TSTP Solution File: SEU559^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU559^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.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 : Tue May 21 03:28:10 EDT 2024
% Result : Timeout 0.56s 300.09s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 221
% Syntax : Number of formulae : 266 ( 25 unt; 142 typ; 0 def)
% Number of atoms : 1003 ( 315 equ; 0 cnn)
% Maximal formula atoms : 309 ( 8 avg)
% Number of connectives : 4134 ( 369 ~; 429 |; 260 &;2449 @)
% ( 137 <=>; 490 =>; 0 <=; 0 <~>)
% Maximal formula depth : 360 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 301 >; 0 *; 0 +; 0 <<)
% Number of symbols : 145 ( 142 usr; 83 con; 0-4 aty)
% Number of variables : 907 ( 120 ^ 683 !; 104 ?; 907 :)
% 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_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,
epred1_0: $o ).
thf(decl_113,type,
esk1_2: $i > $i > $i ).
thf(decl_114,type,
esk2_2: $i > $i > $i ).
thf(decl_115,type,
esk3_2: $i > $i > $i ).
thf(decl_116,type,
esk4_1: $i > $i ).
thf(decl_117,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_118,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_119,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_120,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_121,type,
esk9_1: $i > $i ).
thf(decl_122,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_123,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_124,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_125,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_126,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_127,type,
esk15_2: $i > $i > $i ).
thf(decl_128,type,
esk16_2: $i > $i > $i ).
thf(decl_129,type,
esk17_1: $i > $i ).
thf(decl_130,type,
esk18_1: $i > $i ).
thf(decl_131,type,
esk19_1: $i > $i ).
thf(decl_132,type,
esk20_2: $i > $i > $i ).
thf(decl_133,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_134,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_135,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk24_1: $i > $i ).
thf(decl_137,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_138,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_139,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_140,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_141,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_142,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_143,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_144,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_145,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_146,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_147,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_148,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_149,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_150,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_151,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_152,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_153,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_154,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_155,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_156,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_157,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_158,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_159,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_160,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_161,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_162,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_163,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_164,type,
esk52_0: $i ).
thf(decl_165,type,
esk53_0: $i ).
thf(decl_166,type,
esk54_0: $i ).
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/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
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/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
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/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(subset,axiom,
( subset
= ( ^ [X4: $i,X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
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/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
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/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
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/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
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/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(subsetI1,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
=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
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/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
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/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
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/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
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/sandbox/benchmark/theBenchmark.p',foundationAx) ).
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/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_78,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_79,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_80,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_81,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_82,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_83,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_84,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_85,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_86,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_87,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_88,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_89,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_90,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_91,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_92,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_93,plain,
( subset
= ( ^ [Z0: $i,Z1: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ( in @ X2 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_94,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X245: $i] :
( ( X1 @ X245 )
& ! [X246: $i] :
( ( X1 @ X246 )
=> ( X245 = X246 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_95,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X247: $i] :
( ( X1 @ X247 )
& ! [X248: $i] :
( ( X1 @ X248 )
=> ( X247 = X248 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_80,c_0_79]) ).
thf(c_0_96,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X249: $i] :
( ( X1 @ X249 )
& ! [X250: $i] :
( ( X1 @ X250 )
=> ( X249 = X250 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_81,c_0_79]) ).
thf(c_0_97,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_98,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X251: $i] :
( ( X1 @ X251 )
& ! [X252: $i] :
( ( X1 @ X252 )
=> ( X251 = X252 ) ) )
<=> ? [X253: $i] :
( ( X17 @ X253 )
& ! [X254: $i] :
( ( X17 @ X254 )
=> ( X253 = X254 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_82,c_0_79]) ).
thf(c_0_99,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_83]) ).
thf(c_0_100,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_84,c_0_83]) ).
thf(c_0_101,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_83]) ).
thf(c_0_102,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X255: $i] :
( ( X1 @ X255 )
& ! [X256: $i] :
( ( X1 @ X256 )
=> ( X255 = X256 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_85,c_0_79]) ).
thf(c_0_103,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X257: $i] :
( ( X1 @ X257 )
& ! [X258: $i] :
( ( X1 @ X258 )
=> ( X257 = X258 ) ) )
=> ( ? [X259: $i] :
( ( X17 @ X259 )
& ! [X260: $i] :
( ( X17 @ X260 )
=> ( X259 = X260 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_86,c_0_79]) ).
thf(c_0_104,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_105,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_106,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X241: $i] :
( ( X1 @ X241 )
& ! [X242: $i] :
( ( X1 @ X242 )
=> ( X241 = X242 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_87,c_0_79]) ).
thf(c_0_107,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_83]) ).
thf(c_0_108,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_109,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X243: $i] :
( ( X1 @ X243 )
& ! [X244: $i] :
( ( X1 @ X244 )
=> ( X243 = X244 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_88,c_0_79]) ).
thf(c_0_110,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X239: $i] :
( ( X1 @ X239 )
& ! [X240: $i] :
( ( X1 @ X240 )
=> ( X239 = X240 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_89,c_0_79]) ).
thf(c_0_111,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X237: $i] :
( ( X1 @ X237 )
& ! [X238: $i] :
( ( X1 @ X238 )
=> ( X237 = X238 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_90,c_0_79]) ).
thf(c_0_112,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_113,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_114,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_115,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X235: $i] :
( ( X1 @ X235 )
& ! [X236: $i] :
( ( X1 @ X236 )
=> ( X235 = X236 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_79]) ).
thf(c_0_116,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X233: $i] :
( ( X6 @ X2 @ X233 )
& ! [X234: $i] :
( ( X6 @ X2 @ X234 )
=> ( X233 = X234 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_92,c_0_79]) ).
thf(c_0_117,plain,
( epred1_0
<=> ! [X290: $i] :
? [X291: $i] :
( ! [X292: $i] :
( ( in @ X292 @ X291 )
=> ! [X293: $i] :
( ( in @ X293 @ X292 )
=> ( in @ X293 @ X290 ) ) )
& ! [X294: $i,X295: $i] :
( ( ( in @ X294 @ X290 )
& ( in @ X295 @ X290 ) )
=> ( ! [X296: $i] :
( ( in @ X296 @ X291 )
=> ( ( in @ X294 @ X296 )
<=> ( in @ X295 @ X296 ) ) )
=> ( X294 = X295 ) ) )
& ! [X297: $i,X298: $i] :
( ( ( in @ X297 @ X291 )
& ( in @ X298 @ X291 ) )
=> ( ! [X299: $i] :
( ( in @ X299 @ X297 )
=> ( in @ X299 @ X298 ) )
| ! [X300: $i] :
( ( in @ X300 @ X298 )
=> ( in @ X300 @ X297 ) ) ) )
& ! [X301: $i] :
( ( ! [X302: $i] :
( ( in @ X302 @ X301 )
=> ( in @ X302 @ X290 ) )
& ? [X303: $i] : ( in @ X303 @ X301 ) )
=> ? [X304: $i,X305: $i] :
( ( in @ X304 @ X291 )
& ( in @ X305 @ X301 )
& ~ ? [X306: $i] :
( ( in @ X306 @ X304 )
& ( in @ X306 @ X301 ) )
& ! [X307: $i] :
( ( in @ X307 @ X291 )
=> ( ! [X308: $i] :
( ( in @ X308 @ X307 )
=> ( in @ X308 @ X304 ) )
| ( in @ X305 @ X307 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_118,negated_conjecture,
~ ( ! [X261: $i,X262: $i] :
( ! [X263: $i] :
( ( in @ X263 @ X261 )
<=> ( in @ X263 @ X262 ) )
=> ( X261 = X262 ) )
=> ( ! [X264: $i] :
~ ( in @ X264 @ emptyset )
=> ( ! [X265: $i,X266: $i,X267: $i] :
( ( in @ X267 @ ( setadjoin @ X265 @ X266 ) )
<=> ( ( X267 = X265 )
| ( in @ X267 @ X266 ) ) )
=> ( ! [X268: $i,X269: $i] :
( ( in @ X269 @ ( powerset @ X268 ) )
<=> ! [X270: $i] :
( ( in @ X270 @ X269 )
=> ( in @ X270 @ X268 ) ) )
=> ( ! [X271: $i,X272: $i] :
( ( in @ X272 @ ( setunion @ X271 ) )
<=> ? [X273: $i] :
( ( in @ X272 @ X273 )
& ( in @ X273 @ X271 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X274: $i] :
( ( in @ X274 @ omega )
=> ( in @ ( setadjoin @ X274 @ X274 ) @ omega ) )
=> ( ! [X275: $i] :
( ( ( in @ emptyset @ X275 )
& ! [X276: $i] :
( ( ( in @ X276 @ omega )
& ( in @ X276 @ X275 ) )
=> ( in @ ( setadjoin @ X276 @ X276 ) @ X275 ) ) )
=> ! [X277: $i] :
( ( in @ X277 @ omega )
=> ( in @ X277 @ X275 ) ) )
=> ( ! [X278: $i > $i > $o,X279: $i] :
( ! [X280: $i] :
( ( in @ X280 @ X279 )
=> ? [X281: $i] :
( ( X278 @ X280 @ X281 )
& ! [X282: $i] :
( ( X278 @ X280 @ X282 )
=> ( X281 = X282 ) ) ) )
=> ? [X283: $i] :
! [X284: $i] :
( ( in @ X284 @ X283 )
<=> ? [X285: $i] :
( ( in @ X285 @ X279 )
& ( X278 @ X285 @ X284 ) ) ) )
=> ( ! [X286: $i] :
( ? [X287: $i] : ( in @ X287 @ X286 )
=> ? [X288: $i] :
( ( in @ X288 @ X286 )
& ~ ? [X289: $i] :
( ( in @ X289 @ X288 )
& ( in @ X289 @ X286 ) ) ) )
=> ( epred1_0
=> ( ! [X309: $i > $o] :
( ? [X310: $i] :
( ( X309 @ X310 )
& ! [X311: $i] :
( ( X309 @ X311 )
=> ( X310 = X311 ) ) )
=> ( X309
@ ( descr
@ ^ [Z0: $i] : ( X309 @ Z0 ) ) ) )
=> ( ! [X312: $i,X313: $i > $o,X314: $i] :
( ( in @ X314 @ X312 )
=> ( ( X313 @ X314 )
=> ( in @ X314
@ ( dsetconstr @ X312
@ ^ [Z0: $i] : ( X313 @ Z0 ) ) ) ) )
=> ( ! [X315: $i,X316: $i > $o,X317: $i] :
( ( in @ X317
@ ( dsetconstr @ X315
@ ^ [Z0: $i] : ( X316 @ Z0 ) ) )
=> ( in @ X317 @ X315 ) )
=> ( ! [X318: $i,X319: $i > $o,X320: $i] :
( ( in @ X320
@ ( dsetconstr @ X318
@ ^ [Z0: $i] : ( X319 @ Z0 ) ) )
=> ( X319 @ X320 ) )
=> ( ! [X321: $i > $o] :
( ? [X322: $i] :
( ( X321 @ X322 )
& ! [X323: $i] :
( ( X321 @ X323 )
=> ( X322 = X323 ) ) )
=> ? [X324: $i] :
( ( X321 @ X324 )
& ! [X325: $i] :
( ( X321 @ X325 )
=> ( X324 = X325 ) ) ) )
=> ( ! [X326: $o,X327: $i] :
( ( in @ X327 @ ( prop2set @ X326 ) )
=> X326 )
=> ( ! [X328: $i] :
( ( in @ X328 @ emptyset )
=> ! [X329: $o] : X329 )
=> ( ! [X330: $i] :
~ ( in @ X330 @ emptyset )
=> ( ! [X331: $i] :
~ ( in @ X331 @ emptyset )
=> ( ! [X332: $i > $o] :
( ? [X333: $i] :
( ( X332 @ X333 )
& ! [X334: $i] :
( ( X332 @ X334 )
=> ( X333 = X334 ) ) )
=> ? [X335: $i] : ( X332 @ X335 ) )
=> ( ! [X336: $i,X337: $i] :
( ! [X338: $i] :
( ( in @ X338 @ X336 )
=> ( in @ X338 @ X337 ) )
=> ( ! [X339: $i] :
( ( in @ X339 @ X337 )
=> ( in @ X339 @ X336 ) )
=> ( X336 = X337 ) ) )
=> ( ! [X340: $i] :
( ! [X341: $i] :
~ ( in @ X341 @ X340 )
=> ( X340 = emptyset ) )
=> ( ! [X342: $i] :
( ! [X343: $i] :
~ ( in @ X343 @ X342 )
=> ( X342 = emptyset ) )
=> ( ! [X344: $i,X345: $i > $o,X346: $i] :
( ( in @ X346 @ X344 )
=> ( ( in @ X346
@ ( dsetconstr @ X344
@ ^ [Z0: $i] : ( X345 @ Z0 ) ) )
<=> ( X345 @ X346 ) ) )
=> ( ! [X347: $i] :
( ( X347 != emptyset )
=> ? [X348: $i] : ( in @ X348 @ X347 ) )
=> ( ! [X349: $i,X350: $i > $o,X351: $i] :
( ( in @ X351 @ X349 )
=> ( ( X350 @ X351 )
=> ( ( dsetconstr @ X349
@ ^ [Z0: $i] : ( X350 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X352: $i] :
( ? [X353: $i] : ( in @ X353 @ X352 )
=> ( X352 != emptyset ) )
=> ( ! [X354: $i,X355: $i] : ( in @ X354 @ ( setadjoin @ X354 @ X355 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X356: $i,X357: $i,X358: $i] :
( ( in @ X358 @ X357 )
=> ( in @ X358 @ ( setadjoin @ X356 @ X357 ) ) )
=> ( ! [X359: $i,X360: $i,X361: $i] :
( ( in @ X361 @ ( setadjoin @ X359 @ X360 ) )
=> ! [X362: $o] :
( ( ( X361 = X359 )
=> X362 )
=> ( ( ( in @ X361 @ X360 )
=> X362 )
=> X362 ) ) )
=> ( ! [X363: $i,X364: $i,X365: $i] :
( ( in @ X365 @ ( setadjoin @ X363 @ X364 ) )
=> ( ( X365 = X363 )
| ( in @ X365 @ X364 ) ) )
=> ( ! [X366: $i] :
( ( dsetconstr @ X366
@ ^ [Z0: $i] : $true )
= X366 )
=> ( ! [X367: $i,X368: $i] :
( ! [X369: $i] :
( ( in @ X369 @ X368 )
=> ( in @ X369 @ X367 ) )
=> ( in @ X368 @ ( powerset @ X367 ) ) )
=> ( ! [X370: $i] : ( in @ emptyset @ ( powerset @ X370 ) )
=> ( ! [X371: $i] : ( in @ emptyset @ ( powerset @ X371 ) )
=> ( ! [X372: $i,X373: $i,X374: $i] :
( ( in @ X373 @ ( powerset @ X372 ) )
=> ( ( in @ X374 @ X373 )
=> ( in @ X374 @ X372 ) ) )
=> ( ! [X375: $i,X376: $i,X377: $i] :
( ( in @ X376 @ X377 )
=> ( ( in @ X377 @ X375 )
=> ( in @ X376 @ ( setunion @ X375 ) ) ) )
=> ( ! [X378: $i,X379: $i] :
( ( in @ X379 @ ( setunion @ X378 ) )
=> ! [X380: $o] :
( ! [X381: $i] :
( ( in @ X379 @ X381 )
=> ( ( in @ X381 @ X378 )
=> X380 ) )
=> X380 ) )
=> ( ! [X382: $i,X383: $i] :
( ( in @ X383 @ X382 )
=> ( in @ X383 @ ( powerset @ ( setunion @ X382 ) ) ) )
=> ( ! [X384: $i > $o] :
( ? [X385: $i] :
( ( X384 @ X385 )
& ! [X386: $i] :
( ( X384 @ X386 )
=> ( X385 = X386 ) ) )
=> ? [X387: $i] :
! [X388: $i] :
( ( X384 @ X388 )
<=> ( X388 = X387 ) ) )
=> ( ! [X389: $i] :
( ( X389 != emptyset )
=> ? [X390: $i] : ( in @ X390 @ X389 ) )
=> ( ! [X391: $i,X392: $i] :
( ( in @ X391 @ ( setadjoin @ X392 @ emptyset ) )
=> ( X391 = X392 ) )
=> ( ! [X393: $i,X394: $i] :
( ( X393 != X394 )
=> ~ ( in @ X394 @ ( setadjoin @ X393 @ emptyset ) ) )
=> ( ! [X395: $i,X396: $i] :
( ( X395 = X396 )
=> ( in @ X395 @ ( setadjoin @ X396 @ emptyset ) ) )
=> ( ! [X397: $i,X398: $i] :
( ( in @ X397 @ ( setadjoin @ X398 @ emptyset ) )
=> ( in @ X398 @ ( setadjoin @ X397 @ emptyset ) ) )
=> ( ! [X399: $i,X400: $i,X401: $i] :
( ( in @ X401 @ ( setadjoin @ X399 @ ( setadjoin @ X400 @ emptyset ) ) )
=> ( ( X401 = X399 )
| ( X401 = X400 ) ) )
=> ( ! [X402: $i,X403: $i] : ( in @ X402 @ ( setadjoin @ X402 @ ( setadjoin @ X403 @ emptyset ) ) )
=> ( ! [X404: $i,X405: $i] : ( in @ X405 @ ( setadjoin @ X404 @ ( setadjoin @ X405 @ emptyset ) ) )
=> ( ! [X406: $i,X407: $i > $o] :
( ? [X408: $i] :
( ( in @ X408 @ X406 )
& ( X407 @ X408 ) )
=> ( ( dsetconstr @ X406
@ ^ [Z0: $i] : ( X407 @ Z0 ) )
!= emptyset ) )
=> ( ! [X409: $i > $o,X410: $i] :
( ( in @ X410 @ emptyset )
=> ( X409 @ X410 ) )
=> ( ! [X411: $i,X412: $i > $o] :
( ~ ! [X413: $i] :
( ( in @ X413 @ X411 )
=> ( X412 @ X413 ) )
=> ? [X414: $i] :
( ( in @ X414 @ X411 )
& ~ ( X412 @ X414 ) ) )
=> ( ! [X415: $i,X416: $i > $o] :
( ! [X417: $i] :
( ( in @ X417 @ X415 )
=> ~ ( X416 @ X417 ) )
=> ~ ? [X418: $i] :
( ( in @ X418 @ X415 )
& ( X416 @ X418 ) ) )
=> ( ! [X419: $i,X420: $i > $o] :
( ~ ? [X421: $i] :
( ( in @ X421 @ X419 )
& ( X420 @ X421 ) )
=> ! [X422: $i] :
( ( in @ X422 @ X419 )
=> ~ ( X420 @ X422 ) ) )
=> ( ! [X423: $i,X424: $i > $o] :
( ? [X425: $i] :
( ( in @ X425 @ X423 )
& ~ ( X424 @ X425 ) )
=> ~ ! [X426: $i] :
( ( in @ X426 @ X423 )
=> ( X424 @ X426 ) ) )
=> ( ! [X427: $o] :
( X427
=> ( in @ emptyset @ ( prop2set @ X427 ) ) )
=> ( prop2set2propI
=> ( ! [X428: $i,X429: $i > $o] :
( ~ ? [X430: $i] :
( ( in @ X430 @ X428 )
& ( X429 @ X430 ) )
=> ! [X431: $i] :
( ( in @ X431 @ X428 )
=> ~ ( X429 @ X431 ) ) )
=> ( ! [X432: $i,X433: $i > $o] :
( ~ ! [X434: $i] :
( ( in @ X434 @ X432 )
=> ( X433 @ X434 ) )
=> ? [X435: $i] :
( ( in @ X435 @ X432 )
& ~ ( X433 @ X435 ) ) )
=> ( ! [X436: $i > $o] :
( ? [X437: $i] :
( ( X436 @ X437 )
& ! [X438: $i] :
( ( X436 @ X438 )
=> ( X437 = X438 ) ) )
=> ? [X439: $i] :
( ( X436 @ X439 )
& ! [X440: $i] :
( ( X436 @ X440 )
=> ( X439 = X440 ) ) ) )
=> ( ! [X441: $i > $o] :
( ? [X442: $i] : ( X441 @ X442 )
=> ( ! [X443: $i,X444: $i] :
( ( X441 @ X443 )
=> ( ( X441 @ X444 )
=> ( X443 = X444 ) ) )
=> ? [X445: $i] :
( ( X441 @ X445 )
& ! [X446: $i] :
( ( X441 @ X446 )
=> ( X445 = X446 ) ) ) ) )
=> ( ! [X447: $i > $o] :
( ? [X448: $i] :
! [X449: $i] :
( ( X447 @ X449 )
<=> ( X449 = X448 ) )
=> ? [X450: $i] :
( ( X447 @ X450 )
& ! [X451: $i] :
( ( X447 @ X451 )
=> ( X450 = X451 ) ) ) )
=> ( ! [X452: $i,X453: $i] :
( ( X452 = X453 )
=> ! [X454: $i,X455: $i] :
( ( X454 = X455 )
=> ( ( in @ X454 @ X452 )
=> ( in @ X455 @ X453 ) ) ) )
=> ( ! [X456: $i,X457: $i] :
( ( X456 = X457 )
=> ! [X458: $i,X459: $i] :
( ( X458 = X459 )
=> ( ( in @ X458 @ X456 )
<=> ( in @ X459 @ X457 ) ) ) )
=> ( ! [X460: $i > $o] :
( ? [X461: $i] :
( ( X460 @ X461 )
& ! [X462: $i] :
( ( X460 @ X462 )
=> ( X461 = X462 ) ) )
=> ! [X463: $i,X464: $i] :
( ( X460 @ X463 )
=> ( ( X460 @ X464 )
=> ( X463 = X464 ) ) ) )
=> ( ! [X465: $i > $o,X466: $i > $o] :
( ! [X467: $i,X468: $i] :
( ( X467 = X468 )
=> ( ( X465 @ X467 )
<=> ( X466 @ X468 ) ) )
=> ( ? [X469: $i] :
( ( X465 @ X469 )
& ! [X470: $i] :
( ( X465 @ X470 )
=> ( X469 = X470 ) ) )
<=> ? [X471: $i] :
( ( X466 @ X471 )
& ! [X472: $i] :
( ( X466 @ X472 )
=> ( X471 = X472 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X473: $i,X474: $i] :
( ( X473 = X474 )
=> ! [X475: $i,X476: $i] :
( ( X475 = X476 )
=> ( ( setadjoin @ X473 @ X475 )
= ( setadjoin @ X474 @ X476 ) ) ) )
=> ( ! [X477: $i,X478: $i] :
( ( X477 = X478 )
=> ( ( powerset @ X477 )
= ( powerset @ X478 ) ) )
=> ( ! [X479: $i,X480: $i] :
( ( X479 = X480 )
=> ( ( setunion @ X479 )
= ( setunion @ X480 ) ) )
=> ( ( omega = omega )
=> ( ! [X481: $i > $o] :
( ? [X482: $i] :
( ( X481 @ X482 )
& ! [X483: $i] :
( ( X481 @ X483 )
=> ( X482 = X483 ) ) )
=> ! [X484: $i,X485: $i] :
( ( X481 @ X484 )
=> ( ( X481 @ X485 )
=> ( X484 = X485 ) ) ) )
=> ( ! [X486: $i > $o,X487: $i > $o] :
( ! [X488: $i,X489: $i] :
( ( X488 = X489 )
=> ( ( X486 @ X488 )
<=> ( X487 @ X489 ) ) )
=> ( ? [X490: $i] :
( ( X486 @ X490 )
& ! [X491: $i] :
( ( X486 @ X491 )
=> ( X490 = X491 ) ) )
=> ( ? [X492: $i] :
( ( X487 @ X492 )
& ! [X493: $i] :
( ( X487 @ X493 )
=> ( X492 = X493 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X486 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X487 @ Z0 ) ) ) ) ) )
=> ( ! [X494: $i,X495: $i] :
( ( X494 = X495 )
=> ! [X496: $i > $o,X497: $i > $o] :
( ! [X498: $i] :
( ( in @ X498 @ X494 )
=> ! [X499: $i] :
( ( in @ X499 @ X495 )
=> ( ( X498 = X499 )
=> ( ( X496 @ X498 )
<=> ( X497 @ X499 ) ) ) ) )
=> ( ( dsetconstr @ X494
@ ^ [Z0: $i] : ( X496 @ Z0 ) )
= ( dsetconstr @ X495
@ ^ [Z0: $i] : ( X497 @ Z0 ) ) ) ) )
=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ! [X500: $i] :
( ( in @ X500 @ X4 )
=> ( in @ X500 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[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)],[subsetI1]),c_0_93]),c_0_94]),c_0_95]),inCongP]),noeltsimpempty]),in__Cong]),c_0_96]),c_0_97]),c_0_98]),emptyset__Cong]),c_0_99]),setadjoin__Cong]),powerset__Cong]),c_0_100]),setunion__Cong]),omega__Cong]),c_0_101]),c_0_102]),c_0_103]),setadjoinIL]),c_0_104]),emptyinunitempty]),setadjoinIR]),setadjoinE]),upairsetIR]),setadjoinOr]),c_0_105]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_106]),c_0_107]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),c_0_108]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_109]),emptyI]),setext]),c_0_110]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_111]),c_0_112]),c_0_113]),c_0_114]),c_0_115]),wellorderingAx]),foundationAx]),c_0_116]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_117]) ).
thf(c_0_119,negated_conjecture,
! [X501: $i,X502: $i,X504: $i,X505: $i,X506: $i,X507: $i,X508: $i,X509: $i,X510: $i,X511: $i,X512: $i,X514: $i,X515: $i,X517: $i,X518: $i,X519: $i,X520: $i,X521: $i,X523: $i,X524: $i > $i > $o,X525: $i,X527: $i,X530: $i,X532: $i,X533: $i,X534: $i,X535: $i,X537: $i,X538: $i > $o,X539: $i,X541: $i,X542: $i > $o,X543: $i,X544: $i,X545: $i > $o,X546: $i,X547: $i,X548: $i > $o,X549: $i,X550: $i > $o,X551: $i,X554: $i,X555: $o,X556: $i,X557: $i,X558: $o,X559: $i,X560: $i,X561: $i > $o,X562: $i,X565: $i,X566: $i,X569: $i,X571: $i,X573: $i,X574: $i > $o,X575: $i,X576: $i,X578: $i,X579: $i > $o,X580: $i,X581: $i,X582: $i,X583: $i,X584: $i,X585: $i,X586: $i,X587: $i,X588: $i,X589: $i,X590: $i,X591: $o,X592: $i,X593: $i,X594: $i,X595: $i,X596: $i,X597: $i,X599: $i,X600: $i,X601: $i,X602: $i,X603: $i,X604: $i,X605: $i,X606: $i,X607: $i,X608: $i,X609: $o,X611: $i,X612: $i,X613: $i > $o,X614: $i,X617: $i,X618: $i,X619: $i,X621: $i,X622: $i,X623: $i,X624: $i,X625: $i,X626: $i,X627: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i > $o,X638: $i,X639: $i > $o,X640: $i,X641: $i,X642: $i > $o,X643: $i,X645: $i,X646: $i > $o,X648: $i,X649: $i,X650: $i > $o,X652: $i,X653: $i,X654: $i > $o,X655: $i,X657: $o,X658: $i,X659: $i > $o,X661: $i,X662: $i,X663: $i > $o,X664: $i,X666: $i > $o,X667: $i,X670: $i,X671: $i > $o,X672: $i,X676: $i,X677: $i > $o,X678: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $i,X686: $i,X687: $i,X688: $i,X689: $i,X690: $i > $o,X691: $i,X693: $i,X694: $i,X695: $i > $o,X696: $i > $o,X699: $i,X702: $i,X703: $i,X706: $i,X707: $i,X708: $i,X709: $i,X710: $i,X711: $i,X712: $i,X713: $i,X714: $i,X715: $i > $o,X716: $i,X718: $i,X719: $i,X720: $i > $o,X721: $i > $o,X724: $i,X726: $i,X728: $i,X729: $i,X730: $i > $o,X731: $i > $o,X736: $i] :
( ( ~ ( in @ ( esk1_2 @ X501 @ X502 ) @ X501 )
| ~ ( in @ ( esk1_2 @ X501 @ X502 ) @ X502 )
| ( X501 = X502 ) )
& ( ( in @ ( esk1_2 @ X501 @ X502 ) @ X501 )
| ( in @ ( esk1_2 @ X501 @ X502 ) @ X502 )
| ( X501 = X502 ) )
& ~ ( in @ X504 @ emptyset )
& ( ~ ( in @ X507 @ ( setadjoin @ X505 @ X506 ) )
| ( X507 = X505 )
| ( in @ X507 @ X506 ) )
& ( ( X507 != X505 )
| ( in @ X507 @ ( setadjoin @ X505 @ X506 ) ) )
& ( ~ ( in @ X507 @ X506 )
| ( in @ X507 @ ( setadjoin @ X505 @ X506 ) ) )
& ( ~ ( in @ X509 @ ( powerset @ X508 ) )
| ~ ( in @ X510 @ X509 )
| ( in @ X510 @ X508 ) )
& ( ( in @ ( esk2_2 @ X511 @ X512 ) @ X512 )
| ( in @ X512 @ ( powerset @ X511 ) ) )
& ( ~ ( in @ ( esk2_2 @ X511 @ X512 ) @ X511 )
| ( in @ X512 @ ( powerset @ X511 ) ) )
& ( ( in @ X515 @ ( esk3_2 @ X514 @ X515 ) )
| ~ ( in @ X515 @ ( setunion @ X514 ) ) )
& ( ( in @ ( esk3_2 @ X514 @ X515 ) @ X514 )
| ~ ( in @ X515 @ ( setunion @ X514 ) ) )
& ( ~ ( in @ X518 @ X519 )
| ~ ( in @ X519 @ X517 )
| ( in @ X518 @ ( setunion @ X517 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X520 @ omega )
| ( in @ ( setadjoin @ X520 @ X520 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X521 ) @ omega )
| ~ ( in @ emptyset @ X521 )
| ~ ( in @ X523 @ omega )
| ( in @ X523 @ X521 ) )
& ( ( in @ ( esk4_1 @ X521 ) @ X521 )
| ~ ( in @ emptyset @ X521 )
| ~ ( in @ X523 @ omega )
| ( in @ X523 @ X521 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X521 ) @ ( esk4_1 @ X521 ) ) @ X521 )
| ~ ( in @ emptyset @ X521 )
| ~ ( in @ X523 @ omega )
| ( in @ X523 @ X521 ) )
& ( ( in @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X525 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( in @ ( esk5_2 @ X524 @ X525 ) @ X525 ) )
& ( ( X524 @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X530 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( in @ ( esk5_2 @ X524 @ X525 ) @ X525 ) )
& ( ~ ( in @ X533 @ X525 )
| ~ ( X524 @ X533 @ X532 )
| ( in @ X532 @ ( esk7_2 @ X524 @ X525 ) )
| ( in @ ( esk5_2 @ X524 @ X525 ) @ X525 ) )
& ( ( in @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X525 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( X524 @ ( esk5_2 @ X524 @ X525 ) @ ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ( X524 @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X530 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( X524 @ ( esk5_2 @ X524 @ X525 ) @ ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ~ ( in @ X533 @ X525 )
| ~ ( X524 @ X533 @ X532 )
| ( in @ X532 @ ( esk7_2 @ X524 @ X525 ) )
| ( X524 @ ( esk5_2 @ X524 @ X525 ) @ ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ( in @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X525 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( X527
!= ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ( X524 @ ( esk8_3 @ X524 @ X525 @ X530 ) @ X530 )
| ~ ( in @ X530 @ ( esk7_2 @ X524 @ X525 ) )
| ( X527
!= ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ~ ( in @ X533 @ X525 )
| ~ ( X524 @ X533 @ X532 )
| ( in @ X532 @ ( esk7_2 @ X524 @ X525 ) )
| ( X527
!= ( esk6_3 @ X524 @ X525 @ X527 ) )
| ~ ( X524 @ ( esk5_2 @ X524 @ X525 ) @ X527 ) )
& ( ( in @ ( esk9_1 @ X534 ) @ X534 )
| ~ ( in @ X535 @ X534 ) )
& ( ~ ( in @ X537 @ ( esk9_1 @ X534 ) )
| ~ ( in @ X537 @ X534 )
| ~ ( in @ X535 @ X534 ) )
& epred1_0
& ( ( X538 @ ( esk10_2 @ X538 @ X539 ) )
| ~ ( X538 @ X539 )
| ( X538
@ ( descr
@ ^ [Z0: $i] : ( X538 @ Z0 ) ) ) )
& ( ( X539
!= ( esk10_2 @ X538 @ X539 ) )
| ~ ( X538 @ X539 )
| ( X538
@ ( descr
@ ^ [Z0: $i] : ( X538 @ Z0 ) ) ) )
& ( ~ ( in @ X543 @ X541 )
| ~ ( X542 @ X543 )
| ( in @ X543
@ ( dsetconstr @ X541
@ ^ [Z0: $i] : ( X542 @ Z0 ) ) ) )
& ( ~ ( in @ X546
@ ( dsetconstr @ X544
@ ^ [Z0: $i] : ( X545 @ Z0 ) ) )
| ( in @ X546 @ X544 ) )
& ( ~ ( in @ X549
@ ( dsetconstr @ X547
@ ^ [Z0: $i] : ( X548 @ Z0 ) ) )
| ( X548 @ X549 ) )
& ( ( X550 @ ( esk12_1 @ X550 ) )
| ( X550 @ ( esk11_2 @ X550 @ X551 ) )
| ~ ( X550 @ X551 ) )
& ( ~ ( X550 @ X554 )
| ( ( esk12_1 @ X550 )
= X554 )
| ( X550 @ ( esk11_2 @ X550 @ X551 ) )
| ~ ( X550 @ X551 ) )
& ( ( X550 @ ( esk12_1 @ X550 ) )
| ( X551
!= ( esk11_2 @ X550 @ X551 ) )
| ~ ( X550 @ X551 ) )
& ( ~ ( X550 @ X554 )
| ( ( esk12_1 @ X550 )
= X554 )
| ( X551
!= ( esk11_2 @ X550 @ X551 ) )
| ~ ( X550 @ X551 ) )
& ( ~ ( in @ X556 @ ( prop2set @ X555 ) )
| X555 )
& ( ~ ( in @ X557 @ emptyset )
| X558 )
& ~ ( in @ X559 @ emptyset )
& ~ ( in @ X560 @ emptyset )
& ( ( X561 @ ( esk13_2 @ X561 @ X562 ) )
| ~ ( X561 @ X562 )
| ( X561 @ ( esk14_1 @ X561 ) ) )
& ( ( X562
!= ( esk13_2 @ X561 @ X562 ) )
| ~ ( X561 @ X562 )
| ( X561 @ ( esk14_1 @ X561 ) ) )
& ( ( in @ ( esk16_2 @ X565 @ X566 ) @ X566 )
| ( X565 = X566 )
| ( in @ ( esk15_2 @ X565 @ X566 ) @ X565 ) )
& ( ~ ( in @ ( esk16_2 @ X565 @ X566 ) @ X565 )
| ( X565 = X566 )
| ( in @ ( esk15_2 @ X565 @ X566 ) @ X565 ) )
& ( ( in @ ( esk16_2 @ X565 @ X566 ) @ X566 )
| ( X565 = X566 )
| ~ ( in @ ( esk15_2 @ X565 @ X566 ) @ X566 ) )
& ( ~ ( in @ ( esk16_2 @ X565 @ X566 ) @ X565 )
| ( X565 = X566 )
| ~ ( in @ ( esk15_2 @ X565 @ X566 ) @ X566 ) )
& ( ( in @ ( esk17_1 @ X569 ) @ X569 )
| ( X569 = emptyset ) )
& ( ( in @ ( esk18_1 @ X571 ) @ X571 )
| ( X571 = emptyset ) )
& ( ~ ( in @ X575
@ ( dsetconstr @ X573
@ ^ [Z0: $i] : ( X574 @ Z0 ) ) )
| ( X574 @ X575 )
| ~ ( in @ X575 @ X573 ) )
& ( ~ ( X574 @ X575 )
| ( in @ X575
@ ( dsetconstr @ X573
@ ^ [Z0: $i] : ( X574 @ Z0 ) ) )
| ~ ( in @ X575 @ X573 ) )
& ( ( X576 = emptyset )
| ( in @ ( esk19_1 @ X576 ) @ X576 ) )
& ( ~ ( in @ X580 @ X578 )
| ~ ( X579 @ X580 )
| ( ( dsetconstr @ X578
@ ^ [Z0: $i] : ( X579 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X582 @ X581 )
| ( X581 != emptyset ) )
& ( in @ X583 @ ( setadjoin @ X583 @ X584 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X587 @ X586 )
| ( in @ X587 @ ( setadjoin @ X585 @ X586 ) ) )
& ( ( in @ X590 @ X589 )
| X591
| ( X590 = X588 )
| ~ ( in @ X590 @ ( setadjoin @ X588 @ X589 ) ) )
& ( ~ X591
| X591
| ( X590 = X588 )
| ~ ( in @ X590 @ ( setadjoin @ X588 @ X589 ) ) )
& ( ( in @ X590 @ X589 )
| X591
| ~ X591
| ~ ( in @ X590 @ ( setadjoin @ X588 @ X589 ) ) )
& ( ~ X591
| X591
| ~ X591
| ~ ( in @ X590 @ ( setadjoin @ X588 @ X589 ) ) )
& ( ~ ( in @ X594 @ ( setadjoin @ X592 @ X593 ) )
| ( X594 = X592 )
| ( in @ X594 @ X593 ) )
& ( ( dsetconstr @ X595
@ ^ [Z0: $i] : $true )
= X595 )
& ( ( in @ ( esk20_2 @ X596 @ X597 ) @ X597 )
| ( in @ X597 @ ( powerset @ X596 ) ) )
& ( ~ ( in @ ( esk20_2 @ X596 @ X597 ) @ X596 )
| ( in @ X597 @ ( powerset @ X596 ) ) )
& ( in @ emptyset @ ( powerset @ X599 ) )
& ( in @ emptyset @ ( powerset @ X600 ) )
& ( ~ ( in @ X602 @ ( powerset @ X601 ) )
| ~ ( in @ X603 @ X602 )
| ( in @ X603 @ X601 ) )
& ( ~ ( in @ X605 @ X606 )
| ~ ( in @ X606 @ X604 )
| ( in @ X605 @ ( setunion @ X604 ) ) )
& ( ( in @ X608 @ ( esk21_3 @ X607 @ X608 @ X609 ) )
| X609
| ~ ( in @ X608 @ ( setunion @ X607 ) ) )
& ( ( in @ ( esk21_3 @ X607 @ X608 @ X609 ) @ X607 )
| X609
| ~ ( in @ X608 @ ( setunion @ X607 ) ) )
& ( ~ X609
| X609
| ~ ( in @ X608 @ ( setunion @ X607 ) ) )
& ( ~ ( in @ X612 @ X611 )
| ( in @ X612 @ ( powerset @ ( setunion @ X611 ) ) ) )
& ( ~ ( X613 @ X617 )
| ( X617
= ( esk23_1 @ X613 ) )
| ( X613 @ ( esk22_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ( X618
!= ( esk23_1 @ X613 ) )
| ( X613 @ X618 )
| ( X613 @ ( esk22_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ~ ( X613 @ X617 )
| ( X617
= ( esk23_1 @ X613 ) )
| ( X614
!= ( esk22_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ( X618
!= ( esk23_1 @ X613 ) )
| ( X613 @ X618 )
| ( X614
!= ( esk22_2 @ X613 @ X614 ) )
| ~ ( X613 @ X614 ) )
& ( ( X619 = emptyset )
| ( in @ ( esk24_1 @ X619 ) @ X619 ) )
& ( ~ ( in @ X621 @ ( setadjoin @ X622 @ emptyset ) )
| ( X621 = X622 ) )
& ( ( X623 = X624 )
| ~ ( in @ X624 @ ( setadjoin @ X623 @ emptyset ) ) )
& ( ( X625 != X626 )
| ( in @ X625 @ ( setadjoin @ X626 @ emptyset ) ) )
& ( ~ ( in @ X627 @ ( setadjoin @ X628 @ emptyset ) )
| ( in @ X628 @ ( setadjoin @ X627 @ emptyset ) ) )
& ( ~ ( in @ X631 @ ( setadjoin @ X629 @ ( setadjoin @ X630 @ emptyset ) ) )
| ( X631 = X629 )
| ( X631 = X630 ) )
& ( in @ X632 @ ( setadjoin @ X632 @ ( setadjoin @ X633 @ emptyset ) ) )
& ( in @ X635 @ ( setadjoin @ X634 @ ( setadjoin @ X635 @ emptyset ) ) )
& ( ~ ( in @ X638 @ X636 )
| ~ ( X637 @ X638 )
| ( ( dsetconstr @ X636
@ ^ [Z0: $i] : ( X637 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X640 @ emptyset )
| ( X639 @ X640 ) )
& ( ( in @ ( esk25_2 @ X641 @ X642 ) @ X641 )
| ~ ( in @ X643 @ X641 )
| ( X642 @ X643 ) )
& ( ~ ( X642 @ ( esk25_2 @ X641 @ X642 ) )
| ~ ( in @ X643 @ X641 )
| ( X642 @ X643 ) )
& ( ( in @ ( esk26_2 @ X645 @ X646 ) @ X645 )
| ~ ( in @ X648 @ X645 )
| ~ ( X646 @ X648 ) )
& ( ( X646 @ ( esk26_2 @ X645 @ X646 ) )
| ~ ( in @ X648 @ X645 )
| ~ ( X646 @ X648 ) )
& ( ( in @ ( esk27_2 @ X649 @ X650 ) @ X649 )
| ~ ( in @ X652 @ X649 )
| ~ ( X650 @ X652 ) )
& ( ( X650 @ ( esk27_2 @ X649 @ X650 ) )
| ~ ( in @ X652 @ X649 )
| ~ ( X650 @ X652 ) )
& ( ( in @ ( esk28_2 @ X653 @ X654 ) @ X653 )
| ~ ( in @ X655 @ X653 )
| ( X654 @ X655 ) )
& ( ~ ( X654 @ ( esk28_2 @ X653 @ X654 ) )
| ~ ( in @ X655 @ X653 )
| ( X654 @ X655 ) )
& ( ~ X657
| ( in @ emptyset @ ( prop2set @ X657 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X658 @ X659 ) @ X658 )
| ~ ( in @ X661 @ X658 )
| ~ ( X659 @ X661 ) )
& ( ( X659 @ ( esk29_2 @ X658 @ X659 ) )
| ~ ( in @ X661 @ X658 )
| ~ ( X659 @ X661 ) )
& ( ( in @ ( esk30_2 @ X662 @ X663 ) @ X662 )
| ~ ( in @ X664 @ X662 )
| ( X663 @ X664 ) )
& ( ~ ( X663 @ ( esk30_2 @ X662 @ X663 ) )
| ~ ( in @ X664 @ X662 )
| ( X663 @ X664 ) )
& ( ( X666 @ ( esk32_1 @ X666 ) )
| ( X666 @ ( esk31_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ~ ( X666 @ X670 )
| ( ( esk32_1 @ X666 )
= X670 )
| ( X666 @ ( esk31_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ( X666 @ ( esk32_1 @ X666 ) )
| ( X667
!= ( esk31_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ~ ( X666 @ X670 )
| ( ( esk32_1 @ X666 )
= X670 )
| ( X667
!= ( esk31_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ( X671 @ ( esk35_1 @ X671 ) )
| ( X671 @ ( esk33_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ~ ( X671 @ X676 )
| ( ( esk35_1 @ X671 )
= X676 )
| ( X671 @ ( esk33_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ( X671 @ ( esk35_1 @ X671 ) )
| ( X671 @ ( esk34_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ~ ( X671 @ X676 )
| ( ( esk35_1 @ X671 )
= X676 )
| ( X671 @ ( esk34_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ( X671 @ ( esk35_1 @ X671 ) )
| ( ( esk33_1 @ X671 )
!= ( esk34_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ~ ( X671 @ X676 )
| ( ( esk35_1 @ X671 )
= X676 )
| ( ( esk33_1 @ X671 )
!= ( esk34_1 @ X671 ) )
| ~ ( X671 @ X672 ) )
& ( ( X677 @ ( esk37_1 @ X677 ) )
| ~ ( X677 @ ( esk36_2 @ X677 @ X678 ) )
| ( ( esk36_2 @ X677 @ X678 )
!= X678 ) )
& ( ~ ( X677 @ X681 )
| ( ( esk37_1 @ X677 )
= X681 )
| ~ ( X677 @ ( esk36_2 @ X677 @ X678 ) )
| ( ( esk36_2 @ X677 @ X678 )
!= X678 ) )
& ( ( X677 @ ( esk37_1 @ X677 ) )
| ( X677 @ ( esk36_2 @ X677 @ X678 ) )
| ( ( esk36_2 @ X677 @ X678 )
= X678 ) )
& ( ~ ( X677 @ X681 )
| ( ( esk37_1 @ X677 )
= X681 )
| ( X677 @ ( esk36_2 @ X677 @ X678 ) )
| ( ( esk36_2 @ X677 @ X678 )
= X678 ) )
& ( ( X682 != X683 )
| ( X684 != X685 )
| ~ ( in @ X684 @ X682 )
| ( in @ X685 @ X683 ) )
& ( ~ ( in @ X688 @ X686 )
| ( in @ X689 @ X687 )
| ( X688 != X689 )
| ( X686 != X687 ) )
& ( ~ ( in @ X689 @ X687 )
| ( in @ X688 @ X686 )
| ( X688 != X689 )
| ( X686 != X687 ) )
& ( ( X690 @ ( esk38_2 @ X690 @ X691 ) )
| ~ ( X690 @ X691 )
| ~ ( X690 @ X693 )
| ~ ( X690 @ X694 )
| ( X693 = X694 ) )
& ( ( X691
!= ( esk38_2 @ X690 @ X691 ) )
| ~ ( X690 @ X691 )
| ~ ( X690 @ X693 )
| ~ ( X690 @ X694 )
| ( X693 = X694 ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( ( esk39_2 @ X695 @ X696 )
= ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ~ ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ~ ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X695 @ ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X696 @ ( esk42_2 @ X695 @ X696 ) )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X696 @ X702 )
| ( ( esk42_2 @ X695 @ X696 )
= X702 )
| ( X699
!= ( esk41_3 @ X695 @ X696 @ X699 ) )
| ~ ( X695 @ X699 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X696 @ ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ( X695 @ ( esk44_2 @ X695 @ X696 ) )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( ~ ( X695 @ X706 )
| ( ( esk44_2 @ X695 @ X696 )
= X706 )
| ( X703
!= ( esk43_3 @ X695 @ X696 @ X703 ) )
| ~ ( X696 @ X703 )
| ( X695 @ ( esk39_2 @ X695 @ X696 ) )
| ( X696 @ ( esk40_2 @ X695 @ X696 ) ) )
& ( emptyset = emptyset )
& ( ( X707 != X708 )
| ( X709 != X710 )
| ( ( setadjoin @ X707 @ X709 )
= ( setadjoin @ X708 @ X710 ) ) )
& ( ( X711 != X712 )
| ( ( powerset @ X711 )
= ( powerset @ X712 ) ) )
& ( ( X713 != X714 )
| ( ( setunion @ X713 )
= ( setunion @ X714 ) ) )
& ( omega = omega )
& ( ( X715 @ ( esk45_2 @ X715 @ X716 ) )
| ~ ( X715 @ X716 )
| ~ ( X715 @ X718 )
| ~ ( X715 @ X719 )
| ( X718 = X719 ) )
& ( ( X716
!= ( esk45_2 @ X715 @ X716 ) )
| ~ ( X715 @ X716 )
| ~ ( X715 @ X718 )
| ~ ( X715 @ X719 )
| ( X718 = X719 ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( ( esk46_2 @ X720 @ X721 )
= ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( ( esk46_2 @ X720 @ X721 )
= ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( ( esk46_2 @ X720 @ X721 )
= ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( ( esk46_2 @ X720 @ X721 )
= ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ~ ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ~ ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ~ ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ~ ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ~ ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ~ ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ~ ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ~ ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X720 @ ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X721 @ ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( X726
!= ( esk49_3 @ X720 @ X721 @ X726 ) )
| ~ ( X721 @ X726 )
| ( ( descr
@ ^ [Z0: $i] : ( X720 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X721 @ Z0 ) ) )
| ( X724
!= ( esk48_3 @ X720 @ X721 @ X724 ) )
| ~ ( X720 @ X724 )
| ( X720 @ ( esk46_2 @ X720 @ X721 ) )
| ( X721 @ ( esk47_2 @ X720 @ X721 ) ) )
& ( ( in @ ( esk50_4 @ X728 @ X729 @ X730 @ X731 ) @ X728 )
| ( ( dsetconstr @ X728
@ ^ [Z0: $i] : ( X730 @ Z0 ) )
= ( dsetconstr @ X729
@ ^ [Z0: $i] : ( X731 @ Z0 ) ) )
| ( X728 != X729 ) )
& ( ( in @ ( esk51_4 @ X728 @ X729 @ X730 @ X731 ) @ X729 )
| ( ( dsetconstr @ X728
@ ^ [Z0: $i] : ( X730 @ Z0 ) )
= ( dsetconstr @ X729
@ ^ [Z0: $i] : ( X731 @ Z0 ) ) )
| ( X728 != X729 ) )
& ( ( ( esk50_4 @ X728 @ X729 @ X730 @ X731 )
= ( esk51_4 @ X728 @ X729 @ X730 @ X731 ) )
| ( ( dsetconstr @ X728
@ ^ [Z0: $i] : ( X730 @ Z0 ) )
= ( dsetconstr @ X729
@ ^ [Z0: $i] : ( X731 @ Z0 ) ) )
| ( X728 != X729 ) )
& ( ~ ( X730 @ ( esk50_4 @ X728 @ X729 @ X730 @ X731 ) )
| ~ ( X731 @ ( esk51_4 @ X728 @ X729 @ X730 @ X731 ) )
| ( ( dsetconstr @ X728
@ ^ [Z0: $i] : ( X730 @ Z0 ) )
= ( dsetconstr @ X729
@ ^ [Z0: $i] : ( X731 @ Z0 ) ) )
| ( X728 != X729 ) )
& ( ( X730 @ ( esk50_4 @ X728 @ X729 @ X730 @ X731 ) )
| ( X731 @ ( esk51_4 @ X728 @ X729 @ X730 @ X731 ) )
| ( ( dsetconstr @ X728
@ ^ [Z0: $i] : ( X730 @ Z0 ) )
= ( dsetconstr @ X729
@ ^ [Z0: $i] : ( X731 @ Z0 ) ) )
| ( X728 != X729 ) )
& ( ~ ( in @ X736 @ esk52_0 )
| ( in @ X736 @ esk53_0 ) )
& ( in @ esk54_0 @ esk52_0 )
& ~ ( in @ esk54_0 @ esk53_0 ) ),
inference(distribute,[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_118])])])])])]) ).
thf(c_0_120,negated_conjecture,
~ ( in @ esk54_0 @ esk53_0 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_121,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk53_0 )
| ~ ( in @ X2 @ esk52_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_122,negated_conjecture,
in @ esk54_0 @ esk52_0,
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_123,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU559^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 17:19:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.56/300.09 # Version: 3.1.0-ho
% 0.56/300.09 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.56/300.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/300.09 # Starting new_ho_10 with 1500s (5) cores
% 0.56/300.09 # Starting sh5l with 300s (1) cores
% 0.56/300.09 # Starting new_bool_1 with 300s (1) cores
% 0.56/300.09 # Starting new_bool_2 with 300s (1) cores
% 0.56/300.09 # new_bool_2 with pid 25892 completed with status 0
% 0.56/300.09 # Result found by new_bool_2
% 0.56/300.09 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.56/300.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/300.09 # Starting new_ho_10 with 1500s (5) cores
% 0.56/300.09 # Starting sh5l with 300s (1) cores
% 0.56/300.09 # Starting new_bool_1 with 300s (1) cores
% 0.56/300.09 # Starting new_bool_2 with 300s (1) cores
% 0.56/300.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.56/300.09 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.56/300.09 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.56/300.09 # Starting ho_unfolding_3 with 163s (1) cores
% 0.56/300.09 # ho_unfolding_3 with pid 25906 completed with status 0
% 0.56/300.09 # Result found by ho_unfolding_3
% 0.56/300.09 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.56/300.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/300.09 # Starting new_ho_10 with 1500s (5) cores
% 0.56/300.09 # Starting sh5l with 300s (1) cores
% 0.56/300.09 # Starting new_bool_1 with 300s (1) cores
% 0.56/300.09 # Starting new_bool_2 with 300s (1) cores
% 0.56/300.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.56/300.09 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.56/300.09 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.56/300.09 # Starting ho_unfolding_3 with 163s (1) cores
% 0.56/300.09 # Preprocessing time : 0.005 s
% 0.56/300.09 # Presaturation interreduction done
% 0.56/300.09
% 0.56/300.09 # Proof found!
% 0.56/300.09 # SZS status Theorem
% 0.56/300.09 # SZS output start CNFRefutation
% See solution above
% 0.56/300.09 # Parsed axioms : 169
% 0.56/300.09 # Removed by relevancy pruning/SinE : 91
% 0.56/300.09 # Initial clauses : 185
% 0.56/300.09 # Removed in clause preprocessing : 12
% 0.56/300.09 # Initial clauses in saturation : 173
% 0.56/300.09 # Processed clauses : 192
% 0.56/300.09 # ...of these trivial : 2
% 0.56/300.09 # ...subsumed : 14
% 0.56/300.09 # ...remaining for further processing : 176
% 0.56/300.09 # Other redundant clauses eliminated : 10
% 0.56/300.09 # Clauses deleted for lack of memory : 0
% 0.56/300.09 # Backward-subsumed : 0
% 0.56/300.09 # Backward-rewritten : 1
% 0.56/300.09 # Generated clauses : 12
% 0.56/300.09 # ...of the previous two non-redundant : 8
% 0.56/300.09 # ...aggressively subsumed : 0
% 0.56/300.09 # Contextual simplify-reflections : 0
% 0.56/300.09 # Paramodulations : 1
% 0.56/300.09 # Factorizations : 0
% 0.56/300.09 # NegExts : 0
% 0.56/300.09 # Equation resolutions : 10
% 0.56/300.09 # Disequality decompositions : 0
% 0.56/300.09 # Total rewrite steps : 19
% 0.56/300.09 # ...of those cached : 12
% 0.56/300.09 # Propositional unsat checks : 0
% 0.56/300.09 # Propositional check models : 0
% 0.56/300.09 # Propositional check unsatisfiable : 0
% 0.56/300.09 # Propositional clauses : 0
% 0.56/300.09 # Propositional clauses after purity: 0
% 0.56/300.09 # Propositional unsat core size : 0
% 0.56/300.09 # Propositional preprocessing time : 0.000
% 0.56/300.09 # Propositional encoding time : 0.000
% 0.56/300.09 # Propositional solver time : 0.000
% 0.56/300.09 # Success case prop preproc time : 0.000
% 0.56/300.09 # Success case prop encoding time : 0.000
% 0.56/300.09 # Success case prop solver time : 0.000
% 0.56/300.09 # Current number of processed clauses : 11
% 0.56/300.09 # Positive orientable unit clauses : 6
% 0.56/300.09 # Positive unorientable unit clauses: 0
% 0.56/300.09 # Negative unit clauses : 3
% 0.56/300.09 # Non-unit-clauses : 2
% 0.56/300.09 # Current number of unprocessed clauses: 143
% 0.56/300.09 # ...number of literals in the above : 541
% 0.56/300.09 # Current number of archived formulas : 0
% 0.56/300.09 # Current number of archived clauses : 155
% 0.56/300.09 # Clause-clause subsumption calls (NU) : 4096
% 0.56/300.09 # Rec. Clause-clause subsumption calls : 959
% 0.56/300.09 # Non-unit clause-clause subsumptions : 12
% 0.56/300.09 # Unit Clause-clause subsumption calls : 6
% 0.56/300.09 # Rewrite failures with RHS unbound : 0
% 0.56/300.09 # BW rewrite match attempts : 2
% 0.56/300.09 # BW rewrite match successes : 1
% 0.56/300.09 # Condensation attempts : 192
% 0.56/300.09 # Condensation successes : 3
% 0.56/300.09 # Termbank termtop insertions : 27669
% 0.56/300.09 # Search garbage collected termcells : 7556
% 0.56/300.09
% 0.56/300.09 # -------------------------------------------------
% 0.56/300.09 # User time : 0.042 s
% 0.56/300.09 # System time : 0.005 s
% 0.56/300.09 # Total time : 0.047 s
% 0.56/300.09 # Maximum resident set size: 4196 pages
% 0.56/300.09
% 0.56/300.09 # -------------------------------------------------
% 0.56/300.09 # User time : 0.047 s
% 0.56/300.09 # System time : 0.008 s
% 0.56/300.09 # Total time : 0.055 s
% 0.56/300.09 # Maximum resident set size: 1924 pages
% 0.56/300.09 % E---3.1 exiting
% 0.56/300.09 % E exiting
%------------------------------------------------------------------------------