%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM615+1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 10:34:38 AM UTC 2026
% Result : Theorem 2.37s 0.67s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 32
% Syntax : Number of formulae : 350 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 2507 ( 858 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 4351 ( 833 ~; 713 |; 62 &;2641 @)
% ( 6 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 18 con; 0-2 aty)
% Number of variables : 551 ( 0 ^; 540 !; 11 ?; 551 :)
% 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_SY41,type,
sK1_SY41: $i > $i ).
thf(tp_sK2_SY40,type,
sK2_SY40: $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_xP,type,
xP: $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(tp_xp,type,
xp: $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/sandbox/benchmark/theBenchmark.p',mImgRng) ).
thf(5,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgElm) ).
thf(13,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
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/sandbox/benchmark/theBenchmark.p',mSegSucc) ).
thf(18,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSegFin) ).
thf(27,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(28,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
thf(32,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRefl) ).
thf(33,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mSuccLess) ).
thf(36,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
thf(37,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessRel) ).
thf(38,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(41,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
thf(42,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
thf(59,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(66,axiom,
aElementOf0 @ xp @ xO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
thf(67,axiom,
aElementOf0 @ xp @ xQ,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
thf(69,axiom,
( xp
= ( szmzizndt0 @ xQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
thf(70,axiom,
aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5116) ).
thf(75,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W1 )
= W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
thf(77,axiom,
( ( aSet0 @ xO )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
thf(78,axiom,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
thf(88,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0 != W1 ) )
=> ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W0 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3821) ).
thf(98,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
thf(100,conjecture,
? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(101,negated_conjecture,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[100]) ).
thf(102,plain,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $false ),
inference(unfold_def,[status(thm)],[101]) ).
thf(103,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(104,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(105,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(106,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(107,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(108,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(109,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(110,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(111,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(112,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(113,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(114,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(115,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(116,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(117,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(118,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(119,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(120,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(121,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(122,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(123,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ W0 @ W1 ) @ W1 )
= W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(124,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(125,plain,
( ( aElementOf0 @ xp @ xO )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(126,plain,
( ( aElementOf0 @ xp @ xQ )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(127,plain,
( ( xp
= ( szmzizndt0 @ xQ ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(128,plain,
( ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(129,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W1 )
= W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(130,plain,
( ( ( aSet0 @ xO )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(131,plain,
( ( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(132,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0 != W1 ) )
=> ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W0 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(133,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(134,plain,
( ( ~ ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[102]) ).
thf(135,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(136,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0 != W1 ) )
=> ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W0 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(137,plain,
( ( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
& ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(138,plain,
( ( ( aSet0 @ xO )
& ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(139,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xO )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W1 )
= W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(140,plain,
( ( aElementOf0 @ xQ @ ( szDzozmdt0 @ xc ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(141,plain,
( ( xp
= ( szmzizndt0 @ xQ ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(142,plain,
( ( aElementOf0 @ xp @ xQ )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(143,plain,
( ( aElementOf0 @ xp @ xO )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(144,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(145,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( ( sdtpldt0 @ ( sdtmndt0 @ W0 @ W1 ) @ W1 )
= W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(146,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(147,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(148,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(149,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(150,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(151,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(152,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ sz00 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(153,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(154,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(155,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(156,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(157,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)],[111]) ).
thf(158,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(159,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(160,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(161,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( isFinite0 @ ( slbdtrb0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(162,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)],[106]) ).
thf(163,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( sbrdtbr0 @ ( slbdtrb0 @ W0 ) )
= W0 ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(164,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElement0 @ ( sdtlpdtrp0 @ W0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(165,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( sdtlcdtrc0 @ W0 @ ( szDzozmdt0 @ W0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(166,plain,
( ( ~ ? [W0: $i] :
( ( aElementOf0 @ W0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
& ( ( sdtlpdtrp0 @ xe @ W0 )
= xp ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(167,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0 = sz00 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElementOf0 @ SX1 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( ( sbrdtbr0 @ ( slbdtrb0 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(169,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SX0 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(170,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xO )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX1 )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(171,plain,
( ( ~ ( ~ ( aSet0 @ xO )
| ( xO
!= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(174,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(175,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(176,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)],[165]) ).
thf(177,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)],[156]) ).
thf(178,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ SX0 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(179,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(180,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)],[153]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SX0 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(182,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)],[162]) ).
thf(183,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SX0 )
!= ( szszuzczcdt0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(184,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)],[157]) ).
thf(185,plain,
( ( ~ ( ~ ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
| ~ ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(186,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElement0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(187,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( isFinite0 @ ( slbdtrb0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(188,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(190,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( iLess0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(191,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SX0 @ SX1 ) @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(193,plain,
! [SV1: $i] :
( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ( SV1 = sz00 )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( aElementOf0 @ SY40 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(194,plain,
! [SV2: $i] :
( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ( ( sbrdtbr0 @ ( slbdtrb0 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(195,plain,
! [SV3: $i] :
( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(196,plain,
! [SV4: $i] :
( ( ~ ( aElementOf0 @ SV4 @ xO )
| ~ ! [SY41: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY41 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY41 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SY41 )
!= SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(197,plain,
( ( ~ ( aSet0 @ xO )
| ( xO
!= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(198,plain,
! [SV5: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY42 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV5 @ SY42 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SY42 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(199,plain,
! [SV6: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY43 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV6 @ SY43 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(200,plain,
! [SV7: $i] :
( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV7 @ ( szszuzczcdt0 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(201,plain,
! [SV8: $i] :
( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV8 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(202,plain,
! [SV9: $i] :
( ( ~ ( aFunction0 @ SV9 )
| ! [SY44: $i] :
( ~ ( aElementOf0 @ SY44 @ ( szDzozmdt0 @ SV9 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SY44 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(203,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY45 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SY45 )
| ~ ( sdtlseqdt0 @ SY45 @ SV10 ) )
| ( SV10 = SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(204,plain,
! [SV11: $i] :
( ( ~ ( aFunction0 @ SV11 )
| ! [SY46: $i] :
( ~ ( aElementOf0 @ SY46 @ ( szDzozmdt0 @ SV11 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(205,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(206,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY47 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SY47 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SY47 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SY47 ) )
| ( sdtlseqdt0 @ SV12 @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(207,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY48 @ szNzAzT0 ) )
| ~ ( ( SV13 != SY48 ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(208,plain,
! [SV14: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY49 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY49 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SY49 ) )
| ( SV14 = SY49 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SY49 ) )
| ( SV14 = SY49 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY49 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(209,plain,
! [SV15: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY50 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SY50 ) )
| ( SV15 = SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(210,plain,
! [SV16: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY51 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY52 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SY51 )
| ~ ( sdtlseqdt0 @ SY51 @ SY52 ) )
| ( sdtlseqdt0 @ SV16 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(211,plain,
( ( ~ ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
| ~ ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(212,plain,
! [SV17: $i] :
( ( ~ ( aSet0 @ SV17 )
| ! [SY53: $i] :
( ~ ( aElementOf0 @ SY53 @ SV17 )
| ( aElement0 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(213,plain,
! [SV18: $i] :
( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 )
| ( isFinite0 @ ( slbdtrb0 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(214,plain,
! [SV19: $i] :
( ( ~ ( aElementOf0 @ SV19 @ szNzAzT0 )
| ( SV19
!= ( szszuzczcdt0 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(215,plain,
! [SV20: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY54 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV20 @ SY54 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(216,plain,
! [SV21: $i] :
( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 )
| ( iLess0 @ SV21 @ ( szszuzczcdt0 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV22: $i] :
( ( ~ ( aElementOf0 @ SV22 @ szNzAzT0 )
| ( sdtlseqdt0 @ sz00 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV23: $i] :
( ( ~ ( aSet0 @ SV23 )
| ! [SY55: $i] :
( ~ ( aElementOf0 @ SY55 @ SV23 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SY55 ) @ SY55 )
= SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 ) )
= $true )
| ( ( ( SV1 = sz00 )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( aElementOf0 @ SY40 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(220,plain,
! [SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 ) )
= $true )
| ( ( ( sbrdtbr0 @ ( slbdtrb0 @ SV2 ) )
= SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(221,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(222,plain,
! [SV4: $i] :
( ( ( ~ ( aElementOf0 @ SV4 @ xO ) )
= $true )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY41 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY41 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SY41 )
!= SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(223,plain,
( ( ~ ( aSet0 @ xO ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(224,plain,
( ( xO
!= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(225,plain,
! [SV24: $i,SV5: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(226,plain,
! [SV25: $i,SV6: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(227,plain,
! [SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV7 @ ( szszuzczcdt0 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(228,plain,
! [SV8: $i] :
( ( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(229,plain,
! [SV9: $i] :
( ( ( ~ ( aFunction0 @ SV9 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( aElementOf0 @ SY44 @ ( szDzozmdt0 @ SV9 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SY44 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(230,plain,
! [SV26: $i,SV10: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(231,plain,
! [SV11: $i] :
( ( ( ~ ( aFunction0 @ SV11 ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( aElementOf0 @ SY46 @ ( szDzozmdt0 @ SV11 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(232,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SX0 )
!= xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(233,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(234,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
| ~ ( ( SV13 != SV28 ) ) )
| ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(235,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(236,plain,
! [SV30: $i,SV15: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(237,plain,
! [SV31: $i,SV16: $i] :
( ( ! [SY56: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY56 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SY56 ) )
| ( sdtlseqdt0 @ SV16 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(238,plain,
( ( ~ ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(239,plain,
( ( ~ ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(240,plain,
! [SV17: $i] :
( ( ( ~ ( aSet0 @ SV17 ) )
= $true )
| ( ( ! [SY53: $i] :
( ~ ( aElementOf0 @ SY53 @ SV17 )
| ( aElement0 @ SY53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(241,plain,
! [SV18: $i] :
( ( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
= $true )
| ( ( isFinite0 @ ( slbdtrb0 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(242,plain,
! [SV19: $i] :
( ( ( ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) )
= $true )
| ( ( SV19
!= ( szszuzczcdt0 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(243,plain,
! [SV32: $i,SV20: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(244,plain,
! [SV21: $i] :
( ( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
= $true )
| ( ( iLess0 @ SV21 @ ( szszuzczcdt0 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(245,plain,
! [SV22: $i] :
( ( ( ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ sz00 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(246,plain,
! [SV23: $i] :
( ( ( ~ ( aSet0 @ SV23 ) )
= $true )
| ( ( ! [SY55: $i] :
( ~ ( aElementOf0 @ SY55 @ SV23 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SY55 ) @ SY55 )
= SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(247,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( ( SV1 = sz00 )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( aElementOf0 @ SY40 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(248,plain,
! [SV2: $i] :
( ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( ( sbrdtbr0 @ ( slbdtrb0 @ SV2 ) )
= SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(249,plain,
! [SV3: $i] :
( ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(250,plain,
! [SV4: $i] :
( ( ( aElementOf0 @ SV4 @ xO )
= $false )
| ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY41 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY41 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SY41 )
!= SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(251,plain,
( ( aSet0 @ xO )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(252,plain,
( ( xO
= ( sdtlcdtrc0 @ xe @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(253,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(254,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(255,plain,
! [SV7: $i] :
( ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV7 @ ( szszuzczcdt0 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(256,plain,
! [SV8: $i] :
( ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(257,plain,
! [SV9: $i] :
( ( ( aFunction0 @ SV9 )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( aElementOf0 @ SY44 @ ( szDzozmdt0 @ SV9 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SY44 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(258,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(259,plain,
! [SV11: $i] :
( ( ( aFunction0 @ SV11 )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( aElementOf0 @ SY46 @ ( szDzozmdt0 @ SV11 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(260,plain,
! [SV33: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV33 )
!= xp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(261,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(262,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
| ~ ( ( SV13 != SV28 ) ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(263,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(264,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(266,plain,
( ( aElementOf0 @ ( szDzizrdt0 @ xd ) @ xT )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(267,plain,
( ( isCountable0 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(268,plain,
! [SV17: $i] :
( ( ( aSet0 @ SV17 )
= $false )
| ( ( ! [SY53: $i] :
( ~ ( aElementOf0 @ SY53 @ SV17 )
| ( aElement0 @ SY53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(269,plain,
! [SV18: $i] :
( ( ( aElementOf0 @ SV18 @ szNzAzT0 )
= $false )
| ( ( isFinite0 @ ( slbdtrb0 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(270,plain,
! [SV19: $i] :
( ( ( aElementOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( SV19
!= ( szszuzczcdt0 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(271,plain,
! [SV32: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(272,plain,
! [SV21: $i] :
( ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( iLess0 @ SV21 @ ( szszuzczcdt0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(273,plain,
! [SV22: $i] :
( ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ sz00 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(274,plain,
! [SV23: $i] :
( ( ( aSet0 @ SV23 )
= $false )
| ( ( ! [SY55: $i] :
( ~ ( aElementOf0 @ SY55 @ SV23 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SY55 ) @ SY55 )
= SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(275,plain,
! [SV1: $i] :
( ( ( SV1 = sz00 )
= $true )
| ( ( ~ ! [SY40: $i] :
~ ~ ( ~ ( aElementOf0 @ SY40 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SY40 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(276,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(277,plain,
! [SV4: $i] :
( ( ( ! [SY41: $i] :
~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY41 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY41 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ SY41 )
!= SV4 ) ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(278,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) ) )
= $false )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(279,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(280,plain,
! [SV9: $i,SV35: $i] :
( ( ( ~ ( aElementOf0 @ SV35 @ ( szDzozmdt0 @ SV9 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SV35 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) ) )
= $true )
| ( ( aFunction0 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(281,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(282,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ SV11 ) )
| ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SV36 ) ) )
= $true )
| ( ( aFunction0 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(283,plain,
! [SV33: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV33 )
!= xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(284,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(285,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
| ~ ( ( SV13 != SV28 ) ) ) )
= $false )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(286,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(287,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) ) )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(288,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(289,plain,
! [SV17: $i,SV37: $i] :
( ( ( ~ ( aElementOf0 @ SV37 @ SV17 )
| ( aElement0 @ SV37 ) )
= $true )
| ( ( aSet0 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV19: $i] :
( ( ( SV19
= ( szszuzczcdt0 @ SV19 ) )
= $false )
| ( ( aElementOf0 @ SV19 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(291,plain,
! [SV32: $i,SV20: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(292,plain,
! [SV23: $i,SV38: $i] :
( ( ( ~ ( aElementOf0 @ SV38 @ SV23 )
| ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SV38 ) @ SV38 )
= SV23 ) )
= $true )
| ( ( aSet0 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(293,plain,
! [SV1: $i] :
( ( ( ! [SY40: $i] :
~ ~ ( ~ ( aElementOf0 @ SY40 @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ SY40 ) ) ) )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(294,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 ) )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(295,plain,
! [SV3: $i] :
( ( ( ~ ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(296,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ ( sK1_SY41 @ SV4 ) )
!= SV4 ) ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[277]) ).
thf(297,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(298,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(299,plain,
! [SV9: $i,SV35: $i] :
( ( ( ~ ( aElementOf0 @ SV35 @ ( szDzozmdt0 @ SV9 ) ) )
= $true )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SV35 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) )
= $true )
| ( ( aFunction0 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(300,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(301,plain,
! [SV11: $i,SV36: $i] :
( ( ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ SV11 ) ) )
= $true )
| ( ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SV36 ) )
= $true )
| ( ( aFunction0 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(302,plain,
! [SV33: $i] :
( ( ~ ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
| ( ( sdtlpdtrp0 @ xe @ SV33 )
!= xp ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(303,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(304,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
| ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(305,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(306,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(307,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(308,plain,
! [SV17: $i,SV37: $i] :
( ( ( ~ ( aElementOf0 @ SV37 @ SV17 ) )
= $true )
| ( ( aElement0 @ SV37 )
= $true )
| ( ( aSet0 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(309,plain,
! [SV32: $i,SV20: $i] :
( ( ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(310,plain,
! [SV23: $i,SV38: $i] :
( ( ( ~ ( aElementOf0 @ SV38 @ SV23 ) )
= $true )
| ( ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SV38 ) @ SV38 )
= SV23 )
= $true )
| ( ( aSet0 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(311,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK2_SY40 @ SV1 ) @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ ( sK2_SY40 @ SV1 ) ) ) ) )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(312,plain,
! [SV3: $i] :
( ( ( aElementOf0 @ ( szszuzczcdt0 @ SV3 ) @ szNzAzT0 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(313,plain,
! [SV3: $i] :
( ( ( ( szszuzczcdt0 @ SV3 )
!= sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(314,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ ( sK1_SY41 @ SV4 ) )
!= SV4 ) ) )
= $true )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(315,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(316,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV9: $i,SV35: $i] :
( ( ( aElementOf0 @ SV35 @ ( szDzozmdt0 @ SV9 ) )
= $false )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV9 @ SV35 ) @ ( sdtlcdtrc0 @ SV9 @ ( szDzozmdt0 @ SV9 ) ) )
= $true )
| ( ( aFunction0 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(319,plain,
! [SV11: $i,SV36: $i] :
( ( ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ SV11 ) )
= $false )
| ( ( aElement0 @ ( sdtlpdtrp0 @ SV11 @ SV36 ) )
= $true )
| ( ( aFunction0 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(320,plain,
! [SV33: $i] :
( ( ( ~ ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xe @ SV33 )
!= xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(321,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(324,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(325,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(326,plain,
! [SV17: $i,SV37: $i] :
( ( ( aElementOf0 @ SV37 @ SV17 )
= $false )
| ( ( aElement0 @ SV37 )
= $true )
| ( ( aSet0 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(327,plain,
! [SV32: $i,SV20: $i] :
( ( ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(328,plain,
! [SV23: $i,SV38: $i] :
( ( ( aElementOf0 @ SV38 @ SV23 )
= $false )
| ( ( ( sdtpldt0 @ ( sdtmndt0 @ SV23 @ SV38 ) @ SV38 )
= SV23 )
= $true )
| ( ( aSet0 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(329,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK2_SY40 @ SV1 ) @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ ( sK2_SY40 @ SV1 ) ) ) ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(330,plain,
! [SV3: $i] :
( ( ( ( szszuzczcdt0 @ SV3 )
= sz00 )
= $false )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(331,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
| ( ( sdtlpdtrp0 @ xe @ ( sK1_SY41 @ SV4 ) )
!= SV4 ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(332,plain,
! [SV24: $i,SV5: $i] :
( ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(333,plain,
! [SV25: $i,SV6: $i] :
( ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV25 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(334,plain,
! [SV26: $i,SV10: $i] :
( ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV26 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(335,plain,
! [SV33: $i] :
( ( ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xe @ SV33 )
!= xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(336,plain,
! [SV27: $i,SV12: $i] :
( ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV27 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(337,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(338,plain,
! [SV29: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV29 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(339,plain,
! [SV30: $i,SV15: $i] :
( ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV30 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(340,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(341,plain,
! [SV32: $i,SV20: $i] :
( ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV32 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(342,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SY40 @ SV1 ) @ szNzAzT0 )
| ( SV1
!= ( szszuzczcdt0 @ ( sK2_SY40 @ SV1 ) ) ) )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(343,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(344,plain,
! [SV4: $i] :
( ( ( ( sdtlpdtrp0 @ xe @ ( sK1_SY41 @ SV4 ) )
!= SV4 )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(345,plain,
! [SV5: $i,SV24: $i] :
( ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( ( sdtlseqdt0 @ SV5 @ SV24 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(346,plain,
! [SV6: $i,SV25: $i] :
( ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(347,plain,
! [SV10: $i,SV26: $i] :
( ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
| ( SV10 = SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(348,plain,
! [SV33: $i] :
( ( ( ( sdtlpdtrp0 @ xe @ SV33 )
= xp )
= $false )
| ( ( aElementOf0 @ SV33 @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(349,plain,
! [SV12: $i,SV27: $i] :
( ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(350,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(351,plain,
! [SV14: $i,SV29: $i] :
( ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV15: $i,SV30: $i] :
( ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
| ( SV15 = SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(353,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(354,plain,
! [SV20: $i,SV32: $i] :
( ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false )
| ( ( ~ ( iLess0 @ SV20 @ SV32 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(355,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SY40 @ SV1 ) @ szNzAzT0 ) )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(356,plain,
! [SV1: $i] :
( ( ( SV1
!= ( szszuzczcdt0 @ ( sK2_SY40 @ SV1 ) ) )
= $false )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(357,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(358,plain,
! [SV4: $i] :
( ( ( ( sdtlpdtrp0 @ xe @ ( sK1_SY41 @ SV4 ) )
= SV4 )
= $true )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(359,plain,
! [SV24: $i,SV5: $i] :
( ( ( sdtlseqdt0 @ SV5 @ SV24 )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV24 ) @ SV5 )
= $true )
| ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(360,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV6 @ SV25 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(361,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) ) )
= $true )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(362,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) )
= $false )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(365,plain,
! [SV30: $i,SV15: $i] :
( ( ( ( szszuzczcdt0 @ SV15 )
!= ( szszuzczcdt0 @ SV30 ) )
= $true )
| ( ( SV15 = SV30 )
= $true )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(366,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(367,plain,
! [SV32: $i,SV20: $i] :
( ( ( ~ ( iLess0 @ SV20 @ SV32 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(368,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ ( sK2_SY40 @ SV1 ) @ szNzAzT0 )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(369,plain,
! [SV1: $i] :
( ( ( SV1
= ( szszuzczcdt0 @ ( sK2_SY40 @ SV1 ) ) )
= $true )
| ( ( SV1 = sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(370,plain,
! [SV4: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
| ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(371,plain,
! [SV25: $i,SV6: $i] :
( ( ( sdtlseqdt0 @ SV6 @ SV25 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV25 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) ) )
= $false )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(374,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) ) )
= $false )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(375,plain,
! [SV28: $i,SV13: $i] :
( ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV28 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(377,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(378,plain,
! [SV30: $i,SV15: $i] :
( ( ( ( szszuzczcdt0 @ SV15 )
= ( szszuzczcdt0 @ SV30 ) )
= $false )
| ( ( SV15 = SV30 )
= $true )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV30 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(379,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(380,plain,
! [SV32: $i,SV20: $i] :
( ( ( iLess0 @ SV20 @ SV32 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV32 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(381,plain,
! [SV4: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(382,plain,
! [SV4: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) ) )
= $false )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(383,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV10 @ SV26 )
| ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
= $true )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(384,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(385,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
| ( sdtlseqdt0 @ SV12 @ SV27 ) )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(386,plain,
! [SV13: $i,SV28: $i] :
( ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( ~ ( ( SV13 != SV28 ) ) )
= $true )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(387,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(388,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(389,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV31 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(390,plain,
! [SV4: $i] :
( ( ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ szNzAzT0 )
= $true )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(391,plain,
! [SV4: $i] :
( ( ( aElementOf0 @ ( sK1_SY41 @ SV4 ) @ ( sdtlbdtrb0 @ xd @ ( szDzizrdt0 @ xd ) ) )
= $true )
| ( ( aElementOf0 @ SV4 @ xO )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(392,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV10 @ SV26 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
= $true )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(393,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV27 ) )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(394,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV12 @ SV27 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(395,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 != SV28 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(396,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) ) )
= $true )
| ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(397,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(398,plain,
! [SV34: $i,SV16: $i,SV31: $i] :
( ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV34 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(399,plain,
! [SV26: $i,SV10: $i] :
( ( ( sdtlseqdt0 @ SV10 @ SV26 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV26 @ SV10 ) )
= $true )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(400,plain,
! [SV27: $i,SV12: $i] :
( ( ( sdtlseqdt0 @ SV12 @ SV27 )
= $false )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(401,plain,
! [SV27: $i,SV12: $i] :
( ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV12 ) @ ( szszuzczcdt0 @ SV27 ) )
= $false )
| ( ( sdtlseqdt0 @ SV12 @ SV27 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV27 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(402,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 = SV28 )
= $true )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
!= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(403,plain,
! [SV29: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $false )
| ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(404,plain,
! [SV29: $i,SV14: $i] :
( ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
| ( SV14 = SV29 ) )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(405,plain,
! [SV31: $i,SV16: $i,SV34: $i] :
( ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
| ( sdtlseqdt0 @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(406,plain,
! [SV10: $i,SV26: $i] :
( ( ( sdtlseqdt0 @ SV26 @ SV10 )
= $false )
| ( ( sdtlseqdt0 @ SV10 @ SV26 )
= $false )
| ( ( SV10 = SV26 )
= $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV26 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(407,plain,
! [SV28: $i,SV13: $i] :
( ( ( ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV13 ) )
= ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ SV28 ) ) )
= $false )
| ( ( aElementOf0 @ SV28 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( SV13 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(408,plain,
! [SV29: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
= $true )
| ( ( SV14 = SV29 )
= $true )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(409,plain,
! [SV29: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV29 ) )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(410,plain,
! [SV29: $i,SV14: $i] :
( ( ( SV14 = SV29 )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV29 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV29 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(411,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(412,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(413,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV16 @ SV31 )
| ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
= $true )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(414,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV16 @ SV31 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
= $true )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(415,plain,
! [SV34: $i,SV31: $i,SV16: $i] :
( ( ( sdtlseqdt0 @ SV16 @ SV31 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV31 @ SV34 ) )
= $true )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(416,plain,
! [SV16: $i,SV34: $i,SV31: $i] :
( ( ( sdtlseqdt0 @ SV31 @ SV34 )
= $false )
| ( ( sdtlseqdt0 @ SV16 @ SV31 )
= $false )
| ( ( sdtlseqdt0 @ SV16 @ SV34 )
= $true )
| ( ( aElementOf0 @ SV31 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV34 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(417,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[135,416,410,409,408,407,406,401,400,391,390,380,378,371,369,368,359,358,348,330,328,326,319,317,312,290,273,272,269,267,266,256,255,252,251,248,146,143,142,141,140]) ).
thf(418,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM615+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 13:28:32 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.37/0.67
% 2.37/0.67 No.of.Axioms: 31
% 2.37/0.67
% 2.37/0.67 Length.of.Defs: 0
% 2.37/0.67
% 2.37/0.67 Contains.Choice.Funs: false
% 2.37/0.67 ..........
% 2.37/0.67
% 2.37/0.67 ********************************
% 2.37/0.67 * All subproblems solved! *
% 2.37/0.67 ********************************
% 2.37/0.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:31,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:417,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.37/0.67
% 2.37/0.67 %**** Beginning of derivation protocol ****
% 2.37/0.67 % SZS output start CNFRefutation
% See solution above
% 2.37/0.67
% 2.37/0.67 %**** End of derivation protocol ****
% 2.37/0.67 %**** no. of clauses in derivation: 350 ****
% 2.37/0.67 %**** clause counter: 417 ****
% 2.37/0.67
% 2.37/0.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:31,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:417,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------