%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM572+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:26:04 PM UTC 2026
% Result : Theorem 145.85s 32.48s
% Output : CNFRefutation 145.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 199 ( 19 unt; 2 def)
% Number of atoms : 850 ( 138 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1046 ( 395 ~; 425 |; 167 &)
% ( 10 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 292 ( 0 sgn 274 !; 18 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(f34,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(f39,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
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))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
& 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)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f83,conjecture,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2,X3] :
( ( aElementOf0(X3,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X3,X2)
=> ( iLess0(X2,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X3))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X2))
=> aElementOf0(X4,sdtlpdtrp0(xN,X3)) ) ) ) ) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f84,negated_conjecture,
~ ! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2,X3] :
( ( aElementOf0(X3,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X3,X2)
=> ( iLess0(X2,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X3))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X2))
=> aElementOf0(X4,sdtlpdtrp0(xN,X3)) ) ) ) ) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f83]) ).
fof(f94,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))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,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))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(rectify,[],[f81]) ).
fof(f95,plain,
~ ! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2,X3] :
( ( aElementOf0(X3,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X3,X2)
=> ( iLess0(X2,X0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X3))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X2))
=> aElementOf0(X4,sdtlpdtrp0(xN,X3)) ) ) ) ) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ! [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X0))
=> aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) ) ) ) ),
inference(rectify,[],[f84]) ).
fof(f102,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f105,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f128,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(ennf_transformation,[],[f27]) ).
fof(f129,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(flattening,[],[f128]) ).
fof(f131,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f134,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(flattening,[],[f133]) ).
fof(f136,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f142,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f200,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))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,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))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(ennf_transformation,[],[f94]) ).
fof(f201,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))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,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))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(flattening,[],[f200]) ).
fof(f202,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)) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f203,plain,
? [X0,X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(X1,X0)
& ! [X2,X3] :
( ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X3,X2)
| ~ iLess0(X2,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X3))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,X2))
| aElementOf0(X4,sdtlpdtrp0(xN,X3)) ) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ? [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f204,plain,
? [X0,X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(X1,X0)
& ! [X2,X3] :
( ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X3,X2)
| ~ iLess0(X2,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X3))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,X2))
| aElementOf0(X4,sdtlpdtrp0(xN,X3)) ) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ? [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) ),
inference(flattening,[],[f203]) ).
fof(f223,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f224,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f223]) ).
fof(f225,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f224]) ).
fof(f226,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK11(X0,X1),X1)
& ~ aElementOf0(sK11(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f225]) ).
fof(f239,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) )
| X0 = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f129]) ).
fof(f240,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( ( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f294,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& 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)) ) ),
inference(nnf_transformation,[],[f217]) ).
fof(f295,plain,
! [X0] :
( ~ sP9(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)))
& sP8(X0)
& 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)) ) ),
inference(rectify,[],[f294]) ).
fof(f299,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK39(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f218]) ).
fof(f300,plain,
? [X0,X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(X1,X0)
& ! [X3,X4] :
( ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(X4,X3)
| ~ iLess0(X3,X0)
| ( aSubsetOf0(sdtlpdtrp0(xN,X3),sdtlpdtrp0(xN,X4))
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| aElementOf0(X5,sdtlpdtrp0(xN,X4)) ) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ? [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ),
inference(rectify,[],[f204]) ).
fof(f301,plain,
( aElementOf0(sK41,szNzAzT0)
& aElementOf0(sK40,szNzAzT0)
& sdtlseqdt0(sK41,sK40)
& ! [X3,X4] :
( ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(X4,X3)
| ~ iLess0(X3,sK40)
| ( aSubsetOf0(sdtlpdtrp0(xN,X3),sdtlpdtrp0(xN,X4))
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| aElementOf0(X5,sdtlpdtrp0(xN,X4)) ) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41))
& aElementOf0(sK42,sdtlpdtrp0(xN,sK40))
& ~ aElementOf0(sK42,sdtlpdtrp0(xN,sK41)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42]),skolemize(X0,sK40),skolemize(X1,sK41),skolemize(X2,sK42)],[f300]) ).
fof(f309,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f314,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f349,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f353,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f239]) ).
fof(f354,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f239]) ).
fof(f356,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f358,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ),
inference(cnf_transformation,[],[f240]) ).
fof(f361,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f362,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f363,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f140]) ).
fof(f364,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f365,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f503,plain,
! [X0] :
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
! [X0] :
( ~ sP9(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
! [X0] :
( ~ sP9(X0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f520,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f521,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f523,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f202]) ).
fof(f524,plain,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f301]) ).
fof(f525,plain,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f301]) ).
fof(f526,plain,
sdtlseqdt0(sK41,sK40),
inference(cnf_transformation,[],[f301]) ).
fof(f528,plain,
! [X3,X4,X5] :
( ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(X4,X3)
| ~ iLess0(X3,sK40)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| aElementOf0(X5,sdtlpdtrp0(xN,X4)) ),
inference(cnf_transformation,[],[f301]) ).
fof(f529,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f301]) ).
fof(f530,plain,
aElementOf0(sK42,sdtlpdtrp0(xN,sK40)),
inference(cnf_transformation,[],[f301]) ).
fof(f531,plain,
~ aElementOf0(sK42,sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f301]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_61,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f349]) ).
tcf(c_100,plain,
! [X0: $i] :
( aElementOf0(sK14(X0),szNzAzT0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK14(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_103,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f358]) ).
tcf(c_108,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f362]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f364]) ).
tcf(c_112,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_251,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_252,plain,
! [X0: $i] :
( sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_255,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_266,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_267,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f523]) ).
tcf(c_269,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_270,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_271,negated_conjecture,
~ aElementOf0(sK42,sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f531]) ).
tcf(c_272,negated_conjecture,
aElementOf0(sK42,sdtlpdtrp0(xN,sK40)),
inference(cnf_transformation,[],[f530]) ).
tcf(c_273,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f529]) ).
tcf(c_274,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X2))
| ~ iLess0(X1,sK40)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f528]) ).
tcf(c_276,negated_conjecture,
sdtlseqdt0(sK41,sK40),
inference(cnf_transformation,[],[f526]) ).
tcf(c_277,negated_conjecture,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f525]) ).
tcf(c_278,negated_conjecture,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f524]) ).
tcf(c_495,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_575,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(prop_impl_just,[status(thm)],[c_251]) ).
tcf(c_577,plain,
! [X0: $i] :
( sP8(X0)
| ~ sP9(X0) ),
inference(prop_impl_just,[status(thm)],[c_252]) ).
tcf(c_581,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(prop_impl_just,[status(thm)],[c_255]) ).
tcf(c_661,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_266,c_270,c_269,c_266]) ).
tcf(c_2377,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_661,c_581]) ).
tcf(c_2378,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_2377]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_661,c_575]) ).
tcf(c_2396,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_2395]) ).
tcf(c_2700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X3,X1)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(resolution_lifted,[status(thm)],[c_495,c_274]) ).
tcf(c_2701,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,sdtlpdtrp0(xN,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X2,X0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(unflattening,[status(thm)],[c_2700]) ).
tcf(c_12139,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(prop_impl_just,[status(thm)],[c_2396]) ).
tcf(c_12143,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(prop_impl_just,[status(thm)],[c_2378]) ).
tcf(c_22849,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_22851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_22857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_22863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_22870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtlpdtrp0(X0,X2) = sdtlpdtrp0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_26663,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_26667,plain,
( sdtlseqdt0(sz00,sK41)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_26682,plain,
( aSet0(sdtlpdtrp0(xN,sK41))
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_267]) ).
tcf(c_26717,plain,
( aElementOf0(sK14(sK40),szNzAzT0)
| ( sK40 = sz00 )
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_26735,plain,
( sdtlseqdt0(sK40,sK40)
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_26736,plain,
( sdtlseqdt0(sK41,sK41)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_26787,plain,
( ( sK40 = sz00 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 )
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_26943,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_27083,plain,
( ( sK40 = sK41 )
| ~ sdtlseqdt0(sK40,sK41)
| ~ sdtlseqdt0(sK41,sK40)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_27122,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41))
| ~ aSubsetOf0(X1,X0)
| ( sdtlpdtrp0(xN,sK40) != X1 )
| ( sdtlpdtrp0(xN,sK41) != X0 ) ),
inference(instantiation,[status(thm)],[c_22857]) ).
tcf(c_27730,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz00,sK41)
| ( X1 != sK41 )
| ( X0 != sz00 ) ),
inference(instantiation,[status(thm)],[c_22863]) ).
tcf(c_27814,plain,
( ( sK40 = sK40 )
| ~ sdtlseqdt0(sK40,sK40)
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_27818,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sK40,sK40)
| ( X1 != sK40 )
| ( X0 != sK40 ) ),
inference(instantiation,[status(thm)],[c_22863]) ).
tcf(c_27820,plain,
( ( sK41 = sK41 )
| ~ sdtlseqdt0(sK41,sK41)
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_28276,plain,
( ( sz00 = sz00 )
| ~ sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_29320,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK40 )
| ( sK40 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_22851]) ).
tcf(c_29620,plain,
( ( sz00 = sK41 )
| ( szszuzczcdt0(sK14(sK41)) = sK41 ) ),
inference(superposition,[status(thm)],[c_278,c_101]) ).
tcf(c_30084,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(X0,sK14(sK41))
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK41),szNzAzT0) ),
inference(superposition,[status(thm)],[c_29620,c_111]) ).
tcf(c_31061,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(X0,sK14(sK41))
| ( sz00 = sK41 )
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_100,c_30084]) ).
tcf(c_32940,plain,
! [X0: $i] :
( aElementOf0(sK42,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_272,c_59]) ).
tcf(c_32987,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_277,c_101]) ).
tcf(c_32988,plain,
( ( sz00 = sK41 )
| ( szszuzczcdt0(sK14(sK41)) = sK41 ) ),
inference(superposition,[status(thm)],[c_278,c_101]) ).
tcf(c_34674,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK41),szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(superposition,[status(thm)],[c_32988,c_106]) ).
tcf(c_35454,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(superposition,[status(thm)],[c_100,c_34674]) ).
tcf(c_35460,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_32987,c_12143]) ).
tcf(c_35816,plain,
( aElementOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_35460,c_32940]) ).
tcf(c_37916,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sK41)
| ~ sdtlseqdt0(sz00,sK41)
| ( sK41 != sK41 )
| ( X0 != sz00 ) ),
inference(instantiation,[status(thm)],[c_27730]) ).
tcf(c_40251,plain,
! [X0: $i] :
( ( X0 = sK40 )
| ( sK40 != sz00 )
| ( X0 != sz00 ) ),
inference(instantiation,[status(thm)],[c_29320]) ).
tcf(c_40595,plain,
xN = xN,
inference(instantiation,[status(thm)],[c_22849]) ).
tcf(c_40920,plain,
! [X0: $i] :
( aElementOf0(sK42,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_272,c_59]) ).
tcf(c_40941,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_277,c_101]) ).
tcf(c_40942,plain,
( ( sz00 = sK41 )
| ( szszuzczcdt0(sK14(sK41)) = sK41 ) ),
inference(superposition,[status(thm)],[c_278,c_101]) ).
tcf(c_42194,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK41),szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(superposition,[status(thm)],[c_40942,c_106]) ).
tcf(c_42734,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(global_subsumption_just,[status(thm)],[c_42194,c_278,c_35454]) ).
tcf(c_42766,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_40941,c_12143]) ).
tcf(c_42976,plain,
( sdtlseqdt0(sK40,sK41)
| ~ sdtlseqdt0(sz00,sK41)
| ( sK40 != sz00 )
| ( sK41 != sK41 ) ),
inference(instantiation,[status(thm)],[c_37916]) ).
tcf(c_43235,plain,
( aElementOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_42766,c_40920]) ).
tcf(c_43247,plain,
( ( sz00 = sK40 )
| ( sK40 != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_40251]) ).
tcf(c_44293,plain,
( aElementOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_43235,c_277,c_96,c_26663,c_26717,c_28276,c_35816,c_43247]) ).
tcf(c_45376,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41))
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,sK41))
| ( sdtlpdtrp0(xN,sK40) != X0 )
| ( sdtlpdtrp0(xN,sK41) != sdtlpdtrp0(xN,sK41) ) ),
inference(instantiation,[status(thm)],[c_27122]) ).
tcf(c_45377,plain,
sdtlpdtrp0(xN,sK41) = sdtlpdtrp0(xN,sK41),
inference(instantiation,[status(thm)],[c_22849]) ).
tcf(c_45488,plain,
! [X0: $i] :
( sdtlseqdt0(sK40,X0)
| ~ sdtlseqdt0(sK40,sK40)
| ( sK40 != sK40 )
| ( X0 != sK40 ) ),
inference(instantiation,[status(thm)],[c_27818]) ).
tcf(c_46070,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sK41)
| ~ sdtlseqdt0(X1,sK41)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_278,c_110]) ).
tcf(c_46166,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ sdtlseqdt0(X1,sK14(sK40))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| ( szszuzczcdt0(sK14(sK40)) != sK40 ) ),
inference(instantiation,[status(thm)],[c_2701]) ).
tcf(c_46777,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sK41)
| ~ sdtlseqdt0(sz00,sK41)
| ~ sdtlseqdt0(X0,sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_96,c_46070]) ).
tcf(c_48853,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtlpdtrp0(xN,sK41))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK41),sdtlpdtrp0(xN,sK41))
| ( sdtlpdtrp0(xN,sK40) != sdtlpdtrp0(xN,sK41) )
| ( sdtlpdtrp0(xN,sK41) != sdtlpdtrp0(xN,sK41) ) ),
inference(instantiation,[status(thm)],[c_45376]) ).
tcf(c_48854,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK41),sdtlpdtrp0(xN,sK41))
| ~ aSet0(sdtlpdtrp0(xN,sK41)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_51426,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sK41)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(global_subsumption_just,[status(thm)],[c_46777,c_278,c_26667,c_46777]) ).
tcf(c_51427,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sK41)
| ~ sdtlseqdt0(X0,sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(renaming,[status(thm)],[c_51426]) ).
tcf(c_51457,plain,
( sdtlseqdt0(sK40,sK41)
| ~ sdtlseqdt0(sK40,sz00) ),
inference(superposition,[status(thm)],[c_277,c_51427]) ).
tcf(c_53312,plain,
( aElementOf0(sK42,sdtlpdtrp0(xN,sK41))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ sdtlseqdt0(sK41,sK14(sK40))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(sK42,sdtlpdtrp0(xN,sK14(sK40)))
| ( szszuzczcdt0(sK14(sK40)) != sK40 ) ),
inference(instantiation,[status(thm)],[c_46166]) ).
tcf(c_58739,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_277,c_101]) ).
tcf(c_58740,plain,
( ( sz00 = sK41 )
| ( szszuzczcdt0(sK14(sK41)) = sK41 ) ),
inference(superposition,[status(thm)],[c_278,c_101]) ).
tcf(c_59122,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(X0,sK14(sK41))
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK41),szNzAzT0) ),
inference(superposition,[status(thm)],[c_58740,c_111]) ).
tcf(c_59937,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(X0,sK14(sK41))
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_59122,c_278,c_31061]) ).
tcf(c_60126,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK41),szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(superposition,[status(thm)],[c_58740,c_106]) ).
tcf(c_60458,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sK14(sK41)) ),
inference(global_subsumption_just,[status(thm)],[c_60126,c_42734]) ).
tcf(c_60462,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ( sz00 = sK41 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_59937,c_60458]) ).
tcf(c_67082,plain,
( sdtlseqdt0(sK40,sz00)
| ~ sdtlseqdt0(sK40,sK40)
| ( sK40 != sK40 )
| ( sz00 != sK40 ) ),
inference(instantiation,[status(thm)],[c_45488]) ).
tcf(c_82509,plain,
! [X0: $i,X1: $i] :
( ( sdtlpdtrp0(xN,sK40) = sdtlpdtrp0(X0,X1) )
| ( sK40 != X1 )
| ( xN != X0 ) ),
inference(instantiation,[status(thm)],[c_22870]) ).
tcf(c_86726,plain,
! [X0: $i] :
( sdtlseqdt0(sK41,X0)
| sdtlseqdt0(szszuzczcdt0(X0),sK41)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_60462,c_278,c_26943]) ).
tcf(c_86732,plain,
( sdtlseqdt0(sK40,sK41)
| sdtlseqdt0(sK41,sK14(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_58739,c_86726]) ).
tcf(c_86884,plain,
( sdtlseqdt0(sK40,sK41)
| sdtlseqdt0(sK41,sK14(sK40)) ),
inference(global_subsumption_just,[status(thm)],[c_86732,c_278,c_277,c_26667,c_26717,c_26735,c_26736,c_27814,c_27820,c_42976,c_51457,c_67082,c_86732]) ).
tcf(c_90891,plain,
! [X0: $i] :
( ( sdtlpdtrp0(xN,sK40) = sdtlpdtrp0(X0,sK41) )
| ( sK40 != sK41 )
| ( xN != X0 ) ),
inference(instantiation,[status(thm)],[c_82509]) ).
tcf(c_97052,plain,
( ( sdtlpdtrp0(xN,sK40) = sdtlpdtrp0(xN,sK41) )
| ( sK40 != sK41 )
| ( xN != xN ) ),
inference(instantiation,[status(thm)],[c_90891]) ).
tcf(c_139950,plain,
( aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_12139]) ).
fof(f216,definition,
! [X0] :
( ~ sP8(X0)
| ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f217,definition,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& 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)) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f218,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)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(definition_folding,[],[f201,f217,f216]) ).
fof(f296,plain,
! [X0] :
( ~ sP8(X0)
| ! [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)))) ) ) ),
inference(nnf_transformation,[],[f216]) ).
fof(f297,plain,
! [X0] :
( ~ sP8(X0)
| ! [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)))) ) ) ),
inference(flattening,[],[f296]) ).
fof(f298,plain,
! [X0] :
( ~ sP8(X0)
| ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ),
inference(rectify,[],[f297]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sP8(X0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X1,sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP8(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_2304,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ sP9(X1)
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_259,c_577]) ).
tcf(c_2305,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP9(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(unflattening,[status(thm)],[c_2304]) ).
tcf(c_2443,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2305,c_661]) ).
tcf(c_2444,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(unflattening,[status(thm)],[c_2443]) ).
tcf(c_28732,plain,
! [X0: $i] :
( aElementOf0(sK42,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(instantiation,[status(thm)],[c_2444]) ).
tcf(c_72387,plain,
( aElementOf0(sK42,sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(sK42,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(instantiation,[status(thm)],[c_28732]) ).
tcf(c_139951,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_139950,c_97052,c_86884,c_72387,c_67082,c_53312,c_51457,c_48854,c_48853,c_45377,c_44293,c_42976,c_40595,c_27820,c_27814,c_27083,c_26787,c_26736,c_26735,c_26717,c_26682,c_26667,c_273,c_271,c_276,c_277,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM572+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n014.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 04:41:44 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 145.85/32.48 % SZS status Started for theBenchmark.p
% 145.85/32.48 % SZS status Theorem for theBenchmark.p
% 145.85/32.48
% 145.85/32.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 145.85/32.48
% 145.85/32.48 % ------ iProver source info
% 145.85/32.48
% 145.85/32.48 % git: date: 2026-07-19 20:42:38 +0200
% 145.85/32.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 145.85/32.48 % git: non_committed_changes: false
% 145.85/32.48
% 145.85/32.48 % ------ Parsing...
% 145.85/32.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 145.85/32.48
% 145.85/32.48 % ------ Preprocessing... sup_sim: 0 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 %
% 145.85/32.48
% 145.85/32.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 145.85/32.48
% 145.85/32.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 145.85/32.48 % ------ Proving...
% 145.85/32.48 % ------ Problem Properties
% 145.85/32.48
% 145.85/32.48 %
% 145.85/32.48 % clauses 222
% 145.85/32.48 % conjectures 6
% 145.85/32.48 % EPR 46
% 145.85/32.48 % Horn 172
% 145.85/32.48 % unary 31
% 145.85/32.48 % binary 46
% 145.85/32.48 % lits 748
% 145.85/32.48 % lits eq 105
% 145.85/32.48 % fd_pure 0
% 145.85/32.48 % fd_pseudo 0
% 145.85/32.48 % fd_cond 10
% 145.85/32.48 % fd_pseudo_cond 30
% 145.85/32.48 % AC symbols 0
% 145.85/32.48
% 145.85/32.48 % ------ Input Options Time Limit: Unbounded
% 145.85/32.48
% 145.85/32.48
% 145.85/32.48 % ------
% 145.85/32.48 % Current options:
% 145.85/32.48 % ------
% 145.85/32.48
% 145.85/32.48
% 145.85/32.48 %
% 145.85/32.48
% 145.85/32.48 % ------ Proving...
% 145.85/32.48 %
% 145.85/32.48
% 145.85/32.48 % SZS status Theorem for theBenchmark.p
% 145.85/32.48
% 145.85/32.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 145.85/32.48
% 145.85/32.48
%------------------------------------------------------------------------------