TSTP Solution File: SEU568^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU568^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.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 03:28:14 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 240
% Syntax : Number of formulae : 285 ( 25 unt; 153 typ; 0 def)
% Number of atoms : 1079 ( 326 equ; 0 cnn)
% Maximal formula atoms : 332 ( 8 avg)
% Number of connectives : 4338 ( 395 ~; 440 |; 271 &;2555 @)
% ( 146 <=>; 531 =>; 0 <=; 0 <~>)
% Maximal formula depth : 388 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 305 ( 305 >; 0 *; 0 +; 0 <<)
% Number of symbols : 156 ( 153 usr; 92 con; 0-4 aty)
% Number of variables : 962 ( 116 ^ 742 !; 104 ?; 962 :)
% 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,
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,
epred1_0: $o ).
thf(decl_122,type,
esk1_2: $i > $i > $i ).
thf(decl_123,type,
esk2_2: $i > $i > $i ).
thf(decl_124,type,
esk3_2: $i > $i > $i ).
thf(decl_125,type,
esk4_1: $i > $i ).
thf(decl_126,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_127,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_128,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_129,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_130,type,
esk9_1: $i > $i ).
thf(decl_131,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_132,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_133,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_134,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_135,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_136,type,
esk15_2: $i > $i > $i ).
thf(decl_137,type,
esk16_2: $i > $i > $i ).
thf(decl_138,type,
esk17_1: $i > $i ).
thf(decl_139,type,
esk18_1: $i > $i ).
thf(decl_140,type,
esk19_1: $i > $i ).
thf(decl_141,type,
esk20_2: $i > $i > $i ).
thf(decl_142,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_143,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_144,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_145,type,
esk24_1: $i > $i ).
thf(decl_146,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_147,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_148,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_149,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_150,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_151,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_152,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_153,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_154,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_155,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_156,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_157,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_158,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_159,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_160,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_161,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_162,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_163,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_164,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_165,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_166,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_167,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_168,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_169,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_170,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_171,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_172,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_173,type,
esk52_2: $i > $i > $i ).
thf(decl_174,type,
esk53_2: $i > $i > $i ).
thf(decl_175,type,
esk54_0: $i ).
thf(decl_176,type,
esk55_0: $i ).
thf(decl_177,type,
esk56_0: $i ).
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(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
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(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(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(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(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(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(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(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
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(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(notequalI2,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
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
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(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI2) ).
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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetE) ).
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(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
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(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
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(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(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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
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_86,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_87,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_88,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_89,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_90,plain,
( 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_91,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_92,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_93,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_94,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_95,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_96,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_97,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_98,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_99,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_100,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_101,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_86,c_0_87]) ).
thf(c_0_102,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X277: $i] :
( ( X1 @ X277 )
& ! [X278: $i] :
( ( X1 @ X278 )
=> ( X277 = X278 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_103,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_87]) ).
thf(c_0_104,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X279: $i] :
( ( X1 @ X279 )
& ! [X280: $i] :
( ( X1 @ X280 )
=> ( X279 = X280 ) ) )
=> ( ? [X281: $i] :
( ( X17 @ X281 )
& ! [X282: $i] :
( ( X17 @ X282 )
=> ( X281 = X282 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_90,c_0_89]) ).
thf(c_0_105,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_106,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_107,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X263: $i] :
( ( X1 @ X263 )
& ! [X264: $i] :
( ( X1 @ X264 )
=> ( X263 = X264 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_89]) ).
thf(c_0_108,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_87]) ).
thf(c_0_109,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_110,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X265: $i] :
( ( X1 @ X265 )
& ! [X266: $i] :
( ( X1 @ X266 )
=> ( X265 = X266 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_92,c_0_89]) ).
thf(c_0_111,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X267: $i] :
( ( X1 @ X267 )
& ! [X268: $i] :
( ( X1 @ X268 )
=> ( X267 = X268 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_93,c_0_89]) ).
thf(c_0_112,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X269: $i] :
( ( X1 @ X269 )
& ! [X270: $i] :
( ( X1 @ X270 )
=> ( X269 = X270 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_94,c_0_89]) ).
thf(c_0_113,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X271: $i] :
( ( X1 @ X271 )
& ! [X272: $i] :
( ( X1 @ X272 )
=> ( X271 = X272 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_95,c_0_89]) ).
thf(c_0_114,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X273: $i] :
( ( X1 @ X273 )
& ! [X274: $i] :
( ( X1 @ X274 )
=> ( X273 = X274 ) ) )
<=> ? [X275: $i] :
( ( X17 @ X275 )
& ! [X276: $i] :
( ( X17 @ X276 )
=> ( X275 = X276 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_96,c_0_89]) ).
thf(c_0_115,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_87]) ).
thf(c_0_116,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_117,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X261: $i] :
( ( X1 @ X261 )
& ! [X262: $i] :
( ( X1 @ X262 )
=> ( X261 = X262 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_97,c_0_89]) ).
thf(c_0_118,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X259: $i] :
( ( X1 @ X259 )
& ! [X260: $i] :
( ( X1 @ X260 )
=> ( X259 = X260 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_98,c_0_89]) ).
thf(c_0_119,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_120,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_121,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_122,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X257: $i] :
( ( X1 @ X257 )
& ! [X258: $i] :
( ( X1 @ X258 )
=> ( X257 = X258 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_99,c_0_89]) ).
thf(c_0_123,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X255: $i] :
( ( X6 @ X2 @ X255 )
& ! [X256: $i] :
( ( X6 @ X2 @ X256 )
=> ( X255 = X256 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_100,c_0_89]) ).
thf(c_0_124,plain,
( epred1_0
<=> ! [X312: $i] :
? [X313: $i] :
( ! [X314: $i] :
( ( in @ X314 @ X313 )
=> ! [X315: $i] :
( ( in @ X315 @ X314 )
=> ( in @ X315 @ X312 ) ) )
& ! [X316: $i,X317: $i] :
( ( ( in @ X316 @ X312 )
& ( in @ X317 @ X312 ) )
=> ( ! [X318: $i] :
( ( in @ X318 @ X313 )
=> ( ( in @ X316 @ X318 )
<=> ( in @ X317 @ X318 ) ) )
=> ( X316 = X317 ) ) )
& ! [X319: $i,X320: $i] :
( ( ( in @ X319 @ X313 )
& ( in @ X320 @ X313 ) )
=> ( ! [X321: $i] :
( ( in @ X321 @ X319 )
=> ( in @ X321 @ X320 ) )
| ! [X322: $i] :
( ( in @ X322 @ X320 )
=> ( in @ X322 @ X319 ) ) ) )
& ! [X323: $i] :
( ( ! [X324: $i] :
( ( in @ X324 @ X323 )
=> ( in @ X324 @ X312 ) )
& ? [X325: $i] : ( in @ X325 @ X323 ) )
=> ? [X326: $i,X327: $i] :
( ( in @ X326 @ X313 )
& ( in @ X327 @ X323 )
& ~ ? [X328: $i] :
( ( in @ X328 @ X326 )
& ( in @ X328 @ X323 ) )
& ! [X329: $i] :
( ( in @ X329 @ X313 )
=> ( ! [X330: $i] :
( ( in @ X330 @ X329 )
=> ( in @ X330 @ X326 ) )
| ( in @ X327 @ X329 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_125,negated_conjecture,
~ ( ! [X283: $i,X284: $i] :
( ! [X285: $i] :
( ( in @ X285 @ X283 )
<=> ( in @ X285 @ X284 ) )
=> ( X283 = X284 ) )
=> ( ! [X286: $i] :
~ ( in @ X286 @ emptyset )
=> ( ! [X287: $i,X288: $i,X289: $i] :
( ( in @ X289 @ ( setadjoin @ X287 @ X288 ) )
<=> ( ( X289 = X287 )
| ( in @ X289 @ X288 ) ) )
=> ( ! [X290: $i,X291: $i] :
( ( in @ X291 @ ( powerset @ X290 ) )
<=> ! [X292: $i] :
( ( in @ X292 @ X291 )
=> ( in @ X292 @ X290 ) ) )
=> ( ! [X293: $i,X294: $i] :
( ( in @ X294 @ ( setunion @ X293 ) )
<=> ? [X295: $i] :
( ( in @ X294 @ X295 )
& ( in @ X295 @ X293 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X296: $i] :
( ( in @ X296 @ omega )
=> ( in @ ( setadjoin @ X296 @ X296 ) @ omega ) )
=> ( ! [X297: $i] :
( ( ( in @ emptyset @ X297 )
& ! [X298: $i] :
( ( ( in @ X298 @ omega )
& ( in @ X298 @ X297 ) )
=> ( in @ ( setadjoin @ X298 @ X298 ) @ X297 ) ) )
=> ! [X299: $i] :
( ( in @ X299 @ omega )
=> ( in @ X299 @ X297 ) ) )
=> ( ! [X300: $i > $i > $o,X301: $i] :
( ! [X302: $i] :
( ( in @ X302 @ X301 )
=> ? [X303: $i] :
( ( X300 @ X302 @ X303 )
& ! [X304: $i] :
( ( X300 @ X302 @ X304 )
=> ( X303 = X304 ) ) ) )
=> ? [X305: $i] :
! [X306: $i] :
( ( in @ X306 @ X305 )
<=> ? [X307: $i] :
( ( in @ X307 @ X301 )
& ( X300 @ X307 @ X306 ) ) ) )
=> ( ! [X308: $i] :
( ? [X309: $i] : ( in @ X309 @ X308 )
=> ? [X310: $i] :
( ( in @ X310 @ X308 )
& ~ ? [X311: $i] :
( ( in @ X311 @ X310 )
& ( in @ X311 @ X308 ) ) ) )
=> ( epred1_0
=> ( ! [X331: $i > $o] :
( ? [X332: $i] :
( ( X331 @ X332 )
& ! [X333: $i] :
( ( X331 @ X333 )
=> ( X332 = X333 ) ) )
=> ( X331
@ ( descr
@ ^ [Z0: $i] : ( X331 @ Z0 ) ) ) )
=> ( ! [X334: $i,X335: $i > $o,X336: $i] :
( ( in @ X336 @ X334 )
=> ( ( X335 @ X336 )
=> ( in @ X336
@ ( dsetconstr @ X334
@ ^ [Z0: $i] : ( X335 @ Z0 ) ) ) ) )
=> ( ! [X337: $i,X338: $i > $o,X339: $i] :
( ( in @ X339
@ ( dsetconstr @ X337
@ ^ [Z0: $i] : ( X338 @ Z0 ) ) )
=> ( in @ X339 @ X337 ) )
=> ( ! [X340: $i,X341: $i > $o,X342: $i] :
( ( in @ X342
@ ( dsetconstr @ X340
@ ^ [Z0: $i] : ( X341 @ Z0 ) ) )
=> ( X341 @ X342 ) )
=> ( ! [X343: $i > $o] :
( ? [X344: $i] :
( ( X343 @ X344 )
& ! [X345: $i] :
( ( X343 @ X345 )
=> ( X344 = X345 ) ) )
=> ? [X346: $i] :
( ( X343 @ X346 )
& ! [X347: $i] :
( ( X343 @ X347 )
=> ( X346 = X347 ) ) ) )
=> ( ! [X348: $o,X349: $i] :
( ( in @ X349 @ ( prop2set @ X348 ) )
=> X348 )
=> ( ! [X350: $i] :
( ( in @ X350 @ emptyset )
=> ! [X351: $o] : X351 )
=> ( ! [X352: $i] :
~ ( in @ X352 @ emptyset )
=> ( ! [X353: $i] :
~ ( in @ X353 @ emptyset )
=> ( ! [X354: $i > $o] :
( ? [X355: $i] :
( ( X354 @ X355 )
& ! [X356: $i] :
( ( X354 @ X356 )
=> ( X355 = X356 ) ) )
=> ? [X357: $i] : ( X354 @ X357 ) )
=> ( ! [X358: $i,X359: $i] :
( ! [X360: $i] :
( ( in @ X360 @ X358 )
=> ( in @ X360 @ X359 ) )
=> ( ! [X361: $i] :
( ( in @ X361 @ X359 )
=> ( in @ X361 @ X358 ) )
=> ( X358 = X359 ) ) )
=> ( ! [X362: $i] :
( ! [X363: $i] :
~ ( in @ X363 @ X362 )
=> ( X362 = emptyset ) )
=> ( ! [X364: $i] :
( ! [X365: $i] :
~ ( in @ X365 @ X364 )
=> ( X364 = emptyset ) )
=> ( ! [X366: $i,X367: $i > $o,X368: $i] :
( ( in @ X368 @ X366 )
=> ( ( in @ X368
@ ( dsetconstr @ X366
@ ^ [Z0: $i] : ( X367 @ Z0 ) ) )
<=> ( X367 @ X368 ) ) )
=> ( ! [X369: $i] :
( ( X369 != emptyset )
=> ? [X370: $i] : ( in @ X370 @ X369 ) )
=> ( ! [X371: $i,X372: $i > $o,X373: $i] :
( ( in @ X373 @ X371 )
=> ( ( X372 @ X373 )
=> ( ( dsetconstr @ X371
@ ^ [Z0: $i] : ( X372 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X374: $i] :
( ? [X375: $i] : ( in @ X375 @ X374 )
=> ( X374 != emptyset ) )
=> ( ! [X376: $i,X377: $i] : ( in @ X376 @ ( setadjoin @ X376 @ X377 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X378: $i,X379: $i,X380: $i] :
( ( in @ X380 @ X379 )
=> ( in @ X380 @ ( setadjoin @ X378 @ X379 ) ) )
=> ( ! [X381: $i,X382: $i,X383: $i] :
( ( in @ X383 @ ( setadjoin @ X381 @ X382 ) )
=> ! [X384: $o] :
( ( ( X383 = X381 )
=> X384 )
=> ( ( ( in @ X383 @ X382 )
=> X384 )
=> X384 ) ) )
=> ( ! [X385: $i,X386: $i,X387: $i] :
( ( in @ X387 @ ( setadjoin @ X385 @ X386 ) )
=> ( ( X387 = X385 )
| ( in @ X387 @ X386 ) ) )
=> ( ! [X388: $i] :
( ( dsetconstr @ X388
@ ^ [Z0: $i] : $true )
= X388 )
=> ( ! [X389: $i,X390: $i] :
( ! [X391: $i] :
( ( in @ X391 @ X390 )
=> ( in @ X391 @ X389 ) )
=> ( in @ X390 @ ( powerset @ X389 ) ) )
=> ( ! [X392: $i] : ( in @ emptyset @ ( powerset @ X392 ) )
=> ( ! [X393: $i] : ( in @ emptyset @ ( powerset @ X393 ) )
=> ( ! [X394: $i,X395: $i,X396: $i] :
( ( in @ X395 @ ( powerset @ X394 ) )
=> ( ( in @ X396 @ X395 )
=> ( in @ X396 @ X394 ) ) )
=> ( ! [X397: $i,X398: $i,X399: $i] :
( ( in @ X398 @ X399 )
=> ( ( in @ X399 @ X397 )
=> ( in @ X398 @ ( setunion @ X397 ) ) ) )
=> ( ! [X400: $i,X401: $i] :
( ( in @ X401 @ ( setunion @ X400 ) )
=> ! [X402: $o] :
( ! [X403: $i] :
( ( in @ X401 @ X403 )
=> ( ( in @ X403 @ X400 )
=> X402 ) )
=> X402 ) )
=> ( ! [X404: $i,X405: $i] :
( ( in @ X405 @ X404 )
=> ( in @ X405 @ ( powerset @ ( setunion @ X404 ) ) ) )
=> ( ! [X406: $i > $o] :
( ? [X407: $i] :
( ( X406 @ X407 )
& ! [X408: $i] :
( ( X406 @ X408 )
=> ( X407 = X408 ) ) )
=> ? [X409: $i] :
! [X410: $i] :
( ( X406 @ X410 )
<=> ( X410 = X409 ) ) )
=> ( ! [X411: $i] :
( ( X411 != emptyset )
=> ? [X412: $i] : ( in @ X412 @ X411 ) )
=> ( ! [X413: $i,X414: $i] :
( ( in @ X413 @ ( setadjoin @ X414 @ emptyset ) )
=> ( X413 = X414 ) )
=> ( ! [X415: $i,X416: $i] :
( ( X415 != X416 )
=> ~ ( in @ X416 @ ( setadjoin @ X415 @ emptyset ) ) )
=> ( ! [X417: $i,X418: $i] :
( ( X417 = X418 )
=> ( in @ X417 @ ( setadjoin @ X418 @ emptyset ) ) )
=> ( ! [X419: $i,X420: $i] :
( ( in @ X419 @ ( setadjoin @ X420 @ emptyset ) )
=> ( in @ X420 @ ( setadjoin @ X419 @ emptyset ) ) )
=> ( ! [X421: $i,X422: $i,X423: $i] :
( ( in @ X423 @ ( setadjoin @ X421 @ ( setadjoin @ X422 @ emptyset ) ) )
=> ( ( X423 = X421 )
| ( X423 = X422 ) ) )
=> ( ! [X424: $i,X425: $i] : ( in @ X424 @ ( setadjoin @ X424 @ ( setadjoin @ X425 @ emptyset ) ) )
=> ( ! [X426: $i,X427: $i] : ( in @ X427 @ ( setadjoin @ X426 @ ( setadjoin @ X427 @ emptyset ) ) )
=> ( ! [X428: $i,X429: $i > $o] :
( ? [X430: $i] :
( ( in @ X430 @ X428 )
& ( X429 @ X430 ) )
=> ( ( dsetconstr @ X428
@ ^ [Z0: $i] : ( X429 @ Z0 ) )
!= emptyset ) )
=> ( ! [X431: $i > $o,X432: $i] :
( ( in @ X432 @ emptyset )
=> ( X431 @ X432 ) )
=> ( ! [X433: $i,X434: $i > $o] :
( ~ ! [X435: $i] :
( ( in @ X435 @ X433 )
=> ( X434 @ X435 ) )
=> ? [X436: $i] :
( ( in @ X436 @ X433 )
& ~ ( X434 @ X436 ) ) )
=> ( ! [X437: $i,X438: $i > $o] :
( ! [X439: $i] :
( ( in @ X439 @ X437 )
=> ~ ( X438 @ X439 ) )
=> ~ ? [X440: $i] :
( ( in @ X440 @ X437 )
& ( X438 @ X440 ) ) )
=> ( ! [X441: $i,X442: $i > $o] :
( ~ ? [X443: $i] :
( ( in @ X443 @ X441 )
& ( X442 @ X443 ) )
=> ! [X444: $i] :
( ( in @ X444 @ X441 )
=> ~ ( X442 @ X444 ) ) )
=> ( ! [X445: $i,X446: $i > $o] :
( ? [X447: $i] :
( ( in @ X447 @ X445 )
& ~ ( X446 @ X447 ) )
=> ~ ! [X448: $i] :
( ( in @ X448 @ X445 )
=> ( X446 @ X448 ) ) )
=> ( ! [X449: $o] :
( X449
=> ( in @ emptyset @ ( prop2set @ X449 ) ) )
=> ( prop2set2propI
=> ( ! [X450: $i,X451: $i > $o] :
( ~ ? [X452: $i] :
( ( in @ X452 @ X450 )
& ( X451 @ X452 ) )
=> ! [X453: $i] :
( ( in @ X453 @ X450 )
=> ~ ( X451 @ X453 ) ) )
=> ( ! [X454: $i,X455: $i > $o] :
( ~ ! [X456: $i] :
( ( in @ X456 @ X454 )
=> ( X455 @ X456 ) )
=> ? [X457: $i] :
( ( in @ X457 @ X454 )
& ~ ( X455 @ X457 ) ) )
=> ( ! [X458: $i > $o] :
( ? [X459: $i] :
( ( X458 @ X459 )
& ! [X460: $i] :
( ( X458 @ X460 )
=> ( X459 = X460 ) ) )
=> ? [X461: $i] :
( ( X458 @ X461 )
& ! [X462: $i] :
( ( X458 @ X462 )
=> ( X461 = X462 ) ) ) )
=> ( ! [X463: $i > $o] :
( ? [X464: $i] : ( X463 @ X464 )
=> ( ! [X465: $i,X466: $i] :
( ( X463 @ X465 )
=> ( ( X463 @ X466 )
=> ( X465 = X466 ) ) )
=> ? [X467: $i] :
( ( X463 @ X467 )
& ! [X468: $i] :
( ( X463 @ X468 )
=> ( X467 = X468 ) ) ) ) )
=> ( ! [X469: $i > $o] :
( ? [X470: $i] :
! [X471: $i] :
( ( X469 @ X471 )
<=> ( X471 = X470 ) )
=> ? [X472: $i] :
( ( X469 @ X472 )
& ! [X473: $i] :
( ( X469 @ X473 )
=> ( X472 = X473 ) ) ) )
=> ( ! [X474: $i,X475: $i] :
( ( X474 = X475 )
=> ! [X476: $i,X477: $i] :
( ( X476 = X477 )
=> ( ( in @ X476 @ X474 )
=> ( in @ X477 @ X475 ) ) ) )
=> ( ! [X478: $i,X479: $i] :
( ( X478 = X479 )
=> ! [X480: $i,X481: $i] :
( ( X480 = X481 )
=> ( ( in @ X480 @ X478 )
<=> ( in @ X481 @ X479 ) ) ) )
=> ( ! [X482: $i > $o] :
( ? [X483: $i] :
( ( X482 @ X483 )
& ! [X484: $i] :
( ( X482 @ X484 )
=> ( X483 = X484 ) ) )
=> ! [X485: $i,X486: $i] :
( ( X482 @ X485 )
=> ( ( X482 @ X486 )
=> ( X485 = X486 ) ) ) )
=> ( ! [X487: $i > $o,X488: $i > $o] :
( ! [X489: $i,X490: $i] :
( ( X489 = X490 )
=> ( ( X487 @ X489 )
<=> ( X488 @ X490 ) ) )
=> ( ? [X491: $i] :
( ( X487 @ X491 )
& ! [X492: $i] :
( ( X487 @ X492 )
=> ( X491 = X492 ) ) )
<=> ? [X493: $i] :
( ( X488 @ X493 )
& ! [X494: $i] :
( ( X488 @ X494 )
=> ( X493 = X494 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X495: $i,X496: $i] :
( ( X495 = X496 )
=> ! [X497: $i,X498: $i] :
( ( X497 = X498 )
=> ( ( setadjoin @ X495 @ X497 )
= ( setadjoin @ X496 @ X498 ) ) ) )
=> ( ! [X499: $i,X500: $i] :
( ( X499 = X500 )
=> ( ( powerset @ X499 )
= ( powerset @ X500 ) ) )
=> ( ! [X501: $i,X502: $i] :
( ( X501 = X502 )
=> ( ( setunion @ X501 )
= ( setunion @ X502 ) ) )
=> ( ( omega = omega )
=> ( ! [X503: $i > $o] :
( ? [X504: $i] :
( ( X503 @ X504 )
& ! [X505: $i] :
( ( X503 @ X505 )
=> ( X504 = X505 ) ) )
=> ! [X506: $i,X507: $i] :
( ( X503 @ X506 )
=> ( ( X503 @ X507 )
=> ( X506 = X507 ) ) ) )
=> ( ! [X508: $i > $o,X509: $i > $o] :
( ! [X510: $i,X511: $i] :
( ( X510 = X511 )
=> ( ( X508 @ X510 )
<=> ( X509 @ X511 ) ) )
=> ( ? [X512: $i] :
( ( X508 @ X512 )
& ! [X513: $i] :
( ( X508 @ X513 )
=> ( X512 = X513 ) ) )
=> ( ? [X514: $i] :
( ( X509 @ X514 )
& ! [X515: $i] :
( ( X509 @ X515 )
=> ( X514 = X515 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X508 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X509 @ Z0 ) ) ) ) ) )
=> ( ! [X516: $i,X517: $i] :
( ( X516 = X517 )
=> ! [X518: $i > $o,X519: $i > $o] :
( ! [X520: $i] :
( ( in @ X520 @ X516 )
=> ! [X521: $i] :
( ( in @ X521 @ X517 )
=> ( ( X520 = X521 )
=> ( ( X518 @ X520 )
<=> ( X519 @ X521 ) ) ) ) )
=> ( ( dsetconstr @ X516
@ ^ [Z0: $i] : ( X518 @ Z0 ) )
= ( dsetconstr @ X517
@ ^ [Z0: $i] : ( X519 @ Z0 ) ) ) ) )
=> ( ! [X522: $i,X523: $i] :
( ! [X524: $i] :
( ( in @ X524 @ X522 )
=> ( in @ X524 @ X523 ) )
=> ( subset @ X522 @ X523 ) )
=> ( ! [X525: $i,X526: $i] :
( ( X525 = X526 )
=> ( subset @ X526 @ X525 ) )
=> ( ! [X527: $i,X528: $i] :
( ( X527 = X528 )
=> ( subset @ X527 @ X528 ) )
=> ( ! [X529: $i,X530: $i] :
( ! [X531: $i] :
( ( in @ X531 @ X529 )
=> ( in @ X531 @ X530 ) )
=> ( subset @ X529 @ X530 ) )
=> ( ! [X532: $i] : ( subset @ emptyset @ X532 )
=> ( ! [X533: $i,X534: $i,X535: $i] :
( ( subset @ X533 @ X534 )
=> ( ( in @ X535 @ X533 )
=> ( in @ X535 @ X534 ) ) )
=> ( ! [X536: $i,X537: $i,X538: $i] :
( ( subset @ X536 @ X537 )
=> ( ~ ( in @ X538 @ X537 )
=> ~ ( in @ X538 @ X536 ) ) )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( in @ X541 @ X539 )
=> ( ~ ( in @ X541 @ X540 )
=> ~ ( subset @ X539 @ X540 ) ) )
=> ( ! [X542: $i,X543: $i] :
( ~ ( subset @ X542 @ X543 )
=> ( X542 != X543 ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != 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(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)],[notequalI2]),notequalI1]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),c_0_101]),omega__Cong]),c_0_102]),c_0_103]),c_0_104]),c_0_105]),setadjoinIL]),subsetI1]),eqimpsubset2]),emptyinunitempty]),eqimpsubset1]),subsetI2]),setadjoinIR]),emptysetsubset]),subsetE]),setadjoinE]),subsetE2]),setadjoinOr]),notsubsetI]),c_0_106]),powersetI]),quantDeMorgan1]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_107]),c_0_108]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_109]),vacuousDall]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_110]),c_0_111]),c_0_112]),inCongP]),in__Cong]),c_0_113]),c_0_114]),emptyset__Cong]),c_0_115]),c_0_116]),noeltsimpempty]),emptyI]),setext]),c_0_117]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_118]),c_0_119]),c_0_120]),c_0_121]),c_0_122]),wellorderingAx]),foundationAx]),c_0_123]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_124]) ).
thf(c_0_126,negated_conjecture,
! [X544: $i,X545: $i,X547: $i,X548: $i,X549: $i,X550: $i,X551: $i,X552: $i,X553: $i,X554: $i,X555: $i,X557: $i,X558: $i,X560: $i,X561: $i,X562: $i,X563: $i,X564: $i,X566: $i,X567: $i > $i > $o,X568: $i,X570: $i,X573: $i,X575: $i,X576: $i,X577: $i,X578: $i,X580: $i,X581: $i > $o,X582: $i,X584: $i,X585: $i > $o,X586: $i,X587: $i,X588: $i > $o,X589: $i,X590: $i,X591: $i > $o,X592: $i,X593: $i > $o,X594: $i,X597: $i,X598: $o,X599: $i,X600: $i,X601: $o,X602: $i,X603: $i,X604: $i > $o,X605: $i,X608: $i,X609: $i,X612: $i,X614: $i,X616: $i,X617: $i > $o,X618: $i,X619: $i,X621: $i,X622: $i > $o,X623: $i,X624: $i,X625: $i,X626: $i,X627: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $o,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X642: $i,X643: $i,X644: $i,X645: $i,X646: $i,X647: $i,X648: $i,X649: $i,X650: $i,X651: $i,X652: $o,X654: $i,X655: $i,X656: $i > $o,X657: $i,X660: $i,X661: $i,X662: $i,X664: $i,X665: $i,X666: $i,X667: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $i,X674: $i,X675: $i,X676: $i,X677: $i,X678: $i,X679: $i,X680: $i > $o,X681: $i,X682: $i > $o,X683: $i,X684: $i,X685: $i > $o,X686: $i,X688: $i,X689: $i > $o,X691: $i,X692: $i,X693: $i > $o,X695: $i,X696: $i,X697: $i > $o,X698: $i,X700: $o,X701: $i,X702: $i > $o,X704: $i,X705: $i,X706: $i > $o,X707: $i,X709: $i > $o,X710: $i,X713: $i,X714: $i > $o,X715: $i,X719: $i,X720: $i > $o,X721: $i,X724: $i,X725: $i,X726: $i,X727: $i,X728: $i,X729: $i,X730: $i,X731: $i,X732: $i,X733: $i > $o,X734: $i,X736: $i,X737: $i,X738: $i > $o,X739: $i > $o,X742: $i,X745: $i,X746: $i,X749: $i,X750: $i,X751: $i,X752: $i,X753: $i,X754: $i,X755: $i,X756: $i,X757: $i,X758: $i > $o,X759: $i,X761: $i,X762: $i,X763: $i > $o,X764: $i > $o,X767: $i,X769: $i,X771: $i,X772: $i,X773: $i > $o,X774: $i > $o,X777: $i,X778: $i,X780: $i,X781: $i,X782: $i,X783: $i,X784: $i,X785: $i,X787: $i,X788: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i] :
( ( ~ ( in @ ( esk1_2 @ X544 @ X545 ) @ X544 )
| ~ ( in @ ( esk1_2 @ X544 @ X545 ) @ X545 )
| ( X544 = X545 ) )
& ( ( in @ ( esk1_2 @ X544 @ X545 ) @ X544 )
| ( in @ ( esk1_2 @ X544 @ X545 ) @ X545 )
| ( X544 = X545 ) )
& ~ ( in @ X547 @ emptyset )
& ( ~ ( in @ X550 @ ( setadjoin @ X548 @ X549 ) )
| ( X550 = X548 )
| ( in @ X550 @ X549 ) )
& ( ( X550 != X548 )
| ( in @ X550 @ ( setadjoin @ X548 @ X549 ) ) )
& ( ~ ( in @ X550 @ X549 )
| ( in @ X550 @ ( setadjoin @ X548 @ X549 ) ) )
& ( ~ ( in @ X552 @ ( powerset @ X551 ) )
| ~ ( in @ X553 @ X552 )
| ( in @ X553 @ X551 ) )
& ( ( in @ ( esk2_2 @ X554 @ X555 ) @ X555 )
| ( in @ X555 @ ( powerset @ X554 ) ) )
& ( ~ ( in @ ( esk2_2 @ X554 @ X555 ) @ X554 )
| ( in @ X555 @ ( powerset @ X554 ) ) )
& ( ( in @ X558 @ ( esk3_2 @ X557 @ X558 ) )
| ~ ( in @ X558 @ ( setunion @ X557 ) ) )
& ( ( in @ ( esk3_2 @ X557 @ X558 ) @ X557 )
| ~ ( in @ X558 @ ( setunion @ X557 ) ) )
& ( ~ ( in @ X561 @ X562 )
| ~ ( in @ X562 @ X560 )
| ( in @ X561 @ ( setunion @ X560 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X563 @ omega )
| ( in @ ( setadjoin @ X563 @ X563 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X564 ) @ omega )
| ~ ( in @ emptyset @ X564 )
| ~ ( in @ X566 @ omega )
| ( in @ X566 @ X564 ) )
& ( ( in @ ( esk4_1 @ X564 ) @ X564 )
| ~ ( in @ emptyset @ X564 )
| ~ ( in @ X566 @ omega )
| ( in @ X566 @ X564 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X564 ) @ ( esk4_1 @ X564 ) ) @ X564 )
| ~ ( in @ emptyset @ X564 )
| ~ ( in @ X566 @ omega )
| ( in @ X566 @ X564 ) )
& ( ( in @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X568 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( in @ ( esk5_2 @ X567 @ X568 ) @ X568 ) )
& ( ( X567 @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X573 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( in @ ( esk5_2 @ X567 @ X568 ) @ X568 ) )
& ( ~ ( in @ X576 @ X568 )
| ~ ( X567 @ X576 @ X575 )
| ( in @ X575 @ ( esk7_2 @ X567 @ X568 ) )
| ( in @ ( esk5_2 @ X567 @ X568 ) @ X568 ) )
& ( ( in @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X568 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( X567 @ ( esk5_2 @ X567 @ X568 ) @ ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ( X567 @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X573 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( X567 @ ( esk5_2 @ X567 @ X568 ) @ ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ~ ( in @ X576 @ X568 )
| ~ ( X567 @ X576 @ X575 )
| ( in @ X575 @ ( esk7_2 @ X567 @ X568 ) )
| ( X567 @ ( esk5_2 @ X567 @ X568 ) @ ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ( in @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X568 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( X570
!= ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ( X567 @ ( esk8_3 @ X567 @ X568 @ X573 ) @ X573 )
| ~ ( in @ X573 @ ( esk7_2 @ X567 @ X568 ) )
| ( X570
!= ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ~ ( in @ X576 @ X568 )
| ~ ( X567 @ X576 @ X575 )
| ( in @ X575 @ ( esk7_2 @ X567 @ X568 ) )
| ( X570
!= ( esk6_3 @ X567 @ X568 @ X570 ) )
| ~ ( X567 @ ( esk5_2 @ X567 @ X568 ) @ X570 ) )
& ( ( in @ ( esk9_1 @ X577 ) @ X577 )
| ~ ( in @ X578 @ X577 ) )
& ( ~ ( in @ X580 @ ( esk9_1 @ X577 ) )
| ~ ( in @ X580 @ X577 )
| ~ ( in @ X578 @ X577 ) )
& epred1_0
& ( ( X581 @ ( esk10_2 @ X581 @ X582 ) )
| ~ ( X581 @ X582 )
| ( X581
@ ( descr
@ ^ [Z0: $i] : ( X581 @ Z0 ) ) ) )
& ( ( X582
!= ( esk10_2 @ X581 @ X582 ) )
| ~ ( X581 @ X582 )
| ( X581
@ ( descr
@ ^ [Z0: $i] : ( X581 @ Z0 ) ) ) )
& ( ~ ( in @ X586 @ X584 )
| ~ ( X585 @ X586 )
| ( in @ X586
@ ( dsetconstr @ X584
@ ^ [Z0: $i] : ( X585 @ Z0 ) ) ) )
& ( ~ ( in @ X589
@ ( dsetconstr @ X587
@ ^ [Z0: $i] : ( X588 @ Z0 ) ) )
| ( in @ X589 @ X587 ) )
& ( ~ ( in @ X592
@ ( dsetconstr @ X590
@ ^ [Z0: $i] : ( X591 @ Z0 ) ) )
| ( X591 @ X592 ) )
& ( ( X593 @ ( esk12_1 @ X593 ) )
| ( X593 @ ( esk11_2 @ X593 @ X594 ) )
| ~ ( X593 @ X594 ) )
& ( ~ ( X593 @ X597 )
| ( ( esk12_1 @ X593 )
= X597 )
| ( X593 @ ( esk11_2 @ X593 @ X594 ) )
| ~ ( X593 @ X594 ) )
& ( ( X593 @ ( esk12_1 @ X593 ) )
| ( X594
!= ( esk11_2 @ X593 @ X594 ) )
| ~ ( X593 @ X594 ) )
& ( ~ ( X593 @ X597 )
| ( ( esk12_1 @ X593 )
= X597 )
| ( X594
!= ( esk11_2 @ X593 @ X594 ) )
| ~ ( X593 @ X594 ) )
& ( ~ ( in @ X599 @ ( prop2set @ X598 ) )
| X598 )
& ( ~ ( in @ X600 @ emptyset )
| X601 )
& ~ ( in @ X602 @ emptyset )
& ~ ( in @ X603 @ emptyset )
& ( ( X604 @ ( esk13_2 @ X604 @ X605 ) )
| ~ ( X604 @ X605 )
| ( X604 @ ( esk14_1 @ X604 ) ) )
& ( ( X605
!= ( esk13_2 @ X604 @ X605 ) )
| ~ ( X604 @ X605 )
| ( X604 @ ( esk14_1 @ X604 ) ) )
& ( ( in @ ( esk16_2 @ X608 @ X609 ) @ X609 )
| ( X608 = X609 )
| ( in @ ( esk15_2 @ X608 @ X609 ) @ X608 ) )
& ( ~ ( in @ ( esk16_2 @ X608 @ X609 ) @ X608 )
| ( X608 = X609 )
| ( in @ ( esk15_2 @ X608 @ X609 ) @ X608 ) )
& ( ( in @ ( esk16_2 @ X608 @ X609 ) @ X609 )
| ( X608 = X609 )
| ~ ( in @ ( esk15_2 @ X608 @ X609 ) @ X609 ) )
& ( ~ ( in @ ( esk16_2 @ X608 @ X609 ) @ X608 )
| ( X608 = X609 )
| ~ ( in @ ( esk15_2 @ X608 @ X609 ) @ X609 ) )
& ( ( in @ ( esk17_1 @ X612 ) @ X612 )
| ( X612 = emptyset ) )
& ( ( in @ ( esk18_1 @ X614 ) @ X614 )
| ( X614 = emptyset ) )
& ( ~ ( in @ X618
@ ( dsetconstr @ X616
@ ^ [Z0: $i] : ( X617 @ Z0 ) ) )
| ( X617 @ X618 )
| ~ ( in @ X618 @ X616 ) )
& ( ~ ( X617 @ X618 )
| ( in @ X618
@ ( dsetconstr @ X616
@ ^ [Z0: $i] : ( X617 @ Z0 ) ) )
| ~ ( in @ X618 @ X616 ) )
& ( ( X619 = emptyset )
| ( in @ ( esk19_1 @ X619 ) @ X619 ) )
& ( ~ ( in @ X623 @ X621 )
| ~ ( X622 @ X623 )
| ( ( dsetconstr @ X621
@ ^ [Z0: $i] : ( X622 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X625 @ X624 )
| ( X624 != emptyset ) )
& ( in @ X626 @ ( setadjoin @ X626 @ X627 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X630 @ X629 )
| ( in @ X630 @ ( setadjoin @ X628 @ X629 ) ) )
& ( ( in @ X633 @ X632 )
| X634
| ( X633 = X631 )
| ~ ( in @ X633 @ ( setadjoin @ X631 @ X632 ) ) )
& ( ~ X634
| X634
| ( X633 = X631 )
| ~ ( in @ X633 @ ( setadjoin @ X631 @ X632 ) ) )
& ( ( in @ X633 @ X632 )
| X634
| ~ X634
| ~ ( in @ X633 @ ( setadjoin @ X631 @ X632 ) ) )
& ( ~ X634
| X634
| ~ X634
| ~ ( in @ X633 @ ( setadjoin @ X631 @ X632 ) ) )
& ( ~ ( in @ X637 @ ( setadjoin @ X635 @ X636 ) )
| ( X637 = X635 )
| ( in @ X637 @ X636 ) )
& ( ( dsetconstr @ X638
@ ^ [Z0: $i] : $true )
= X638 )
& ( ( in @ ( esk20_2 @ X639 @ X640 ) @ X640 )
| ( in @ X640 @ ( powerset @ X639 ) ) )
& ( ~ ( in @ ( esk20_2 @ X639 @ X640 ) @ X639 )
| ( in @ X640 @ ( powerset @ X639 ) ) )
& ( in @ emptyset @ ( powerset @ X642 ) )
& ( in @ emptyset @ ( powerset @ X643 ) )
& ( ~ ( in @ X645 @ ( powerset @ X644 ) )
| ~ ( in @ X646 @ X645 )
| ( in @ X646 @ X644 ) )
& ( ~ ( in @ X648 @ X649 )
| ~ ( in @ X649 @ X647 )
| ( in @ X648 @ ( setunion @ X647 ) ) )
& ( ( in @ X651 @ ( esk21_3 @ X650 @ X651 @ X652 ) )
| X652
| ~ ( in @ X651 @ ( setunion @ X650 ) ) )
& ( ( in @ ( esk21_3 @ X650 @ X651 @ X652 ) @ X650 )
| X652
| ~ ( in @ X651 @ ( setunion @ X650 ) ) )
& ( ~ X652
| X652
| ~ ( in @ X651 @ ( setunion @ X650 ) ) )
& ( ~ ( in @ X655 @ X654 )
| ( in @ X655 @ ( powerset @ ( setunion @ X654 ) ) ) )
& ( ~ ( X656 @ X660 )
| ( X660
= ( esk23_1 @ X656 ) )
| ( X656 @ ( esk22_2 @ X656 @ X657 ) )
| ~ ( X656 @ X657 ) )
& ( ( X661
!= ( esk23_1 @ X656 ) )
| ( X656 @ X661 )
| ( X656 @ ( esk22_2 @ X656 @ X657 ) )
| ~ ( X656 @ X657 ) )
& ( ~ ( X656 @ X660 )
| ( X660
= ( esk23_1 @ X656 ) )
| ( X657
!= ( esk22_2 @ X656 @ X657 ) )
| ~ ( X656 @ X657 ) )
& ( ( X661
!= ( esk23_1 @ X656 ) )
| ( X656 @ X661 )
| ( X657
!= ( esk22_2 @ X656 @ X657 ) )
| ~ ( X656 @ X657 ) )
& ( ( X662 = emptyset )
| ( in @ ( esk24_1 @ X662 ) @ X662 ) )
& ( ~ ( in @ X664 @ ( setadjoin @ X665 @ emptyset ) )
| ( X664 = X665 ) )
& ( ( X666 = X667 )
| ~ ( in @ X667 @ ( setadjoin @ X666 @ emptyset ) ) )
& ( ( X668 != X669 )
| ( in @ X668 @ ( setadjoin @ X669 @ emptyset ) ) )
& ( ~ ( in @ X670 @ ( setadjoin @ X671 @ emptyset ) )
| ( in @ X671 @ ( setadjoin @ X670 @ emptyset ) ) )
& ( ~ ( in @ X674 @ ( setadjoin @ X672 @ ( setadjoin @ X673 @ emptyset ) ) )
| ( X674 = X672 )
| ( X674 = X673 ) )
& ( in @ X675 @ ( setadjoin @ X675 @ ( setadjoin @ X676 @ emptyset ) ) )
& ( in @ X678 @ ( setadjoin @ X677 @ ( setadjoin @ X678 @ emptyset ) ) )
& ( ~ ( in @ X681 @ X679 )
| ~ ( X680 @ X681 )
| ( ( dsetconstr @ X679
@ ^ [Z0: $i] : ( X680 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X683 @ emptyset )
| ( X682 @ X683 ) )
& ( ( in @ ( esk25_2 @ X684 @ X685 ) @ X684 )
| ~ ( in @ X686 @ X684 )
| ( X685 @ X686 ) )
& ( ~ ( X685 @ ( esk25_2 @ X684 @ X685 ) )
| ~ ( in @ X686 @ X684 )
| ( X685 @ X686 ) )
& ( ( in @ ( esk26_2 @ X688 @ X689 ) @ X688 )
| ~ ( in @ X691 @ X688 )
| ~ ( X689 @ X691 ) )
& ( ( X689 @ ( esk26_2 @ X688 @ X689 ) )
| ~ ( in @ X691 @ X688 )
| ~ ( X689 @ X691 ) )
& ( ( in @ ( esk27_2 @ X692 @ X693 ) @ X692 )
| ~ ( in @ X695 @ X692 )
| ~ ( X693 @ X695 ) )
& ( ( X693 @ ( esk27_2 @ X692 @ X693 ) )
| ~ ( in @ X695 @ X692 )
| ~ ( X693 @ X695 ) )
& ( ( in @ ( esk28_2 @ X696 @ X697 ) @ X696 )
| ~ ( in @ X698 @ X696 )
| ( X697 @ X698 ) )
& ( ~ ( X697 @ ( esk28_2 @ X696 @ X697 ) )
| ~ ( in @ X698 @ X696 )
| ( X697 @ X698 ) )
& ( ~ X700
| ( in @ emptyset @ ( prop2set @ X700 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X701 @ X702 ) @ X701 )
| ~ ( in @ X704 @ X701 )
| ~ ( X702 @ X704 ) )
& ( ( X702 @ ( esk29_2 @ X701 @ X702 ) )
| ~ ( in @ X704 @ X701 )
| ~ ( X702 @ X704 ) )
& ( ( in @ ( esk30_2 @ X705 @ X706 ) @ X705 )
| ~ ( in @ X707 @ X705 )
| ( X706 @ X707 ) )
& ( ~ ( X706 @ ( esk30_2 @ X705 @ X706 ) )
| ~ ( in @ X707 @ X705 )
| ( X706 @ X707 ) )
& ( ( X709 @ ( esk32_1 @ X709 ) )
| ( X709 @ ( esk31_2 @ X709 @ X710 ) )
| ~ ( X709 @ X710 ) )
& ( ~ ( X709 @ X713 )
| ( ( esk32_1 @ X709 )
= X713 )
| ( X709 @ ( esk31_2 @ X709 @ X710 ) )
| ~ ( X709 @ X710 ) )
& ( ( X709 @ ( esk32_1 @ X709 ) )
| ( X710
!= ( esk31_2 @ X709 @ X710 ) )
| ~ ( X709 @ X710 ) )
& ( ~ ( X709 @ X713 )
| ( ( esk32_1 @ X709 )
= X713 )
| ( X710
!= ( esk31_2 @ X709 @ X710 ) )
| ~ ( X709 @ X710 ) )
& ( ( X714 @ ( esk35_1 @ X714 ) )
| ( X714 @ ( esk33_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ~ ( X714 @ X719 )
| ( ( esk35_1 @ X714 )
= X719 )
| ( X714 @ ( esk33_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ( X714 @ ( esk35_1 @ X714 ) )
| ( X714 @ ( esk34_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ~ ( X714 @ X719 )
| ( ( esk35_1 @ X714 )
= X719 )
| ( X714 @ ( esk34_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ( X714 @ ( esk35_1 @ X714 ) )
| ( ( esk33_1 @ X714 )
!= ( esk34_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ~ ( X714 @ X719 )
| ( ( esk35_1 @ X714 )
= X719 )
| ( ( esk33_1 @ X714 )
!= ( esk34_1 @ X714 ) )
| ~ ( X714 @ X715 ) )
& ( ( X720 @ ( esk37_1 @ X720 ) )
| ~ ( X720 @ ( esk36_2 @ X720 @ X721 ) )
| ( ( esk36_2 @ X720 @ X721 )
!= X721 ) )
& ( ~ ( X720 @ X724 )
| ( ( esk37_1 @ X720 )
= X724 )
| ~ ( X720 @ ( esk36_2 @ X720 @ X721 ) )
| ( ( esk36_2 @ X720 @ X721 )
!= X721 ) )
& ( ( X720 @ ( esk37_1 @ X720 ) )
| ( X720 @ ( esk36_2 @ X720 @ X721 ) )
| ( ( esk36_2 @ X720 @ X721 )
= X721 ) )
& ( ~ ( X720 @ X724 )
| ( ( esk37_1 @ X720 )
= X724 )
| ( X720 @ ( esk36_2 @ X720 @ X721 ) )
| ( ( esk36_2 @ X720 @ X721 )
= X721 ) )
& ( ( X725 != X726 )
| ( X727 != X728 )
| ~ ( in @ X727 @ X725 )
| ( in @ X728 @ X726 ) )
& ( ~ ( in @ X731 @ X729 )
| ( in @ X732 @ X730 )
| ( X731 != X732 )
| ( X729 != X730 ) )
& ( ~ ( in @ X732 @ X730 )
| ( in @ X731 @ X729 )
| ( X731 != X732 )
| ( X729 != X730 ) )
& ( ( X733 @ ( esk38_2 @ X733 @ X734 ) )
| ~ ( X733 @ X734 )
| ~ ( X733 @ X736 )
| ~ ( X733 @ X737 )
| ( X736 = X737 ) )
& ( ( X734
!= ( esk38_2 @ X733 @ X734 ) )
| ~ ( X733 @ X734 )
| ~ ( X733 @ X736 )
| ~ ( X733 @ X737 )
| ( X736 = X737 ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( ( esk39_2 @ X738 @ X739 )
= ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ~ ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ~ ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X738 @ ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X739 @ ( esk42_2 @ X738 @ X739 ) )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X739 @ X745 )
| ( ( esk42_2 @ X738 @ X739 )
= X745 )
| ( X742
!= ( esk41_3 @ X738 @ X739 @ X742 ) )
| ~ ( X738 @ X742 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X739 @ ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ( X738 @ ( esk44_2 @ X738 @ X739 ) )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( ~ ( X738 @ X749 )
| ( ( esk44_2 @ X738 @ X739 )
= X749 )
| ( X746
!= ( esk43_3 @ X738 @ X739 @ X746 ) )
| ~ ( X739 @ X746 )
| ( X738 @ ( esk39_2 @ X738 @ X739 ) )
| ( X739 @ ( esk40_2 @ X738 @ X739 ) ) )
& ( emptyset = emptyset )
& ( ( X750 != X751 )
| ( X752 != X753 )
| ( ( setadjoin @ X750 @ X752 )
= ( setadjoin @ X751 @ X753 ) ) )
& ( ( X754 != X755 )
| ( ( powerset @ X754 )
= ( powerset @ X755 ) ) )
& ( ( X756 != X757 )
| ( ( setunion @ X756 )
= ( setunion @ X757 ) ) )
& ( omega = omega )
& ( ( X758 @ ( esk45_2 @ X758 @ X759 ) )
| ~ ( X758 @ X759 )
| ~ ( X758 @ X761 )
| ~ ( X758 @ X762 )
| ( X761 = X762 ) )
& ( ( X759
!= ( esk45_2 @ X758 @ X759 ) )
| ~ ( X758 @ X759 )
| ~ ( X758 @ X761 )
| ~ ( X758 @ X762 )
| ( X761 = X762 ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( ( esk46_2 @ X763 @ X764 )
= ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( ( esk46_2 @ X763 @ X764 )
= ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( ( esk46_2 @ X763 @ X764 )
= ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( ( esk46_2 @ X763 @ X764 )
= ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ~ ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ~ ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ~ ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ~ ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ~ ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ~ ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ~ ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ~ ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X763 @ ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X764 @ ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( X769
!= ( esk49_3 @ X763 @ X764 @ X769 ) )
| ~ ( X764 @ X769 )
| ( ( descr
@ ^ [Z0: $i] : ( X763 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X764 @ Z0 ) ) )
| ( X767
!= ( esk48_3 @ X763 @ X764 @ X767 ) )
| ~ ( X763 @ X767 )
| ( X763 @ ( esk46_2 @ X763 @ X764 ) )
| ( X764 @ ( esk47_2 @ X763 @ X764 ) ) )
& ( ( in @ ( esk50_4 @ X771 @ X772 @ X773 @ X774 ) @ X771 )
| ( ( dsetconstr @ X771
@ ^ [Z0: $i] : ( X773 @ Z0 ) )
= ( dsetconstr @ X772
@ ^ [Z0: $i] : ( X774 @ Z0 ) ) )
| ( X771 != X772 ) )
& ( ( in @ ( esk51_4 @ X771 @ X772 @ X773 @ X774 ) @ X772 )
| ( ( dsetconstr @ X771
@ ^ [Z0: $i] : ( X773 @ Z0 ) )
= ( dsetconstr @ X772
@ ^ [Z0: $i] : ( X774 @ Z0 ) ) )
| ( X771 != X772 ) )
& ( ( ( esk50_4 @ X771 @ X772 @ X773 @ X774 )
= ( esk51_4 @ X771 @ X772 @ X773 @ X774 ) )
| ( ( dsetconstr @ X771
@ ^ [Z0: $i] : ( X773 @ Z0 ) )
= ( dsetconstr @ X772
@ ^ [Z0: $i] : ( X774 @ Z0 ) ) )
| ( X771 != X772 ) )
& ( ~ ( X773 @ ( esk50_4 @ X771 @ X772 @ X773 @ X774 ) )
| ~ ( X774 @ ( esk51_4 @ X771 @ X772 @ X773 @ X774 ) )
| ( ( dsetconstr @ X771
@ ^ [Z0: $i] : ( X773 @ Z0 ) )
= ( dsetconstr @ X772
@ ^ [Z0: $i] : ( X774 @ Z0 ) ) )
| ( X771 != X772 ) )
& ( ( X773 @ ( esk50_4 @ X771 @ X772 @ X773 @ X774 ) )
| ( X774 @ ( esk51_4 @ X771 @ X772 @ X773 @ X774 ) )
| ( ( dsetconstr @ X771
@ ^ [Z0: $i] : ( X773 @ Z0 ) )
= ( dsetconstr @ X772
@ ^ [Z0: $i] : ( X774 @ Z0 ) ) )
| ( X771 != X772 ) )
& ( ( in @ ( esk52_2 @ X777 @ X778 ) @ X777 )
| ( subset @ X777 @ X778 ) )
& ( ~ ( in @ ( esk52_2 @ X777 @ X778 ) @ X778 )
| ( subset @ X777 @ X778 ) )
& ( ( X780 != X781 )
| ( subset @ X781 @ X780 ) )
& ( ( X782 != X783 )
| ( subset @ X782 @ X783 ) )
& ( ( in @ ( esk53_2 @ X784 @ X785 ) @ X784 )
| ( subset @ X784 @ X785 ) )
& ( ~ ( in @ ( esk53_2 @ X784 @ X785 ) @ X785 )
| ( subset @ X784 @ X785 ) )
& ( subset @ emptyset @ X787 )
& ( ~ ( subset @ X788 @ X789 )
| ~ ( in @ X790 @ X788 )
| ( in @ X790 @ X789 ) )
& ( ~ ( subset @ X791 @ X792 )
| ( in @ X793 @ X792 )
| ~ ( in @ X793 @ X791 ) )
& ( ~ ( in @ X796 @ X794 )
| ( in @ X796 @ X795 )
| ~ ( subset @ X794 @ X795 ) )
& ( ( subset @ X797 @ X798 )
| ( X797 != X798 ) )
& ( in @ esk56_0 @ esk54_0 )
& ~ ( in @ esk56_0 @ esk55_0 )
& ( esk54_0 = esk55_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_125])])])])])]) ).
thf(c_0_127,negated_conjecture,
~ ( in @ esk56_0 @ esk55_0 ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_128,negated_conjecture,
esk54_0 = esk55_0,
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_129,negated_conjecture,
in @ esk56_0 @ esk54_0,
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_130,negated_conjecture,
~ ( in @ esk56_0 @ esk54_0 ),
inference(rw,[status(thm)],[c_0_127,c_0_128]) ).
thf(c_0_131,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_129,c_0_130]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU568^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 18:12:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.20/0.53 # Version: 3.1.0-ho
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # new_bool_2 with pid 20756 completed with status 0
% 0.20/0.53 # Result found by new_bool_2
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53 # ho_unfolding_3 with pid 20772 completed with status 0
% 0.20/0.53 # Result found by ho_unfolding_3
% 0.20/0.53 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.20/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting ho_unfolding_3 with 163s (1) cores
% 0.20/0.53 # Preprocessing time : 0.005 s
% 0.20/0.53 # Presaturation interreduction done
% 0.20/0.53
% 0.20/0.53 # Proof found!
% 0.20/0.53 # SZS status Theorem
% 0.20/0.53 # SZS output start CNFRefutation
% See solution above
% 0.20/0.53 # Parsed axioms : 186
% 0.20/0.53 # Removed by relevancy pruning/SinE : 100
% 0.20/0.53 # Initial clauses : 196
% 0.20/0.53 # Removed in clause preprocessing : 12
% 0.20/0.53 # Initial clauses in saturation : 184
% 0.20/0.53 # Processed clauses : 6
% 0.20/0.53 # ...of these trivial : 0
% 0.20/0.53 # ...subsumed : 0
% 0.20/0.53 # ...remaining for further processing : 5
% 0.20/0.53 # Other redundant clauses eliminated : 0
% 0.20/0.53 # Clauses deleted for lack of memory : 0
% 0.20/0.53 # Backward-subsumed : 0
% 0.20/0.53 # Backward-rewritten : 0
% 0.20/0.53 # Generated clauses : 0
% 0.20/0.53 # ...of the previous two non-redundant : 0
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 0
% 0.20/0.53 # Paramodulations : 0
% 0.20/0.53 # Factorizations : 0
% 0.20/0.53 # NegExts : 0
% 0.20/0.53 # Equation resolutions : 0
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 1
% 0.20/0.53 # ...of those cached : 0
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 5
% 0.20/0.53 # Positive orientable unit clauses : 4
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 1
% 0.20/0.53 # Non-unit-clauses : 0
% 0.20/0.53 # Current number of unprocessed clauses: 178
% 0.20/0.53 # ...number of literals in the above : 633
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 0
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 0
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 0
% 0.20/0.53 # Non-unit clause-clause subsumptions : 0
% 0.20/0.53 # Unit Clause-clause subsumption calls : 0
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 0
% 0.20/0.53 # BW rewrite match successes : 0
% 0.20/0.53 # Condensation attempts : 6
% 0.20/0.53 # Condensation successes : 0
% 0.20/0.53 # Termbank termtop insertions : 22395
% 0.20/0.53 # Search garbage collected termcells : 8111
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.024 s
% 0.20/0.53 # System time : 0.006 s
% 0.20/0.53 # Total time : 0.030 s
% 0.20/0.53 # Maximum resident set size: 4368 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.029 s
% 0.20/0.53 # System time : 0.008 s
% 0.20/0.53 # Total time : 0.038 s
% 0.20/0.53 # Maximum resident set size: 1912 pages
% 0.20/0.53 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------