TSTP Solution File: NUM579+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM579+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 02:50:02 EDT 2024
% Result : Theorem 17.17s 3.12s
% Output : CNFRefutation 17.17s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
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(f18,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aElement0(X0) )
=> ( ~ aElementOf0(X0,X1)
=> sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDiffCons) ).
fof(f21,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(f44,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f80,axiom,
( xK = szszuzczcdt0(xk)
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
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(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f85,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [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,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(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))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| aElementOf0(X2,X1) )
& aElement0(X2) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ( xK = sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
| ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X2,xS) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f86,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [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,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(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))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X2
| aElementOf0(X2,X1) )
& aElement0(X2) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ( xK = sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
| ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X2,xS) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f85]) ).
fof(f96,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(f98,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [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,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(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))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
=> ( ( ! [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
=> ( ( ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| aElementOf0(X6,X1) )
& aElement0(X6) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
=> ( aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ( xK = sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
| ! [X7] :
( aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
=> aElementOf0(X7,xS) ) ) ) ) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f118,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f119,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f118]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f124]) ).
fof(f134,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f148,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f152]) ).
fof(f198,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f203,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,[],[f96]) ).
fof(f204,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,[],[f203]) ).
fof(f205,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(f206,plain,
! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f207,plain,
! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f206]) ).
fof(f210,plain,
? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| aElementOf0(X6,X1) )
& aElement0(X6) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,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))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f211,plain,
? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X6] :
( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| aElementOf0(X6,X1) )
& aElement0(X6) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,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))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f210]) ).
fof(f223,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(f224,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(f225,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,[],[f204,f224,f223]) ).
fof(f231,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,[],[f105]) ).
fof(f232,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,[],[f231]) ).
fof(f233,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,[],[f232]) ).
fof(f234,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK11(X0,X1),X0)
& aElementOf0(sK11(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK11(X0,X1),X0)
& aElementOf0(sK11(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,[sK11])],[f233,f234]) ).
fof(f251,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f332,plain,
! [X0] :
( ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
=> ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
( ! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(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,[sK39])],[f225,f332]) ).
fof(f337,plain,
? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X6] :
( ( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& ~ aElementOf0(X6,X1) )
| ~ aElement0(X6) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| aElementOf0(X6,X1) )
& aElement0(X6) )
| ~ aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,X1) )
& ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,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))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f211]) ).
fof(f338,plain,
? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X7] :
( ~ aElementOf0(X7,xS)
& aElementOf0(X7,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X6] :
( ( aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& ~ aElementOf0(X6,X1) )
| ~ aElement0(X6) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| aElementOf0(X6,X1) )
& aElement0(X6) )
| ~ aElementOf0(X6,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,X1) )
& ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,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))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f337]) ).
fof(f339,plain,
? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,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))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X5,X1) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,X0))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f338]) ).
fof(f340,plain,
( ? [X0] :
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),xS)
& ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
| ~ aElementOf0(X4,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))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X5,X1) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X0))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,X0))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& aSet0(X1) )
& aElementOf0(X0,szNzAzT0) )
=> ( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))),xS)
& ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))),xk))
& sbrdtbr0(X1) = xk
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X5,X1) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK41))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aSet0(X1) )
& aElementOf0(sK41,szNzAzT0) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
( ? [X1] :
( ~ aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( ~ aSubsetOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))),xS)
& ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| aElementOf0(X3,X1) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))),xk))
& sbrdtbr0(X1) = xk
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X5,X1) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK41))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aSet0(X1) )
=> ( ~ aElementOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( ~ aSubsetOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),xS)
& ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3
& ~ aElementOf0(X3,sK42) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| aElementOf0(X3,sK42) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aElementOf0(sK42,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))),xk))
& xk = sbrdtbr0(sK42)
& aSubsetOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X5,sK42) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK41))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aSet0(sK42) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
( ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) )
=> ( ~ aElementOf0(sK43,xS)
& aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
( ~ aElementOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),slbdtsldtrb0(xS,xK))
& ( xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( ~ aSubsetOf0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))),xS)
& ~ aElementOf0(sK43,xS)
& aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& ! [X3] :
( ( aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3
& ~ aElementOf0(X3,sK42) )
| ~ aElement0(X3) )
& ( ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| aElementOf0(X3,sK42) )
& aElement0(X3) )
| ~ aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aElementOf0(sK42,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))),xk))
& xk = sbrdtbr0(sK42)
& aSubsetOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X5,sK42) )
& ! [X6] :
( ( aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X6
| ~ aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElement0(X6) )
& ( ( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
& aElementOf0(X6,sdtlpdtrp0(xN,sK41))
& aElement0(X6) )
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK41)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK41)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41))
& aSet0(sK42)
& aElementOf0(sK41,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43])],[f339,f342,f341,f340]) ).
fof(f344,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f352,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f384,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f387,plain,
! [X0,X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f391,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f398,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f409,plain,
! [X0] :
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f414,plain,
! [X0,X1] :
( sbrdtbr0(X0) = szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1)))
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f490,plain,
aSet0(xS),
inference(cnf_transformation,[],[f198]) ).
fof(f542,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f543,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f558,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f333]) ).
fof(f562,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f566,plain,
! [X2,X0,X1] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f567,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f573,plain,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f343]) ).
fof(f574,plain,
aSet0(sK42),
inference(cnf_transformation,[],[f343]) ).
fof(f575,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f343]) ).
fof(f579,plain,
! [X6] :
( aElementOf0(X6,sdtlpdtrp0(xN,sK41))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f343]) ).
fof(f580,plain,
! [X6] :
( szmzizndt0(sdtlpdtrp0(xN,sK41)) != X6
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f343]) ).
fof(f582,plain,
! [X5] :
( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(X5,sK42) ),
inference(cnf_transformation,[],[f343]) ).
fof(f584,plain,
xk = sbrdtbr0(sK42),
inference(cnf_transformation,[],[f343]) ).
fof(f588,plain,
aSet0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))),
inference(cnf_transformation,[],[f343]) ).
fof(f590,plain,
! [X3] :
( szmzizndt0(sdtlpdtrp0(xN,sK41)) = X3
| aElementOf0(X3,sK42)
| ~ aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f343]) ).
fof(f592,plain,
! [X3] :
( aElementOf0(X3,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) != X3
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f343]) ).
fof(f593,plain,
( xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f343]) ).
fof(f594,plain,
( xK != sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElementOf0(sK43,xS) ),
inference(cnf_transformation,[],[f343]) ).
fof(f640,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK41))) ),
inference(equality_resolution,[],[f592]) ).
fof(f641,plain,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))),
inference(equality_resolution,[],[f580]) ).
cnf(c_49,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f344]) ).
cnf(c_58,plain,
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f352]) ).
cnf(c_89,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f384]) ).
cnf(c_92,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| isFinite0(sdtpldt0(X1,X0)) ),
inference(cnf_transformation,[],[f387]) ).
cnf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f391]) ).
cnf(c_103,plain,
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f398]) ).
cnf(c_115,plain,
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0)
| isFinite0(X0) ),
inference(cnf_transformation,[],[f409]) ).
cnf(c_119,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X0))) = sbrdtbr0(X1) ),
inference(cnf_transformation,[],[f414]) ).
cnf(c_198,plain,
aSet0(xS),
inference(cnf_transformation,[],[f490]) ).
cnf(c_247,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[],[f543]) ).
cnf(c_248,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f542]) ).
cnf(c_264,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f558]) ).
cnf(c_270,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_271,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_272,plain,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X0,sdtlpdtrp0(xN,X2)) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_280,negated_conjecture,
( sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) != xK
| ~ aElementOf0(sK43,xS) ),
inference(cnf_transformation,[],[f594]) ).
cnf(c_281,negated_conjecture,
( sbrdtbr0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) != xK
| aElementOf0(sK43,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f593]) ).
cnf(c_282,negated_conjecture,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK41)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f640]) ).
cnf(c_284,negated_conjecture,
( ~ aElementOf0(X0,sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41))))
| szmzizndt0(sdtlpdtrp0(xN,sK41)) = X0
| aElementOf0(X0,sK42) ),
inference(cnf_transformation,[],[f590]) ).
cnf(c_286,negated_conjecture,
aSet0(sdtpldt0(sK42,szmzizndt0(sdtlpdtrp0(xN,sK41)))),
inference(cnf_transformation,[],[f588]) ).
cnf(c_290,negated_conjecture,
sbrdtbr0(sK42) = xk,
inference(cnf_transformation,[],[f584]) ).
cnf(c_292,negated_conjecture,
( ~ aElementOf0(X0,sK42)
| aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))) ),
inference(cnf_transformation,[],[f582]) ).
cnf(c_294,negated_conjecture,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41)))),
inference(cnf_transformation,[],[f641]) ).
cnf(c_295,negated_conjecture,
( ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK41),szmzizndt0(sdtlpdtrp0(xN,sK41))))
| aElementOf0(X0,sdtlpdtrp0(xN,sK41)) ),
inference(cnf_transformation,[],[f579]) ).
cnf(c_299,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK41)),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f575]) ).
cnf(c_300,negated_conjecture,
aSet0(sK42),
inference(cnf_transformation,[],[f574]) ).
cnf(c_301,negated_conjecture,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f573]) ).
cnf(c_16884,plain,
sdtlpdtrp0(xN,sK41) = sP0_iProver_def,
definition ).
cnf(c_16886,plain,
sdtpldt0(sK42,sP1_iProver_def) = sP2_iProver_def,
definition ).
cnf(c_16888,plain,
sbrdtbr0(sK42) = sP4_iProver_def,
definition ).
cnf(c_16890,plain,
sbrdtbr0(sP2_iProver_def) = sP6_iProver_def,
definition ).
cnf(c_16892,negated_conjecture,
aElementOf0(sK41,szNzAzT0),
inference(demodulation,[status(thm)],[c_301]) ).
cnf(c_16893,negated_conjecture,
aSet0(sK42),
inference(demodulation,[status(thm)],[c_300]) ).
cnf(c_16896,negated_conjecture,
( ~ aElementOf0(X0,sP3_iProver_def)
| aElementOf0(X0,sP0_iProver_def) ),
inference(demodulation,[status(thm)],[c_295]) ).
cnf(c_16897,negated_conjecture,
~ aElementOf0(sP1_iProver_def,sP3_iProver_def),
inference(demodulation,[status(thm)],[c_294]) ).
cnf(c_16899,negated_conjecture,
( ~ aElementOf0(X0,sK42)
| aElementOf0(X0,sP3_iProver_def) ),
inference(demodulation,[status(thm)],[c_292]) ).
cnf(c_16901,negated_conjecture,
sP4_iProver_def = xk,
inference(demodulation,[status(thm)],[c_290,c_16888]) ).
cnf(c_16903,negated_conjecture,
aElementOf0(sP1_iProver_def,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_299]) ).
cnf(c_16905,negated_conjecture,
aSet0(sP2_iProver_def),
inference(demodulation,[status(thm)],[c_286]) ).
cnf(c_16907,negated_conjecture,
( ~ aElementOf0(X0,sP2_iProver_def)
| sP1_iProver_def = X0
| aElementOf0(X0,sK42) ),
inference(demodulation,[status(thm)],[c_284]) ).
cnf(c_16908,negated_conjecture,
( ~ aElement0(sP1_iProver_def)
| aElementOf0(sP1_iProver_def,sP2_iProver_def) ),
inference(demodulation,[status(thm)],[c_282]) ).
cnf(c_16909,negated_conjecture,
( sP6_iProver_def != xK
| aElementOf0(sK43,sP2_iProver_def) ),
inference(demodulation,[status(thm)],[c_281,c_16890]) ).
cnf(c_16910,negated_conjecture,
( sP6_iProver_def != xK
| ~ aElementOf0(sK43,xS) ),
inference(demodulation,[status(thm)],[c_280]) ).
cnf(c_20505,plain,
aElementOf0(sP4_iProver_def,szNzAzT0),
inference(light_normalisation,[status(thm)],[c_248,c_16901]) ).
cnf(c_20535,plain,
szszuzczcdt0(sP4_iProver_def) = xK,
inference(light_normalisation,[status(thm)],[c_247,c_16901]) ).
cnf(c_20570,plain,
sdtlseqdt0(sz00,sK41),
inference(superposition,[status(thm)],[c_16892,c_103]) ).
cnf(c_20697,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| aSet0(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_16884,c_270]) ).
cnf(c_20698,plain,
aSet0(sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_20697,c_16892]) ).
cnf(c_20711,plain,
( ~ aSet0(sP0_iProver_def)
| aElement0(sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_16903,c_49]) ).
cnf(c_20795,plain,
aElement0(sP1_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_20711,c_20698,c_20711]) ).
cnf(c_20797,plain,
aElementOf0(sP1_iProver_def,sP2_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_16908,c_20795]) ).
cnf(c_21000,plain,
( ~ aElementOf0(sP4_iProver_def,szNzAzT0)
| ~ aSet0(sK42)
| isFinite0(sK42) ),
inference(superposition,[status(thm)],[c_16888,c_115]) ).
cnf(c_21005,plain,
isFinite0(sK42),
inference(forward_subsumption_resolution,[status(thm)],[c_21000,c_16893,c_20505]) ).
cnf(c_22373,plain,
( ~ aElement0(sP1_iProver_def)
| ~ aSet0(sK42)
| ~ isFinite0(sK42)
| isFinite0(sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_16886,c_92]) ).
cnf(c_22374,plain,
isFinite0(sP2_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_22373,c_21005,c_16893,c_20795]) ).
cnf(c_22878,plain,
( ~ aSubsetOf0(sP0_iProver_def,X0)
| ~ aSet0(X0)
| aElementOf0(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_16903,c_58]) ).
cnf(c_25881,plain,
( ~ aElement0(X0)
| ~ aSet0(sK42)
| sdtmndt0(sdtpldt0(sK42,X0),X0) = sK42
| aElementOf0(X0,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_89,c_16899]) ).
cnf(c_25922,plain,
( ~ aElement0(X0)
| sdtmndt0(sdtpldt0(sK42,X0),X0) = sK42
| aElementOf0(X0,sP3_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25881,c_16893]) ).
cnf(c_26647,plain,
( ~ aElement0(sP1_iProver_def)
| sdtmndt0(sdtpldt0(sK42,sP1_iProver_def),sP1_iProver_def) = sK42 ),
inference(superposition,[status(thm)],[c_25922,c_16897]) ).
cnf(c_26648,plain,
( ~ aElement0(sP1_iProver_def)
| sdtmndt0(sP2_iProver_def,sP1_iProver_def) = sK42 ),
inference(light_normalisation,[status(thm)],[c_26647,c_16886]) ).
cnf(c_26649,plain,
sdtmndt0(sP2_iProver_def,sP1_iProver_def) = sK42,
inference(forward_subsumption_resolution,[status(thm)],[c_26648,c_20795]) ).
cnf(c_29495,plain,
( ~ aSet0(sP2_iProver_def)
| ~ isFinite0(sP2_iProver_def)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(sP2_iProver_def,sP1_iProver_def))) = sbrdtbr0(sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_20797,c_119]) ).
cnf(c_29544,plain,
( ~ aSet0(sP2_iProver_def)
| ~ isFinite0(sP2_iProver_def)
| xK = sP6_iProver_def ),
inference(light_normalisation,[status(thm)],[c_29495,c_16888,c_16890,c_20535,c_26649]) ).
cnf(c_29545,plain,
xK = sP6_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_29544,c_22374,c_16905]) ).
cnf(c_29772,plain,
( sP6_iProver_def != sP6_iProver_def
| ~ aElementOf0(sK43,xS) ),
inference(demodulation,[status(thm)],[c_16910,c_29545]) ).
cnf(c_29773,plain,
( sP6_iProver_def != sP6_iProver_def
| aElementOf0(sK43,sP2_iProver_def) ),
inference(demodulation,[status(thm)],[c_16909,c_29545]) ).
cnf(c_29775,plain,
aElementOf0(sK43,sP2_iProver_def),
inference(equality_resolution_simp,[status(thm)],[c_29773]) ).
cnf(c_29776,plain,
~ aElementOf0(sK43,xS),
inference(equality_resolution_simp,[status(thm)],[c_29772]) ).
cnf(c_29895,plain,
( sK43 = sP1_iProver_def
| aElementOf0(sK43,sK42) ),
inference(superposition,[status(thm)],[c_29775,c_16907]) ).
cnf(c_29937,plain,
( sK43 = sP1_iProver_def
| aElementOf0(sK43,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_29895,c_16899]) ).
cnf(c_29972,plain,
( sK43 = sP1_iProver_def
| aElementOf0(sK43,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_29937,c_16896]) ).
cnf(c_30304,plain,
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK41)
| ~ aElementOf0(sK41,szNzAzT0)
| aSubsetOf0(sP0_iProver_def,sdtlpdtrp0(xN,X0)) ),
inference(superposition,[status(thm)],[c_16884,c_271]) ).
cnf(c_30317,plain,
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK41)
| aSubsetOf0(sP0_iProver_def,sdtlpdtrp0(xN,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30304,c_16892]) ).
cnf(c_31967,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sK41)
| aSubsetOf0(sP0_iProver_def,xS) ),
inference(superposition,[status(thm)],[c_264,c_30317]) ).
cnf(c_31972,plain,
aSubsetOf0(sP0_iProver_def,xS),
inference(forward_subsumption_resolution,[status(thm)],[c_31967,c_20570,c_96]) ).
cnf(c_32947,plain,
( ~ aSet0(xS)
| aElementOf0(sP1_iProver_def,xS) ),
inference(superposition,[status(thm)],[c_31972,c_22878]) ).
cnf(c_32948,plain,
aElementOf0(sP1_iProver_def,xS),
inference(forward_subsumption_resolution,[status(thm)],[c_32947,c_198]) ).
cnf(c_39589,plain,
( ~ aElementOf0(X0,sP0_iProver_def)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,sK41)
| ~ aElementOf0(sK41,szNzAzT0)
| aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(superposition,[status(thm)],[c_16884,c_272]) ).
cnf(c_39594,plain,
( ~ aElementOf0(X0,sP0_iProver_def)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,sK41)
| aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39589,c_16892]) ).
cnf(c_46176,plain,
( ~ aElementOf0(X0,sP0_iProver_def)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ sdtlseqdt0(sz00,sK41)
| aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_264,c_39594]) ).
cnf(c_46192,plain,
( ~ aElementOf0(X0,sP0_iProver_def)
| aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_46176,c_20570,c_96]) ).
cnf(c_48587,plain,
( sK43 = sP1_iProver_def
| aElementOf0(sK43,xS) ),
inference(superposition,[status(thm)],[c_29972,c_46192]) ).
cnf(c_48594,plain,
sK43 = sP1_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_48587,c_29776]) ).
cnf(c_48751,plain,
~ aElementOf0(sP1_iProver_def,xS),
inference(demodulation,[status(thm)],[c_29776,c_48594]) ).
cnf(c_48757,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_48751,c_32948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM579+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 19:29:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 17.17/3.12 % SZS status Started for theBenchmark.p
% 17.17/3.12 % SZS status Theorem for theBenchmark.p
% 17.17/3.12
% 17.17/3.12 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.17/3.12
% 17.17/3.12 ------ iProver source info
% 17.17/3.12
% 17.17/3.12 git: date: 2024-05-02 19:28:25 +0000
% 17.17/3.12 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.17/3.12 git: non_committed_changes: false
% 17.17/3.12
% 17.17/3.12 ------ Parsing...
% 17.17/3.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.17/3.12
% 17.17/3.12 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 17.17/3.12
% 17.17/3.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.17/3.12
% 17.17/3.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.17/3.12 ------ Proving...
% 17.17/3.12 ------ Problem Properties
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12 clauses 248
% 17.17/3.12 conjectures 21
% 17.17/3.12 EPR 64
% 17.17/3.12 Horn 195
% 17.17/3.12 unary 42
% 17.17/3.12 binary 56
% 17.17/3.12 lits 798
% 17.17/3.12 lits eq 120
% 17.17/3.12 fd_pure 0
% 17.17/3.12 fd_pseudo 0
% 17.17/3.12 fd_cond 12
% 17.17/3.12 fd_pseudo_cond 33
% 17.17/3.12 AC symbols 0
% 17.17/3.12
% 17.17/3.12 ------ Schedule dynamic 5 is on
% 17.17/3.12
% 17.17/3.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12 ------
% 17.17/3.12 Current options:
% 17.17/3.12 ------
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12 ------ Proving...
% 17.17/3.12
% 17.17/3.12
% 17.17/3.12 % SZS status Theorem for theBenchmark.p
% 17.17/3.12
% 17.17/3.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.17/3.12
% 17.17/3.12
%------------------------------------------------------------------------------