%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM607+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Wed Oct 7 10:34:36 AM UTC 2026
% Result : Theorem 2.58s 0.68s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 37
% Syntax : Number of formulae : 505 ( 218 unt; 0 typ; 0 def)
% Number of atoms : 3972 (1252 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 6668 (1429 ~;1216 |; 99 &;3764 @)
% ( 9 <=>; 151 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 19 con; 0-2 aty)
% Number of variables : 851 ( 0 ^; 842 !; 9 ?; 851 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aFunction0,type,
aFunction0: $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_iLess0,type,
iLess0: $i > $i > $o ).
thf(tp_isCountable0,type,
isCountable0: $i > $o ).
thf(tp_isFinite0,type,
isFinite0: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY80,type,
sK3_SY80: $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY73,type,
sK5_SY73: $i > $i ).
thf(tp_sbrdtbr0,type,
sbrdtbr0: $i > $i ).
thf(tp_sdtexdt0,type,
sdtexdt0: $i > $i > $i ).
thf(tp_sdtlbdtrb0,type,
sdtlbdtrb0: $i > $i > $i ).
thf(tp_sdtlcdtrc0,type,
sdtlcdtrc0: $i > $i > $i ).
thf(tp_sdtlpdtrp0,type,
sdtlpdtrp0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_sdtmndt0,type,
sdtmndt0: $i > $i > $i ).
thf(tp_sdtpldt0,type,
sdtpldt0: $i > $i > $i ).
thf(tp_slbdtrb0,type,
slbdtrb0: $i > $i ).
thf(tp_slbdtsldtrb0,type,
slbdtsldtrb0: $i > $i > $i ).
thf(tp_slcrc0,type,
slcrc0: $i ).
thf(tp_sz00,type,
sz00: $i ).
thf(tp_szDzizrdt0,type,
szDzizrdt0: $i > $i ).
thf(tp_szDzozmdt0,type,
szDzozmdt0: $i > $i ).
thf(tp_szNzAzT0,type,
szNzAzT0: $i ).
thf(tp_szmzazxdt0,type,
szmzazxdt0: $i > $i ).
thf(tp_szmzizndt0,type,
szmzizndt0: $i > $i ).
thf(tp_szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
thf(tp_xC,type,
xC: $i ).
thf(tp_xK,type,
xK: $i ).
thf(tp_xN,type,
xN: $i ).
thf(tp_xO,type,
xO: $i ).
thf(tp_xQ,type,
xQ: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xc,type,
xc: $i ).
thf(tp_xd,type,
xd: $i ).
thf(tp_xe,type,
xe: $i ).
thf(tp_xk,type,
xk: $i ).
thf(3,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( sdtlcdtrc0 @ W0 @ ( szDzozmdt0 @ W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
thf(4,axiom,
! [W0: $i,W1: $i] :
( ( ( aFunction0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ W0 @ W1 ) @ ( szDzozmdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
thf(5,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgElm) ).
thf(6,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
thf(13,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
thf(14,axiom,
! [W0: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( isFinite0 @ W0 ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aSubsetOf0 @ W0 @ ( slbdtrb0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFinSubSeg) ).
thf(15,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ W0 ) @ ( slbdtrb0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegLess) ).
thf(16,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ W1 ) ) )
<=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ W1 ) )
| ( W0 = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).
thf(18,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).
thf(19,axiom,
! [W0: $i,W1: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( aSubsetOf0 @ W1 @ szNzAzT0 )
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ W0 ) @ W1 )
& ( aElementOf0 @ ( szmzizndt0 @ W1 ) @ W0 ) )
=> ( ( szmzizndt0 @ W0 )
= ( szmzizndt0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMinMin) ).
thf(27,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(28,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).
thf(29,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
thf(30,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W2 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
thf(31,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
thf(32,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
thf(33,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
thf(34,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
thf(36,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
thf(37,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(38,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
thf(39,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
thf(40,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(41,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
thf(42,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
thf(49,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ W0 @ W1 ) @ W1 )
= W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
thf(50,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
thf(51,axiom,
! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
thf(52,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
thf(53,axiom,
! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isFinite0 @ W0 ) )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ( isFinite0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
thf(59,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(62,axiom,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xQ @ szNzAzT0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
thf(63,axiom,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xO ) )
& ~ ( ~ ? [W0: $i] : ( aElementOf0 @ W0 @ xQ )
| ( xQ = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
thf(65,axiom,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xO @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
thf(88,axiom,
( ( aSet0 @ xS )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xS )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
thf(89,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
thf(91,conjecture,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(92,negated_conjecture,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[91]) ).
thf(93,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) )
= $false ),
inference(unfold_def,[status(thm)],[92]) ).
thf(94,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( sdtlcdtrc0 @ W0 @ ( szDzozmdt0 @ W0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aFunction0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ W0 @ W1 ) @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(96,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(97,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(98,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(99,plain,
( ( ! [W0: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( isFinite0 @ W0 ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aSubsetOf0 @ W0 @ ( slbdtrb0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(100,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ W0 ) @ ( slbdtrb0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(101,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ W1 ) ) )
<=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ W1 ) )
| ( W0 = W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(102,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(103,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( aSubsetOf0 @ W1 @ szNzAzT0 )
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ W0 ) @ W1 )
& ( aElementOf0 @ ( szmzizndt0 @ W1 ) @ W0 ) )
=> ( ( szmzizndt0 @ W0 )
= ( szmzizndt0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(104,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(105,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(106,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(107,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W2 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(108,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(109,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(110,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(111,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(112,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(113,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(115,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(116,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(117,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(118,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(119,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ W0 @ W1 ) @ W1 )
= W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(120,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(121,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(122,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(123,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isFinite0 @ W0 ) )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ( isFinite0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(124,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(125,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xQ @ szNzAzT0 ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(126,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xO ) )
& ~ ( ~ ? [W0: $i] : ( aElementOf0 @ W0 @ xQ )
| ( xQ = slcrc0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(127,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xO @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(128,plain,
( ( ( aSet0 @ xS )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xS )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(129,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(130,plain,
( ( ~ ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[93]) ).
thf(131,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(132,plain,
( ( ( aSet0 @ xS )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xS )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xS @ szNzAzT0 )
& ( isCountable0 @ xS ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(133,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xO @ xS ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(134,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xO ) )
& ~ ( ~ ? [W0: $i] : ( aElementOf0 @ W0 @ xQ )
| ( xQ = slcrc0 ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(135,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ szNzAzT0 ) )
& ( aSubsetOf0 @ xQ @ szNzAzT0 ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(136,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(137,plain,
( ( ! [W0: $i] :
( ( ( aSet0 @ W0 )
& ( isFinite0 @ W0 ) )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ( isFinite0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(138,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ( aSubsetOf0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(139,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(140,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aSet0 @ W0 )
& ( aSet0 @ W1 )
& ( aSet0 @ W2 ) )
=> ( ( ( aSubsetOf0 @ W0 @ W1 )
& ( aSubsetOf0 @ W1 @ W2 ) )
=> ( aSubsetOf0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(141,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ W0 @ W1 ) @ W1 )
= W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(142,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(143,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(144,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(145,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(146,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(147,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(148,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(149,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(150,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(151,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(152,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(153,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W2 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(154,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(155,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(156,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(157,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( aSubsetOf0 @ W1 @ szNzAzT0 )
& ( W0 != slcrc0 )
& ( W1 != slcrc0 ) )
=> ( ( ( aElementOf0 @ ( szmzizndt0 @ W0 ) @ W1 )
& ( aElementOf0 @ ( szmzizndt0 @ W1 ) @ W0 ) )
=> ( ( szmzizndt0 @ W0 )
= ( szmzizndt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(158,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(159,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ W1 ) ) )
<=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ W1 ) )
| ( W0 = W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(160,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( aSubsetOf0 @ ( slbdtrb0 @ W0 ) @ ( slbdtrb0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(161,plain,
( ( ! [W0: $i] :
( ( ( aSubsetOf0 @ W0 @ szNzAzT0 )
& ( isFinite0 @ W0 ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aSubsetOf0 @ W0 @ ( slbdtrb0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(162,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(163,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(164,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(165,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aFunction0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( aSubsetOf0 @ ( sdtlbdtrb0 @ W0 @ W1 ) @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(166,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( sdtlcdtrc0 @ W0 @ ( szDzozmdt0 @ W0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(167,plain,
( ( ~ ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [W0: $i] :
( ( aElementOf0 @ W0 @ xQ )
=> ( aElementOf0 @ W0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SX0 ) @ ( szszuzczcdt0 @ SX1 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SX0 ) @ ( szszuzczcdt0 @ SX1 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(169,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ( aSet0 @ ( szDzozmdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ SX1 )
| ~ ( aSubsetOf0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(172,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ( aSubsetOf0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(173,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( isFinite0 @ ( slbdtrb0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(174,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(176,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aFunction0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ( aSubsetOf0 @ ( sdtlbdtrb0 @ SX0 @ SX1 ) @ ( szDzozmdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(178,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
| ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) )
| ~ ( isCountable0 @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(179,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(180,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( iLess0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(181,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(182,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xO ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ )
| ( xQ = slcrc0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(183,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ SX0 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(184,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xO )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xO @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(185,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ SX0 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SX0 @ SX1 ) @ ( sdtlcdtrc0 @ SX0 @ ( szDzozmdt0 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(186,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SX2 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 ) )
| ( sdtlseqdt0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(187,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElement0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(188,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( ( sbrdtbr0 @ ( slbdtrb0 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(189,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( ( SX0 != slcrc0 ) ) )
| ~ ( ( SX1 != slcrc0 ) ) )
| ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SX0 ) @ SX1 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SX1 ) @ SX0 ) )
| ( ( szmzizndt0 @ SX0 )
= ( szmzizndt0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(191,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( isFinite0 @ SX0 ) )
| ! [SX1: $i] :
( ~ ( aSubsetOf0 @ SX1 @ SX0 )
| ( isFinite0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(192,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SX0 )
!= ( szszuzczcdt0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(193,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ szNzAzT0 )
| ~ ( isFinite0 @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElementOf0 @ SX1 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SX0 @ ( slbdtrb0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(194,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(195,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SX0 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(196,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) )
| ~ ( aSubsetOf0 @ xQ @ szNzAzT0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SX1 ) ) )
| ( aElementOf0 @ SX0 @ ( slbdtrb0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ~ ( ( aElementOf0 @ SX0 @ ( slbdtrb0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ( aElementOf0 @ SX0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SX0 )
| ~ ( aSet0 @ SX1 ) )
| ~ ( aSet0 @ SX2 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SX0 @ SX1 )
| ~ ( aSubsetOf0 @ SX1 @ SX2 ) )
| ( aSubsetOf0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(199,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SX0 ) @ ( slbdtrb0 @ SX1 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SX0 ) @ ( slbdtrb0 @ SX1 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(200,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(201,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SX0 @ SX1 ) @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0 = sz00 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElementOf0 @ SX1 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(203,plain,
! [SV1: $i] :
( ( ! [SY59: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY59 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SY59 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SY59 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SY59 ) )
| ( sdtlseqdt0 @ SV1 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(204,plain,
! [SV2: $i] :
( ( ~ ( aFunction0 @ SV2 )
| ( aSet0 @ ( szDzozmdt0 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(205,plain,
! [SV3: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY60 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV3 @ SY60 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(206,plain,
! [SV4: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ( aSet0 @ SV4 )
| ~ ( aSet0 @ SY61 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SY61 )
| ~ ( aSubsetOf0 @ SY61 @ SV4 ) )
| ( SV4 = SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(207,plain,
! [SV5: $i] :
( ( ~ ( aSet0 @ SV5 )
| ( aSubsetOf0 @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(208,plain,
! [SV6: $i] :
( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ( isFinite0 @ ( slbdtrb0 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(209,plain,
! [SV7: $i] :
( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV7 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(210,plain,
! [SV8: $i] :
( ( ! [SY62: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY62 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV8 @ SY62 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SY62 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(211,plain,
! [SV9: $i] :
( ( ! [SY63: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY63 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV9 @ SY63 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(212,plain,
! [SV10: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( aFunction0 @ SV10 )
| ~ ( aElement0 @ SY64 ) )
| ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SY64 ) @ ( szDzozmdt0 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(213,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
| ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) )
| ~ ( isCountable0 @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(214,plain,
! [SV11: $i] :
( ( ~ ( aElementOf0 @ SV11 @ szNzAzT0 )
| ( SV11
!= ( szszuzczcdt0 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(215,plain,
! [SV12: $i] :
( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ( iLess0 @ SV12 @ ( szszuzczcdt0 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(216,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(217,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xO ) )
| ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ )
| ( xQ = slcrc0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(218,plain,
! [SV13: $i] :
( ( ~ ( aFunction0 @ SV13 )
| ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ ( szDzozmdt0 @ SV13 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(219,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xO )
| ( aElementOf0 @ SX0 @ xS ) )
| ~ ( aSubsetOf0 @ xO @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(220,plain,
! [SV14: $i] :
( ( ~ ( aFunction0 @ SV14 )
| ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ ( szDzozmdt0 @ SV14 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SY66 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(221,plain,
! [SV15: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY67 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY68 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SY67 )
| ~ ( sdtlseqdt0 @ SY67 @ SY68 ) )
| ( sdtlseqdt0 @ SV15 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(222,plain,
! [SV16: $i] :
( ( ~ ( aSet0 @ SV16 )
| ! [SY69: $i] :
( ~ ( aElementOf0 @ SY69 @ SV16 )
| ( aElement0 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(223,plain,
! [SV17: $i] :
( ( ~ ( aElementOf0 @ SV17 @ szNzAzT0 )
| ( ( sbrdtbr0 @ ( slbdtrb0 @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(224,plain,
! [SV18: $i] :
( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(225,plain,
! [SV19: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SY70 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
| ~ ( ( SY70 != slcrc0 ) ) )
| ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SY70 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SY70 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(226,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ( aSet0 @ SV20 )
| ~ ( isFinite0 @ SV20 ) )
| ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(227,plain,
! [SV21: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY72 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SY72 ) )
| ( SV21 = SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(228,plain,
! [SV22: $i] :
( ( ~ ~ ( ~ ( aSubsetOf0 @ SV22 @ szNzAzT0 )
| ~ ( isFinite0 @ SV22 ) )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(229,plain,
! [SV23: $i] :
( ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV23 @ ( szszuzczcdt0 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(230,plain,
! [SV24: $i] :
( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(231,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) )
| ~ ( aSubsetOf0 @ xQ @ szNzAzT0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(232,plain,
! [SV25: $i] :
( ( ! [SY74: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY74 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY74 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SY74 ) )
| ( SV25 = SY74 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SY74 ) )
| ( SV25 = SY74 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY74 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(233,plain,
! [SV26: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SY75 ) )
| ~ ( aSet0 @ SY76 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SY75 )
| ~ ( aSubsetOf0 @ SY75 @ SY76 ) )
| ( aSubsetOf0 @ SV26 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(234,plain,
! [SV27: $i] :
( ( ! [SY77: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY77 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SY77 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SY77 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SY77 ) )
| ( sdtlseqdt0 @ SV27 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(235,plain,
! [SV28: $i] :
( ( ! [SY78: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY78 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SY78 )
| ~ ( sdtlseqdt0 @ SY78 @ SV28 ) )
| ( SV28 = SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(236,plain,
! [SV29: $i] :
( ( ~ ( aSet0 @ SV29 )
| ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ SV29 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SY79 ) @ SY79 )
= SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(237,plain,
! [SV30: $i] :
( ( ~ ( aElementOf0 @ SV30 @ szNzAzT0 )
| ( SV30 = sz00 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( aElementOf0 @ SY80 @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(238,plain,
! [SV31: $i,SV1: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(239,plain,
! [SV2: $i] :
( ( ( ~ ( aFunction0 @ SV2 ) )
= $true )
| ( ( aSet0 @ ( szDzozmdt0 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(240,plain,
! [SV32: $i,SV3: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(241,plain,
! [SV33: $i,SV4: $i] :
( ( ~ ~ ( ~ ( aSet0 @ SV4 )
| ~ ( aSet0 @ SV33 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(242,plain,
! [SV5: $i] :
( ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( aSubsetOf0 @ SV5 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(243,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 ) )
= $true )
| ( ( isFinite0 @ ( slbdtrb0 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(244,plain,
! [SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV7 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(245,plain,
! [SV34: $i,SV8: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(246,plain,
! [SV35: $i,SV9: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(247,plain,
! [SV36: $i,SV10: $i] :
( ( ~ ~ ( ~ ( aFunction0 @ SV10 )
| ~ ( aElement0 @ SV36 ) )
| ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(248,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
| ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(249,plain,
( ( ~ ( isCountable0 @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(250,plain,
! [SV11: $i] :
( ( ( ~ ( aElementOf0 @ SV11 @ szNzAzT0 ) )
= $true )
| ( ( SV11
!= ( szszuzczcdt0 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV12: $i] :
( ( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 ) )
= $true )
| ( ( iLess0 @ SV12 @ ( szszuzczcdt0 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(252,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(253,plain,
( ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xO ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(255,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ )
| ( xQ = slcrc0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(256,plain,
! [SV13: $i] :
( ( ( ~ ( aFunction0 @ SV13 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ ( szDzozmdt0 @ SV13 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(257,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xO )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(258,plain,
( ( ~ ( aSubsetOf0 @ xO @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(259,plain,
! [SV14: $i] :
( ( ( ~ ( aFunction0 @ SV14 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ ( szDzozmdt0 @ SV14 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SY66 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(260,plain,
! [SV37: $i,SV15: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY81 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SY81 ) )
| ( sdtlseqdt0 @ SV15 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(261,plain,
! [SV16: $i] :
( ( ( ~ ( aSet0 @ SV16 ) )
= $true )
| ( ( ! [SY69: $i] :
( ~ ( aElementOf0 @ SY69 @ SV16 )
| ( aElement0 @ SY69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(262,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) )
= $true )
| ( ( ( sbrdtbr0 @ ( slbdtrb0 @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(263,plain,
! [SV18: $i] :
( ( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ sz00 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(264,plain,
! [SV38: $i,SV19: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
| ~ ( ( SV38 != slcrc0 ) ) )
| ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(265,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV20 )
| ~ ( isFinite0 @ SV20 ) ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(266,plain,
! [SV39: $i,SV21: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(267,plain,
! [SV22: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV22 @ szNzAzT0 )
| ~ ( isFinite0 @ SV22 ) ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(268,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV23 @ ( szszuzczcdt0 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(269,plain,
! [SV24: $i] :
( ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(270,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(271,plain,
( ( ~ ( aSubsetOf0 @ xQ @ szNzAzT0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(272,plain,
! [SV40: $i,SV25: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(273,plain,
! [SV41: $i,SV26: $i] :
( ( ! [SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
| ~ ( aSet0 @ SY82 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SY82 ) )
| ( aSubsetOf0 @ SV26 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(274,plain,
! [SV42: $i,SV27: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(275,plain,
! [SV43: $i,SV28: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(276,plain,
! [SV29: $i] :
( ( ( ~ ( aSet0 @ SV29 ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ SV29 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SY79 ) @ SY79 )
= SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(277,plain,
! [SV30: $i] :
( ( ( ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) )
= $true )
| ( ( ( SV30 = sz00 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( aElementOf0 @ SY80 @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ SY80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(278,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(279,plain,
! [SV2: $i] :
( ( ( aFunction0 @ SV2 )
= $false )
| ( ( aSet0 @ ( szDzozmdt0 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(280,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(281,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV4 )
| ~ ( aSet0 @ SV33 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(282,plain,
! [SV5: $i] :
( ( ( aSet0 @ SV5 )
= $false )
| ( ( aSubsetOf0 @ SV5 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(283,plain,
! [SV6: $i] :
( ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ ( slbdtrb0 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(284,plain,
! [SV7: $i] :
( ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV7 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(285,plain,
! [SV34: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(286,plain,
! [SV35: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(287,plain,
! [SV36: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aFunction0 @ SV10 )
| ~ ( aElement0 @ SV36 ) ) )
= $true )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(288,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
| ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(289,plain,
( ( isCountable0 @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(290,plain,
! [SV11: $i] :
( ( ( aElementOf0 @ SV11 @ szNzAzT0 )
= $false )
| ( ( SV11
!= ( szszuzczcdt0 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(291,plain,
! [SV12: $i] :
( ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( iLess0 @ SV12 @ ( szszuzczcdt0 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(292,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS )
| ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(293,plain,
( ( aSubsetOf0 @ xQ @ xS )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(294,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xO ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(295,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ )
| ( xQ = slcrc0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(296,plain,
! [SV13: $i] :
( ( ( aFunction0 @ SV13 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ ( szDzozmdt0 @ SV13 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(297,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xO )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(298,plain,
( ( aSubsetOf0 @ xO @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(299,plain,
! [SV14: $i] :
( ( ( aFunction0 @ SV14 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( aElementOf0 @ SY66 @ ( szDzozmdt0 @ SV14 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SY66 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(300,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(301,plain,
! [SV16: $i] :
( ( ( aSet0 @ SV16 )
= $false )
| ( ( ! [SY69: $i] :
( ~ ( aElementOf0 @ SY69 @ SV16 )
| ( aElement0 @ SY69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(302,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false )
| ( ( ( sbrdtbr0 @ ( slbdtrb0 @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(303,plain,
! [SV18: $i] :
( ( ( aElementOf0 @ SV18 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ sz00 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(304,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
| ~ ( ( SV38 != slcrc0 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(305,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV20 )
| ~ ( isFinite0 @ SV20 ) ) )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(306,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(307,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV22 @ szNzAzT0 )
| ~ ( isFinite0 @ SV22 ) ) )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(308,plain,
! [SV23: $i] :
( ( ( aElementOf0 @ SV23 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV23 @ ( szszuzczcdt0 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(309,plain,
! [SV24: $i] :
( ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(311,plain,
( ( aSubsetOf0 @ xQ @ szNzAzT0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(312,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(313,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
| ~ ( aSet0 @ SV45 ) )
| ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(314,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(315,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(316,plain,
! [SV29: $i] :
( ( ( aSet0 @ SV29 )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ SV29 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SY79 ) @ SY79 )
= SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(317,plain,
! [SV30: $i] :
( ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false )
| ( ( ( SV30 = sz00 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( aElementOf0 @ SY80 @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ SY80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(318,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(319,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(320,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV4 )
| ~ ( aSet0 @ SV33 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(321,plain,
! [SV34: $i,SV8: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) ) )
= $false )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(322,plain,
! [SV35: $i,SV9: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(323,plain,
! [SV36: $i,SV10: $i] :
( ( ( ~ ( ~ ( aFunction0 @ SV10 )
| ~ ( aElement0 @ SV36 ) ) )
= $false )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(324,plain,
( ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
| ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(325,plain,
! [SV11: $i] :
( ( ( SV11
= ( szszuzczcdt0 @ SV11 ) )
= $false )
| ( ( aElementOf0 @ SV11 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) )
| ( aSubsetOf0 @ xQ @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(327,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(328,plain,
! [SV46: $i] :
( ( ~ ( aElementOf0 @ SV46 @ xQ )
| ( aElementOf0 @ SV46 @ xO ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(329,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ )
| ( xQ = slcrc0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(330,plain,
! [SV13: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ SV47 @ ( szDzozmdt0 @ SV13 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SV47 ) ) )
= $true )
| ( ( aFunction0 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV48: $i] :
( ( ~ ( aElementOf0 @ SV48 @ xO )
| ( aElementOf0 @ SV48 @ xS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV14: $i,SV49: $i] :
( ( ( ~ ( aElementOf0 @ SV49 @ ( szDzozmdt0 @ SV14 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SV49 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) ) )
= $true )
| ( ( aFunction0 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(333,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(334,plain,
! [SV16: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ SV50 @ SV16 )
| ( aElement0 @ SV50 ) )
= $true )
| ( ( aSet0 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(335,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
| ~ ( ( SV38 != slcrc0 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(336,plain,
! [SV20: $i] :
( ( ( ~ ( aSet0 @ SV20 )
| ~ ( isFinite0 @ SV20 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(337,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) ) )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(338,plain,
! [SV22: $i] :
( ( ( ~ ( aSubsetOf0 @ SV22 @ szNzAzT0 )
| ~ ( isFinite0 @ SV22 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(339,plain,
! [SV24: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(340,plain,
! [SV51: $i] :
( ( ~ ( aElementOf0 @ SV51 @ xQ )
| ( aElementOf0 @ SV51 @ szNzAzT0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(341,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(342,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
| ~ ( aSet0 @ SV45 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(343,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(344,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(345,plain,
! [SV29: $i,SV52: $i] :
( ( ( ~ ( aElementOf0 @ SV52 @ SV29 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SV52 ) @ SV52 )
= SV29 ) )
= $true )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(346,plain,
! [SV30: $i] :
( ( ( SV30 = sz00 )
= $true )
| ( ( ~ ! [SY80: $i] :
~ ~ ( ~ ( aElementOf0 @ SY80 @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ SY80 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(347,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(348,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(349,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 )
| ~ ( aSet0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(350,plain,
! [SV34: $i,SV8: $i] :
( ( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(351,plain,
! [SV35: $i,SV9: $i] :
( ( ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(352,plain,
! [SV36: $i,SV10: $i] :
( ( ( ~ ( aFunction0 @ SV10 )
| ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(353,plain,
( ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(354,plain,
( ( ~ ( aSubsetOf0 @ xS @ szNzAzT0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(355,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xQ )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(356,plain,
( ( aSubsetOf0 @ xQ @ xS )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(357,plain,
( ( ~ ( aElementOf0 @ sK1_SX0 @ xQ )
| ( aElementOf0 @ sK1_SX0 @ xS ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[327]) ).
thf(358,plain,
! [SV46: $i] :
( ( ( ~ ( aElementOf0 @ SV46 @ xQ ) )
= $true )
| ( ( aElementOf0 @ SV46 @ xO )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(359,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(360,plain,
( ( xQ = slcrc0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(361,plain,
! [SV13: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ SV47 @ ( szDzozmdt0 @ SV13 ) ) )
= $true )
| ( ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SV47 ) )
= $true )
| ( ( aFunction0 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(362,plain,
! [SV48: $i] :
( ( ( ~ ( aElementOf0 @ SV48 @ xO ) )
= $true )
| ( ( aElementOf0 @ SV48 @ xS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(363,plain,
! [SV14: $i,SV49: $i] :
( ( ( ~ ( aElementOf0 @ SV49 @ ( szDzozmdt0 @ SV14 ) ) )
= $true )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SV49 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) )
= $true )
| ( ( aFunction0 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(364,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(365,plain,
! [SV16: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ SV50 @ SV16 ) )
= $true )
| ( ( aElement0 @ SV50 )
= $true )
| ( ( aSet0 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(366,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
| ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(367,plain,
! [SV20: $i] :
( ( ( ~ ( aSet0 @ SV20 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV20 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(368,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(369,plain,
! [SV22: $i] :
( ( ( ~ ( aSubsetOf0 @ SV22 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( isFinite0 @ SV22 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(370,plain,
! [SV24: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 ) )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(371,plain,
! [SV24: $i] :
( ( ( ~ ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(372,plain,
! [SV51: $i] :
( ( ( ~ ( aElementOf0 @ SV51 @ xQ ) )
= $true )
| ( ( aElementOf0 @ SV51 @ szNzAzT0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(373,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(374,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
| ~ ( aSet0 @ SV45 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(376,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(377,plain,
! [SV29: $i,SV52: $i] :
( ( ( ~ ( aElementOf0 @ SV52 @ SV29 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SV52 ) @ SV52 )
= SV29 )
= $true )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(378,plain,
! [SV30: $i] :
( ( ( ! [SY80: $i] :
~ ~ ( ~ ( aElementOf0 @ SY80 @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ SY80 ) ) ) )
= $false )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(379,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(380,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(381,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( aSet0 @ SV4 ) )
= $true )
| ( ( ~ ( aSet0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(382,plain,
! [SV34: $i,SV8: $i] :
( ( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(383,plain,
! [SV35: $i,SV9: $i] :
( ( ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(384,plain,
! [SV36: $i,SV10: $i] :
( ( ( ~ ( aFunction0 @ SV10 ) )
= $true )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(385,plain,
( ( ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(386,plain,
( ( aSubsetOf0 @ xS @ szNzAzT0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(387,plain,
( ( ~ ( aElementOf0 @ sK2_SX0 @ xQ )
| ( aElementOf0 @ sK2_SX0 @ xS ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[355]) ).
thf(388,plain,
( ( ~ ( aElementOf0 @ sK1_SX0 @ xQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(389,plain,
( ( aElementOf0 @ sK1_SX0 @ xS )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(390,plain,
! [SV46: $i] :
( ( ( aElementOf0 @ SV46 @ xQ )
= $false )
| ( ( aElementOf0 @ SV46 @ xO )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(391,plain,
( ( ~ ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(392,plain,
! [SV13: $i,SV47: $i] :
( ( ( aElementOf0 @ SV47 @ ( szDzozmdt0 @ SV13 ) )
= $false )
| ( ( aElement0 @ ( sdtlpdtrp0 @ SV13 @ SV47 ) )
= $true )
| ( ( aFunction0 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(393,plain,
! [SV48: $i] :
( ( ( aElementOf0 @ SV48 @ xO )
= $false )
| ( ( aElementOf0 @ SV48 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(394,plain,
! [SV14: $i,SV49: $i] :
( ( ( aElementOf0 @ SV49 @ ( szDzozmdt0 @ SV14 ) )
= $false )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV14 @ SV49 ) @ ( sdtlcdtrc0 @ SV14 @ ( szDzozmdt0 @ SV14 ) ) )
= $true )
| ( ( aFunction0 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(395,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(396,plain,
! [SV16: $i,SV50: $i] :
( ( ( aElementOf0 @ SV50 @ SV16 )
= $false )
| ( ( aElement0 @ SV50 )
= $true )
| ( ( aSet0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(397,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(398,plain,
! [SV20: $i] :
( ( ( aSet0 @ SV20 )
= $false )
| ( ( ~ ( isFinite0 @ SV20 ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(399,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(400,plain,
! [SV22: $i] :
( ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( ~ ( isFinite0 @ SV22 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(401,plain,
! [SV24: $i] :
( ( ( aElementOf0 @ ( szszuzczcdt0 @ SV24 ) @ szNzAzT0 )
= $true )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(402,plain,
! [SV24: $i] :
( ( ( ( szszuzczcdt0 @ SV24 )
!= sz00 )
= $true )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(403,plain,
! [SV51: $i] :
( ( ( aElementOf0 @ SV51 @ xQ )
= $false )
| ( ( aElementOf0 @ SV51 @ szNzAzT0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(404,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(405,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
| ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(406,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(407,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(408,plain,
! [SV29: $i,SV52: $i] :
( ( ( aElementOf0 @ SV52 @ SV29 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtmndt0 @ SV29 @ SV52 ) @ SV52 )
= SV29 )
= $true )
| ( ( aSet0 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(409,plain,
! [SV30: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK3_SY80 @ SV30 ) @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ ( sK3_SY80 @ SV30 ) ) ) ) )
= $false )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[378]) ).
thf(410,plain,
! [SV31: $i,SV1: $i] :
( ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(411,plain,
! [SV32: $i,SV3: $i] :
( ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(412,plain,
! [SV33: $i,SV4: $i] :
( ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ( aSet0 @ SV33 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(413,plain,
! [SV34: $i,SV8: $i] :
( ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(414,plain,
! [SV35: $i,SV9: $i] :
( ( ( aElementOf0 @ SV9 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV35 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(415,plain,
! [SV36: $i,SV10: $i] :
( ( ( aFunction0 @ SV10 )
= $false )
| ( ( ~ ( aElement0 @ SV36 ) )
= $true )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(416,plain,
( ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(417,plain,
( ( ~ ( aElementOf0 @ sK2_SX0 @ xQ ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(418,plain,
( ( aElementOf0 @ sK2_SX0 @ xS )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(419,plain,
( ( aElementOf0 @ sK1_SX0 @ xQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(420,plain,
( ( ! [SX0: $i] :
~ ( aElementOf0 @ SX0 @ xQ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(421,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(422,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) ) )
= $false )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(423,plain,
! [SV20: $i] :
( ( ( isFinite0 @ SV20 )
= $false )
| ( ( aSet0 @ SV20 )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( aSubsetOf0 @ SY71 @ SV20 )
| ( isFinite0 @ SY71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(424,plain,
! [SV39: $i,SV21: $i] :
( ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV39 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(425,plain,
! [SV22: $i] :
( ( ( isFinite0 @ SV22 )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(426,plain,
! [SV24: $i] :
( ( ( ( szszuzczcdt0 @ SV24 )
= sz00 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(427,plain,
! [SV40: $i,SV25: $i] :
( ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV40 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(428,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) ) )
= $true )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(429,plain,
! [SV42: $i,SV27: $i] :
( ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV42 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(430,plain,
! [SV43: $i,SV28: $i] :
( ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV43 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(431,plain,
! [SV30: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK3_SY80 @ SV30 ) @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ ( sK3_SY80 @ SV30 ) ) ) ) )
= $true )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(432,plain,
! [SV1: $i,SV31: $i] :
( ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(433,plain,
! [SV3: $i,SV32: $i] :
( ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(434,plain,
! [SV4: $i,SV33: $i] :
( ( ( aSet0 @ SV33 )
= $false )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
| ( SV4 = SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(435,plain,
! [SV8: $i,SV34: $i] :
( ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( ( sdtlseqdt0 @ SV8 @ SV34 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(436,plain,
! [SV9: $i,SV35: $i] :
( ( ( aElementOf0 @ SV35 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV9 @ szNzAzT0 )
= $false )
| ( ( ~ ( iLess0 @ SV9 @ SV35 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(437,plain,
! [SV10: $i,SV36: $i] :
( ( ( aElement0 @ SV36 )
= $false )
| ( ( aFunction0 @ SV10 )
= $false )
| ( ( aSubsetOf0 @ ( sdtlbdtrb0 @ SV10 @ SV36 ) @ ( szDzozmdt0 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(438,plain,
( ( ~ ( aSet0 @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(439,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(440,plain,
( ( aElementOf0 @ sK2_SX0 @ xQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(441,plain,
( ( ~ ( aElementOf0 @ sK4_SX0 @ xQ ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[420]) ).
thf(442,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(443,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
| ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(444,plain,
! [SV20: $i,SV53: $i] :
( ( ( ~ ( aSubsetOf0 @ SV53 @ SV20 )
| ( isFinite0 @ SV53 ) )
= $true )
| ( ( aSet0 @ SV20 )
= $false )
| ( ( isFinite0 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(445,plain,
! [SV21: $i,SV39: $i] :
( ( ( aElementOf0 @ SV39 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
| ( SV21 = SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(446,plain,
! [SV22: $i] :
( ( ( ! [SY73: $i] :
~ ~ ( ~ ( aElementOf0 @ SY73 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ SY73 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(447,plain,
! [SV25: $i,SV40: $i] :
( ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(448,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) ) )
= $false )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(449,plain,
! [SV27: $i,SV42: $i] :
( ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(450,plain,
! [SV28: $i,SV43: $i] :
( ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
| ( SV28 = SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(451,plain,
! [SV30: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY80 @ SV30 ) @ szNzAzT0 )
| ( SV30
!= ( szszuzczcdt0 @ ( sK3_SY80 @ SV30 ) ) ) )
= $false )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(452,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(453,plain,
! [SV32: $i,SV3: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV3 @ SV32 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(454,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) ) )
= $true )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(455,plain,
! [SV34: $i,SV8: $i] :
( ( ( sdtlseqdt0 @ SV8 @ SV34 )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV34 ) @ SV8 )
= $true )
| ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(456,plain,
! [SV35: $i,SV9: $i] :
( ( ( ~ ( iLess0 @ SV9 @ SV35 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV9 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV35 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(457,plain,
( ( aSet0 @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(458,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xS )
| ( aElementOf0 @ SX0 @ szNzAzT0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(459,plain,
( ( aElementOf0 @ sK4_SX0 @ xQ )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(460,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(461,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(462,plain,
! [SV20: $i,SV53: $i] :
( ( ( ~ ( aSubsetOf0 @ SV53 @ SV20 ) )
= $true )
| ( ( isFinite0 @ SV53 )
= $true )
| ( ( aSet0 @ SV20 )
= $false )
| ( ( isFinite0 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(463,plain,
! [SV39: $i,SV21: $i] :
( ( ( ( szszuzczcdt0 @ SV21 )
!= ( szszuzczcdt0 @ SV39 ) )
= $true )
| ( ( SV21 = SV39 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV39 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(464,plain,
! [SV22: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY73 @ SV22 ) @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ ( sK5_SY73 @ SV22 ) ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[446]) ).
thf(465,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(466,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( aSet0 @ SV26 )
| ~ ( aSet0 @ SV41 ) )
= $true )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(467,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
| ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(468,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(469,plain,
! [SV30: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY80 @ SV30 ) @ szNzAzT0 ) )
= $false )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(470,plain,
! [SV30: $i] :
( ( ( SV30
!= ( szszuzczcdt0 @ ( sK3_SY80 @ SV30 ) ) )
= $false )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(471,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(472,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(473,plain,
! [SV32: $i,SV3: $i] :
( ( ( sdtlseqdt0 @ SV3 @ SV32 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(474,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) ) )
= $false )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(475,plain,
! [SV35: $i,SV9: $i] :
( ( ( iLess0 @ SV9 @ SV35 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV9 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV35 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(476,plain,
! [SV54: $i] :
( ( ~ ( aElementOf0 @ SV54 @ xS )
| ( aElementOf0 @ SV54 @ szNzAzT0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(477,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(478,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(479,plain,
! [SV20: $i,SV53: $i] :
( ( ( aSubsetOf0 @ SV53 @ SV20 )
= $false )
| ( ( isFinite0 @ SV53 )
= $true )
| ( ( aSet0 @ SV20 )
= $false )
| ( ( isFinite0 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(480,plain,
! [SV39: $i,SV21: $i] :
( ( ( ( szszuzczcdt0 @ SV21 )
= ( szszuzczcdt0 @ SV39 ) )
= $false )
| ( ( SV21 = SV39 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV39 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(481,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK5_SY73 @ SV22 ) @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ ( sK5_SY73 @ SV22 ) ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(482,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(483,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(484,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( aSet0 @ SV26 ) )
= $true )
| ( ( ~ ( aSet0 @ SV41 ) )
= $true )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(485,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(486,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) ) )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(487,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(488,plain,
! [SV30: $i] :
( ( ( aElementOf0 @ ( sK3_SY80 @ SV30 ) @ szNzAzT0 )
= $true )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(489,plain,
! [SV30: $i] :
( ( ( SV30
= ( szszuzczcdt0 @ ( sK3_SY80 @ SV30 ) ) )
= $true )
| ( ( SV30 = sz00 )
= $true )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(490,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV1 @ SV31 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(491,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
| ( sdtlseqdt0 @ SV1 @ SV31 ) )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(492,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( aSubsetOf0 @ SV4 @ SV33 )
| ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
= $true )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(493,plain,
! [SV54: $i] :
( ( ( ~ ( aElementOf0 @ SV54 @ xS ) )
= $true )
| ( ( aElementOf0 @ SV54 @ szNzAzT0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(494,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV37 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(495,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(496,plain,
! [SV22: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY73 @ SV22 ) @ szNzAzT0 )
| ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ ( sK5_SY73 @ SV22 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(497,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(498,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
| ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(499,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( aSet0 @ SV26 )
= $false )
| ( ( ~ ( aSet0 @ SV41 ) )
= $true )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(500,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV27 @ SV42 )
| ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(501,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
| ( sdtlseqdt0 @ SV27 @ SV42 ) )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(502,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV28 @ SV43 )
| ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
= $true )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(503,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV1 @ SV31 ) )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(504,plain,
! [SV31: $i,SV1: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV1 @ SV31 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(505,plain,
! [SV33: $i,SV4: $i] :
( ( ( ~ ( aSubsetOf0 @ SV4 @ SV33 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
= $true )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(506,plain,
! [SV54: $i] :
( ( ( aElementOf0 @ SV54 @ xS )
= $false )
| ( ( aElementOf0 @ SV54 @ szNzAzT0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(507,plain,
! [SV44: $i,SV15: $i,SV37: $i] :
( ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV44 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(508,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( aSubsetOf0 @ SV19 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(509,plain,
! [SV22: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY73 @ SV22 ) @ szNzAzT0 ) )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(510,plain,
! [SV22: $i] :
( ( ( ~ ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ ( sK5_SY73 @ SV22 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(511,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) ) )
= $true )
| ( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(512,plain,
! [SV40: $i,SV25: $i] :
( ( ( ~ ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(513,plain,
! [SV45: $i,SV26: $i,SV41: $i] :
( ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( ~ ( aSet0 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(514,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV27 @ SV42 ) )
= $true )
| ( ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(515,plain,
! [SV42: $i,SV27: $i] :
( ( ( ~ ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV27 @ SV42 )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(516,plain,
! [SV43: $i,SV28: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV28 @ SV43 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
= $true )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(517,plain,
! [SV31: $i,SV1: $i] :
( ( ( sdtlseqdt0 @ SV1 @ SV31 )
= $false )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(518,plain,
! [SV31: $i,SV1: $i] :
( ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV1 ) @ ( szszuzczcdt0 @ SV31 ) )
= $false )
| ( ( sdtlseqdt0 @ SV1 @ SV31 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(519,plain,
! [SV33: $i,SV4: $i] :
( ( ( aSubsetOf0 @ SV4 @ SV33 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV33 @ SV4 ) )
= $true )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(520,plain,
! [SV37: $i,SV15: $i,SV44: $i] :
( ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
| ( sdtlseqdt0 @ SV15 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(521,plain,
! [SV38: $i,SV19: $i] :
( ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV38 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(522,plain,
! [SV22: $i] :
( ( ( aElementOf0 @ ( sK5_SY73 @ SV22 ) @ szNzAzT0 )
= $true )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(523,plain,
! [SV22: $i] :
( ( ( aSubsetOf0 @ SV22 @ ( slbdtrb0 @ ( sK5_SY73 @ SV22 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(524,plain,
! [SV40: $i,SV25: $i] :
( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $false )
| ( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(525,plain,
! [SV40: $i,SV25: $i] :
( ( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
| ( SV25 = SV40 ) )
= $false )
| ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(526,plain,
! [SV41: $i,SV26: $i,SV45: $i] :
( ( ( aSet0 @ SV45 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
| ( aSubsetOf0 @ SV26 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(527,plain,
! [SV42: $i,SV27: $i] :
( ( ( sdtlseqdt0 @ SV27 @ SV42 )
= $false )
| ( ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(528,plain,
! [SV42: $i,SV27: $i] :
( ( ( aSubsetOf0 @ ( slbdtrb0 @ SV27 ) @ ( slbdtrb0 @ SV42 ) )
= $false )
| ( ( sdtlseqdt0 @ SV27 @ SV42 )
= $true )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV42 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(529,plain,
! [SV43: $i,SV28: $i] :
( ( ( sdtlseqdt0 @ SV28 @ SV43 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV43 @ SV28 ) )
= $true )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(530,plain,
! [SV4: $i,SV33: $i] :
( ( ( aSubsetOf0 @ SV33 @ SV4 )
= $false )
| ( ( aSubsetOf0 @ SV4 @ SV33 )
= $false )
| ( ( SV4 = SV33 )
= $true )
| ( ( aSet0 @ SV4 )
= $false )
| ( ( aSet0 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(531,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(532,plain,
! [SV19: $i,SV38: $i] :
( ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( ~ ( ( SV19 != slcrc0 ) ) )
= $true )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(533,plain,
! [SV40: $i,SV25: $i] :
( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
= $true )
| ( ( SV25 = SV40 )
= $true )
| ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(534,plain,
! [SV40: $i,SV25: $i] :
( ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(535,plain,
! [SV40: $i,SV25: $i] :
( ( ( SV25 = SV40 )
= $false )
| ( ( aElementOf0 @ SV25 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV40 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV40 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(536,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(537,plain,
! [SV28: $i,SV43: $i] :
( ( ( sdtlseqdt0 @ SV43 @ SV28 )
= $false )
| ( ( sdtlseqdt0 @ SV28 @ SV43 )
= $false )
| ( ( SV28 = SV43 )
= $true )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV43 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(538,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(539,plain,
! [SV38: $i,SV19: $i] :
( ( ( SV19 != slcrc0 )
= $false )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(540,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(541,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV15 @ SV37 )
| ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
= $true )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(542,plain,
! [SV38: $i,SV19: $i] :
( ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( ~ ( ( SV38 != slcrc0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(543,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( aSubsetOf0 @ SV26 @ SV41 )
| ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
= $true )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(544,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV15 @ SV37 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
= $true )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(545,plain,
! [SV19: $i,SV38: $i] :
( ( ( SV38 != slcrc0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(546,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( aSubsetOf0 @ SV26 @ SV41 ) )
= $true )
| ( ( ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
= $true )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(547,plain,
! [SV44: $i,SV37: $i,SV15: $i] :
( ( ( sdtlseqdt0 @ SV15 @ SV37 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV37 @ SV44 ) )
= $true )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(548,plain,
! [SV19: $i,SV38: $i] :
( ( ( SV38 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
| ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(549,plain,
! [SV45: $i,SV41: $i,SV26: $i] :
( ( ( aSubsetOf0 @ SV26 @ SV41 )
= $false )
| ( ( ~ ( aSubsetOf0 @ SV41 @ SV45 ) )
= $true )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(550,plain,
! [SV15: $i,SV44: $i,SV37: $i] :
( ( ( sdtlseqdt0 @ SV37 @ SV44 )
= $false )
| ( ( sdtlseqdt0 @ SV15 @ SV37 )
= $false )
| ( ( sdtlseqdt0 @ SV15 @ SV44 )
= $true )
| ( ( aElementOf0 @ SV37 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV44 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(551,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) ) )
= $true )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(552,plain,
! [SV26: $i,SV45: $i,SV41: $i] :
( ( ( aSubsetOf0 @ SV41 @ SV45 )
= $false )
| ( ( aSubsetOf0 @ SV26 @ SV41 )
= $false )
| ( ( aSubsetOf0 @ SV26 @ SV45 )
= $true )
| ( ( aSet0 @ SV41 )
= $false )
| ( ( aSet0 @ SV26 )
= $false )
| ( ( aSet0 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(553,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) ) )
= $false )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(554,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
| ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
= $true )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(555,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 ) )
= $true )
| ( ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
= $true )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(556,plain,
! [SV38: $i,SV19: $i] :
( ( ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
= $false )
| ( ( ~ ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 ) )
= $true )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(557,plain,
! [SV19: $i,SV38: $i] :
( ( ( aElementOf0 @ ( szmzizndt0 @ SV38 ) @ SV19 )
= $false )
| ( ( aElementOf0 @ ( szmzizndt0 @ SV19 ) @ SV38 )
= $false )
| ( ( ( szmzizndt0 @ SV19 )
= ( szmzizndt0 @ SV38 ) )
= $true )
| ( ( SV19 = slcrc0 )
= $true )
| ( ( aSubsetOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aSubsetOf0 @ SV38 @ szNzAzT0 )
= $false )
| ( ( SV38 = slcrc0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(558,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[131,557,552,550,537,535,534,533,530,528,527,523,522,518,517,506,489,488,480,479,475,473,459,457,455,440,437,426,419,418,408,403,401,396,394,393,392,390,389,386,360,356,325,311,308,303,302,298,293,291,289,284,283,282,279,253,142]) ).
thf(559,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM607+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n026.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 13:31:01 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/0.68
% 2.58/0.68 No.of.Axioms: 36
% 2.58/0.68
% 2.58/0.68 Length.of.Defs: 0
% 2.58/0.68
% 2.58/0.68 Contains.Choice.Funs: false
% 2.58/0.68 ...............
% 2.58/0.68
% 2.58/0.68 ********************************
% 2.58/0.68 * All subproblems solved! *
% 2.58/0.68 ********************************
% 2.58/0.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:36,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:558,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.58/0.68
% 2.58/0.68 %**** Beginning of derivation protocol ****
% 2.58/0.68 % SZS output start CNFRefutation
% See solution above
% 2.58/0.68
% 2.58/0.68 %**** End of derivation protocol ****
% 2.58/0.68 %**** no. of clauses in derivation: 505 ****
% 2.58/0.68 %**** clause counter: 558 ****
% 2.58/0.68
% 2.58/0.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:36,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:558,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------