TSTP Solution File: SEU570^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU570^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 03:28:15 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 246
% Syntax : Number of formulae : 297 ( 24 unt; 156 typ; 0 def)
% Number of atoms : 1118 ( 326 equ; 0 cnn)
% Maximal formula atoms : 340 ( 7 avg)
% Number of connectives : 4397 ( 406 ~; 454 |; 275 &;2570 @)
% ( 149 <=>; 543 =>; 0 <=; 0 <~>)
% Maximal formula depth : 396 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 156 usr; 94 con; 0-4 aty)
% Number of variables : 935 ( 63 ^ 768 !; 104 ?; 935 :)
% 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,
subsetRefl: $o ).
thf(decl_123,type,
epred1_0: $o ).
thf(decl_124,type,
esk1_2: $i > $i > $i ).
thf(decl_125,type,
esk2_2: $i > $i > $i ).
thf(decl_126,type,
esk3_2: $i > $i > $i ).
thf(decl_127,type,
esk4_1: $i > $i ).
thf(decl_128,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_129,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_130,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_131,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_132,type,
esk9_1: $i > $i ).
thf(decl_133,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_134,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_135,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_137,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_138,type,
esk15_2: $i > $i > $i ).
thf(decl_139,type,
esk16_2: $i > $i > $i ).
thf(decl_140,type,
esk17_1: $i > $i ).
thf(decl_141,type,
esk18_1: $i > $i ).
thf(decl_142,type,
esk19_1: $i > $i ).
thf(decl_143,type,
esk20_2: $i > $i > $i ).
thf(decl_144,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_145,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_146,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_147,type,
esk24_1: $i > $i ).
thf(decl_148,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_149,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_150,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_151,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_152,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_153,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_154,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_155,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_156,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_157,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_158,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_159,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_160,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_161,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_162,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_163,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_164,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_165,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_166,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_167,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_168,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_169,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_170,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_171,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_172,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_173,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_174,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_175,type,
esk52_2: $i > $i > $i ).
thf(decl_176,type,
esk53_2: $i > $i > $i ).
thf(decl_177,type,
esk54_0: $i ).
thf(decl_178,type,
esk55_0: $i ).
thf(decl_179,type,
esk56_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/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.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/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/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/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/sandbox2/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/sandbox2/benchmark/theBenchmark.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/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/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(subsetTrans,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
=> ( subsetRefl
=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.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/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/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/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/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(c_0_89,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_90,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
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,
( 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_93,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_94,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_95,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_96,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_97,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_98,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_99,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_100,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_101,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_102,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_103,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_104,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X260: $i] :
( ( X6 @ X2 @ X260 )
& ! [X261: $i] :
( ( X6 @ X2 @ X261 )
=> ( X260 = X261 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_105,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X262: $i] :
( ( X1 @ X262 )
& ! [X263: $i] :
( ( X1 @ X263 )
=> ( X262 = X263 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_90]) ).
thf(c_0_106,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_107,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_108,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_109,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X264: $i] :
( ( X1 @ X264 )
& ! [X265: $i] :
( ( X1 @ X265 )
=> ( X264 = X265 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_92,c_0_90]) ).
thf(c_0_110,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X266: $i] :
( ( X1 @ X266 )
& ! [X267: $i] :
( ( X1 @ X267 )
=> ( X266 = X267 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_93,c_0_90]) ).
thf(c_0_111,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_112,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_94]) ).
thf(c_0_113,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_95,c_0_94]) ).
thf(c_0_114,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_94]) ).
thf(c_0_115,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_116,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X268: $i] :
( ( X1 @ X268 )
& ! [X269: $i] :
( ( X1 @ X269 )
=> ( X268 = X269 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_96,c_0_90]) ).
thf(c_0_117,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_94]) ).
thf(c_0_118,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_119,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X270: $i] :
( ( X1 @ X270 )
& ! [X271: $i] :
( ( X1 @ X271 )
=> ( X270 = X271 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_97,c_0_90]) ).
thf(c_0_120,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X272: $i] :
( ( X1 @ X272 )
& ! [X273: $i] :
( ( X1 @ X273 )
=> ( X272 = X273 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_98,c_0_90]) ).
thf(c_0_121,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X274: $i] :
( ( X1 @ X274 )
& ! [X275: $i] :
( ( X1 @ X275 )
=> ( X274 = X275 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_99,c_0_90]) ).
thf(c_0_122,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X276: $i] :
( ( X1 @ X276 )
& ! [X277: $i] :
( ( X1 @ X277 )
=> ( X276 = X277 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_100,c_0_90]) ).
thf(c_0_123,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X278: $i] :
( ( X1 @ X278 )
& ! [X279: $i] :
( ( X1 @ X279 )
=> ( X278 = X279 ) ) )
<=> ? [X280: $i] :
( ( X17 @ X280 )
& ! [X281: $i] :
( ( X17 @ X281 )
=> ( X280 = X281 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_101,c_0_90]) ).
thf(c_0_124,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X282: $i] :
( ( X1 @ X282 )
& ! [X283: $i] :
( ( X1 @ X283 )
=> ( X282 = X283 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_102,c_0_90]) ).
thf(c_0_125,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X284: $i] :
( ( X1 @ X284 )
& ! [X285: $i] :
( ( X1 @ X285 )
=> ( X284 = X285 ) ) )
=> ( ? [X286: $i] :
( ( X17 @ X286 )
& ! [X287: $i] :
( ( X17 @ X287 )
=> ( X286 = X287 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_103,c_0_90]) ).
thf(c_0_126,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_127,plain,
( epred1_0
<=> ! [X317: $i] :
? [X318: $i] :
( ! [X319: $i] :
( ( in @ X319 @ X318 )
=> ! [X320: $i] :
( ( in @ X320 @ X319 )
=> ( in @ X320 @ X317 ) ) )
& ! [X321: $i,X322: $i] :
( ( ( in @ X321 @ X317 )
& ( in @ X322 @ X317 ) )
=> ( ! [X323: $i] :
( ( in @ X323 @ X318 )
=> ( ( in @ X321 @ X323 )
<=> ( in @ X322 @ X323 ) ) )
=> ( X321 = X322 ) ) )
& ! [X324: $i,X325: $i] :
( ( ( in @ X324 @ X318 )
& ( in @ X325 @ X318 ) )
=> ( ! [X326: $i] :
( ( in @ X326 @ X324 )
=> ( in @ X326 @ X325 ) )
| ! [X327: $i] :
( ( in @ X327 @ X325 )
=> ( in @ X327 @ X324 ) ) ) )
& ! [X328: $i] :
( ( ! [X329: $i] :
( ( in @ X329 @ X328 )
=> ( in @ X329 @ X317 ) )
& ? [X330: $i] : ( in @ X330 @ X328 ) )
=> ? [X331: $i,X332: $i] :
( ( in @ X331 @ X318 )
& ( in @ X332 @ X328 )
& ~ ? [X333: $i] :
( ( in @ X333 @ X331 )
& ( in @ X333 @ X328 ) )
& ! [X334: $i] :
( ( in @ X334 @ X318 )
=> ( ! [X335: $i] :
( ( in @ X335 @ X334 )
=> ( in @ X335 @ X331 ) )
| ( in @ X332 @ X334 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_128,negated_conjecture,
~ ( ! [X288: $i,X289: $i] :
( ! [X290: $i] :
( ( in @ X290 @ X288 )
<=> ( in @ X290 @ X289 ) )
=> ( X288 = X289 ) )
=> ( ! [X291: $i] :
~ ( in @ X291 @ emptyset )
=> ( ! [X292: $i,X293: $i,X294: $i] :
( ( in @ X294 @ ( setadjoin @ X292 @ X293 ) )
<=> ( ( X294 = X292 )
| ( in @ X294 @ X293 ) ) )
=> ( ! [X295: $i,X296: $i] :
( ( in @ X296 @ ( powerset @ X295 ) )
<=> ! [X297: $i] :
( ( in @ X297 @ X296 )
=> ( in @ X297 @ X295 ) ) )
=> ( ! [X298: $i,X299: $i] :
( ( in @ X299 @ ( setunion @ X298 ) )
<=> ? [X300: $i] :
( ( in @ X299 @ X300 )
& ( in @ X300 @ X298 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X301: $i] :
( ( in @ X301 @ omega )
=> ( in @ ( setadjoin @ X301 @ X301 ) @ omega ) )
=> ( ! [X302: $i] :
( ( ( in @ emptyset @ X302 )
& ! [X303: $i] :
( ( ( in @ X303 @ omega )
& ( in @ X303 @ X302 ) )
=> ( in @ ( setadjoin @ X303 @ X303 ) @ X302 ) ) )
=> ! [X304: $i] :
( ( in @ X304 @ omega )
=> ( in @ X304 @ X302 ) ) )
=> ( ! [X305: $i > $i > $o,X306: $i] :
( ! [X307: $i] :
( ( in @ X307 @ X306 )
=> ? [X308: $i] :
( ( X305 @ X307 @ X308 )
& ! [X309: $i] :
( ( X305 @ X307 @ X309 )
=> ( X308 = X309 ) ) ) )
=> ? [X310: $i] :
! [X311: $i] :
( ( in @ X311 @ X310 )
<=> ? [X312: $i] :
( ( in @ X312 @ X306 )
& ( X305 @ X312 @ X311 ) ) ) )
=> ( ! [X313: $i] :
( ? [X314: $i] : ( in @ X314 @ X313 )
=> ? [X315: $i] :
( ( in @ X315 @ X313 )
& ~ ? [X316: $i] :
( ( in @ X316 @ X315 )
& ( in @ X316 @ X313 ) ) ) )
=> ( epred1_0
=> ( ! [X336: $i > $o] :
( ? [X337: $i] :
( ( X336 @ X337 )
& ! [X338: $i] :
( ( X336 @ X338 )
=> ( X337 = X338 ) ) )
=> ( X336
@ ( descr
@ ^ [Z0: $i] : ( X336 @ Z0 ) ) ) )
=> ( ! [X339: $i,X340: $i > $o,X341: $i] :
( ( in @ X341 @ X339 )
=> ( ( X340 @ X341 )
=> ( in @ X341 @ ( dsetconstr @ X339 @ X340 ) ) ) )
=> ( ! [X342: $i,X343: $i > $o,X344: $i] :
( ( in @ X344 @ ( dsetconstr @ X342 @ X343 ) )
=> ( in @ X344 @ X342 ) )
=> ( ! [X345: $i,X346: $i > $o,X347: $i] :
( ( in @ X347 @ ( dsetconstr @ X345 @ X346 ) )
=> ( X346 @ X347 ) )
=> ( ! [X348: $i > $o] :
( ? [X349: $i] :
( ( X348 @ X349 )
& ! [X350: $i] :
( ( X348 @ X350 )
=> ( X349 = X350 ) ) )
=> ? [X351: $i] :
( ( X348 @ X351 )
& ! [X352: $i] :
( ( X348 @ X352 )
=> ( X351 = X352 ) ) ) )
=> ( ! [X353: $o,X354: $i] :
( ( in @ X354 @ ( prop2set @ X353 ) )
=> X353 )
=> ( ! [X355: $i] :
( ( in @ X355 @ emptyset )
=> ! [X356: $o] : X356 )
=> ( ! [X357: $i] :
( ( in @ X357 @ emptyset )
=> ~ $true )
=> ( ! [X358: $i] :
~ ( in @ X358 @ emptyset )
=> ( ! [X359: $i > $o] :
( ? [X360: $i] :
( ( X359 @ X360 )
& ! [X361: $i] :
( ( X359 @ X361 )
=> ( X360 = X361 ) ) )
=> ? [X362: $i] : ( X359 @ X362 ) )
=> ( ! [X363: $i,X364: $i] :
( ! [X365: $i] :
( ( in @ X365 @ X363 )
=> ( in @ X365 @ X364 ) )
=> ( ! [X366: $i] :
( ( in @ X366 @ X364 )
=> ( in @ X366 @ X363 ) )
=> ( X363 = X364 ) ) )
=> ( ! [X367: $i] :
( ! [X368: $i] :
~ ( in @ X368 @ X367 )
=> ( X367 = emptyset ) )
=> ( ! [X369: $i] :
( ! [X370: $i] :
~ ( in @ X370 @ X369 )
=> ( X369 = emptyset ) )
=> ( ! [X371: $i,X372: $i > $o,X373: $i] :
( ( in @ X373 @ X371 )
=> ( ( in @ X373 @ ( dsetconstr @ X371 @ X372 ) )
<=> ( X372 @ X373 ) ) )
=> ( ! [X374: $i] :
( ( X374 != emptyset )
=> ? [X375: $i] : ( in @ X375 @ X374 ) )
=> ( ! [X376: $i,X377: $i > $o,X378: $i] :
( ( in @ X378 @ X376 )
=> ( ( X377 @ X378 )
=> ( ( dsetconstr @ X376 @ X377 )
!= emptyset ) ) )
=> ( ! [X379: $i] :
( ? [X380: $i] : ( in @ X380 @ X379 )
=> ( X379 != emptyset ) )
=> ( ! [X381: $i,X382: $i] : ( in @ X381 @ ( setadjoin @ X381 @ X382 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X383: $i,X384: $i,X385: $i] :
( ( in @ X385 @ X384 )
=> ( in @ X385 @ ( setadjoin @ X383 @ X384 ) ) )
=> ( ! [X386: $i,X387: $i,X388: $i] :
( ( in @ X388 @ ( setadjoin @ X386 @ X387 ) )
=> ! [X389: $o] :
( ( ( X388 = X386 )
=> X389 )
=> ( ( ( in @ X388 @ X387 )
=> X389 )
=> X389 ) ) )
=> ( ! [X390: $i,X391: $i,X392: $i] :
( ( in @ X392 @ ( setadjoin @ X390 @ X391 ) )
=> ( ( X392 = X390 )
| ( in @ X392 @ X391 ) ) )
=> ( ! [X393: $i] :
( ( dsetconstr @ X393
@ ^ [Z0: $i] : $true )
= X393 )
=> ( ! [X394: $i,X395: $i] :
( ! [X396: $i] :
( ( in @ X396 @ X395 )
=> ( in @ X396 @ X394 ) )
=> ( in @ X395 @ ( powerset @ X394 ) ) )
=> ( ! [X397: $i] : ( in @ emptyset @ ( powerset @ X397 ) )
=> ( ! [X398: $i] : ( in @ emptyset @ ( powerset @ X398 ) )
=> ( ! [X399: $i,X400: $i,X401: $i] :
( ( in @ X400 @ ( powerset @ X399 ) )
=> ( ( in @ X401 @ X400 )
=> ( in @ X401 @ X399 ) ) )
=> ( ! [X402: $i,X403: $i,X404: $i] :
( ( in @ X403 @ X404 )
=> ( ( in @ X404 @ X402 )
=> ( in @ X403 @ ( setunion @ X402 ) ) ) )
=> ( ! [X405: $i,X406: $i] :
( ( in @ X406 @ ( setunion @ X405 ) )
=> ! [X407: $o] :
( ! [X408: $i] :
( ( in @ X406 @ X408 )
=> ( ( in @ X408 @ X405 )
=> X407 ) )
=> X407 ) )
=> ( ! [X409: $i,X410: $i] :
( ( in @ X410 @ X409 )
=> ( in @ X410 @ ( powerset @ ( setunion @ X409 ) ) ) )
=> ( ! [X411: $i > $o] :
( ? [X412: $i] :
( ( X411 @ X412 )
& ! [X413: $i] :
( ( X411 @ X413 )
=> ( X412 = X413 ) ) )
=> ? [X414: $i] :
! [X415: $i] :
( ( X411 @ X415 )
<=> ( X415 = X414 ) ) )
=> ( ! [X416: $i] :
( ( X416 != emptyset )
=> ? [X417: $i] :
( ( in @ X417 @ X416 )
& $true ) )
=> ( ! [X418: $i,X419: $i] :
( ( in @ X418 @ ( setadjoin @ X419 @ emptyset ) )
=> ( X418 = X419 ) )
=> ( ! [X420: $i,X421: $i] :
( ( X420 != X421 )
=> ~ ( in @ X421 @ ( setadjoin @ X420 @ emptyset ) ) )
=> ( ! [X422: $i,X423: $i] :
( ( X422 = X423 )
=> ( in @ X422 @ ( setadjoin @ X423 @ emptyset ) ) )
=> ( ! [X424: $i,X425: $i] :
( ( in @ X424 @ ( setadjoin @ X425 @ emptyset ) )
=> ( in @ X425 @ ( setadjoin @ X424 @ emptyset ) ) )
=> ( ! [X426: $i,X427: $i,X428: $i] :
( ( in @ X428 @ ( setadjoin @ X426 @ ( setadjoin @ X427 @ emptyset ) ) )
=> ( ( X428 = X426 )
| ( X428 = X427 ) ) )
=> ( ! [X429: $i,X430: $i] : ( in @ X429 @ ( setadjoin @ X429 @ ( setadjoin @ X430 @ emptyset ) ) )
=> ( ! [X431: $i,X432: $i] : ( in @ X432 @ ( setadjoin @ X431 @ ( setadjoin @ X432 @ emptyset ) ) )
=> ( ! [X433: $i,X434: $i > $o] :
( ? [X435: $i] :
( ( in @ X435 @ X433 )
& ( X434 @ X435 ) )
=> ( ( ( dsetconstr @ X433 @ X434 )
= emptyset )
=> ~ $true ) )
=> ( ! [X436: $i > $o,X437: $i] :
( ( in @ X437 @ emptyset )
=> ( X436 @ X437 ) )
=> ( ! [X438: $i,X439: $i > $o] :
( ~ ! [X440: $i] :
( ( in @ X440 @ X438 )
=> ( X439 @ X440 ) )
=> ? [X441: $i] :
( ( in @ X441 @ X438 )
& ~ ( X439 @ X441 ) ) )
=> ( ! [X442: $i,X443: $i > $o] :
( ! [X444: $i] :
( ( in @ X444 @ X442 )
=> ~ ( X443 @ X444 ) )
=> ~ ? [X445: $i] :
( ( in @ X445 @ X442 )
& ( X443 @ X445 ) ) )
=> ( ! [X446: $i,X447: $i > $o] :
( ~ ? [X448: $i] :
( ( in @ X448 @ X446 )
& ( X447 @ X448 ) )
=> ! [X449: $i] :
( ( in @ X449 @ X446 )
=> ~ ( X447 @ X449 ) ) )
=> ( ! [X450: $i,X451: $i > $o] :
( ? [X452: $i] :
( ( in @ X452 @ X450 )
& ~ ( X451 @ X452 ) )
=> ~ ! [X453: $i] :
( ( in @ X453 @ X450 )
=> ( X451 @ X453 ) ) )
=> ( ! [X454: $o] :
( X454
=> ( in @ emptyset @ ( prop2set @ X454 ) ) )
=> ( ! [X455: $o] :
( X455
=> ( set2prop @ ( prop2set @ X455 ) ) )
=> ( ! [X456: $i,X457: $i > $o] :
( ~ ? [X458: $i] :
( ( in @ X458 @ X456 )
& ( X457 @ X458 ) )
=> ! [X459: $i] :
( ( in @ X459 @ X456 )
=> ~ ( X457 @ X459 ) ) )
=> ( ! [X460: $i,X461: $i > $o] :
( ~ ! [X462: $i] :
( ( in @ X462 @ X460 )
=> ( X461 @ X462 ) )
=> ? [X463: $i] :
( ( in @ X463 @ X460 )
& ~ ( X461 @ X463 ) ) )
=> ( ! [X464: $i > $o] :
( ? [X465: $i] :
( ( X464 @ X465 )
& ! [X466: $i] :
( ( X464 @ X466 )
=> ( X465 = X466 ) ) )
=> ? [X467: $i] :
( ( X464 @ X467 )
& ! [X468: $i] :
( ( X464 @ X468 )
=> ( X467 = X468 ) ) ) )
=> ( ! [X469: $i > $o] :
( ? [X470: $i] : ( X469 @ X470 )
=> ( ! [X471: $i,X472: $i] :
( ( X469 @ X471 )
=> ( ( X469 @ X472 )
=> ( X471 = X472 ) ) )
=> ? [X473: $i] :
( ( X469 @ X473 )
& ! [X474: $i] :
( ( X469 @ X474 )
=> ( X473 = X474 ) ) ) ) )
=> ( ! [X475: $i > $o] :
( ? [X476: $i] :
! [X477: $i] :
( ( X475 @ X477 )
<=> ( X477 = X476 ) )
=> ? [X478: $i] :
( ( X475 @ X478 )
& ! [X479: $i] :
( ( X475 @ X479 )
=> ( X478 = X479 ) ) ) )
=> ( ! [X480: $i,X481: $i] :
( ( X480 = X481 )
=> ! [X482: $i,X483: $i] :
( ( X482 = X483 )
=> ( ( in @ X482 @ X480 )
=> ( in @ X483 @ X481 ) ) ) )
=> ( ! [X484: $i,X485: $i] :
( ( X484 = X485 )
=> ! [X486: $i,X487: $i] :
( ( X486 = X487 )
=> ( ( in @ X486 @ X484 )
<=> ( in @ X487 @ X485 ) ) ) )
=> ( ! [X488: $i > $o] :
( ? [X489: $i] :
( ( X488 @ X489 )
& ! [X490: $i] :
( ( X488 @ X490 )
=> ( X489 = X490 ) ) )
=> ! [X491: $i,X492: $i] :
( ( X488 @ X491 )
=> ( ( X488 @ X492 )
=> ( X491 = X492 ) ) ) )
=> ( ! [X493: $i > $o,X494: $i > $o] :
( ! [X495: $i,X496: $i] :
( ( X495 = X496 )
=> ( ( X493 @ X495 )
<=> ( X494 @ X496 ) ) )
=> ( ? [X497: $i] :
( ( X493 @ X497 )
& ! [X498: $i] :
( ( X493 @ X498 )
=> ( X497 = X498 ) ) )
<=> ? [X499: $i] :
( ( X494 @ X499 )
& ! [X500: $i] :
( ( X494 @ X500 )
=> ( X499 = X500 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X501: $i,X502: $i] :
( ( X501 = X502 )
=> ! [X503: $i,X504: $i] :
( ( X503 = X504 )
=> ( ( setadjoin @ X501 @ X503 )
= ( setadjoin @ X502 @ X504 ) ) ) )
=> ( ! [X505: $i,X506: $i] :
( ( X505 = X506 )
=> ( ( powerset @ X505 )
= ( powerset @ X506 ) ) )
=> ( ! [X507: $i,X508: $i] :
( ( X507 = X508 )
=> ( ( setunion @ X507 )
= ( setunion @ X508 ) ) )
=> ( ( omega = omega )
=> ( ! [X509: $i > $o] :
( ? [X510: $i] :
( ( X509 @ X510 )
& ! [X511: $i] :
( ( X509 @ X511 )
=> ( X510 = X511 ) ) )
=> ! [X512: $i,X513: $i] :
( ( X509 @ X512 )
=> ( ( X509 @ X513 )
=> ( X512 = X513 ) ) ) )
=> ( ! [X514: $i > $o,X515: $i > $o] :
( ! [X516: $i,X517: $i] :
( ( X516 = X517 )
=> ( ( X514 @ X516 )
<=> ( X515 @ X517 ) ) )
=> ( ? [X518: $i] :
( ( X514 @ X518 )
& ! [X519: $i] :
( ( X514 @ X519 )
=> ( X518 = X519 ) ) )
=> ( ? [X520: $i] :
( ( X515 @ X520 )
& ! [X521: $i] :
( ( X515 @ X521 )
=> ( X520 = X521 ) ) )
=> ( ( descr @ X514 )
= ( descr @ X515 ) ) ) ) )
=> ( ! [X522: $i,X523: $i] :
( ( X522 = X523 )
=> ! [X524: $i > $o,X525: $i > $o] :
( ! [X526: $i] :
( ( in @ X526 @ X522 )
=> ! [X527: $i] :
( ( in @ X527 @ X523 )
=> ( ( X526 = X527 )
=> ( ( X524 @ X526 )
<=> ( X525 @ X527 ) ) ) ) )
=> ( ( dsetconstr @ X522 @ X524 )
= ( dsetconstr @ X523 @ X525 ) ) ) )
=> ( ! [X528: $i,X529: $i] :
( ! [X530: $i] :
( ( in @ X530 @ X528 )
=> ( in @ X530 @ X529 ) )
=> ( subset @ X528 @ X529 ) )
=> ( ! [X531: $i,X532: $i] :
( ( X531 = X532 )
=> ( subset @ X532 @ X531 ) )
=> ( ! [X533: $i,X534: $i] :
( ( X533 = X534 )
=> ( subset @ X533 @ X534 ) )
=> ( ! [X535: $i,X536: $i] :
( ! [X537: $i] :
( ( in @ X537 @ X535 )
=> ( in @ X537 @ X536 ) )
=> ( subset @ X535 @ X536 ) )
=> ( ! [X538: $i] : ( subset @ emptyset @ X538 )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( subset @ X539 @ X540 )
=> ( ( in @ X541 @ X539 )
=> ( in @ X541 @ X540 ) ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( subset @ X542 @ X543 )
=> ( ~ ( in @ X544 @ X543 )
=> ~ ( in @ X544 @ X542 ) ) )
=> ( ! [X545: $i,X546: $i,X547: $i] :
( ( in @ X547 @ X545 )
=> ( ~ ( in @ X547 @ X546 )
=> ~ ( subset @ X545 @ X546 ) ) )
=> ( ! [X548: $i,X549: $i] :
( ~ ( subset @ X548 @ X549 )
=> ( X548 != X549 ) )
=> ( ! [X550: $i,X551: $i,X552: $i] :
( ( in @ X552 @ X550 )
=> ( ~ ( in @ X552 @ X551 )
=> ( X550 != X551 ) ) )
=> ( ! [X553: $i] : ( subset @ X553 @ X553 )
=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[subsetTrans]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_104]),foundationAx]),wellorderingAx]),c_0_105]),c_0_106]),c_0_107]),c_0_108]),c_0_109]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_110]),setext]),emptyI]),noeltsimpempty]),c_0_111]),c_0_112]),c_0_113]),c_0_114]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_115]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_116]),c_0_117]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_118]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_119]),c_0_120]),c_0_121]),inCongP]),in__Cong]),c_0_122]),c_0_123]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_124]),c_0_125]),c_0_126]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl])])]),c_0_127]) ).
thf(c_0_129,negated_conjecture,
! [X554: $i,X555: $i,X557: $i,X558: $i,X559: $i,X560: $i,X561: $i,X562: $i,X563: $i,X564: $i,X565: $i,X567: $i,X568: $i,X570: $i,X571: $i,X572: $i,X573: $i,X574: $i,X576: $i,X577: $i > $i > $o,X578: $i,X580: $i,X583: $i,X585: $i,X586: $i,X587: $i,X588: $i,X590: $i,X591: $i > $o,X592: $i,X594: $i,X595: $i > $o,X596: $i,X597: $i,X598: $i > $o,X599: $i,X600: $i,X601: $i > $o,X602: $i,X603: $i > $o,X604: $i,X607: $i,X608: $o,X609: $i,X610: $i,X611: $o,X612: $i,X613: $i,X614: $i > $o,X615: $i,X618: $i,X619: $i,X622: $i,X624: $i,X626: $i,X627: $i > $o,X628: $i,X629: $i,X631: $i,X632: $i > $o,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X641: $i,X642: $i,X643: $i,X644: $o,X645: $i,X646: $i,X647: $i,X648: $i,X649: $i,X650: $i,X652: $i,X653: $i,X654: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i,X660: $i,X661: $i,X662: $o,X664: $i,X665: $i,X666: $i > $o,X667: $i,X670: $i,X671: $i,X672: $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,X687: $i,X688: $i,X689: $i,X690: $i > $o,X691: $i,X692: $i > $o,X693: $i,X694: $i,X695: $i > $o,X696: $i,X698: $i,X699: $i > $o,X701: $i,X702: $i,X703: $i > $o,X705: $i,X706: $i,X707: $i > $o,X708: $i,X710: $o,X711: $o,X712: $i,X713: $i > $o,X715: $i,X716: $i,X717: $i > $o,X718: $i,X720: $i > $o,X721: $i,X724: $i,X725: $i > $o,X726: $i,X730: $i,X731: $i > $o,X732: $i,X735: $i,X736: $i,X737: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $i,X743: $i,X744: $i > $o,X745: $i,X747: $i,X748: $i,X749: $i > $o,X750: $i > $o,X753: $i,X756: $i,X757: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i > $o,X770: $i,X772: $i,X773: $i,X774: $i > $o,X775: $i > $o,X778: $i,X780: $i,X782: $i,X783: $i,X784: $i > $o,X785: $i > $o,X788: $i,X789: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X798: $i,X799: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i] :
( ( ~ ( in @ ( esk1_2 @ X554 @ X555 ) @ X554 )
| ~ ( in @ ( esk1_2 @ X554 @ X555 ) @ X555 )
| ( X554 = X555 ) )
& ( ( in @ ( esk1_2 @ X554 @ X555 ) @ X554 )
| ( in @ ( esk1_2 @ X554 @ X555 ) @ X555 )
| ( X554 = X555 ) )
& ~ ( in @ X557 @ emptyset )
& ( ~ ( in @ X560 @ ( setadjoin @ X558 @ X559 ) )
| ( X560 = X558 )
| ( in @ X560 @ X559 ) )
& ( ( X560 != X558 )
| ( in @ X560 @ ( setadjoin @ X558 @ X559 ) ) )
& ( ~ ( in @ X560 @ X559 )
| ( in @ X560 @ ( setadjoin @ X558 @ X559 ) ) )
& ( ~ ( in @ X562 @ ( powerset @ X561 ) )
| ~ ( in @ X563 @ X562 )
| ( in @ X563 @ X561 ) )
& ( ( in @ ( esk2_2 @ X564 @ X565 ) @ X565 )
| ( in @ X565 @ ( powerset @ X564 ) ) )
& ( ~ ( in @ ( esk2_2 @ X564 @ X565 ) @ X564 )
| ( in @ X565 @ ( powerset @ X564 ) ) )
& ( ( in @ X568 @ ( esk3_2 @ X567 @ X568 ) )
| ~ ( in @ X568 @ ( setunion @ X567 ) ) )
& ( ( in @ ( esk3_2 @ X567 @ X568 ) @ X567 )
| ~ ( in @ X568 @ ( setunion @ X567 ) ) )
& ( ~ ( in @ X571 @ X572 )
| ~ ( in @ X572 @ X570 )
| ( in @ X571 @ ( setunion @ X570 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X573 @ omega )
| ( in @ ( setadjoin @ X573 @ X573 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X574 ) @ omega )
| ~ ( in @ emptyset @ X574 )
| ~ ( in @ X576 @ omega )
| ( in @ X576 @ X574 ) )
& ( ( in @ ( esk4_1 @ X574 ) @ X574 )
| ~ ( in @ emptyset @ X574 )
| ~ ( in @ X576 @ omega )
| ( in @ X576 @ X574 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X574 ) @ ( esk4_1 @ X574 ) ) @ X574 )
| ~ ( in @ emptyset @ X574 )
| ~ ( in @ X576 @ omega )
| ( in @ X576 @ X574 ) )
& ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
& ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
& ( ~ ( in @ X586 @ X578 )
| ~ ( X577 @ X586 @ X585 )
| ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
| ( in @ ( esk5_2 @ X577 @ X578 ) @ X578 ) )
& ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ~ ( in @ X586 @ X578 )
| ~ ( X577 @ X586 @ X585 )
| ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
| ( X577 @ ( esk5_2 @ X577 @ X578 ) @ ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ( in @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X578 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( X580
!= ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ( X577 @ ( esk8_3 @ X577 @ X578 @ X583 ) @ X583 )
| ~ ( in @ X583 @ ( esk7_2 @ X577 @ X578 ) )
| ( X580
!= ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ~ ( in @ X586 @ X578 )
| ~ ( X577 @ X586 @ X585 )
| ( in @ X585 @ ( esk7_2 @ X577 @ X578 ) )
| ( X580
!= ( esk6_3 @ X577 @ X578 @ X580 ) )
| ~ ( X577 @ ( esk5_2 @ X577 @ X578 ) @ X580 ) )
& ( ( in @ ( esk9_1 @ X587 ) @ X587 )
| ~ ( in @ X588 @ X587 ) )
& ( ~ ( in @ X590 @ ( esk9_1 @ X587 ) )
| ~ ( in @ X590 @ X587 )
| ~ ( in @ X588 @ X587 ) )
& epred1_0
& ( ( X591 @ ( esk10_2 @ X591 @ X592 ) )
| ~ ( X591 @ X592 )
| ( X591 @ ( descr @ X591 ) ) )
& ( ( X592
!= ( esk10_2 @ X591 @ X592 ) )
| ~ ( X591 @ X592 )
| ( X591 @ ( descr @ X591 ) ) )
& ( ~ ( in @ X596 @ X594 )
| ~ ( X595 @ X596 )
| ( in @ X596 @ ( dsetconstr @ X594 @ X595 ) ) )
& ( ~ ( in @ X599 @ ( dsetconstr @ X597 @ X598 ) )
| ( in @ X599 @ X597 ) )
& ( ~ ( in @ X602 @ ( dsetconstr @ X600 @ X601 ) )
| ( X601 @ X602 ) )
& ( ( X603 @ ( esk12_1 @ X603 ) )
| ( X603 @ ( esk11_2 @ X603 @ X604 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( X603 @ X607 )
| ( ( esk12_1 @ X603 )
= X607 )
| ( X603 @ ( esk11_2 @ X603 @ X604 ) )
| ~ ( X603 @ X604 ) )
& ( ( X603 @ ( esk12_1 @ X603 ) )
| ( X604
!= ( esk11_2 @ X603 @ X604 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( X603 @ X607 )
| ( ( esk12_1 @ X603 )
= X607 )
| ( X604
!= ( esk11_2 @ X603 @ X604 ) )
| ~ ( X603 @ X604 ) )
& ( ~ ( in @ X609 @ ( prop2set @ X608 ) )
| X608 )
& ( ~ ( in @ X610 @ emptyset )
| X611 )
& ( ~ ( in @ X612 @ emptyset )
| ~ $true )
& ~ ( in @ X613 @ emptyset )
& ( ( X614 @ ( esk13_2 @ X614 @ X615 ) )
| ~ ( X614 @ X615 )
| ( X614 @ ( esk14_1 @ X614 ) ) )
& ( ( X615
!= ( esk13_2 @ X614 @ X615 ) )
| ~ ( X614 @ X615 )
| ( X614 @ ( esk14_1 @ X614 ) ) )
& ( ( in @ ( esk16_2 @ X618 @ X619 ) @ X619 )
| ( X618 = X619 )
| ( in @ ( esk15_2 @ X618 @ X619 ) @ X618 ) )
& ( ~ ( in @ ( esk16_2 @ X618 @ X619 ) @ X618 )
| ( X618 = X619 )
| ( in @ ( esk15_2 @ X618 @ X619 ) @ X618 ) )
& ( ( in @ ( esk16_2 @ X618 @ X619 ) @ X619 )
| ( X618 = X619 )
| ~ ( in @ ( esk15_2 @ X618 @ X619 ) @ X619 ) )
& ( ~ ( in @ ( esk16_2 @ X618 @ X619 ) @ X618 )
| ( X618 = X619 )
| ~ ( in @ ( esk15_2 @ X618 @ X619 ) @ X619 ) )
& ( ( in @ ( esk17_1 @ X622 ) @ X622 )
| ( X622 = emptyset ) )
& ( ( in @ ( esk18_1 @ X624 ) @ X624 )
| ( X624 = emptyset ) )
& ( ~ ( in @ X628 @ ( dsetconstr @ X626 @ X627 ) )
| ( X627 @ X628 )
| ~ ( in @ X628 @ X626 ) )
& ( ~ ( X627 @ X628 )
| ( in @ X628 @ ( dsetconstr @ X626 @ X627 ) )
| ~ ( in @ X628 @ X626 ) )
& ( ( X629 = emptyset )
| ( in @ ( esk19_1 @ X629 ) @ X629 ) )
& ( ~ ( in @ X633 @ X631 )
| ~ ( X632 @ X633 )
| ( ( dsetconstr @ X631 @ X632 )
!= emptyset ) )
& ( ~ ( in @ X635 @ X634 )
| ( X634 != emptyset ) )
& ( in @ X636 @ ( setadjoin @ X636 @ X637 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X640 @ X639 )
| ( in @ X640 @ ( setadjoin @ X638 @ X639 ) ) )
& ( ( in @ X643 @ X642 )
| X644
| ( X643 = X641 )
| ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
& ( ~ X644
| X644
| ( X643 = X641 )
| ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
& ( ( in @ X643 @ X642 )
| X644
| ~ X644
| ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
& ( ~ X644
| X644
| ~ X644
| ~ ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
& ( ~ ( in @ X647 @ ( setadjoin @ X645 @ X646 ) )
| ( X647 = X645 )
| ( in @ X647 @ X646 ) )
& ( ( dsetconstr @ X648
@ ^ [Z0: $i] : $true )
= X648 )
& ( ( in @ ( esk20_2 @ X649 @ X650 ) @ X650 )
| ( in @ X650 @ ( powerset @ X649 ) ) )
& ( ~ ( in @ ( esk20_2 @ X649 @ X650 ) @ X649 )
| ( in @ X650 @ ( powerset @ X649 ) ) )
& ( in @ emptyset @ ( powerset @ X652 ) )
& ( in @ emptyset @ ( powerset @ X653 ) )
& ( ~ ( in @ X655 @ ( powerset @ X654 ) )
| ~ ( in @ X656 @ X655 )
| ( in @ X656 @ X654 ) )
& ( ~ ( in @ X658 @ X659 )
| ~ ( in @ X659 @ X657 )
| ( in @ X658 @ ( setunion @ X657 ) ) )
& ( ( in @ X661 @ ( esk21_3 @ X660 @ X661 @ X662 ) )
| X662
| ~ ( in @ X661 @ ( setunion @ X660 ) ) )
& ( ( in @ ( esk21_3 @ X660 @ X661 @ X662 ) @ X660 )
| X662
| ~ ( in @ X661 @ ( setunion @ X660 ) ) )
& ( ~ X662
| X662
| ~ ( in @ X661 @ ( setunion @ X660 ) ) )
& ( ~ ( in @ X665 @ X664 )
| ( in @ X665 @ ( powerset @ ( setunion @ X664 ) ) ) )
& ( ~ ( X666 @ X670 )
| ( X670
= ( esk23_1 @ X666 ) )
| ( X666 @ ( esk22_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ( X671
!= ( esk23_1 @ X666 ) )
| ( X666 @ X671 )
| ( X666 @ ( esk22_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ~ ( X666 @ X670 )
| ( X670
= ( esk23_1 @ X666 ) )
| ( X667
!= ( esk22_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ( X671
!= ( esk23_1 @ X666 ) )
| ( X666 @ X671 )
| ( X667
!= ( esk22_2 @ X666 @ X667 ) )
| ~ ( X666 @ X667 ) )
& ( ( in @ ( esk24_1 @ X672 ) @ X672 )
| ( X672 = emptyset ) )
& ( $true
| ( X672 = emptyset ) )
& ( ~ ( in @ X674 @ ( setadjoin @ X675 @ emptyset ) )
| ( X674 = X675 ) )
& ( ( X676 = X677 )
| ~ ( in @ X677 @ ( setadjoin @ X676 @ emptyset ) ) )
& ( ( X678 != X679 )
| ( in @ X678 @ ( setadjoin @ X679 @ emptyset ) ) )
& ( ~ ( in @ X680 @ ( setadjoin @ X681 @ emptyset ) )
| ( in @ X681 @ ( setadjoin @ X680 @ emptyset ) ) )
& ( ~ ( in @ X684 @ ( setadjoin @ X682 @ ( setadjoin @ X683 @ emptyset ) ) )
| ( X684 = X682 )
| ( X684 = X683 ) )
& ( in @ X685 @ ( setadjoin @ X685 @ ( setadjoin @ X686 @ emptyset ) ) )
& ( in @ X688 @ ( setadjoin @ X687 @ ( setadjoin @ X688 @ emptyset ) ) )
& ( ~ ( in @ X691 @ X689 )
| ~ ( X690 @ X691 )
| ( ( dsetconstr @ X689 @ X690 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X693 @ emptyset )
| ( X692 @ X693 ) )
& ( ( in @ ( esk25_2 @ X694 @ X695 ) @ X694 )
| ~ ( in @ X696 @ X694 )
| ( X695 @ X696 ) )
& ( ~ ( X695 @ ( esk25_2 @ X694 @ X695 ) )
| ~ ( in @ X696 @ X694 )
| ( X695 @ X696 ) )
& ( ( in @ ( esk26_2 @ X698 @ X699 ) @ X698 )
| ~ ( in @ X701 @ X698 )
| ~ ( X699 @ X701 ) )
& ( ( X699 @ ( esk26_2 @ X698 @ X699 ) )
| ~ ( in @ X701 @ X698 )
| ~ ( X699 @ X701 ) )
& ( ( in @ ( esk27_2 @ X702 @ X703 ) @ X702 )
| ~ ( in @ X705 @ X702 )
| ~ ( X703 @ X705 ) )
& ( ( X703 @ ( esk27_2 @ X702 @ X703 ) )
| ~ ( in @ X705 @ X702 )
| ~ ( X703 @ X705 ) )
& ( ( in @ ( esk28_2 @ X706 @ X707 ) @ X706 )
| ~ ( in @ X708 @ X706 )
| ( X707 @ X708 ) )
& ( ~ ( X707 @ ( esk28_2 @ X706 @ X707 ) )
| ~ ( in @ X708 @ X706 )
| ( X707 @ X708 ) )
& ( ~ X710
| ( in @ emptyset @ ( prop2set @ X710 ) ) )
& ( ~ X711
| ( set2prop @ ( prop2set @ X711 ) ) )
& ( ( in @ ( esk29_2 @ X712 @ X713 ) @ X712 )
| ~ ( in @ X715 @ X712 )
| ~ ( X713 @ X715 ) )
& ( ( X713 @ ( esk29_2 @ X712 @ X713 ) )
| ~ ( in @ X715 @ X712 )
| ~ ( X713 @ X715 ) )
& ( ( in @ ( esk30_2 @ X716 @ X717 ) @ X716 )
| ~ ( in @ X718 @ X716 )
| ( X717 @ X718 ) )
& ( ~ ( X717 @ ( esk30_2 @ X716 @ X717 ) )
| ~ ( in @ X718 @ X716 )
| ( X717 @ X718 ) )
& ( ( X720 @ ( esk32_1 @ X720 ) )
| ( X720 @ ( esk31_2 @ X720 @ X721 ) )
| ~ ( X720 @ X721 ) )
& ( ~ ( X720 @ X724 )
| ( ( esk32_1 @ X720 )
= X724 )
| ( X720 @ ( esk31_2 @ X720 @ X721 ) )
| ~ ( X720 @ X721 ) )
& ( ( X720 @ ( esk32_1 @ X720 ) )
| ( X721
!= ( esk31_2 @ X720 @ X721 ) )
| ~ ( X720 @ X721 ) )
& ( ~ ( X720 @ X724 )
| ( ( esk32_1 @ X720 )
= X724 )
| ( X721
!= ( esk31_2 @ X720 @ X721 ) )
| ~ ( X720 @ X721 ) )
& ( ( X725 @ ( esk35_1 @ X725 ) )
| ( X725 @ ( esk33_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ~ ( X725 @ X730 )
| ( ( esk35_1 @ X725 )
= X730 )
| ( X725 @ ( esk33_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ( X725 @ ( esk35_1 @ X725 ) )
| ( X725 @ ( esk34_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ~ ( X725 @ X730 )
| ( ( esk35_1 @ X725 )
= X730 )
| ( X725 @ ( esk34_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ( X725 @ ( esk35_1 @ X725 ) )
| ( ( esk33_1 @ X725 )
!= ( esk34_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ~ ( X725 @ X730 )
| ( ( esk35_1 @ X725 )
= X730 )
| ( ( esk33_1 @ X725 )
!= ( esk34_1 @ X725 ) )
| ~ ( X725 @ X726 ) )
& ( ( X731 @ ( esk37_1 @ X731 ) )
| ~ ( X731 @ ( esk36_2 @ X731 @ X732 ) )
| ( ( esk36_2 @ X731 @ X732 )
!= X732 ) )
& ( ~ ( X731 @ X735 )
| ( ( esk37_1 @ X731 )
= X735 )
| ~ ( X731 @ ( esk36_2 @ X731 @ X732 ) )
| ( ( esk36_2 @ X731 @ X732 )
!= X732 ) )
& ( ( X731 @ ( esk37_1 @ X731 ) )
| ( X731 @ ( esk36_2 @ X731 @ X732 ) )
| ( ( esk36_2 @ X731 @ X732 )
= X732 ) )
& ( ~ ( X731 @ X735 )
| ( ( esk37_1 @ X731 )
= X735 )
| ( X731 @ ( esk36_2 @ X731 @ X732 ) )
| ( ( esk36_2 @ X731 @ X732 )
= X732 ) )
& ( ( X736 != X737 )
| ( X738 != X739 )
| ~ ( in @ X738 @ X736 )
| ( in @ X739 @ X737 ) )
& ( ~ ( in @ X742 @ X740 )
| ( in @ X743 @ X741 )
| ( X742 != X743 )
| ( X740 != X741 ) )
& ( ~ ( in @ X743 @ X741 )
| ( in @ X742 @ X740 )
| ( X742 != X743 )
| ( X740 != X741 ) )
& ( ( X744 @ ( esk38_2 @ X744 @ X745 ) )
| ~ ( X744 @ X745 )
| ~ ( X744 @ X747 )
| ~ ( X744 @ X748 )
| ( X747 = X748 ) )
& ( ( X745
!= ( esk38_2 @ X744 @ X745 ) )
| ~ ( X744 @ X745 )
| ~ ( X744 @ X747 )
| ~ ( X744 @ X748 )
| ( X747 = X748 ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( ( esk39_2 @ X749 @ X750 )
= ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ~ ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ~ ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X749 @ ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X750 @ ( esk42_2 @ X749 @ X750 ) )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X750 @ X756 )
| ( ( esk42_2 @ X749 @ X750 )
= X756 )
| ( X753
!= ( esk41_3 @ X749 @ X750 @ X753 ) )
| ~ ( X749 @ X753 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X750 @ ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ( X749 @ ( esk44_2 @ X749 @ X750 ) )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( ~ ( X749 @ X760 )
| ( ( esk44_2 @ X749 @ X750 )
= X760 )
| ( X757
!= ( esk43_3 @ X749 @ X750 @ X757 ) )
| ~ ( X750 @ X757 )
| ( X749 @ ( esk39_2 @ X749 @ X750 ) )
| ( X750 @ ( esk40_2 @ X749 @ X750 ) ) )
& ( emptyset = emptyset )
& ( ( X761 != X762 )
| ( X763 != X764 )
| ( ( setadjoin @ X761 @ X763 )
= ( setadjoin @ X762 @ X764 ) ) )
& ( ( X765 != X766 )
| ( ( powerset @ X765 )
= ( powerset @ X766 ) ) )
& ( ( X767 != X768 )
| ( ( setunion @ X767 )
= ( setunion @ X768 ) ) )
& ( omega = omega )
& ( ( X769 @ ( esk45_2 @ X769 @ X770 ) )
| ~ ( X769 @ X770 )
| ~ ( X769 @ X772 )
| ~ ( X769 @ X773 )
| ( X772 = X773 ) )
& ( ( X770
!= ( esk45_2 @ X769 @ X770 ) )
| ~ ( X769 @ X770 )
| ~ ( X769 @ X772 )
| ~ ( X769 @ X773 )
| ( X772 = X773 ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( ( esk46_2 @ X774 @ X775 )
= ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( ( esk46_2 @ X774 @ X775 )
= ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( ( esk46_2 @ X774 @ X775 )
= ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( ( esk46_2 @ X774 @ X775 )
= ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ~ ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ~ ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X774 @ ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X775 @ ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( X780
!= ( esk49_3 @ X774 @ X775 @ X780 ) )
| ~ ( X775 @ X780 )
| ( ( descr @ X774 )
= ( descr @ X775 ) )
| ( X778
!= ( esk48_3 @ X774 @ X775 @ X778 ) )
| ~ ( X774 @ X778 )
| ( X774 @ ( esk46_2 @ X774 @ X775 ) )
| ( X775 @ ( esk47_2 @ X774 @ X775 ) ) )
& ( ( in @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) @ X782 )
| ( ( dsetconstr @ X782 @ X784 )
= ( dsetconstr @ X783 @ X785 ) )
| ( X782 != X783 ) )
& ( ( in @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) @ X783 )
| ( ( dsetconstr @ X782 @ X784 )
= ( dsetconstr @ X783 @ X785 ) )
| ( X782 != X783 ) )
& ( ( ( esk50_4 @ X782 @ X783 @ X784 @ X785 )
= ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
| ( ( dsetconstr @ X782 @ X784 )
= ( dsetconstr @ X783 @ X785 ) )
| ( X782 != X783 ) )
& ( ~ ( X784 @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) )
| ~ ( X785 @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
| ( ( dsetconstr @ X782 @ X784 )
= ( dsetconstr @ X783 @ X785 ) )
| ( X782 != X783 ) )
& ( ( X784 @ ( esk50_4 @ X782 @ X783 @ X784 @ X785 ) )
| ( X785 @ ( esk51_4 @ X782 @ X783 @ X784 @ X785 ) )
| ( ( dsetconstr @ X782 @ X784 )
= ( dsetconstr @ X783 @ X785 ) )
| ( X782 != X783 ) )
& ( ( in @ ( esk52_2 @ X788 @ X789 ) @ X788 )
| ( subset @ X788 @ X789 ) )
& ( ~ ( in @ ( esk52_2 @ X788 @ X789 ) @ X789 )
| ( subset @ X788 @ X789 ) )
& ( ( X791 != X792 )
| ( subset @ X792 @ X791 ) )
& ( ( X793 != X794 )
| ( subset @ X793 @ X794 ) )
& ( ( in @ ( esk53_2 @ X795 @ X796 ) @ X795 )
| ( subset @ X795 @ X796 ) )
& ( ~ ( in @ ( esk53_2 @ X795 @ X796 ) @ X796 )
| ( subset @ X795 @ X796 ) )
& ( subset @ emptyset @ X798 )
& ( ~ ( subset @ X799 @ X800 )
| ~ ( in @ X801 @ X799 )
| ( in @ X801 @ X800 ) )
& ( ~ ( subset @ X802 @ X803 )
| ( in @ X804 @ X803 )
| ~ ( in @ X804 @ X802 ) )
& ( ~ ( in @ X807 @ X805 )
| ( in @ X807 @ X806 )
| ~ ( subset @ X805 @ X806 ) )
& ( ( subset @ X808 @ X809 )
| ( X808 != X809 ) )
& ( ~ ( in @ X812 @ X810 )
| ( in @ X812 @ X811 )
| ( X810 != X811 ) )
& ( subset @ X813 @ X813 )
& ( subset @ esk54_0 @ esk55_0 )
& ( subset @ esk55_0 @ esk56_0 )
& ~ ( subset @ esk54_0 @ esk56_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_128])])])])])])]) ).
thf(c_0_130,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_131,negated_conjecture,
subset @ esk55_0 @ esk56_0,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_132,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk52_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_133,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk56_0 )
| ~ ( in @ X2 @ esk55_0 ) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
thf(c_0_134,negated_conjecture,
subset @ esk54_0 @ esk55_0,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_135,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk56_0 )
| ~ ( in @ ( esk52_2 @ X2 @ esk56_0 ) @ esk55_0 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
thf(c_0_136,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk55_0 )
| ~ ( in @ X2 @ esk54_0 ) ),
inference(spm,[status(thm)],[c_0_130,c_0_134]) ).
thf(c_0_137,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk56_0 )
| ~ ( in @ ( esk52_2 @ X2 @ esk56_0 ) @ esk54_0 ) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
thf(c_0_138,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk52_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_139,negated_conjecture,
~ ( subset @ esk54_0 @ esk56_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_140,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SEU570^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun May 19 17:28:22 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.14/0.37 Running higher-order theorem proving
% 0.14/0.37 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/benchmark/theBenchmark.p
% 0.14/0.42 # Version: 3.1.0-ho
% 0.14/0.42 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42 # Starting ehoh_best3_rw with 300s (1) cores
% 0.14/0.42 # Starting almost_fo_3 with 300s (1) cores
% 0.14/0.42 # Starting new_ho_13 with 300s (1) cores
% 0.14/0.42 # ehoh_best3_avoidappvar with pid 28695 completed with status 0
% 0.14/0.42 # Result found by ehoh_best3_avoidappvar
% 0.14/0.42 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42 # No SInE strategy applied
% 0.14/0.42 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 # Starting ho_unfolding_3 with 811s (1) cores
% 0.14/0.42 # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.14/0.42 # Starting lpo1_def_fix with 136s (1) cores
% 0.14/0.42 # Starting full_lambda_2 with 136s (1) cores
% 0.14/0.42 # Starting new_ho_14 with 136s (1) cores
% 0.14/0.42 # ehoh_best3_avoidappvar with pid 28702 completed with status 0
% 0.14/0.42 # Result found by ehoh_best3_avoidappvar
% 0.14/0.42 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.14/0.42 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.14/0.42 # No SInE strategy applied
% 0.14/0.42 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.14/0.42 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 # Starting ho_unfolding_3 with 811s (1) cores
% 0.14/0.42 # Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.14/0.42 # Preprocessing time : 0.003 s
% 0.14/0.42 # Presaturation interreduction done
% 0.14/0.42
% 0.14/0.42 # Proof found!
% 0.14/0.42 # SZS status Theorem
% 0.14/0.42 # SZS output start CNFRefutation
% See solution above
% 0.14/0.42 # Parsed axioms : 190
% 0.14/0.42 # Removed by relevancy pruning/SinE : 0
% 0.14/0.42 # Initial clauses : 300
% 0.14/0.42 # Removed in clause preprocessing : 115
% 0.14/0.42 # Initial clauses in saturation : 185
% 0.14/0.42 # Processed clauses : 295
% 0.14/0.42 # ...of these trivial : 7
% 0.14/0.42 # ...subsumed : 42
% 0.14/0.42 # ...remaining for further processing : 246
% 0.14/0.42 # Other redundant clauses eliminated : 13
% 0.14/0.42 # Clauses deleted for lack of memory : 0
% 0.14/0.42 # Backward-subsumed : 0
% 0.14/0.42 # Backward-rewritten : 5
% 0.14/0.42 # Generated clauses : 278
% 0.14/0.42 # ...of the previous two non-redundant : 245
% 0.14/0.42 # ...aggressively subsumed : 0
% 0.14/0.42 # Contextual simplify-reflections : 0
% 0.14/0.42 # Paramodulations : 254
% 0.14/0.42 # Factorizations : 2
% 0.14/0.42 # NegExts : 0
% 0.14/0.42 # Equation resolutions : 13
% 0.14/0.42 # Disequality decompositions : 0
% 0.14/0.42 # Total rewrite steps : 52
% 0.14/0.42 # ...of those cached : 29
% 0.14/0.42 # Propositional unsat checks : 0
% 0.14/0.42 # Propositional check models : 0
% 0.14/0.42 # Propositional check unsatisfiable : 0
% 0.14/0.42 # Propositional clauses : 0
% 0.14/0.42 # Propositional clauses after purity: 0
% 0.14/0.42 # Propositional unsat core size : 0
% 0.14/0.42 # Propositional preprocessing time : 0.000
% 0.14/0.42 # Propositional encoding time : 0.000
% 0.14/0.42 # Propositional solver time : 0.000
% 0.14/0.42 # Success case prop preproc time : 0.000
% 0.14/0.42 # Success case prop encoding time : 0.000
% 0.14/0.42 # Success case prop solver time : 0.000
% 0.14/0.42 # Current number of processed clauses : 67
% 0.14/0.42 # Positive orientable unit clauses : 20
% 0.14/0.42 # Positive unorientable unit clauses: 0
% 0.14/0.42 # Negative unit clauses : 2
% 0.14/0.42 # Non-unit-clauses : 45
% 0.14/0.42 # Current number of unprocessed clauses: 288
% 0.14/0.42 # ...number of literals in the above : 897
% 0.14/0.42 # Current number of archived formulas : 0
% 0.14/0.42 # Current number of archived clauses : 166
% 0.14/0.42 # Clause-clause subsumption calls (NU) : 5522
% 0.14/0.42 # Rec. Clause-clause subsumption calls : 1417
% 0.14/0.42 # Non-unit clause-clause subsumptions : 30
% 0.14/0.42 # Unit Clause-clause subsumption calls : 40
% 0.14/0.42 # Rewrite failures with RHS unbound : 0
% 0.14/0.42 # BW rewrite match attempts : 17
% 0.14/0.42 # BW rewrite match successes : 4
% 0.14/0.42 # Condensation attempts : 0
% 0.14/0.42 # Condensation successes : 0
% 0.14/0.42 # Termbank termtop insertions : 43332
% 0.14/0.42 # Search garbage collected termcells : 9904
% 0.14/0.42
% 0.14/0.42 # -------------------------------------------------
% 0.14/0.42 # User time : 0.032 s
% 0.14/0.42 # System time : 0.007 s
% 0.14/0.42 # Total time : 0.039 s
% 0.14/0.42 # Maximum resident set size: 4304 pages
% 0.14/0.42
% 0.14/0.42 # -------------------------------------------------
% 0.14/0.42 # User time : 0.103 s
% 0.14/0.42 # System time : 0.020 s
% 0.14/0.42 # Total time : 0.123 s
% 0.14/0.42 # Maximum resident set size: 1924 pages
% 0.14/0.42 % E---3.1 exiting
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------