plain,
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f725]) ).
cnf(c_261,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f736]) ).
cnf(c_263,plain,
( ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK54(X0),sdtlpdtrp0(xN,X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f734]) ).
cnf(c_267,plain,
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f740]) ).
cnf(c_268,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f739]) ).
cnf(c_306,plain,
( ~ aSet0(X0)
| ~ sP16(X1)
| sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,X1)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X0)
| sP14(X1,X0) ),
inference(cnf_transformation,[],[f782]) ).
cnf(c_321,plain,
( sbrdtbr0(X0) != xk
| ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ sP14(X1,X0) ),
inference(cnf_transformation,[],[f796]) ).
cnf(c_332,plain,
( ~ aElementOf0(X0,szNzAzT0)
| sP16(X0) ),
inference(cnf_transformation,[],[f811]) ).
cnf(c_336,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f807]) ).
cnf(c_465,plain,
aSet0(xP),
inference(cnf_transformation,[],[f929]) ).
cnf(c_473,plain,
sbrdtbr0(xP) = xk,
inference(cnf_transformation,[],[f943]) ).
cnf(c_476,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f948]) ).
cnf(c_481,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f952]) ).
cnf(c_493,negated_conjecture,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f969]) ).
cnf(c_856,plain,
( ~ aSubsetOf0(X2,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_59,c_63]) ).
cnf(c_857,plain,
( ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1) ),
inference(renaming,[status(thm)],[c_856]) ).
cnf(c_865,plain,
( ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(global_subsumption_just,[status(thm)],[c_263,c_267,c_268,c_261]) ).
cnf(c_4367,plain,
( X0 != X1
| ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(resolution_lifted,[status(thm)],[c_865,c_250]) ).
cnf(c_4368,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(unflattening,[status(thm)],[c_4367]) ).
cnf(c_4442,plain,
( X0 != X1
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X2)
| sdtlpdtrp0(xc,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X0)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X2)
| sP14(X0,X2) ),
inference(resolution_lifted,[status(thm)],[c_306,c_332]) ).
cnf(c_4443,plain,
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(X1)
| sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| sP14(X0,X1) ),
inference(unflattening,[status(thm)],[c_4442]) ).
cnf(c_27296,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(instantiation,[status(thm)],[c_336]) ).
cnf(c_27376,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(instantiation,[status(thm)],[c_4368]) ).
cnf(c_27849,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),X0)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(X0)
| ~ aSet0(xP)
| aSubsetOf0(xP,X0) ),
inference(instantiation,[status(thm)],[c_857]) ).
cnf(c_27858,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ aSet0(X0)
| sdtlpdtrp0(xc,sdtpldt0(X0,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),X0)
| sP14(xn,X0) ),
inference(instantiation,[status(thm)],[c_4443]) ).
cnf(c_29879,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(xP)
| aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
inference(instantiation,[status(thm)],[c_27849]) ).
cnf(c_29913,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ aSet0(xP)
| sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
| sP14(xn,xP) ),
inference(instantiation,[status(thm)],[c_27858]) ).
cnf(c_36989,plain,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ sP14(xn,xP) ),
inference(instantiation,[status(thm)],[c_321]) ).
cnf(c_36991,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_36989,c_29913,c_29879,c_27376,c_27296,c_493,c_481,c_473,c_476,c_465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM630+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 19:58:05 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 103.92/14.76 % SZS status Started for theBenchmark.p
% 103.92/14.76 % SZS status Theorem for theBenchmark.p
% 103.92/14.76
% 103.92/14.76 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 103.92/14.76
% 103.92/14.76 ------ iProver source info
% 103.92/14.76
% 103.92/14.76 git: date: 2024-05-02 19:28:25 +0000
% 103.92/14.76 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 103.92/14.76 git: non_committed_changes: false
% 103.92/14.76
% 103.92/14.76 ------ Parsing...
% 103.92/14.76 ------ Clausification by vclausify_rel & Parsing by iProver...
% 103.92/14.76
% 103.92/14.76 ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 103.92/14.76
% 103.92/14.76 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 103.92/14.76
% 103.92/14.76 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 103.92/14.76 ------ Proving...
% 103.92/14.76 ------ Problem Properties
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76 clauses 404
% 103.92/14.76 conjectures 7
% 103.92/14.76 EPR 78
% 103.92/14.76 Horn 327
% 103.92/14.76 unary 72
% 103.92/14.76 binary 111
% 103.92/14.76 lits 1219
% 103.92/14.76 lits eq 177
% 103.92/14.76 fd_pure 0
% 103.92/14.76 fd_pseudo 0
% 103.92/14.76 fd_cond 13
% 103.92/14.76 fd_pseudo_cond 39
% 103.92/14.76 AC symbols 0
% 103.92/14.76
% 103.92/14.76 ------ Input Options Time Limit: Unbounded
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76 ------
% 103.92/14.76 Current options:
% 103.92/14.76 ------
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76 ------ Proving...
% 103.92/14.76
% 103.92/14.76
% 103.92/14.76 % SZS status Theorem for theBenchmark.p
% 103.92/14.76
% 103.92/14.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 103.92/14.76
% 103.92/14.76
%------------------------------------------------------------------------------