%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 10:34:29 AM UTC 2026
% Result : Theorem 0.52s 0.40s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 231 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 1814 ( 610 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3004 ( 620 ~; 560 |; 44 &;1717 @)
% ( 6 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 9 con; 0-2 aty)
% Number of variables : 386 ( 0 ^; 378 !; 8 ?; 386 :)
% 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_SY26,type,
sK1_SY26: $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_xK,type,
xK: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xc,type,
xc: $i ).
thf(16,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ ( szszuzczcdt0 @ W1 ) ) )
<=> ( ( aElementOf0 @ W0 @ ( slbdtrb0 @ W1 ) )
| ( W0 = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).
thf(27,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(28,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHSort) ).
thf(29,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
thf(30,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 )
& ( aElementOf0 @ W2 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
thf(31,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
thf(32,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRefl) ).
thf(33,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
thf(34,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
thf(37,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(38,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
thf(39,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
thf(40,axiom,
! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
thf(41,axiom,
! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
thf(42,axiom,
aElementOf0 @ sz00 @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
thf(62,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3520) ).
thf(63,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
thf(67,axiom,
aElementOf0 @ xK @ szNzAzT0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
thf(69,conjecture,
? [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
= xK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(70,negated_conjecture,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
= xK ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[69]) ).
thf(71,plain,
( ( ? [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
= xK ) ) )
= $false ),
inference(unfold_def,[status(thm)],[70]) ).
thf(72,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(73,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(74,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(75,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(76,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(77,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(78,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(79,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(80,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(81,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,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(85,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(87,plain,
( ( xK != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(88,plain,
( ( xK != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(89,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(90,plain,
( ( ~ ? [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
= xK ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[71]) ).
thf(91,plain,
( ( aElementOf0 @ xK @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(92,plain,
( ( xK != sz00 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(93,plain,
( ( xK != sz00 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(94,plain,
( ( aElementOf0 @ sz00 @ szNzAzT0 )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(95,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( aElementOf0 @ ( szszuzczcdt0 @ W0 ) @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
!= sz00 ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(96,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( szszuzczcdt0 @ W0 )
= ( szszuzczcdt0 @ W1 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(97,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( ( W0 = sz00 )
| ? [W1: $i] :
( ( aElementOf0 @ W1 @ szNzAzT0 )
& ( W0
= ( szszuzczcdt0 @ W1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(98,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( W0
!= ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(99,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(100,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ( sdtlseqdt0 @ ( szszuzczcdt0 @ W0 ) @ ( szszuzczcdt0 @ W1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(101,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(102,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(103,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(104,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)],[76]) ).
thf(105,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ W1 ) @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( aElementOf0 @ W1 @ szNzAzT0 ) )
=> ( ( iLess0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
=> ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,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)],[72]) ).
thf(109,plain,
( ( ~ ? [W0: $i] :
( ( aElementOf0 @ W0 @ szNzAzT0 )
& ( ( szszuzczcdt0 @ W0 )
= xK ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(110,plain,
( ( xK != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(111,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SX0 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SX0 )
!= sz00 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(112,plain,
( ( xK != sz00 )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0 = sz00 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( aElementOf0 @ SX1 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( iLess0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( SX0
!= ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(118,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)],[100]) ).
thf(119,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SX0 )
!= xK ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SX0 )
!= ( szszuzczcdt0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ~ ( aElementOf0 @ SX1 @ szNzAzT0 ) )
| ~ ( iLess0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(123,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(124,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)],[103]) ).
thf(125,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)],[104]) ).
thf(126,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)],[108]) ).
thf(127,plain,
( ( xK = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(128,plain,
! [SV1: $i] :
( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 )
| ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(129,plain,
( ( xK = sz00 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY25 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV2 @ SY25 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(131,plain,
! [SV3: $i] :
( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 )
| ( SV3 = sz00 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( aElementOf0 @ SY26 @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV4: $i] :
( ( ~ ( aElementOf0 @ SV4 @ szNzAzT0 )
| ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV5: $i] :
( ( ! [SY27: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY27 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV5 @ SY27 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SY27 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV6: $i] :
( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 )
| ( SV6
!= ( szszuzczcdt0 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV7: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY28 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SY28 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SY28 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SY28 ) )
| ( sdtlseqdt0 @ SV7 @ SY28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(136,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SX0 )
!= xK ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV8: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY29 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SY29 ) )
| ( SV8 = SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV9: $i] :
( ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV9 @ ( szszuzczcdt0 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV10: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY30 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV10 @ SY30 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV11: $i] :
( ( ~ ( aElementOf0 @ SV11 @ szNzAzT0 )
| ( sdtlseqdt0 @ SV11 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV12: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY31 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SY31 )
| ~ ( sdtlseqdt0 @ SY31 @ SV12 ) )
| ( SV12 = SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV13: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY32 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY33 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SY32 )
| ~ ( sdtlseqdt0 @ SY32 @ SY33 ) )
| ( sdtlseqdt0 @ SV13 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(143,plain,
! [SV14: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SY34 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY34 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SY34 ) )
| ( SV14 = SY34 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SY34 ) )
| ( SV14 = SY34 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SY34 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ SV1 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV15: $i,SV2: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
| ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ SV3 @ szNzAzT0 ) )
= $true )
| ( ( ( SV3 = sz00 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( aElementOf0 @ SY26 @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV4: $i] :
( ( ( ~ ( aElementOf0 @ SV4 @ szNzAzT0 ) )
= $true )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) )
| ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV6: $i] :
( ( ( ~ ( aElementOf0 @ SV6 @ szNzAzT0 ) )
= $true )
| ( ( SV6
!= ( szszuzczcdt0 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV17: $i,SV7: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(151,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( aElementOf0 @ SX0 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SX0 )
!= xK ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV18: $i,SV8: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
| ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV9: $i] :
( ( ( ~ ( aElementOf0 @ SV9 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV9 @ ( szszuzczcdt0 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV19: $i,SV10: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) )
| ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV11: $i] :
( ( ( ~ ( aElementOf0 @ SV11 @ szNzAzT0 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV20: $i,SV12: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV21: $i,SV13: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SY35 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SY35 ) )
| ( sdtlseqdt0 @ SV13 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV22: $i,SV14: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) )
| ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV3: $i] :
( ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false )
| ( ( ( SV3 = sz00 )
| ~ ! [SY26: $i] :
~ ~ ( ~ ( aElementOf0 @ SY26 @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV4: $i] :
( ( ( aElementOf0 @ SV4 @ szNzAzT0 )
= $false )
| ( ( iLess0 @ SV4 @ ( szszuzczcdt0 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV6: $i] :
( ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false )
| ( ( SV6
!= ( szszuzczcdt0 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SV23 )
!= xK ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV9: $i] :
( ( ( aElementOf0 @ SV9 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ ( szszuzczcdt0 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV11: $i] :
( ( ( aElementOf0 @ SV11 @ szNzAzT0 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 )
| ~ ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV3: $i] :
( ( ( SV3 = sz00 )
= $true )
| ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ( aElementOf0 @ SY26 @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ SY26 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) ) )
= $false )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV6: $i] :
( ( ( SV6
= ( szszuzczcdt0 @ SV6 ) )
= $false )
| ( ( aElementOf0 @ SV6 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(179,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(180,plain,
! [SV23: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SV23 )
!= xK ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(181,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) ) )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(182,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV1: $i] :
( ( ( ~ ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV1: $i] :
( ( ( ~ ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 ) ) )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(188,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(189,plain,
! [SV3: $i] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ( aElementOf0 @ SY26 @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ SY26 ) ) ) )
= $false )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(191,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(192,plain,
! [SV23: $i] :
( ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 )
| ( ( szszuzczcdt0 @ SV23 )
!= xK ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(193,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(194,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(195,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(196,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(198,plain,
! [SV1: $i] :
( ( ( aElementOf0 @ ( szszuzczcdt0 @ SV1 ) @ szNzAzT0 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV1: $i] :
( ( ( ( szszuzczcdt0 @ SV1 )
!= sz00 )
= $true )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( aElementOf0 @ SV2 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY26 @ SV3 ) @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ ( sK1_SY26 @ SV3 ) ) ) ) )
= $false )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[189]) ).
thf(202,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( aElementOf0 @ SV5 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( aElementOf0 @ SV7 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ szNzAzT0 ) )
= $true )
| ( ( ( szszuzczcdt0 @ SV23 )
!= xK )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( aElementOf0 @ SV8 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( aElementOf0 @ SV10 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(207,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( aElementOf0 @ SV12 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(208,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
| ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(209,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV1: $i] :
( ( ( ( szszuzczcdt0 @ SV1 )
= sz00 )
= $false )
| ( ( aElementOf0 @ SV1 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV15: $i,SV2: $i] :
( ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV15 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK1_SY26 @ SV3 ) @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ ( sK1_SY26 @ SV3 ) ) ) ) )
= $true )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(213,plain,
! [SV16: $i,SV5: $i] :
( ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV16 @ szNzAzT0 ) )
= $true )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(214,plain,
! [SV17: $i,SV7: $i] :
( ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV17 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(215,plain,
! [SV23: $i] :
( ( ( aElementOf0 @ SV23 @ szNzAzT0 )
= $false )
| ( ( ( szszuzczcdt0 @ SV23 )
!= xK )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(216,plain,
! [SV18: $i,SV8: $i] :
( ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV18 @ szNzAzT0 ) )
= $true )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(217,plain,
! [SV19: $i,SV10: $i] :
( ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV19 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(218,plain,
! [SV20: $i,SV12: $i] :
( ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV20 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(219,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV22: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV22 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV2: $i,SV15: $i] :
( ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(222,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY26 @ SV3 ) @ szNzAzT0 )
| ( SV3
!= ( szszuzczcdt0 @ ( sK1_SY26 @ SV3 ) ) ) )
= $false )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV5: $i,SV16: $i] :
( ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( ( sdtlseqdt0 @ SV5 @ SV16 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV7: $i,SV17: $i] :
( ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(225,plain,
! [SV23: $i] :
( ( ( ( szszuzczcdt0 @ SV23 )
= xK )
= $false )
| ( ( aElementOf0 @ SV23 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(226,plain,
! [SV8: $i,SV18: $i] :
( ( ( aElementOf0 @ SV18 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
| ( SV8 = SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(227,plain,
! [SV10: $i,SV19: $i] :
( ( ( aElementOf0 @ SV19 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( ~ ( iLess0 @ SV10 @ SV19 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(228,plain,
! [SV12: $i,SV20: $i] :
( ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
| ( SV12 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(229,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV14: $i,SV22: $i] :
( ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(231,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV2 @ SV15 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(232,plain,
! [SV3: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY26 @ SV3 ) @ szNzAzT0 ) )
= $false )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(233,plain,
! [SV3: $i] :
( ( ( SV3
!= ( szszuzczcdt0 @ ( sK1_SY26 @ SV3 ) ) )
= $false )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(234,plain,
! [SV16: $i,SV5: $i] :
( ( ( sdtlseqdt0 @ SV5 @ SV16 )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV16 ) @ SV5 )
= $true )
| ( ( aElementOf0 @ SV5 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV16 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(235,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
| ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(236,plain,
! [SV18: $i,SV8: $i] :
( ( ( ( szszuzczcdt0 @ SV8 )
!= ( szszuzczcdt0 @ SV18 ) )
= $true )
| ( ( SV8 = SV18 )
= $true )
| ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV18 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(237,plain,
! [SV19: $i,SV10: $i] :
( ( ( ~ ( iLess0 @ SV10 @ SV19 ) )
= $true )
| ( $true = $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV19 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(238,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) ) )
= $true )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 )
| ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV15: $i,SV2: $i] :
( ( ( sdtlseqdt0 @ SV2 @ SV15 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV2 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV15 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV3: $i] :
( ( ( aElementOf0 @ ( sK1_SY26 @ SV3 ) @ szNzAzT0 )
= $true )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(243,plain,
! [SV3: $i] :
( ( ( SV3
= ( szszuzczcdt0 @ ( sK1_SY26 @ SV3 ) ) )
= $true )
| ( ( SV3 = sz00 )
= $true )
| ( ( aElementOf0 @ SV3 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(244,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(245,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(246,plain,
! [SV18: $i,SV8: $i] :
( ( ( ( szszuzczcdt0 @ SV8 )
= ( szszuzczcdt0 @ SV18 ) )
= $false )
| ( ( SV8 = SV18 )
= $true )
| ( ( aElementOf0 @ SV8 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV18 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV19: $i,SV10: $i] :
( ( ( iLess0 @ SV10 @ SV19 )
= $false )
| ( $true = $true )
| ( ( aElementOf0 @ SV10 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV19 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) ) )
= $false )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( aElementOf0 @ SV13 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(250,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(251,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(252,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV7 @ SV17 )
| ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(253,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
| ( sdtlseqdt0 @ SV7 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(254,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV20 )
| ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
= $true )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(255,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV21 @ szNzAzT0 ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(256,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(257,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
| ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(258,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV7 @ SV17 ) )
= $true )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(259,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV7 @ SV17 )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(260,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
= $true )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(261,plain,
! [SV24: $i,SV13: $i,SV21: $i] :
( ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( ~ ( aElementOf0 @ SV24 @ szNzAzT0 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(262,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) ) )
= $true )
| ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(263,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(264,plain,
! [SV17: $i,SV7: $i] :
( ( ( sdtlseqdt0 @ SV7 @ SV17 )
= $false )
| ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(265,plain,
! [SV17: $i,SV7: $i] :
( ( ( sdtlseqdt0 @ ( szszuzczcdt0 @ SV7 ) @ ( szszuzczcdt0 @ SV17 ) )
= $false )
| ( ( sdtlseqdt0 @ SV7 @ SV17 )
= $true )
| ( ( aElementOf0 @ SV7 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV17 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(266,plain,
! [SV20: $i,SV12: $i] :
( ( ( sdtlseqdt0 @ SV12 @ SV20 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV20 @ SV12 ) )
= $true )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(267,plain,
! [SV21: $i,SV13: $i,SV24: $i] :
( ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
| ( sdtlseqdt0 @ SV13 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(268,plain,
! [SV22: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $false )
| ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(269,plain,
! [SV22: $i,SV14: $i] :
( ( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
| ( SV14 = SV22 ) )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV12: $i,SV20: $i] :
( ( ( sdtlseqdt0 @ SV20 @ SV12 )
= $false )
| ( ( sdtlseqdt0 @ SV12 @ SV20 )
= $false )
| ( ( SV12 = SV20 )
= $true )
| ( ( aElementOf0 @ SV12 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV20 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(271,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(272,plain,
! [SV22: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
= $true )
| ( ( SV14 = SV22 )
= $true )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $false )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(273,plain,
! [SV22: $i,SV14: $i] :
( ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ SV22 ) )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(274,plain,
! [SV22: $i,SV14: $i] :
( ( ( SV14 = SV22 )
= $false )
| ( ( aElementOf0 @ SV14 @ ( slbdtrb0 @ ( szszuzczcdt0 @ SV22 ) ) )
= $true )
| ( ( aElementOf0 @ SV14 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV22 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(275,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(276,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV21 )
| ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(277,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV21 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(278,plain,
! [SV24: $i,SV21: $i,SV13: $i] :
( ( ( sdtlseqdt0 @ SV13 @ SV21 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV21 @ SV24 ) )
= $true )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(279,plain,
! [SV13: $i,SV24: $i,SV21: $i] :
( ( ( sdtlseqdt0 @ SV21 @ SV24 )
= $false )
| ( ( sdtlseqdt0 @ SV13 @ SV21 )
= $false )
| ( ( sdtlseqdt0 @ SV13 @ SV24 )
= $true )
| ( ( aElementOf0 @ SV21 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV13 @ szNzAzT0 )
= $false )
| ( ( aElementOf0 @ SV24 @ szNzAzT0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(280,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,279,274,273,272,270,265,264,247,246,243,242,241,234,225,210,198,178,170,168,162,129,127,94]) ).
thf(281,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 13:26:39 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.40
% 0.52/0.40 No.of.Axioms: 18
% 0.52/0.40
% 0.52/0.40 Length.of.Defs: 0
% 0.52/0.40
% 0.52/0.40 Contains.Choice.Funs: false
% 0.52/0.40 ......
% 0.52/0.40
% 0.52/0.40 ********************************
% 0.52/0.40 * All subproblems solved! *
% 0.52/0.40 ********************************
% 0.52/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:280,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.52/0.40
% 0.52/0.40 %**** Beginning of derivation protocol ****
% 0.52/0.40 % SZS output start CNFRefutation
% See solution above
% 0.52/0.40
% 0.52/0.40 %**** End of derivation protocol ****
% 0.52/0.40 %**** no. of clauses in derivation: 231 ****
% 0.52/0.40 %**** clause counter: 280 ****
% 0.52/0.40
% 0.52/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,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:280,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------