TSTP Solution File: SEU569^1 by E---3.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU569^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:09:03 EDT 2024
% Result : Theorem 0.57s 0.55s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 89
% Syntax : Number of formulae : 133 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 1093 ( 327 equ; 0 cnn)
% Maximal formula atoms : 337 ( 8 avg)
% Number of connectives : 4318 ( 400 ~; 447 |; 272 &;2514 @)
% ( 148 <=>; 537 =>; 0 <=; 0 <~>)
% Maximal formula depth : 393 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 131 ( 131 >; 0 *; 0 +; 0 <<)
% Number of symbols : 156 ( 153 usr; 91 con; 0-4 aty)
% Number of variables : 920 ( 63 ^ 753 !; 104 ?; 920 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
epred1_0: $o ).
thf(decl_123,type,
esk1_2: $i > $i > $i ).
thf(decl_124,type,
esk2_2: $i > $i > $i ).
thf(decl_125,type,
esk3_2: $i > $i > $i ).
thf(decl_126,type,
esk4_1: $i > $i ).
thf(decl_127,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_128,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_129,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_130,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_131,type,
esk9_1: $i > $i ).
thf(decl_132,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_133,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_134,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_135,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_136,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_137,type,
esk15_2: $i > $i > $i ).
thf(decl_138,type,
esk16_2: $i > $i > $i ).
thf(decl_139,type,
esk17_1: $i > $i ).
thf(decl_140,type,
esk18_1: $i > $i ).
thf(decl_141,type,
esk19_1: $i > $i ).
thf(decl_142,type,
esk20_2: $i > $i > $i ).
thf(decl_143,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_144,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_145,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_146,type,
esk24_1: $i > $i ).
thf(decl_147,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_148,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_149,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_150,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_151,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_152,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_153,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_154,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_155,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_156,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_157,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_158,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_159,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_160,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_161,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_162,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_163,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_164,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_165,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_166,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_167,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_168,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_169,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_170,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_171,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_172,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_173,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_174,type,
esk52_2: $i > $i > $i ).
thf(decl_175,type,
esk53_2: $i > $i > $i ).
thf(decl_176,type,
esk54_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',descr__Cong) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',dsetconstr__Cong) ).
thf(subsetRefl,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ! [X4: $i] : ( subset @ X4 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subsetRefl) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p',notequalI2) ).
thf(c_0_88,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_89,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_90,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_91,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_92,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_93,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_94,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_95,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_96,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_97,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_98,plain,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI2]) ).
thf(c_0_99,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_100,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_101,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_102,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_103,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X257: $i] :
( ( X6 @ X2 @ X257 )
& ! [X258: $i] :
( ( X6 @ X2 @ X258 )
=> ( X257 = X258 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_104,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X259: $i] :
( ( X1 @ X259 )
& ! [X260: $i] :
( ( X1 @ X260 )
=> ( X259 = X260 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_90,c_0_89]) ).
thf(c_0_105,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_106,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_107,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_108,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X261: $i] :
( ( X1 @ X261 )
& ! [X262: $i] :
( ( X1 @ X262 )
=> ( X261 = X262 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_89]) ).
thf(c_0_109,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X263: $i] :
( ( X1 @ X263 )
& ! [X264: $i] :
( ( X1 @ X264 )
=> ( X263 = X264 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_92,c_0_89]) ).
thf(c_0_110,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_111,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_93]) ).
thf(c_0_112,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_94,c_0_93]) ).
thf(c_0_113,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_93]) ).
thf(c_0_114,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_115,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X265: $i] :
( ( X1 @ X265 )
& ! [X266: $i] :
( ( X1 @ X266 )
=> ( X265 = X266 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_95,c_0_89]) ).
thf(c_0_116,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_93]) ).
thf(c_0_117,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_118,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X267: $i] :
( ( X1 @ X267 )
& ! [X268: $i] :
( ( X1 @ X268 )
=> ( X267 = X268 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_96,c_0_89]) ).
thf(c_0_119,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X269: $i] :
( ( X1 @ X269 )
& ! [X270: $i] :
( ( X1 @ X270 )
=> ( X269 = X270 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_97,c_0_89]) ).
thf(c_0_120,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X271: $i] :
( ( X1 @ X271 )
& ! [X272: $i] :
( ( X1 @ X272 )
=> ( X271 = X272 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_98,c_0_89]) ).
thf(c_0_121,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X273: $i] :
( ( X1 @ X273 )
& ! [X274: $i] :
( ( X1 @ X274 )
=> ( X273 = X274 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_99,c_0_89]) ).
thf(c_0_122,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X275: $i] :
( ( X1 @ X275 )
& ! [X276: $i] :
( ( X1 @ X276 )
=> ( X275 = X276 ) ) )
<=> ? [X277: $i] :
( ( X17 @ X277 )
& ! [X278: $i] :
( ( X17 @ X278 )
=> ( X277 = X278 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_100,c_0_89]) ).
thf(c_0_123,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X279: $i] :
( ( X1 @ X279 )
& ! [X280: $i] :
( ( X1 @ X280 )
=> ( X279 = X280 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_101,c_0_89]) ).
thf(c_0_124,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X281: $i] :
( ( X1 @ X281 )
& ! [X282: $i] :
( ( X1 @ X282 )
=> ( X281 = X282 ) ) )
=> ( ? [X283: $i] :
( ( X17 @ X283 )
& ! [X284: $i] :
( ( X17 @ X284 )
=> ( X283 = X284 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_102,c_0_89]) ).
thf(c_0_125,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_126,plain,
( epred1_0
<=> ! [X314: $i] :
? [X315: $i] :
( ! [X316: $i] :
( ( in @ X316 @ X315 )
=> ! [X317: $i] :
( ( in @ X317 @ X316 )
=> ( in @ X317 @ X314 ) ) )
& ! [X318: $i,X319: $i] :
( ( ( in @ X318 @ X314 )
& ( in @ X319 @ X314 ) )
=> ( ! [X320: $i] :
( ( in @ X320 @ X315 )
=> ( ( in @ X318 @ X320 )
<=> ( in @ X319 @ X320 ) ) )
=> ( X318 = X319 ) ) )
& ! [X321: $i,X322: $i] :
( ( ( in @ X321 @ X315 )
& ( in @ X322 @ X315 ) )
=> ( ! [X323: $i] :
( ( in @ X323 @ X321 )
=> ( in @ X323 @ X322 ) )
| ! [X324: $i] :
( ( in @ X324 @ X322 )
=> ( in @ X324 @ X321 ) ) ) )
& ! [X325: $i] :
( ( ! [X326: $i] :
( ( in @ X326 @ X325 )
=> ( in @ X326 @ X314 ) )
& ? [X327: $i] : ( in @ X327 @ X325 ) )
=> ? [X328: $i,X329: $i] :
( ( in @ X328 @ X315 )
& ( in @ X329 @ X325 )
& ~ ? [X330: $i] :
( ( in @ X330 @ X328 )
& ( in @ X330 @ X325 ) )
& ! [X331: $i] :
( ( in @ X331 @ X315 )
=> ( ! [X332: $i] :
( ( in @ X332 @ X331 )
=> ( in @ X332 @ X328 ) )
| ( in @ X329 @ X331 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_127,negated_conjecture,
~ ( ! [X285: $i,X286: $i] :
( ! [X287: $i] :
( ( in @ X287 @ X285 )
<=> ( in @ X287 @ X286 ) )
=> ( X285 = X286 ) )
=> ( ! [X288: $i] :
~ ( in @ X288 @ emptyset )
=> ( ! [X289: $i,X290: $i,X291: $i] :
( ( in @ X291 @ ( setadjoin @ X289 @ X290 ) )
<=> ( ( X291 = X289 )
| ( in @ X291 @ X290 ) ) )
=> ( ! [X292: $i,X293: $i] :
( ( in @ X293 @ ( powerset @ X292 ) )
<=> ! [X294: $i] :
( ( in @ X294 @ X293 )
=> ( in @ X294 @ X292 ) ) )
=> ( ! [X295: $i,X296: $i] :
( ( in @ X296 @ ( setunion @ X295 ) )
<=> ? [X297: $i] :
( ( in @ X296 @ X297 )
& ( in @ X297 @ X295 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X298: $i] :
( ( in @ X298 @ omega )
=> ( in @ ( setadjoin @ X298 @ X298 ) @ omega ) )
=> ( ! [X299: $i] :
( ( ( in @ emptyset @ X299 )
& ! [X300: $i] :
( ( ( in @ X300 @ omega )
& ( in @ X300 @ X299 ) )
=> ( in @ ( setadjoin @ X300 @ X300 ) @ X299 ) ) )
=> ! [X301: $i] :
( ( in @ X301 @ omega )
=> ( in @ X301 @ X299 ) ) )
=> ( ! [X302: $i > $i > $o,X303: $i] :
( ! [X304: $i] :
( ( in @ X304 @ X303 )
=> ? [X305: $i] :
( ( X302 @ X304 @ X305 )
& ! [X306: $i] :
( ( X302 @ X304 @ X306 )
=> ( X305 = X306 ) ) ) )
=> ? [X307: $i] :
! [X308: $i] :
( ( in @ X308 @ X307 )
<=> ? [X309: $i] :
( ( in @ X309 @ X303 )
& ( X302 @ X309 @ X308 ) ) ) )
=> ( ! [X310: $i] :
( ? [X311: $i] : ( in @ X311 @ X310 )
=> ? [X312: $i] :
( ( in @ X312 @ X310 )
& ~ ? [X313: $i] :
( ( in @ X313 @ X312 )
& ( in @ X313 @ X310 ) ) ) )
=> ( epred1_0
=> ( ! [X333: $i > $o] :
( ? [X334: $i] :
( ( X333 @ X334 )
& ! [X335: $i] :
( ( X333 @ X335 )
=> ( X334 = X335 ) ) )
=> ( X333
@ ( descr
@ ^ [Z0: $i] : ( X333 @ Z0 ) ) ) )
=> ( ! [X336: $i,X337: $i > $o,X338: $i] :
( ( in @ X338 @ X336 )
=> ( ( X337 @ X338 )
=> ( in @ X338 @ ( dsetconstr @ X336 @ X337 ) ) ) )
=> ( ! [X339: $i,X340: $i > $o,X341: $i] :
( ( in @ X341 @ ( dsetconstr @ X339 @ X340 ) )
=> ( in @ X341 @ X339 ) )
=> ( ! [X342: $i,X343: $i > $o,X344: $i] :
( ( in @ X344 @ ( dsetconstr @ X342 @ X343 ) )
=> ( X343 @ X344 ) )
=> ( ! [X345: $i > $o] :
( ? [X346: $i] :
( ( X345 @ X346 )
& ! [X347: $i] :
( ( X345 @ X347 )
=> ( X346 = X347 ) ) )
=> ? [X348: $i] :
( ( X345 @ X348 )
& ! [X349: $i] :
( ( X345 @ X349 )
=> ( X348 = X349 ) ) ) )
=> ( ! [X350: $o,X351: $i] :
( ( in @ X351 @ ( prop2set @ X350 ) )
=> X350 )
=> ( ! [X352: $i] :
( ( in @ X352 @ emptyset )
=> ! [X353: $o] : X353 )
=> ( ! [X354: $i] :
( ( in @ X354 @ emptyset )
=> ~ $true )
=> ( ! [X355: $i] :
~ ( in @ X355 @ emptyset )
=> ( ! [X356: $i > $o] :
( ? [X357: $i] :
( ( X356 @ X357 )
& ! [X358: $i] :
( ( X356 @ X358 )
=> ( X357 = X358 ) ) )
=> ? [X359: $i] : ( X356 @ X359 ) )
=> ( ! [X360: $i,X361: $i] :
( ! [X362: $i] :
( ( in @ X362 @ X360 )
=> ( in @ X362 @ X361 ) )
=> ( ! [X363: $i] :
( ( in @ X363 @ X361 )
=> ( in @ X363 @ X360 ) )
=> ( X360 = X361 ) ) )
=> ( ! [X364: $i] :
( ! [X365: $i] :
~ ( in @ X365 @ X364 )
=> ( X364 = emptyset ) )
=> ( ! [X366: $i] :
( ! [X367: $i] :
~ ( in @ X367 @ X366 )
=> ( X366 = emptyset ) )
=> ( ! [X368: $i,X369: $i > $o,X370: $i] :
( ( in @ X370 @ X368 )
=> ( ( in @ X370 @ ( dsetconstr @ X368 @ X369 ) )
<=> ( X369 @ X370 ) ) )
=> ( ! [X371: $i] :
( ( X371 != emptyset )
=> ? [X372: $i] : ( in @ X372 @ X371 ) )
=> ( ! [X373: $i,X374: $i > $o,X375: $i] :
( ( in @ X375 @ X373 )
=> ( ( X374 @ X375 )
=> ( ( dsetconstr @ X373 @ X374 )
!= emptyset ) ) )
=> ( ! [X376: $i] :
( ? [X377: $i] : ( in @ X377 @ X376 )
=> ( X376 != emptyset ) )
=> ( ! [X378: $i,X379: $i] : ( in @ X378 @ ( setadjoin @ X378 @ X379 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X380: $i,X381: $i,X382: $i] :
( ( in @ X382 @ X381 )
=> ( in @ X382 @ ( setadjoin @ X380 @ X381 ) ) )
=> ( ! [X383: $i,X384: $i,X385: $i] :
( ( in @ X385 @ ( setadjoin @ X383 @ X384 ) )
=> ! [X386: $o] :
( ( ( X385 = X383 )
=> X386 )
=> ( ( ( in @ X385 @ X384 )
=> X386 )
=> X386 ) ) )
=> ( ! [X387: $i,X388: $i,X389: $i] :
( ( in @ X389 @ ( setadjoin @ X387 @ X388 ) )
=> ( ( X389 = X387 )
| ( in @ X389 @ X388 ) ) )
=> ( ! [X390: $i] :
( ( dsetconstr @ X390
@ ^ [Z0: $i] : $true )
= X390 )
=> ( ! [X391: $i,X392: $i] :
( ! [X393: $i] :
( ( in @ X393 @ X392 )
=> ( in @ X393 @ X391 ) )
=> ( in @ X392 @ ( powerset @ X391 ) ) )
=> ( ! [X394: $i] : ( in @ emptyset @ ( powerset @ X394 ) )
=> ( ! [X395: $i] : ( in @ emptyset @ ( powerset @ X395 ) )
=> ( ! [X396: $i,X397: $i,X398: $i] :
( ( in @ X397 @ ( powerset @ X396 ) )
=> ( ( in @ X398 @ X397 )
=> ( in @ X398 @ X396 ) ) )
=> ( ! [X399: $i,X400: $i,X401: $i] :
( ( in @ X400 @ X401 )
=> ( ( in @ X401 @ X399 )
=> ( in @ X400 @ ( setunion @ X399 ) ) ) )
=> ( ! [X402: $i,X403: $i] :
( ( in @ X403 @ ( setunion @ X402 ) )
=> ! [X404: $o] :
( ! [X405: $i] :
( ( in @ X403 @ X405 )
=> ( ( in @ X405 @ X402 )
=> X404 ) )
=> X404 ) )
=> ( ! [X406: $i,X407: $i] :
( ( in @ X407 @ X406 )
=> ( in @ X407 @ ( powerset @ ( setunion @ X406 ) ) ) )
=> ( ! [X408: $i > $o] :
( ? [X409: $i] :
( ( X408 @ X409 )
& ! [X410: $i] :
( ( X408 @ X410 )
=> ( X409 = X410 ) ) )
=> ? [X411: $i] :
! [X412: $i] :
( ( X408 @ X412 )
<=> ( X412 = X411 ) ) )
=> ( ! [X413: $i] :
( ( X413 != emptyset )
=> ? [X414: $i] :
( ( in @ X414 @ X413 )
& $true ) )
=> ( ! [X415: $i,X416: $i] :
( ( in @ X415 @ ( setadjoin @ X416 @ emptyset ) )
=> ( X415 = X416 ) )
=> ( ! [X417: $i,X418: $i] :
( ( X417 != X418 )
=> ~ ( in @ X418 @ ( setadjoin @ X417 @ emptyset ) ) )
=> ( ! [X419: $i,X420: $i] :
( ( X419 = X420 )
=> ( in @ X419 @ ( setadjoin @ X420 @ emptyset ) ) )
=> ( ! [X421: $i,X422: $i] :
( ( in @ X421 @ ( setadjoin @ X422 @ emptyset ) )
=> ( in @ X422 @ ( setadjoin @ X421 @ emptyset ) ) )
=> ( ! [X423: $i,X424: $i,X425: $i] :
( ( in @ X425 @ ( setadjoin @ X423 @ ( setadjoin @ X424 @ emptyset ) ) )
=> ( ( X425 = X423 )
| ( X425 = X424 ) ) )
=> ( ! [X426: $i,X427: $i] : ( in @ X426 @ ( setadjoin @ X426 @ ( setadjoin @ X427 @ emptyset ) ) )
=> ( ! [X428: $i,X429: $i] : ( in @ X429 @ ( setadjoin @ X428 @ ( setadjoin @ X429 @ emptyset ) ) )
=> ( ! [X430: $i,X431: $i > $o] :
( ? [X432: $i] :
( ( in @ X432 @ X430 )
& ( X431 @ X432 ) )
=> ( ( ( dsetconstr @ X430 @ X431 )
= emptyset )
=> ~ $true ) )
=> ( ! [X433: $i > $o,X434: $i] :
( ( in @ X434 @ emptyset )
=> ( X433 @ X434 ) )
=> ( ! [X435: $i,X436: $i > $o] :
( ~ ! [X437: $i] :
( ( in @ X437 @ X435 )
=> ( X436 @ X437 ) )
=> ? [X438: $i] :
( ( in @ X438 @ X435 )
& ~ ( X436 @ X438 ) ) )
=> ( ! [X439: $i,X440: $i > $o] :
( ! [X441: $i] :
( ( in @ X441 @ X439 )
=> ~ ( X440 @ X441 ) )
=> ~ ? [X442: $i] :
( ( in @ X442 @ X439 )
& ( X440 @ X442 ) ) )
=> ( ! [X443: $i,X444: $i > $o] :
( ~ ? [X445: $i] :
( ( in @ X445 @ X443 )
& ( X444 @ X445 ) )
=> ! [X446: $i] :
( ( in @ X446 @ X443 )
=> ~ ( X444 @ X446 ) ) )
=> ( ! [X447: $i,X448: $i > $o] :
( ? [X449: $i] :
( ( in @ X449 @ X447 )
& ~ ( X448 @ X449 ) )
=> ~ ! [X450: $i] :
( ( in @ X450 @ X447 )
=> ( X448 @ X450 ) ) )
=> ( ! [X451: $o] :
( X451
=> ( in @ emptyset @ ( prop2set @ X451 ) ) )
=> ( ! [X452: $o] :
( X452
=> ( set2prop @ ( prop2set @ X452 ) ) )
=> ( ! [X453: $i,X454: $i > $o] :
( ~ ? [X455: $i] :
( ( in @ X455 @ X453 )
& ( X454 @ X455 ) )
=> ! [X456: $i] :
( ( in @ X456 @ X453 )
=> ~ ( X454 @ X456 ) ) )
=> ( ! [X457: $i,X458: $i > $o] :
( ~ ! [X459: $i] :
( ( in @ X459 @ X457 )
=> ( X458 @ X459 ) )
=> ? [X460: $i] :
( ( in @ X460 @ X457 )
& ~ ( X458 @ X460 ) ) )
=> ( ! [X461: $i > $o] :
( ? [X462: $i] :
( ( X461 @ X462 )
& ! [X463: $i] :
( ( X461 @ X463 )
=> ( X462 = X463 ) ) )
=> ? [X464: $i] :
( ( X461 @ X464 )
& ! [X465: $i] :
( ( X461 @ X465 )
=> ( X464 = X465 ) ) ) )
=> ( ! [X466: $i > $o] :
( ? [X467: $i] : ( X466 @ X467 )
=> ( ! [X468: $i,X469: $i] :
( ( X466 @ X468 )
=> ( ( X466 @ X469 )
=> ( X468 = X469 ) ) )
=> ? [X470: $i] :
( ( X466 @ X470 )
& ! [X471: $i] :
( ( X466 @ X471 )
=> ( X470 = X471 ) ) ) ) )
=> ( ! [X472: $i > $o] :
( ? [X473: $i] :
! [X474: $i] :
( ( X472 @ X474 )
<=> ( X474 = X473 ) )
=> ? [X475: $i] :
( ( X472 @ X475 )
& ! [X476: $i] :
( ( X472 @ X476 )
=> ( X475 = X476 ) ) ) )
=> ( ! [X477: $i,X478: $i] :
( ( X477 = X478 )
=> ! [X479: $i,X480: $i] :
( ( X479 = X480 )
=> ( ( in @ X479 @ X477 )
=> ( in @ X480 @ X478 ) ) ) )
=> ( ! [X481: $i,X482: $i] :
( ( X481 = X482 )
=> ! [X483: $i,X484: $i] :
( ( X483 = X484 )
=> ( ( in @ X483 @ X481 )
<=> ( in @ X484 @ X482 ) ) ) )
=> ( ! [X485: $i > $o] :
( ? [X486: $i] :
( ( X485 @ X486 )
& ! [X487: $i] :
( ( X485 @ X487 )
=> ( X486 = X487 ) ) )
=> ! [X488: $i,X489: $i] :
( ( X485 @ X488 )
=> ( ( X485 @ X489 )
=> ( X488 = X489 ) ) ) )
=> ( ! [X490: $i > $o,X491: $i > $o] :
( ! [X492: $i,X493: $i] :
( ( X492 = X493 )
=> ( ( X490 @ X492 )
<=> ( X491 @ X493 ) ) )
=> ( ? [X494: $i] :
( ( X490 @ X494 )
& ! [X495: $i] :
( ( X490 @ X495 )
=> ( X494 = X495 ) ) )
<=> ? [X496: $i] :
( ( X491 @ X496 )
& ! [X497: $i] :
( ( X491 @ X497 )
=> ( X496 = X497 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X498: $i,X499: $i] :
( ( X498 = X499 )
=> ! [X500: $i,X501: $i] :
( ( X500 = X501 )
=> ( ( setadjoin @ X498 @ X500 )
= ( setadjoin @ X499 @ X501 ) ) ) )
=> ( ! [X502: $i,X503: $i] :
( ( X502 = X503 )
=> ( ( powerset @ X502 )
= ( powerset @ X503 ) ) )
=> ( ! [X504: $i,X505: $i] :
( ( X504 = X505 )
=> ( ( setunion @ X504 )
= ( setunion @ X505 ) ) )
=> ( ( omega = omega )
=> ( ! [X506: $i > $o] :
( ? [X507: $i] :
( ( X506 @ X507 )
& ! [X508: $i] :
( ( X506 @ X508 )
=> ( X507 = X508 ) ) )
=> ! [X509: $i,X510: $i] :
( ( X506 @ X509 )
=> ( ( X506 @ X510 )
=> ( X509 = X510 ) ) ) )
=> ( ! [X511: $i > $o,X512: $i > $o] :
( ! [X513: $i,X514: $i] :
( ( X513 = X514 )
=> ( ( X511 @ X513 )
<=> ( X512 @ X514 ) ) )
=> ( ? [X515: $i] :
( ( X511 @ X515 )
& ! [X516: $i] :
( ( X511 @ X516 )
=> ( X515 = X516 ) ) )
=> ( ? [X517: $i] :
( ( X512 @ X517 )
& ! [X518: $i] :
( ( X512 @ X518 )
=> ( X517 = X518 ) ) )
=> ( ( descr @ X511 )
= ( descr @ X512 ) ) ) ) )
=> ( ! [X519: $i,X520: $i] :
( ( X519 = X520 )
=> ! [X521: $i > $o,X522: $i > $o] :
( ! [X523: $i] :
( ( in @ X523 @ X519 )
=> ! [X524: $i] :
( ( in @ X524 @ X520 )
=> ( ( X523 = X524 )
=> ( ( X521 @ X523 )
<=> ( X522 @ X524 ) ) ) ) )
=> ( ( dsetconstr @ X519 @ X521 )
= ( dsetconstr @ X520 @ X522 ) ) ) )
=> ( ! [X525: $i,X526: $i] :
( ! [X527: $i] :
( ( in @ X527 @ X525 )
=> ( in @ X527 @ X526 ) )
=> ( subset @ X525 @ X526 ) )
=> ( ! [X528: $i,X529: $i] :
( ( X528 = X529 )
=> ( subset @ X529 @ X528 ) )
=> ( ! [X530: $i,X531: $i] :
( ( X530 = X531 )
=> ( subset @ X530 @ X531 ) )
=> ( ! [X532: $i,X533: $i] :
( ! [X534: $i] :
( ( in @ X534 @ X532 )
=> ( in @ X534 @ X533 ) )
=> ( subset @ X532 @ X533 ) )
=> ( ! [X535: $i] : ( subset @ emptyset @ X535 )
=> ( ! [X536: $i,X537: $i,X538: $i] :
( ( subset @ X536 @ X537 )
=> ( ( in @ X538 @ X536 )
=> ( in @ X538 @ X537 ) ) )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( subset @ X539 @ X540 )
=> ( ~ ( in @ X541 @ X540 )
=> ~ ( in @ X541 @ X539 ) ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( in @ X544 @ X542 )
=> ( ~ ( in @ X544 @ X543 )
=> ~ ( subset @ X542 @ X543 ) ) )
=> ( ! [X545: $i,X546: $i] :
( ~ ( subset @ X545 @ X546 )
=> ( X545 != X546 ) )
=> ( ! [X547: $i,X548: $i,X549: $i] :
( ( in @ X549 @ X547 )
=> ( ~ ( in @ X549 @ X548 )
=> ( X547 != X548 ) ) )
=> ! [X4: $i] : ( subset @ X4 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[subsetRefl]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_103]),foundationAx]),wellorderingAx]),c_0_104]),c_0_105]),c_0_106]),c_0_107]),c_0_108]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_109]),setext]),emptyI]),noeltsimpempty]),c_0_110]),c_0_111]),c_0_112]),c_0_113]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_114]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_115]),c_0_116]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_117]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_118]),c_0_119]),c_0_120]),inCongP]),in__Cong]),c_0_121]),c_0_122]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_123]),c_0_124]),c_0_125]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2])])]),c_0_126]) ).
thf(c_0_128,negated_conjecture,
! [X550: $i,X551: $i,X553: $i,X554: $i,X555: $i,X556: $i,X557: $i,X558: $i,X559: $i,X560: $i,X561: $i,X563: $i,X564: $i,X566: $i,X567: $i,X568: $i,X569: $i,X570: $i,X572: $i,X573: $i > $i > $o,X574: $i,X576: $i,X579: $i,X581: $i,X582: $i,X583: $i,X584: $i,X586: $i,X587: $i > $o,X588: $i,X590: $i,X591: $i > $o,X592: $i,X593: $i,X594: $i > $o,X595: $i,X596: $i,X597: $i > $o,X598: $i,X599: $i > $o,X600: $i,X603: $i,X604: $o,X605: $i,X606: $i,X607: $o,X608: $i,X609: $i,X610: $i > $o,X611: $i,X614: $i,X615: $i,X618: $i,X620: $i,X622: $i,X623: $i > $o,X624: $i,X625: $i,X627: $i,X628: $i > $o,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $o,X641: $i,X642: $i,X643: $i,X644: $i,X645: $i,X646: $i,X648: $i,X649: $i,X650: $i,X651: $i,X652: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $o,X660: $i,X661: $i,X662: $i > $o,X663: $i,X666: $i,X667: $i,X668: $i,X670: $i,X671: $i,X672: $i,X673: $i,X674: $i,X675: $i,X676: $i,X677: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $i,X686: $i > $o,X687: $i,X688: $i > $o,X689: $i,X690: $i,X691: $i > $o,X692: $i,X694: $i,X695: $i > $o,X697: $i,X698: $i,X699: $i > $o,X701: $i,X702: $i,X703: $i > $o,X704: $i,X706: $o,X707: $o,X708: $i,X709: $i > $o,X711: $i,X712: $i,X713: $i > $o,X714: $i,X716: $i > $o,X717: $i,X720: $i,X721: $i > $o,X722: $i,X726: $i,X727: $i > $o,X728: $i,X731: $i,X732: $i,X733: $i,X734: $i,X735: $i,X736: $i,X737: $i,X738: $i,X739: $i,X740: $i > $o,X741: $i,X743: $i,X744: $i,X745: $i > $o,X746: $i > $o,X749: $i,X752: $i,X753: $i,X756: $i,X757: $i,X758: $i,X759: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i > $o,X766: $i,X768: $i,X769: $i,X770: $i > $o,X771: $i > $o,X774: $i,X776: $i,X778: $i,X779: $i,X780: $i > $o,X781: $i > $o,X784: $i,X785: $i,X787: $i,X788: $i,X789: $i,X790: $i,X791: $i,X792: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i] :
( ( ~ ( in @ ( esk1_2 @ X550 @ X551 ) @ X550 )
| ~ ( in @ ( esk1_2 @ X550 @ X551 ) @ X551 )
| ( X550 = X551 ) )
& ( ( in @ ( esk1_2 @ X550 @ X551 ) @ X550 )
| ( in @ ( esk1_2 @ X550 @ X551 ) @ X551 )
| ( X550 = X551 ) )
& ~ ( in @ X553 @ emptyset )
& ( ~ ( in @ X556 @ ( setadjoin @ X554 @ X555 ) )
| ( X556 = X554 )
| ( in @ X556 @ X555 ) )
& ( ( X556 != X554 )
| ( in @ X556 @ ( setadjoin @ X554 @ X555 ) ) )
& ( ~ ( in @ X556 @ X555 )
| ( in @ X556 @ ( setadjoin @ X554 @ X555 ) ) )
& ( ~ ( in @ X558 @ ( powerset @ X557 ) )
| ~ ( in @ X559 @ X558 )
| ( in @ X559 @ X557 ) )
& ( ( in @ ( esk2_2 @ X560 @ X561 ) @ X561 )
| ( in @ X561 @ ( powerset @ X560 ) ) )
& ( ~ ( in @ ( esk2_2 @ X560 @ X561 ) @ X560 )
| ( in @ X561 @ ( powerset @ X560 ) ) )
& ( ( in @ X564 @ ( esk3_2 @ X563 @ X564 ) )
| ~ ( in @ X564 @ ( setunion @ X563 ) ) )
& ( ( in @ ( esk3_2 @ X563 @ X564 ) @ X563 )
| ~ ( in @ X564 @ ( setunion @ X563 ) ) )
& ( ~ ( in @ X567 @ X568 )
| ~ ( in @ X568 @ X566 )
| ( in @ X567 @ ( setunion @ X566 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X569 @ omega )
| ( in @ ( setadjoin @ X569 @ X569 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X570 ) @ omega )
| ~ ( in @ emptyset @ X570 )
| ~ ( in @ X572 @ omega )
| ( in @ X572 @ X570 ) )
& ( ( in @ ( esk4_1 @ X570 ) @ X570 )
| ~ ( in @ emptyset @ X570 )
| ~ ( in @ X572 @ omega )
| ( in @ X572 @ X570 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X570 ) @ ( esk4_1 @ X570 ) ) @ X570 )
| ~ ( in @ emptyset @ X570 )
| ~ ( in @ X572 @ omega )
| ( in @ X572 @ X570 ) )
& ( ( in @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X574 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( in @ ( esk5_2 @ X573 @ X574 ) @ X574 ) )
& ( ( X573 @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X579 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( in @ ( esk5_2 @ X573 @ X574 ) @ X574 ) )
& ( ~ ( in @ X582 @ X574 )
| ~ ( X573 @ X582 @ X581 )
| ( in @ X581 @ ( esk7_2 @ X573 @ X574 ) )
| ( in @ ( esk5_2 @ X573 @ X574 ) @ X574 ) )
& ( ( in @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X574 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( X573 @ ( esk5_2 @ X573 @ X574 ) @ ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ( X573 @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X579 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( X573 @ ( esk5_2 @ X573 @ X574 ) @ ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ~ ( in @ X582 @ X574 )
| ~ ( X573 @ X582 @ X581 )
| ( in @ X581 @ ( esk7_2 @ X573 @ X574 ) )
| ( X573 @ ( esk5_2 @ X573 @ X574 ) @ ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ( in @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X574 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( X576
!= ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ( X573 @ ( esk8_3 @ X573 @ X574 @ X579 ) @ X579 )
| ~ ( in @ X579 @ ( esk7_2 @ X573 @ X574 ) )
| ( X576
!= ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ~ ( in @ X582 @ X574 )
| ~ ( X573 @ X582 @ X581 )
| ( in @ X581 @ ( esk7_2 @ X573 @ X574 ) )
| ( X576
!= ( esk6_3 @ X573 @ X574 @ X576 ) )
| ~ ( X573 @ ( esk5_2 @ X573 @ X574 ) @ X576 ) )
& ( ( in @ ( esk9_1 @ X583 ) @ X583 )
| ~ ( in @ X584 @ X583 ) )
& ( ~ ( in @ X586 @ ( esk9_1 @ X583 ) )
| ~ ( in @ X586 @ X583 )
| ~ ( in @ X584 @ X583 ) )
& epred1_0
& ( ( X587 @ ( esk10_2 @ X587 @ X588 ) )
| ~ ( X587 @ X588 )
| ( X587 @ ( descr @ X587 ) ) )
& ( ( X588
!= ( esk10_2 @ X587 @ X588 ) )
| ~ ( X587 @ X588 )
| ( X587 @ ( descr @ X587 ) ) )
& ( ~ ( in @ X592 @ X590 )
| ~ ( X591 @ X592 )
| ( in @ X592 @ ( dsetconstr @ X590 @ X591 ) ) )
& ( ~ ( in @ X595 @ ( dsetconstr @ X593 @ X594 ) )
| ( in @ X595 @ X593 ) )
& ( ~ ( in @ X598 @ ( dsetconstr @ X596 @ X597 ) )
| ( X597 @ X598 ) )
& ( ( X599 @ ( esk12_1 @ X599 ) )
| ( X599 @ ( esk11_2 @ X599 @ X600 ) )
| ~ ( X599 @ X600 ) )
& ( ~ ( X599 @ X603 )
| ( ( esk12_1 @ X599 )
= X603 )
| ( X599 @ ( esk11_2 @ X599 @ X600 ) )
| ~ ( X599 @ X600 ) )
& ( ( X599 @ ( esk12_1 @ X599 ) )
| ( X600
!= ( esk11_2 @ X599 @ X600 ) )
| ~ ( X599 @ X600 ) )
& ( ~ ( X599 @ X603 )
| ( ( esk12_1 @ X599 )
= X603 )
| ( X600
!= ( esk11_2 @ X599 @ X600 ) )
| ~ ( X599 @ X600 ) )
& ( ~ ( in @ X605 @ ( prop2set @ X604 ) )
| X604 )
& ( ~ ( in @ X606 @ emptyset )
| X607 )
& ( ~ ( in @ X608 @ emptyset )
| ~ $true )
& ~ ( in @ X609 @ emptyset )
& ( ( X610 @ ( esk13_2 @ X610 @ X611 ) )
| ~ ( X610 @ X611 )
| ( X610 @ ( esk14_1 @ X610 ) ) )
& ( ( X611
!= ( esk13_2 @ X610 @ X611 ) )
| ~ ( X610 @ X611 )
| ( X610 @ ( esk14_1 @ X610 ) ) )
& ( ( in @ ( esk16_2 @ X614 @ X615 ) @ X615 )
| ( X614 = X615 )
| ( in @ ( esk15_2 @ X614 @ X615 ) @ X614 ) )
& ( ~ ( in @ ( esk16_2 @ X614 @ X615 ) @ X614 )
| ( X614 = X615 )
| ( in @ ( esk15_2 @ X614 @ X615 ) @ X614 ) )
& ( ( in @ ( esk16_2 @ X614 @ X615 ) @ X615 )
| ( X614 = X615 )
| ~ ( in @ ( esk15_2 @ X614 @ X615 ) @ X615 ) )
& ( ~ ( in @ ( esk16_2 @ X614 @ X615 ) @ X614 )
| ( X614 = X615 )
| ~ ( in @ ( esk15_2 @ X614 @ X615 ) @ X615 ) )
& ( ( in @ ( esk17_1 @ X618 ) @ X618 )
| ( X618 = emptyset ) )
& ( ( in @ ( esk18_1 @ X620 ) @ X620 )
| ( X620 = emptyset ) )
& ( ~ ( in @ X624 @ ( dsetconstr @ X622 @ X623 ) )
| ( X623 @ X624 )
| ~ ( in @ X624 @ X622 ) )
& ( ~ ( X623 @ X624 )
| ( in @ X624 @ ( dsetconstr @ X622 @ X623 ) )
| ~ ( in @ X624 @ X622 ) )
& ( ( X625 = emptyset )
| ( in @ ( esk19_1 @ X625 ) @ X625 ) )
& ( ~ ( in @ X629 @ X627 )
| ~ ( X628 @ X629 )
| ( ( dsetconstr @ X627 @ X628 )
!= emptyset ) )
& ( ~ ( in @ X631 @ X630 )
| ( X630 != emptyset ) )
& ( in @ X632 @ ( setadjoin @ X632 @ X633 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X636 @ X635 )
| ( in @ X636 @ ( setadjoin @ X634 @ X635 ) ) )
& ( ( in @ X639 @ X638 )
| X640
| ( X639 = X637 )
| ~ ( in @ X639 @ ( setadjoin @ X637 @ X638 ) ) )
& ( ~ X640
| X640
| ( X639 = X637 )
| ~ ( in @ X639 @ ( setadjoin @ X637 @ X638 ) ) )
& ( ( in @ X639 @ X638 )
| X640
| ~ X640
| ~ ( in @ X639 @ ( setadjoin @ X637 @ X638 ) ) )
& ( ~ X640
| X640
| ~ X640
| ~ ( in @ X639 @ ( setadjoin @ X637 @ X638 ) ) )
& ( ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) )
| ( X643 = X641 )
| ( in @ X643 @ X642 ) )
& ( ( dsetconstr @ X644
@ ^ [Z0: $i] : $true )
= X644 )
& ( ( in @ ( esk20_2 @ X645 @ X646 ) @ X646 )
| ( in @ X646 @ ( powerset @ X645 ) ) )
& ( ~ ( in @ ( esk20_2 @ X645 @ X646 ) @ X645 )
| ( in @ X646 @ ( powerset @ X645 ) ) )
& ( in @ emptyset @ ( powerset @ X648 ) )
& ( in @ emptyset @ ( powerset @ X649 ) )
& ( ~ ( in @ X651 @ ( powerset @ X650 ) )
| ~ ( in @ X652 @ X651 )
| ( in @ X652 @ X650 ) )
& ( ~ ( in @ X654 @ X655 )
| ~ ( in @ X655 @ X653 )
| ( in @ X654 @ ( setunion @ X653 ) ) )
& ( ( in @ X657 @ ( esk21_3 @ X656 @ X657 @ X658 ) )
| X658
| ~ ( in @ X657 @ ( setunion @ X656 ) ) )
& ( ( in @ ( esk21_3 @ X656 @ X657 @ X658 ) @ X656 )
| X658
| ~ ( in @ X657 @ ( setunion @ X656 ) ) )
& ( ~ X658
| X658
| ~ ( in @ X657 @ ( setunion @ X656 ) ) )
& ( ~ ( in @ X661 @ X660 )
| ( in @ X661 @ ( powerset @ ( setunion @ X660 ) ) ) )
& ( ~ ( X662 @ X666 )
| ( X666
= ( esk23_1 @ X662 ) )
| ( X662 @ ( esk22_2 @ X662 @ X663 ) )
| ~ ( X662 @ X663 ) )
& ( ( X667
!= ( esk23_1 @ X662 ) )
| ( X662 @ X667 )
| ( X662 @ ( esk22_2 @ X662 @ X663 ) )
| ~ ( X662 @ X663 ) )
& ( ~ ( X662 @ X666 )
| ( X666
= ( esk23_1 @ X662 ) )
| ( X663
!= ( esk22_2 @ X662 @ X663 ) )
| ~ ( X662 @ X663 ) )
& ( ( X667
!= ( esk23_1 @ X662 ) )
| ( X662 @ X667 )
| ( X663
!= ( esk22_2 @ X662 @ X663 ) )
| ~ ( X662 @ X663 ) )
& ( ( in @ ( esk24_1 @ X668 ) @ X668 )
| ( X668 = emptyset ) )
& ( $true
| ( X668 = emptyset ) )
& ( ~ ( in @ X670 @ ( setadjoin @ X671 @ emptyset ) )
| ( X670 = X671 ) )
& ( ( X672 = X673 )
| ~ ( in @ X673 @ ( setadjoin @ X672 @ emptyset ) ) )
& ( ( X674 != X675 )
| ( in @ X674 @ ( setadjoin @ X675 @ emptyset ) ) )
& ( ~ ( in @ X676 @ ( setadjoin @ X677 @ emptyset ) )
| ( in @ X677 @ ( setadjoin @ X676 @ emptyset ) ) )
& ( ~ ( in @ X680 @ ( setadjoin @ X678 @ ( setadjoin @ X679 @ emptyset ) ) )
| ( X680 = X678 )
| ( X680 = X679 ) )
& ( in @ X681 @ ( setadjoin @ X681 @ ( setadjoin @ X682 @ emptyset ) ) )
& ( in @ X684 @ ( setadjoin @ X683 @ ( setadjoin @ X684 @ emptyset ) ) )
& ( ~ ( in @ X687 @ X685 )
| ~ ( X686 @ X687 )
| ( ( dsetconstr @ X685 @ X686 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X689 @ emptyset )
| ( X688 @ X689 ) )
& ( ( in @ ( esk25_2 @ X690 @ X691 ) @ X690 )
| ~ ( in @ X692 @ X690 )
| ( X691 @ X692 ) )
& ( ~ ( X691 @ ( esk25_2 @ X690 @ X691 ) )
| ~ ( in @ X692 @ X690 )
| ( X691 @ X692 ) )
& ( ( in @ ( esk26_2 @ X694 @ X695 ) @ X694 )
| ~ ( in @ X697 @ X694 )
| ~ ( X695 @ X697 ) )
& ( ( X695 @ ( esk26_2 @ X694 @ X695 ) )
| ~ ( in @ X697 @ X694 )
| ~ ( X695 @ X697 ) )
& ( ( in @ ( esk27_2 @ X698 @ X699 ) @ X698 )
| ~ ( in @ X701 @ X698 )
| ~ ( X699 @ X701 ) )
& ( ( X699 @ ( esk27_2 @ X698 @ X699 ) )
| ~ ( in @ X701 @ X698 )
| ~ ( X699 @ X701 ) )
& ( ( in @ ( esk28_2 @ X702 @ X703 ) @ X702 )
| ~ ( in @ X704 @ X702 )
| ( X703 @ X704 ) )
& ( ~ ( X703 @ ( esk28_2 @ X702 @ X703 ) )
| ~ ( in @ X704 @ X702 )
| ( X703 @ X704 ) )
& ( ~ X706
| ( in @ emptyset @ ( prop2set @ X706 ) ) )
& ( ~ X707
| ( set2prop @ ( prop2set @ X707 ) ) )
& ( ( in @ ( esk29_2 @ X708 @ X709 ) @ X708 )
| ~ ( in @ X711 @ X708 )
| ~ ( X709 @ X711 ) )
& ( ( X709 @ ( esk29_2 @ X708 @ X709 ) )
| ~ ( in @ X711 @ X708 )
| ~ ( X709 @ X711 ) )
& ( ( in @ ( esk30_2 @ X712 @ X713 ) @ X712 )
| ~ ( in @ X714 @ X712 )
| ( X713 @ X714 ) )
& ( ~ ( X713 @ ( esk30_2 @ X712 @ X713 ) )
| ~ ( in @ X714 @ X712 )
| ( X713 @ X714 ) )
& ( ( X716 @ ( esk32_1 @ X716 ) )
| ( X716 @ ( esk31_2 @ X716 @ X717 ) )
| ~ ( X716 @ X717 ) )
& ( ~ ( X716 @ X720 )
| ( ( esk32_1 @ X716 )
= X720 )
| ( X716 @ ( esk31_2 @ X716 @ X717 ) )
| ~ ( X716 @ X717 ) )
& ( ( X716 @ ( esk32_1 @ X716 ) )
| ( X717
!= ( esk31_2 @ X716 @ X717 ) )
| ~ ( X716 @ X717 ) )
& ( ~ ( X716 @ X720 )
| ( ( esk32_1 @ X716 )
= X720 )
| ( X717
!= ( esk31_2 @ X716 @ X717 ) )
| ~ ( X716 @ X717 ) )
& ( ( X721 @ ( esk35_1 @ X721 ) )
| ( X721 @ ( esk33_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ~ ( X721 @ X726 )
| ( ( esk35_1 @ X721 )
= X726 )
| ( X721 @ ( esk33_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ( X721 @ ( esk35_1 @ X721 ) )
| ( X721 @ ( esk34_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ~ ( X721 @ X726 )
| ( ( esk35_1 @ X721 )
= X726 )
| ( X721 @ ( esk34_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ( X721 @ ( esk35_1 @ X721 ) )
| ( ( esk33_1 @ X721 )
!= ( esk34_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ~ ( X721 @ X726 )
| ( ( esk35_1 @ X721 )
= X726 )
| ( ( esk33_1 @ X721 )
!= ( esk34_1 @ X721 ) )
| ~ ( X721 @ X722 ) )
& ( ( X727 @ ( esk37_1 @ X727 ) )
| ~ ( X727 @ ( esk36_2 @ X727 @ X728 ) )
| ( ( esk36_2 @ X727 @ X728 )
!= X728 ) )
& ( ~ ( X727 @ X731 )
| ( ( esk37_1 @ X727 )
= X731 )
| ~ ( X727 @ ( esk36_2 @ X727 @ X728 ) )
| ( ( esk36_2 @ X727 @ X728 )
!= X728 ) )
& ( ( X727 @ ( esk37_1 @ X727 ) )
| ( X727 @ ( esk36_2 @ X727 @ X728 ) )
| ( ( esk36_2 @ X727 @ X728 )
= X728 ) )
& ( ~ ( X727 @ X731 )
| ( ( esk37_1 @ X727 )
= X731 )
| ( X727 @ ( esk36_2 @ X727 @ X728 ) )
| ( ( esk36_2 @ X727 @ X728 )
= X728 ) )
& ( ( X732 != X733 )
| ( X734 != X735 )
| ~ ( in @ X734 @ X732 )
| ( in @ X735 @ X733 ) )
& ( ~ ( in @ X738 @ X736 )
| ( in @ X739 @ X737 )
| ( X738 != X739 )
| ( X736 != X737 ) )
& ( ~ ( in @ X739 @ X737 )
| ( in @ X738 @ X736 )
| ( X738 != X739 )
| ( X736 != X737 ) )
& ( ( X740 @ ( esk38_2 @ X740 @ X741 ) )
| ~ ( X740 @ X741 )
| ~ ( X740 @ X743 )
| ~ ( X740 @ X744 )
| ( X743 = X744 ) )
& ( ( X741
!= ( esk38_2 @ X740 @ X741 ) )
| ~ ( X740 @ X741 )
| ~ ( X740 @ X743 )
| ~ ( X740 @ X744 )
| ( X743 = X744 ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( ( esk39_2 @ X745 @ X746 )
= ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ~ ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ~ ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X745 @ ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X746 @ ( esk42_2 @ X745 @ X746 ) )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X746 @ X752 )
| ( ( esk42_2 @ X745 @ X746 )
= X752 )
| ( X749
!= ( esk41_3 @ X745 @ X746 @ X749 ) )
| ~ ( X745 @ X749 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X746 @ ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ( X745 @ ( esk44_2 @ X745 @ X746 ) )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( ~ ( X745 @ X756 )
| ( ( esk44_2 @ X745 @ X746 )
= X756 )
| ( X753
!= ( esk43_3 @ X745 @ X746 @ X753 ) )
| ~ ( X746 @ X753 )
| ( X745 @ ( esk39_2 @ X745 @ X746 ) )
| ( X746 @ ( esk40_2 @ X745 @ X746 ) ) )
& ( emptyset = emptyset )
& ( ( X757 != X758 )
| ( X759 != X760 )
| ( ( setadjoin @ X757 @ X759 )
= ( setadjoin @ X758 @ X760 ) ) )
& ( ( X761 != X762 )
| ( ( powerset @ X761 )
= ( powerset @ X762 ) ) )
& ( ( X763 != X764 )
| ( ( setunion @ X763 )
= ( setunion @ X764 ) ) )
& ( omega = omega )
& ( ( X765 @ ( esk45_2 @ X765 @ X766 ) )
| ~ ( X765 @ X766 )
| ~ ( X765 @ X768 )
| ~ ( X765 @ X769 )
| ( X768 = X769 ) )
& ( ( X766
!= ( esk45_2 @ X765 @ X766 ) )
| ~ ( X765 @ X766 )
| ~ ( X765 @ X768 )
| ~ ( X765 @ X769 )
| ( X768 = X769 ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( ( esk46_2 @ X770 @ X771 )
= ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( ( esk46_2 @ X770 @ X771 )
= ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( ( esk46_2 @ X770 @ X771 )
= ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( ( esk46_2 @ X770 @ X771 )
= ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ~ ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ~ ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ~ ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ~ ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ~ ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ~ ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ~ ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ~ ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X770 @ ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X771 @ ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( X776
!= ( esk49_3 @ X770 @ X771 @ X776 ) )
| ~ ( X771 @ X776 )
| ( ( descr @ X770 )
= ( descr @ X771 ) )
| ( X774
!= ( esk48_3 @ X770 @ X771 @ X774 ) )
| ~ ( X770 @ X774 )
| ( X770 @ ( esk46_2 @ X770 @ X771 ) )
| ( X771 @ ( esk47_2 @ X770 @ X771 ) ) )
& ( ( in @ ( esk50_4 @ X778 @ X779 @ X780 @ X781 ) @ X778 )
| ( ( dsetconstr @ X778 @ X780 )
= ( dsetconstr @ X779 @ X781 ) )
| ( X778 != X779 ) )
& ( ( in @ ( esk51_4 @ X778 @ X779 @ X780 @ X781 ) @ X779 )
| ( ( dsetconstr @ X778 @ X780 )
= ( dsetconstr @ X779 @ X781 ) )
| ( X778 != X779 ) )
& ( ( ( esk50_4 @ X778 @ X779 @ X780 @ X781 )
= ( esk51_4 @ X778 @ X779 @ X780 @ X781 ) )
| ( ( dsetconstr @ X778 @ X780 )
= ( dsetconstr @ X779 @ X781 ) )
| ( X778 != X779 ) )
& ( ~ ( X780 @ ( esk50_4 @ X778 @ X779 @ X780 @ X781 ) )
| ~ ( X781 @ ( esk51_4 @ X778 @ X779 @ X780 @ X781 ) )
| ( ( dsetconstr @ X778 @ X780 )
= ( dsetconstr @ X779 @ X781 ) )
| ( X778 != X779 ) )
& ( ( X780 @ ( esk50_4 @ X778 @ X779 @ X780 @ X781 ) )
| ( X781 @ ( esk51_4 @ X778 @ X779 @ X780 @ X781 ) )
| ( ( dsetconstr @ X778 @ X780 )
= ( dsetconstr @ X779 @ X781 ) )
| ( X778 != X779 ) )
& ( ( in @ ( esk52_2 @ X784 @ X785 ) @ X784 )
| ( subset @ X784 @ X785 ) )
& ( ~ ( in @ ( esk52_2 @ X784 @ X785 ) @ X785 )
| ( subset @ X784 @ X785 ) )
& ( ( X787 != X788 )
| ( subset @ X788 @ X787 ) )
& ( ( X789 != X790 )
| ( subset @ X789 @ X790 ) )
& ( ( in @ ( esk53_2 @ X791 @ X792 ) @ X791 )
| ( subset @ X791 @ X792 ) )
& ( ~ ( in @ ( esk53_2 @ X791 @ X792 ) @ X792 )
| ( subset @ X791 @ X792 ) )
& ( subset @ emptyset @ X794 )
& ( ~ ( subset @ X795 @ X796 )
| ~ ( in @ X797 @ X795 )
| ( in @ X797 @ X796 ) )
& ( ~ ( subset @ X798 @ X799 )
| ( in @ X800 @ X799 )
| ~ ( in @ X800 @ X798 ) )
& ( ~ ( in @ X803 @ X801 )
| ( in @ X803 @ X802 )
| ~ ( subset @ X801 @ X802 ) )
& ( ( subset @ X804 @ X805 )
| ( X804 != X805 ) )
& ( ~ ( in @ X808 @ X806 )
| ( in @ X808 @ X807 )
| ( X806 != X807 ) )
& ~ ( subset @ esk54_0 @ esk54_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_127])])])])])])]) ).
thf(c_0_129,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X3 @ X2 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_130,negated_conjecture,
~ ( subset @ esk54_0 @ esk54_0 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_131,negated_conjecture,
! [X2: $i] : ( subset @ X2 @ X2 ),
inference(er,[status(thm)],[c_0_129]) ).
thf(c_0_132,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU569^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 13:02:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.22/0.50 Running higher-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.f3EL9BQbEt/E---3.1_32130.p
% 0.57/0.55 # Version: 3.2.0-ho
% 0.57/0.55 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.57/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.55 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.57/0.55 # Starting ehoh_best3_rw with 300s (1) cores
% 0.57/0.55 # Starting almost_fo_3 with 300s (1) cores
% 0.57/0.55 # Starting new_ho_13 with 300s (1) cores
% 0.57/0.55 # almost_fo_3 with pid 32210 completed with status 0
% 0.57/0.55 # Result found by almost_fo_3
% 0.57/0.55 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.57/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.55 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.57/0.55 # Starting ehoh_best3_rw with 300s (1) cores
% 0.57/0.55 # Starting almost_fo_3 with 300s (1) cores
% 0.57/0.55 # No SInE strategy applied
% 0.57/0.55 # Search class: HGHSM-FSLS31-SHFMMMBN
% 0.57/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.55 # Starting new_ho_10 with 163s (1) cores
% 0.57/0.55 # new_ho_10 with pid 32213 completed with status 0
% 0.57/0.55 # Result found by new_ho_10
% 0.57/0.55 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.57/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.55 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.57/0.55 # Starting ehoh_best3_rw with 300s (1) cores
% 0.57/0.55 # Starting almost_fo_3 with 300s (1) cores
% 0.57/0.55 # No SInE strategy applied
% 0.57/0.55 # Search class: HGHSM-FSLS31-SHFMMMBN
% 0.57/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.55 # Starting new_ho_10 with 163s (1) cores
% 0.57/0.55 # Preprocessing time : 0.004 s
% 0.57/0.55 # Presaturation interreduction done
% 0.57/0.55
% 0.57/0.55 # Proof found!
% 0.57/0.55 # SZS status Theorem
% 0.57/0.55 # SZS output start CNFRefutation
% See solution above
% 0.57/0.55 # Parsed axioms : 188
% 0.57/0.55 # Removed by relevancy pruning/SinE : 0
% 0.57/0.55 # Initial clauses : 296
% 0.57/0.55 # Removed in clause preprocessing : 114
% 0.57/0.55 # Initial clauses in saturation : 182
% 0.57/0.55 # Processed clauses : 25
% 0.57/0.55 # ...of these trivial : 1
% 0.57/0.55 # ...subsumed : 7
% 0.57/0.55 # ...remaining for further processing : 17
% 0.57/0.55 # Other redundant clauses eliminated : 2
% 0.57/0.55 # Clauses deleted for lack of memory : 0
% 0.57/0.55 # Backward-subsumed : 0
% 0.57/0.55 # Backward-rewritten : 1
% 0.57/0.55 # Generated clauses : 2
% 0.57/0.55 # ...of the previous two non-redundant : 2
% 0.57/0.55 # ...aggressively subsumed : 0
% 0.57/0.55 # Contextual simplify-reflections : 0
% 0.57/0.55 # Paramodulations : 0
% 0.57/0.55 # Factorizations : 0
% 0.57/0.55 # NegExts : 0
% 0.57/0.55 # Equation resolutions : 2
% 0.57/0.55 # Disequality decompositions : 0
% 0.57/0.55 # Total rewrite steps : 2
% 0.57/0.55 # ...of those cached : 0
% 0.57/0.55 # Propositional unsat checks : 0
% 0.57/0.55 # Propositional check models : 0
% 0.57/0.55 # Propositional check unsatisfiable : 0
% 0.57/0.55 # Propositional clauses : 0
% 0.57/0.55 # Propositional clauses after purity: 0
% 0.57/0.55 # Propositional unsat core size : 0
% 0.57/0.55 # Propositional preprocessing time : 0.000
% 0.57/0.55 # Propositional encoding time : 0.000
% 0.57/0.55 # Propositional solver time : 0.000
% 0.57/0.55 # Success case prop preproc time : 0.000
% 0.57/0.55 # Success case prop encoding time : 0.000
% 0.57/0.55 # Success case prop solver time : 0.000
% 0.57/0.55 # Current number of processed clauses : 14
% 0.57/0.55 # Positive orientable unit clauses : 9
% 0.57/0.55 # Positive unorientable unit clauses: 0
% 0.57/0.55 # Negative unit clauses : 2
% 0.57/0.55 # Non-unit-clauses : 3
% 0.57/0.55 # Current number of unprocessed clauses: 159
% 0.57/0.55 # ...number of literals in the above : 604
% 0.57/0.55 # Current number of archived formulas : 0
% 0.57/0.55 # Current number of archived clauses : 1
% 0.57/0.55 # Clause-clause subsumption calls (NU) : 4
% 0.57/0.55 # Rec. Clause-clause subsumption calls : 2
% 0.57/0.55 # Non-unit clause-clause subsumptions : 2
% 0.57/0.55 # Unit Clause-clause subsumption calls : 2
% 0.57/0.55 # Rewrite failures with RHS unbound : 0
% 0.57/0.55 # BW rewrite match attempts : 2
% 0.57/0.55 # BW rewrite match successes : 1
% 0.57/0.55 # Condensation attempts : 25
% 0.57/0.55 # Condensation successes : 0
% 0.57/0.55 # Termbank termtop insertions : 24243
% 0.57/0.55 # Search garbage collected termcells : 9836
% 0.57/0.55
% 0.57/0.55 # -------------------------------------------------
% 0.57/0.55 # User time : 0.029 s
% 0.57/0.55 # System time : 0.007 s
% 0.57/0.55 # Total time : 0.036 s
% 0.57/0.55 # Maximum resident set size: 4408 pages
% 0.57/0.55
% 0.57/0.55 # -------------------------------------------------
% 0.57/0.55 # User time : 0.033 s
% 0.57/0.55 # System time : 0.011 s
% 0.57/0.55 # Total time : 0.044 s
% 0.57/0.55 # Maximum resident set size: 2128 pages
% 0.57/0.55 % E---3.1 exiting
% 0.57/0.56 % E exiting
%------------------------------------------------------------------------------