TSTP Solution File: SEU560^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU560^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 03:28:11 EDT 2024
% Result : Timeout 0.35s 300.10s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 224
% Syntax : Number of formulae : 270 ( 27 unt; 144 typ; 0 def)
% Number of atoms : 1020 ( 320 equ; 0 cnn)
% Maximal formula atoms : 314 ( 8 avg)
% Number of connectives : 4170 ( 370 ~; 431 |; 262 &;2471 @)
% ( 138 <=>; 498 =>; 0 <=; 0 <~>)
% Maximal formula depth : 363 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% Number of symbols : 147 ( 144 usr; 84 con; 0-4 aty)
% Number of variables : 917 ( 120 ^ 693 !; 104 ?; 917 :)
% 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,
epred1_0: $o ).
thf(decl_114,type,
esk1_2: $i > $i > $i ).
thf(decl_115,type,
esk2_2: $i > $i > $i ).
thf(decl_116,type,
esk3_2: $i > $i > $i ).
thf(decl_117,type,
esk4_1: $i > $i ).
thf(decl_118,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_119,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_120,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_121,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_122,type,
esk9_1: $i > $i ).
thf(decl_123,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_124,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_125,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_126,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_127,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_128,type,
esk15_2: $i > $i > $i ).
thf(decl_129,type,
esk16_2: $i > $i > $i ).
thf(decl_130,type,
esk17_1: $i > $i ).
thf(decl_131,type,
esk18_1: $i > $i ).
thf(decl_132,type,
esk19_1: $i > $i ).
thf(decl_133,type,
esk20_2: $i > $i > $i ).
thf(decl_134,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_135,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_136,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_137,type,
esk24_1: $i > $i ).
thf(decl_138,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_139,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_140,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_141,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_142,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_143,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_144,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_145,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_146,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_147,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_148,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_149,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_150,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_151,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_152,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_153,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_154,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_155,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_156,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_157,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_158,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_159,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_160,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_161,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_162,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_163,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_164,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_165,type,
esk52_2: $i > $i > $i ).
thf(decl_166,type,
esk53_0: $i ).
thf(decl_167,type,
esk54_0: $i ).
thf(decl_168,type,
esk55_0: $i ).
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(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(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(subset,axiom,
( subset
= ( ^ [X4: $i,X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
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(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(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(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(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(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(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(eqimpsubset2,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
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
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(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
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(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(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(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_79,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_80,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_81,plain,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE3u]) ).
thf(c_0_82,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_83,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_84,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_85,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu]) ).
thf(c_0_86,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_87,plain,
( subset
= ( ^ [Z0: $i,Z1: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ( in @ X2 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_88,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_89,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_90,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_91,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
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,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_94,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_95,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X249: $i] :
( ( X1 @ X249 )
& ! [X250: $i] :
( ( X1 @ X250 )
=> ( X249 = X250 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_96,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X251: $i] :
( ( X1 @ X251 )
& ! [X252: $i] :
( ( X1 @ X252 )
=> ( X251 = X252 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_81,c_0_80]) ).
thf(c_0_97,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_98,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X253: $i] :
( ( X1 @ X253 )
& ! [X254: $i] :
( ( X1 @ X254 )
=> ( X253 = X254 ) ) )
<=> ? [X255: $i] :
( ( X17 @ X255 )
& ! [X256: $i] :
( ( X17 @ X256 )
=> ( X255 = X256 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_82,c_0_80]) ).
thf(c_0_99,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_83]) ).
thf(c_0_100,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_84,c_0_83]) ).
thf(c_0_101,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_83]) ).
thf(c_0_102,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X257: $i] :
( ( X1 @ X257 )
& ! [X258: $i] :
( ( X1 @ X258 )
=> ( X257 = X258 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_85,c_0_80]) ).
thf(c_0_103,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X259: $i] :
( ( X1 @ X259 )
& ! [X260: $i] :
( ( X1 @ X260 )
=> ( X259 = X260 ) ) )
=> ( ? [X261: $i] :
( ( X17 @ X261 )
& ! [X262: $i] :
( ( X17 @ X262 )
=> ( X261 = X262 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_86,c_0_80]) ).
thf(c_0_104,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_105,axiom,
( subsetI1
= ( ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ! [X263: $i] :
( ( in @ X263 @ X4 )
=> ( in @ X263 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[subsetI1,c_0_87]) ).
thf(c_0_106,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_107,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_108,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X243: $i] :
( ( X1 @ X243 )
& ! [X244: $i] :
( ( X1 @ X244 )
=> ( X243 = X244 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_88,c_0_80]) ).
thf(c_0_109,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_83]) ).
thf(c_0_110,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X245: $i] :
( ( X1 @ X245 )
& ! [X246: $i] :
( ( X1 @ X246 )
=> ( X245 = X246 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_89,c_0_80]) ).
thf(c_0_111,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X247: $i] :
( ( X1 @ X247 )
& ! [X248: $i] :
( ( X1 @ X248 )
=> ( X247 = X248 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_90,c_0_80]) ).
thf(c_0_112,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X241: $i] :
( ( X1 @ X241 )
& ! [X242: $i] :
( ( X1 @ X242 )
=> ( X241 = X242 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_80]) ).
thf(c_0_113,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X239: $i] :
( ( X1 @ X239 )
& ! [X240: $i] :
( ( X1 @ X240 )
=> ( X239 = X240 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_92,c_0_80]) ).
thf(c_0_114,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_115,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_116,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_117,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X237: $i] :
( ( X1 @ X237 )
& ! [X238: $i] :
( ( X1 @ X238 )
=> ( X237 = X238 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_93,c_0_80]) ).
thf(c_0_118,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X235: $i] :
( ( X6 @ X2 @ X235 )
& ! [X236: $i] :
( ( X6 @ X2 @ X236 )
=> ( X235 = X236 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_94,c_0_80]) ).
thf(c_0_119,plain,
( epred1_0
<=> ! [X293: $i] :
? [X294: $i] :
( ! [X295: $i] :
( ( in @ X295 @ X294 )
=> ! [X296: $i] :
( ( in @ X296 @ X295 )
=> ( in @ X296 @ X293 ) ) )
& ! [X297: $i,X298: $i] :
( ( ( in @ X297 @ X293 )
& ( in @ X298 @ X293 ) )
=> ( ! [X299: $i] :
( ( in @ X299 @ X294 )
=> ( ( in @ X297 @ X299 )
<=> ( in @ X298 @ X299 ) ) )
=> ( X297 = X298 ) ) )
& ! [X300: $i,X301: $i] :
( ( ( in @ X300 @ X294 )
& ( in @ X301 @ X294 ) )
=> ( ! [X302: $i] :
( ( in @ X302 @ X300 )
=> ( in @ X302 @ X301 ) )
| ! [X303: $i] :
( ( in @ X303 @ X301 )
=> ( in @ X303 @ X300 ) ) ) )
& ! [X304: $i] :
( ( ! [X305: $i] :
( ( in @ X305 @ X304 )
=> ( in @ X305 @ X293 ) )
& ? [X306: $i] : ( in @ X306 @ X304 ) )
=> ? [X307: $i,X308: $i] :
( ( in @ X307 @ X294 )
& ( in @ X308 @ X304 )
& ~ ? [X309: $i] :
( ( in @ X309 @ X307 )
& ( in @ X309 @ X304 ) )
& ! [X310: $i] :
( ( in @ X310 @ X294 )
=> ( ! [X311: $i] :
( ( in @ X311 @ X310 )
=> ( in @ X311 @ X307 ) )
| ( in @ X308 @ X310 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_120,negated_conjecture,
~ ( ! [X264: $i,X265: $i] :
( ! [X266: $i] :
( ( in @ X266 @ X264 )
<=> ( in @ X266 @ X265 ) )
=> ( X264 = X265 ) )
=> ( ! [X267: $i] :
~ ( in @ X267 @ emptyset )
=> ( ! [X268: $i,X269: $i,X270: $i] :
( ( in @ X270 @ ( setadjoin @ X268 @ X269 ) )
<=> ( ( X270 = X268 )
| ( in @ X270 @ X269 ) ) )
=> ( ! [X271: $i,X272: $i] :
( ( in @ X272 @ ( powerset @ X271 ) )
<=> ! [X273: $i] :
( ( in @ X273 @ X272 )
=> ( in @ X273 @ X271 ) ) )
=> ( ! [X274: $i,X275: $i] :
( ( in @ X275 @ ( setunion @ X274 ) )
<=> ? [X276: $i] :
( ( in @ X275 @ X276 )
& ( in @ X276 @ X274 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X277: $i] :
( ( in @ X277 @ omega )
=> ( in @ ( setadjoin @ X277 @ X277 ) @ omega ) )
=> ( ! [X278: $i] :
( ( ( in @ emptyset @ X278 )
& ! [X279: $i] :
( ( ( in @ X279 @ omega )
& ( in @ X279 @ X278 ) )
=> ( in @ ( setadjoin @ X279 @ X279 ) @ X278 ) ) )
=> ! [X280: $i] :
( ( in @ X280 @ omega )
=> ( in @ X280 @ X278 ) ) )
=> ( ! [X281: $i > $i > $o,X282: $i] :
( ! [X283: $i] :
( ( in @ X283 @ X282 )
=> ? [X284: $i] :
( ( X281 @ X283 @ X284 )
& ! [X285: $i] :
( ( X281 @ X283 @ X285 )
=> ( X284 = X285 ) ) ) )
=> ? [X286: $i] :
! [X287: $i] :
( ( in @ X287 @ X286 )
<=> ? [X288: $i] :
( ( in @ X288 @ X282 )
& ( X281 @ X288 @ X287 ) ) ) )
=> ( ! [X289: $i] :
( ? [X290: $i] : ( in @ X290 @ X289 )
=> ? [X291: $i] :
( ( in @ X291 @ X289 )
& ~ ? [X292: $i] :
( ( in @ X292 @ X291 )
& ( in @ X292 @ X289 ) ) ) )
=> ( epred1_0
=> ( ! [X312: $i > $o] :
( ? [X313: $i] :
( ( X312 @ X313 )
& ! [X314: $i] :
( ( X312 @ X314 )
=> ( X313 = X314 ) ) )
=> ( X312
@ ( descr
@ ^ [Z0: $i] : ( X312 @ Z0 ) ) ) )
=> ( ! [X315: $i,X316: $i > $o,X317: $i] :
( ( in @ X317 @ X315 )
=> ( ( X316 @ X317 )
=> ( in @ X317
@ ( dsetconstr @ X315
@ ^ [Z0: $i] : ( X316 @ Z0 ) ) ) ) )
=> ( ! [X318: $i,X319: $i > $o,X320: $i] :
( ( in @ X320
@ ( dsetconstr @ X318
@ ^ [Z0: $i] : ( X319 @ Z0 ) ) )
=> ( in @ X320 @ X318 ) )
=> ( ! [X321: $i,X322: $i > $o,X323: $i] :
( ( in @ X323
@ ( dsetconstr @ X321
@ ^ [Z0: $i] : ( X322 @ Z0 ) ) )
=> ( X322 @ X323 ) )
=> ( ! [X324: $i > $o] :
( ? [X325: $i] :
( ( X324 @ X325 )
& ! [X326: $i] :
( ( X324 @ X326 )
=> ( X325 = X326 ) ) )
=> ? [X327: $i] :
( ( X324 @ X327 )
& ! [X328: $i] :
( ( X324 @ X328 )
=> ( X327 = X328 ) ) ) )
=> ( ! [X329: $o,X330: $i] :
( ( in @ X330 @ ( prop2set @ X329 ) )
=> X329 )
=> ( ! [X331: $i] :
( ( in @ X331 @ emptyset )
=> ! [X332: $o] : X332 )
=> ( ! [X333: $i] :
~ ( in @ X333 @ emptyset )
=> ( ! [X334: $i] :
~ ( in @ X334 @ emptyset )
=> ( ! [X335: $i > $o] :
( ? [X336: $i] :
( ( X335 @ X336 )
& ! [X337: $i] :
( ( X335 @ X337 )
=> ( X336 = X337 ) ) )
=> ? [X338: $i] : ( X335 @ X338 ) )
=> ( ! [X339: $i,X340: $i] :
( ! [X341: $i] :
( ( in @ X341 @ X339 )
=> ( in @ X341 @ X340 ) )
=> ( ! [X342: $i] :
( ( in @ X342 @ X340 )
=> ( in @ X342 @ X339 ) )
=> ( X339 = X340 ) ) )
=> ( ! [X343: $i] :
( ! [X344: $i] :
~ ( in @ X344 @ X343 )
=> ( X343 = emptyset ) )
=> ( ! [X345: $i] :
( ! [X346: $i] :
~ ( in @ X346 @ X345 )
=> ( X345 = emptyset ) )
=> ( ! [X347: $i,X348: $i > $o,X349: $i] :
( ( in @ X349 @ X347 )
=> ( ( in @ X349
@ ( dsetconstr @ X347
@ ^ [Z0: $i] : ( X348 @ Z0 ) ) )
<=> ( X348 @ X349 ) ) )
=> ( ! [X350: $i] :
( ( X350 != emptyset )
=> ? [X351: $i] : ( in @ X351 @ X350 ) )
=> ( ! [X352: $i,X353: $i > $o,X354: $i] :
( ( in @ X354 @ X352 )
=> ( ( X353 @ X354 )
=> ( ( dsetconstr @ X352
@ ^ [Z0: $i] : ( X353 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X355: $i] :
( ? [X356: $i] : ( in @ X356 @ X355 )
=> ( X355 != emptyset ) )
=> ( ! [X357: $i,X358: $i] : ( in @ X357 @ ( setadjoin @ X357 @ X358 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X359: $i,X360: $i,X361: $i] :
( ( in @ X361 @ X360 )
=> ( in @ X361 @ ( setadjoin @ X359 @ X360 ) ) )
=> ( ! [X362: $i,X363: $i,X364: $i] :
( ( in @ X364 @ ( setadjoin @ X362 @ X363 ) )
=> ! [X365: $o] :
( ( ( X364 = X362 )
=> X365 )
=> ( ( ( in @ X364 @ X363 )
=> X365 )
=> X365 ) ) )
=> ( ! [X366: $i,X367: $i,X368: $i] :
( ( in @ X368 @ ( setadjoin @ X366 @ X367 ) )
=> ( ( X368 = X366 )
| ( in @ X368 @ X367 ) ) )
=> ( ! [X369: $i] :
( ( dsetconstr @ X369
@ ^ [Z0: $i] : $true )
= X369 )
=> ( ! [X370: $i,X371: $i] :
( ! [X372: $i] :
( ( in @ X372 @ X371 )
=> ( in @ X372 @ X370 ) )
=> ( in @ X371 @ ( powerset @ X370 ) ) )
=> ( ! [X373: $i] : ( in @ emptyset @ ( powerset @ X373 ) )
=> ( ! [X374: $i] : ( in @ emptyset @ ( powerset @ X374 ) )
=> ( ! [X375: $i,X376: $i,X377: $i] :
( ( in @ X376 @ ( powerset @ X375 ) )
=> ( ( in @ X377 @ X376 )
=> ( in @ X377 @ X375 ) ) )
=> ( ! [X378: $i,X379: $i,X380: $i] :
( ( in @ X379 @ X380 )
=> ( ( in @ X380 @ X378 )
=> ( in @ X379 @ ( setunion @ X378 ) ) ) )
=> ( ! [X381: $i,X382: $i] :
( ( in @ X382 @ ( setunion @ X381 ) )
=> ! [X383: $o] :
( ! [X384: $i] :
( ( in @ X382 @ X384 )
=> ( ( in @ X384 @ X381 )
=> X383 ) )
=> X383 ) )
=> ( ! [X385: $i,X386: $i] :
( ( in @ X386 @ X385 )
=> ( in @ X386 @ ( powerset @ ( setunion @ X385 ) ) ) )
=> ( ! [X387: $i > $o] :
( ? [X388: $i] :
( ( X387 @ X388 )
& ! [X389: $i] :
( ( X387 @ X389 )
=> ( X388 = X389 ) ) )
=> ? [X390: $i] :
! [X391: $i] :
( ( X387 @ X391 )
<=> ( X391 = X390 ) ) )
=> ( ! [X392: $i] :
( ( X392 != emptyset )
=> ? [X393: $i] : ( in @ X393 @ X392 ) )
=> ( ! [X394: $i,X395: $i] :
( ( in @ X394 @ ( setadjoin @ X395 @ emptyset ) )
=> ( X394 = X395 ) )
=> ( ! [X396: $i,X397: $i] :
( ( X396 != X397 )
=> ~ ( in @ X397 @ ( setadjoin @ X396 @ emptyset ) ) )
=> ( ! [X398: $i,X399: $i] :
( ( X398 = X399 )
=> ( in @ X398 @ ( setadjoin @ X399 @ emptyset ) ) )
=> ( ! [X400: $i,X401: $i] :
( ( in @ X400 @ ( setadjoin @ X401 @ emptyset ) )
=> ( in @ X401 @ ( setadjoin @ X400 @ emptyset ) ) )
=> ( ! [X402: $i,X403: $i,X404: $i] :
( ( in @ X404 @ ( setadjoin @ X402 @ ( setadjoin @ X403 @ emptyset ) ) )
=> ( ( X404 = X402 )
| ( X404 = X403 ) ) )
=> ( ! [X405: $i,X406: $i] : ( in @ X405 @ ( setadjoin @ X405 @ ( setadjoin @ X406 @ emptyset ) ) )
=> ( ! [X407: $i,X408: $i] : ( in @ X408 @ ( setadjoin @ X407 @ ( setadjoin @ X408 @ emptyset ) ) )
=> ( ! [X409: $i,X410: $i > $o] :
( ? [X411: $i] :
( ( in @ X411 @ X409 )
& ( X410 @ X411 ) )
=> ( ( dsetconstr @ X409
@ ^ [Z0: $i] : ( X410 @ Z0 ) )
!= emptyset ) )
=> ( ! [X412: $i > $o,X413: $i] :
( ( in @ X413 @ emptyset )
=> ( X412 @ X413 ) )
=> ( ! [X414: $i,X415: $i > $o] :
( ~ ! [X416: $i] :
( ( in @ X416 @ X414 )
=> ( X415 @ X416 ) )
=> ? [X417: $i] :
( ( in @ X417 @ X414 )
& ~ ( X415 @ X417 ) ) )
=> ( ! [X418: $i,X419: $i > $o] :
( ! [X420: $i] :
( ( in @ X420 @ X418 )
=> ~ ( X419 @ X420 ) )
=> ~ ? [X421: $i] :
( ( in @ X421 @ X418 )
& ( X419 @ X421 ) ) )
=> ( ! [X422: $i,X423: $i > $o] :
( ~ ? [X424: $i] :
( ( in @ X424 @ X422 )
& ( X423 @ X424 ) )
=> ! [X425: $i] :
( ( in @ X425 @ X422 )
=> ~ ( X423 @ X425 ) ) )
=> ( ! [X426: $i,X427: $i > $o] :
( ? [X428: $i] :
( ( in @ X428 @ X426 )
& ~ ( X427 @ X428 ) )
=> ~ ! [X429: $i] :
( ( in @ X429 @ X426 )
=> ( X427 @ X429 ) ) )
=> ( ! [X430: $o] :
( X430
=> ( in @ emptyset @ ( prop2set @ X430 ) ) )
=> ( prop2set2propI
=> ( ! [X431: $i,X432: $i > $o] :
( ~ ? [X433: $i] :
( ( in @ X433 @ X431 )
& ( X432 @ X433 ) )
=> ! [X434: $i] :
( ( in @ X434 @ X431 )
=> ~ ( X432 @ X434 ) ) )
=> ( ! [X435: $i,X436: $i > $o] :
( ~ ! [X437: $i] :
( ( in @ X437 @ X435 )
=> ( X436 @ X437 ) )
=> ? [X438: $i] :
( ( in @ X438 @ X435 )
& ~ ( X436 @ X438 ) ) )
=> ( ! [X439: $i > $o] :
( ? [X440: $i] :
( ( X439 @ X440 )
& ! [X441: $i] :
( ( X439 @ X441 )
=> ( X440 = X441 ) ) )
=> ? [X442: $i] :
( ( X439 @ X442 )
& ! [X443: $i] :
( ( X439 @ X443 )
=> ( X442 = X443 ) ) ) )
=> ( ! [X444: $i > $o] :
( ? [X445: $i] : ( X444 @ X445 )
=> ( ! [X446: $i,X447: $i] :
( ( X444 @ X446 )
=> ( ( X444 @ X447 )
=> ( X446 = X447 ) ) )
=> ? [X448: $i] :
( ( X444 @ X448 )
& ! [X449: $i] :
( ( X444 @ X449 )
=> ( X448 = X449 ) ) ) ) )
=> ( ! [X450: $i > $o] :
( ? [X451: $i] :
! [X452: $i] :
( ( X450 @ X452 )
<=> ( X452 = X451 ) )
=> ? [X453: $i] :
( ( X450 @ X453 )
& ! [X454: $i] :
( ( X450 @ X454 )
=> ( X453 = X454 ) ) ) )
=> ( ! [X455: $i,X456: $i] :
( ( X455 = X456 )
=> ! [X457: $i,X458: $i] :
( ( X457 = X458 )
=> ( ( in @ X457 @ X455 )
=> ( in @ X458 @ X456 ) ) ) )
=> ( ! [X459: $i,X460: $i] :
( ( X459 = X460 )
=> ! [X461: $i,X462: $i] :
( ( X461 = X462 )
=> ( ( in @ X461 @ X459 )
<=> ( in @ X462 @ X460 ) ) ) )
=> ( ! [X463: $i > $o] :
( ? [X464: $i] :
( ( X463 @ X464 )
& ! [X465: $i] :
( ( X463 @ X465 )
=> ( X464 = X465 ) ) )
=> ! [X466: $i,X467: $i] :
( ( X463 @ X466 )
=> ( ( X463 @ X467 )
=> ( X466 = X467 ) ) ) )
=> ( ! [X468: $i > $o,X469: $i > $o] :
( ! [X470: $i,X471: $i] :
( ( X470 = X471 )
=> ( ( X468 @ X470 )
<=> ( X469 @ X471 ) ) )
=> ( ? [X472: $i] :
( ( X468 @ X472 )
& ! [X473: $i] :
( ( X468 @ X473 )
=> ( X472 = X473 ) ) )
<=> ? [X474: $i] :
( ( X469 @ X474 )
& ! [X475: $i] :
( ( X469 @ X475 )
=> ( X474 = X475 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X476: $i,X477: $i] :
( ( X476 = X477 )
=> ! [X478: $i,X479: $i] :
( ( X478 = X479 )
=> ( ( setadjoin @ X476 @ X478 )
= ( setadjoin @ X477 @ X479 ) ) ) )
=> ( ! [X480: $i,X481: $i] :
( ( X480 = X481 )
=> ( ( powerset @ X480 )
= ( powerset @ X481 ) ) )
=> ( ! [X482: $i,X483: $i] :
( ( X482 = X483 )
=> ( ( setunion @ X482 )
= ( setunion @ X483 ) ) )
=> ( ( omega = omega )
=> ( ! [X484: $i > $o] :
( ? [X485: $i] :
( ( X484 @ X485 )
& ! [X486: $i] :
( ( X484 @ X486 )
=> ( X485 = X486 ) ) )
=> ! [X487: $i,X488: $i] :
( ( X484 @ X487 )
=> ( ( X484 @ X488 )
=> ( X487 = X488 ) ) ) )
=> ( ! [X489: $i > $o,X490: $i > $o] :
( ! [X491: $i,X492: $i] :
( ( X491 = X492 )
=> ( ( X489 @ X491 )
<=> ( X490 @ X492 ) ) )
=> ( ? [X493: $i] :
( ( X489 @ X493 )
& ! [X494: $i] :
( ( X489 @ X494 )
=> ( X493 = X494 ) ) )
=> ( ? [X495: $i] :
( ( X490 @ X495 )
& ! [X496: $i] :
( ( X490 @ X496 )
=> ( X495 = X496 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X489 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X490 @ Z0 ) ) ) ) ) )
=> ( ! [X497: $i,X498: $i] :
( ( X497 = X498 )
=> ! [X499: $i > $o,X500: $i > $o] :
( ! [X501: $i] :
( ( in @ X501 @ X497 )
=> ! [X502: $i] :
( ( in @ X502 @ X498 )
=> ( ( X501 = X502 )
=> ( ( X499 @ X501 )
<=> ( X500 @ X502 ) ) ) ) )
=> ( ( dsetconstr @ X497
@ ^ [Z0: $i] : ( X499 @ Z0 ) )
= ( dsetconstr @ X498
@ ^ [Z0: $i] : ( X500 @ Z0 ) ) ) ) )
=> ( ! [X503: $i,X504: $i] :
( ! [X505: $i] :
( ( in @ X505 @ X503 )
=> ( in @ X505 @ X504 ) )
=> ! [X506: $i] :
( ( in @ X506 @ X503 )
=> ( in @ X506 @ X504 ) ) )
=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X507: $i] :
( ( in @ X507 @ X5 )
=> ( in @ X507 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[eqimpsubset2]),setadjoinOr]),c_0_87]),c_0_95]),noeltsimpempty]),inCongP]),in__Cong]),c_0_96]),c_0_97]),c_0_98]),emptyset__Cong]),c_0_99]),setadjoin__Cong]),powerset__Cong]),c_0_100]),setunion__Cong]),omega__Cong]),c_0_101]),c_0_102]),c_0_103]),setadjoinIL]),c_0_104]),c_0_105]),emptyinunitempty]),setadjoinIR]),setadjoinE]),c_0_106]),c_0_107]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_108]),c_0_109]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_110]),c_0_111]),emptyI]),setext]),c_0_112]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_113]),c_0_114]),c_0_115]),c_0_116]),c_0_117]),wellorderingAx]),foundationAx]),c_0_118]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_119]) ).
thf(c_0_121,negated_conjecture,
! [X508: $i,X509: $i,X511: $i,X512: $i,X513: $i,X514: $i,X515: $i,X516: $i,X517: $i,X518: $i,X519: $i,X521: $i,X522: $i,X524: $i,X525: $i,X526: $i,X527: $i,X528: $i,X530: $i,X531: $i > $i > $o,X532: $i,X534: $i,X537: $i,X539: $i,X540: $i,X541: $i,X542: $i,X544: $i,X545: $i > $o,X546: $i,X548: $i,X549: $i > $o,X550: $i,X551: $i,X552: $i > $o,X553: $i,X554: $i,X555: $i > $o,X556: $i,X557: $i > $o,X558: $i,X561: $i,X562: $o,X563: $i,X564: $i,X565: $o,X566: $i,X567: $i,X568: $i > $o,X569: $i,X572: $i,X573: $i,X576: $i,X578: $i,X580: $i,X581: $i > $o,X582: $i,X583: $i,X585: $i,X586: $i > $o,X587: $i,X588: $i,X589: $i,X590: $i,X591: $i,X592: $i,X593: $i,X594: $i,X595: $i,X596: $i,X597: $i,X598: $o,X599: $i,X600: $i,X601: $i,X602: $i,X603: $i,X604: $i,X606: $i,X607: $i,X608: $i,X609: $i,X610: $i,X611: $i,X612: $i,X613: $i,X614: $i,X615: $i,X616: $o,X618: $i,X619: $i,X620: $i > $o,X621: $i,X624: $i,X625: $i,X626: $i,X628: $i,X629: $i,X630: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X641: $i,X642: $i,X643: $i,X644: $i > $o,X645: $i,X646: $i > $o,X647: $i,X648: $i,X649: $i > $o,X650: $i,X652: $i,X653: $i > $o,X655: $i,X656: $i,X657: $i > $o,X659: $i,X660: $i,X661: $i > $o,X662: $i,X664: $o,X665: $i,X666: $i > $o,X668: $i,X669: $i,X670: $i > $o,X671: $i,X673: $i > $o,X674: $i,X677: $i,X678: $i > $o,X679: $i,X683: $i,X684: $i > $o,X685: $i,X688: $i,X689: $i,X690: $i,X691: $i,X692: $i,X693: $i,X694: $i,X695: $i,X696: $i,X697: $i > $o,X698: $i,X700: $i,X701: $i,X702: $i > $o,X703: $i > $o,X706: $i,X709: $i,X710: $i,X713: $i,X714: $i,X715: $i,X716: $i,X717: $i,X718: $i,X719: $i,X720: $i,X721: $i,X722: $i > $o,X723: $i,X725: $i,X726: $i,X727: $i > $o,X728: $i > $o,X731: $i,X733: $i,X735: $i,X736: $i,X737: $i > $o,X738: $i > $o,X741: $i,X742: $i,X744: $i] :
( ( ~ ( in @ ( esk1_2 @ X508 @ X509 ) @ X508 )
| ~ ( in @ ( esk1_2 @ X508 @ X509 ) @ X509 )
| ( X508 = X509 ) )
& ( ( in @ ( esk1_2 @ X508 @ X509 ) @ X508 )
| ( in @ ( esk1_2 @ X508 @ X509 ) @ X509 )
| ( X508 = X509 ) )
& ~ ( in @ X511 @ emptyset )
& ( ~ ( in @ X514 @ ( setadjoin @ X512 @ X513 ) )
| ( X514 = X512 )
| ( in @ X514 @ X513 ) )
& ( ( X514 != X512 )
| ( in @ X514 @ ( setadjoin @ X512 @ X513 ) ) )
& ( ~ ( in @ X514 @ X513 )
| ( in @ X514 @ ( setadjoin @ X512 @ X513 ) ) )
& ( ~ ( in @ X516 @ ( powerset @ X515 ) )
| ~ ( in @ X517 @ X516 )
| ( in @ X517 @ X515 ) )
& ( ( in @ ( esk2_2 @ X518 @ X519 ) @ X519 )
| ( in @ X519 @ ( powerset @ X518 ) ) )
& ( ~ ( in @ ( esk2_2 @ X518 @ X519 ) @ X518 )
| ( in @ X519 @ ( powerset @ X518 ) ) )
& ( ( in @ X522 @ ( esk3_2 @ X521 @ X522 ) )
| ~ ( in @ X522 @ ( setunion @ X521 ) ) )
& ( ( in @ ( esk3_2 @ X521 @ X522 ) @ X521 )
| ~ ( in @ X522 @ ( setunion @ X521 ) ) )
& ( ~ ( in @ X525 @ X526 )
| ~ ( in @ X526 @ X524 )
| ( in @ X525 @ ( setunion @ X524 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X527 @ omega )
| ( in @ ( setadjoin @ X527 @ X527 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X528 ) @ omega )
| ~ ( in @ emptyset @ X528 )
| ~ ( in @ X530 @ omega )
| ( in @ X530 @ X528 ) )
& ( ( in @ ( esk4_1 @ X528 ) @ X528 )
| ~ ( in @ emptyset @ X528 )
| ~ ( in @ X530 @ omega )
| ( in @ X530 @ X528 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X528 ) @ ( esk4_1 @ X528 ) ) @ X528 )
| ~ ( in @ emptyset @ X528 )
| ~ ( in @ X530 @ omega )
| ( in @ X530 @ X528 ) )
& ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
& ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
& ( ~ ( in @ X540 @ X532 )
| ~ ( X531 @ X540 @ X539 )
| ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
| ( in @ ( esk5_2 @ X531 @ X532 ) @ X532 ) )
& ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ~ ( in @ X540 @ X532 )
| ~ ( X531 @ X540 @ X539 )
| ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
| ( X531 @ ( esk5_2 @ X531 @ X532 ) @ ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ( in @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X532 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( X534
!= ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ( X531 @ ( esk8_3 @ X531 @ X532 @ X537 ) @ X537 )
| ~ ( in @ X537 @ ( esk7_2 @ X531 @ X532 ) )
| ( X534
!= ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ~ ( in @ X540 @ X532 )
| ~ ( X531 @ X540 @ X539 )
| ( in @ X539 @ ( esk7_2 @ X531 @ X532 ) )
| ( X534
!= ( esk6_3 @ X531 @ X532 @ X534 ) )
| ~ ( X531 @ ( esk5_2 @ X531 @ X532 ) @ X534 ) )
& ( ( in @ ( esk9_1 @ X541 ) @ X541 )
| ~ ( in @ X542 @ X541 ) )
& ( ~ ( in @ X544 @ ( esk9_1 @ X541 ) )
| ~ ( in @ X544 @ X541 )
| ~ ( in @ X542 @ X541 ) )
& epred1_0
& ( ( X545 @ ( esk10_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 )
| ( X545
@ ( descr
@ ^ [Z0: $i] : ( X545 @ Z0 ) ) ) )
& ( ( X546
!= ( esk10_2 @ X545 @ X546 ) )
| ~ ( X545 @ X546 )
| ( X545
@ ( descr
@ ^ [Z0: $i] : ( X545 @ Z0 ) ) ) )
& ( ~ ( in @ X550 @ X548 )
| ~ ( X549 @ X550 )
| ( in @ X550
@ ( dsetconstr @ X548
@ ^ [Z0: $i] : ( X549 @ Z0 ) ) ) )
& ( ~ ( in @ X553
@ ( dsetconstr @ X551
@ ^ [Z0: $i] : ( X552 @ Z0 ) ) )
| ( in @ X553 @ X551 ) )
& ( ~ ( in @ X556
@ ( dsetconstr @ X554
@ ^ [Z0: $i] : ( X555 @ Z0 ) ) )
| ( X555 @ X556 ) )
& ( ( X557 @ ( esk12_1 @ X557 ) )
| ( X557 @ ( esk11_2 @ X557 @ X558 ) )
| ~ ( X557 @ X558 ) )
& ( ~ ( X557 @ X561 )
| ( ( esk12_1 @ X557 )
= X561 )
| ( X557 @ ( esk11_2 @ X557 @ X558 ) )
| ~ ( X557 @ X558 ) )
& ( ( X557 @ ( esk12_1 @ X557 ) )
| ( X558
!= ( esk11_2 @ X557 @ X558 ) )
| ~ ( X557 @ X558 ) )
& ( ~ ( X557 @ X561 )
| ( ( esk12_1 @ X557 )
= X561 )
| ( X558
!= ( esk11_2 @ X557 @ X558 ) )
| ~ ( X557 @ X558 ) )
& ( ~ ( in @ X563 @ ( prop2set @ X562 ) )
| X562 )
& ( ~ ( in @ X564 @ emptyset )
| X565 )
& ~ ( in @ X566 @ emptyset )
& ~ ( in @ X567 @ emptyset )
& ( ( X568 @ ( esk13_2 @ X568 @ X569 ) )
| ~ ( X568 @ X569 )
| ( X568 @ ( esk14_1 @ X568 ) ) )
& ( ( X569
!= ( esk13_2 @ X568 @ X569 ) )
| ~ ( X568 @ X569 )
| ( X568 @ ( esk14_1 @ X568 ) ) )
& ( ( in @ ( esk16_2 @ X572 @ X573 ) @ X573 )
| ( X572 = X573 )
| ( in @ ( esk15_2 @ X572 @ X573 ) @ X572 ) )
& ( ~ ( in @ ( esk16_2 @ X572 @ X573 ) @ X572 )
| ( X572 = X573 )
| ( in @ ( esk15_2 @ X572 @ X573 ) @ X572 ) )
& ( ( in @ ( esk16_2 @ X572 @ X573 ) @ X573 )
| ( X572 = X573 )
| ~ ( in @ ( esk15_2 @ X572 @ X573 ) @ X573 ) )
& ( ~ ( in @ ( esk16_2 @ X572 @ X573 ) @ X572 )
| ( X572 = X573 )
| ~ ( in @ ( esk15_2 @ X572 @ X573 ) @ X573 ) )
& ( ( in @ ( esk17_1 @ X576 ) @ X576 )
| ( X576 = emptyset ) )
& ( ( in @ ( esk18_1 @ X578 ) @ X578 )
| ( X578 = emptyset ) )
& ( ~ ( in @ X582
@ ( dsetconstr @ X580
@ ^ [Z0: $i] : ( X581 @ Z0 ) ) )
| ( X581 @ X582 )
| ~ ( in @ X582 @ X580 ) )
& ( ~ ( X581 @ X582 )
| ( in @ X582
@ ( dsetconstr @ X580
@ ^ [Z0: $i] : ( X581 @ Z0 ) ) )
| ~ ( in @ X582 @ X580 ) )
& ( ( X583 = emptyset )
| ( in @ ( esk19_1 @ X583 ) @ X583 ) )
& ( ~ ( in @ X587 @ X585 )
| ~ ( X586 @ X587 )
| ( ( dsetconstr @ X585
@ ^ [Z0: $i] : ( X586 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X589 @ X588 )
| ( X588 != emptyset ) )
& ( in @ X590 @ ( setadjoin @ X590 @ X591 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X594 @ X593 )
| ( in @ X594 @ ( setadjoin @ X592 @ X593 ) ) )
& ( ( in @ X597 @ X596 )
| X598
| ( X597 = X595 )
| ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
& ( ~ X598
| X598
| ( X597 = X595 )
| ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
& ( ( in @ X597 @ X596 )
| X598
| ~ X598
| ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
& ( ~ X598
| X598
| ~ X598
| ~ ( in @ X597 @ ( setadjoin @ X595 @ X596 ) ) )
& ( ~ ( in @ X601 @ ( setadjoin @ X599 @ X600 ) )
| ( X601 = X599 )
| ( in @ X601 @ X600 ) )
& ( ( dsetconstr @ X602
@ ^ [Z0: $i] : $true )
= X602 )
& ( ( in @ ( esk20_2 @ X603 @ X604 ) @ X604 )
| ( in @ X604 @ ( powerset @ X603 ) ) )
& ( ~ ( in @ ( esk20_2 @ X603 @ X604 ) @ X603 )
| ( in @ X604 @ ( powerset @ X603 ) ) )
& ( in @ emptyset @ ( powerset @ X606 ) )
& ( in @ emptyset @ ( powerset @ X607 ) )
& ( ~ ( in @ X609 @ ( powerset @ X608 ) )
| ~ ( in @ X610 @ X609 )
| ( in @ X610 @ X608 ) )
& ( ~ ( in @ X612 @ X613 )
| ~ ( in @ X613 @ X611 )
| ( in @ X612 @ ( setunion @ X611 ) ) )
& ( ( in @ X615 @ ( esk21_3 @ X614 @ X615 @ X616 ) )
| X616
| ~ ( in @ X615 @ ( setunion @ X614 ) ) )
& ( ( in @ ( esk21_3 @ X614 @ X615 @ X616 ) @ X614 )
| X616
| ~ ( in @ X615 @ ( setunion @ X614 ) ) )
& ( ~ X616
| X616
| ~ ( in @ X615 @ ( setunion @ X614 ) ) )
& ( ~ ( in @ X619 @ X618 )
| ( in @ X619 @ ( powerset @ ( setunion @ X618 ) ) ) )
& ( ~ ( X620 @ X624 )
| ( X624
= ( esk23_1 @ X620 ) )
| ( X620 @ ( esk22_2 @ X620 @ X621 ) )
| ~ ( X620 @ X621 ) )
& ( ( X625
!= ( esk23_1 @ X620 ) )
| ( X620 @ X625 )
| ( X620 @ ( esk22_2 @ X620 @ X621 ) )
| ~ ( X620 @ X621 ) )
& ( ~ ( X620 @ X624 )
| ( X624
= ( esk23_1 @ X620 ) )
| ( X621
!= ( esk22_2 @ X620 @ X621 ) )
| ~ ( X620 @ X621 ) )
& ( ( X625
!= ( esk23_1 @ X620 ) )
| ( X620 @ X625 )
| ( X621
!= ( esk22_2 @ X620 @ X621 ) )
| ~ ( X620 @ X621 ) )
& ( ( X626 = emptyset )
| ( in @ ( esk24_1 @ X626 ) @ X626 ) )
& ( ~ ( in @ X628 @ ( setadjoin @ X629 @ emptyset ) )
| ( X628 = X629 ) )
& ( ( X630 = X631 )
| ~ ( in @ X631 @ ( setadjoin @ X630 @ emptyset ) ) )
& ( ( X632 != X633 )
| ( in @ X632 @ ( setadjoin @ X633 @ emptyset ) ) )
& ( ~ ( in @ X634 @ ( setadjoin @ X635 @ emptyset ) )
| ( in @ X635 @ ( setadjoin @ X634 @ emptyset ) ) )
& ( ~ ( in @ X638 @ ( setadjoin @ X636 @ ( setadjoin @ X637 @ emptyset ) ) )
| ( X638 = X636 )
| ( X638 = X637 ) )
& ( in @ X639 @ ( setadjoin @ X639 @ ( setadjoin @ X640 @ emptyset ) ) )
& ( in @ X642 @ ( setadjoin @ X641 @ ( setadjoin @ X642 @ emptyset ) ) )
& ( ~ ( in @ X645 @ X643 )
| ~ ( X644 @ X645 )
| ( ( dsetconstr @ X643
@ ^ [Z0: $i] : ( X644 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X647 @ emptyset )
| ( X646 @ X647 ) )
& ( ( in @ ( esk25_2 @ X648 @ X649 ) @ X648 )
| ~ ( in @ X650 @ X648 )
| ( X649 @ X650 ) )
& ( ~ ( X649 @ ( esk25_2 @ X648 @ X649 ) )
| ~ ( in @ X650 @ X648 )
| ( X649 @ X650 ) )
& ( ( in @ ( esk26_2 @ X652 @ X653 ) @ X652 )
| ~ ( in @ X655 @ X652 )
| ~ ( X653 @ X655 ) )
& ( ( X653 @ ( esk26_2 @ X652 @ X653 ) )
| ~ ( in @ X655 @ X652 )
| ~ ( X653 @ X655 ) )
& ( ( in @ ( esk27_2 @ X656 @ X657 ) @ X656 )
| ~ ( in @ X659 @ X656 )
| ~ ( X657 @ X659 ) )
& ( ( X657 @ ( esk27_2 @ X656 @ X657 ) )
| ~ ( in @ X659 @ X656 )
| ~ ( X657 @ X659 ) )
& ( ( in @ ( esk28_2 @ X660 @ X661 ) @ X660 )
| ~ ( in @ X662 @ X660 )
| ( X661 @ X662 ) )
& ( ~ ( X661 @ ( esk28_2 @ X660 @ X661 ) )
| ~ ( in @ X662 @ X660 )
| ( X661 @ X662 ) )
& ( ~ X664
| ( in @ emptyset @ ( prop2set @ X664 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X665 @ X666 ) @ X665 )
| ~ ( in @ X668 @ X665 )
| ~ ( X666 @ X668 ) )
& ( ( X666 @ ( esk29_2 @ X665 @ X666 ) )
| ~ ( in @ X668 @ X665 )
| ~ ( X666 @ X668 ) )
& ( ( in @ ( esk30_2 @ X669 @ X670 ) @ X669 )
| ~ ( in @ X671 @ X669 )
| ( X670 @ X671 ) )
& ( ~ ( X670 @ ( esk30_2 @ X669 @ X670 ) )
| ~ ( in @ X671 @ X669 )
| ( X670 @ X671 ) )
& ( ( X673 @ ( esk32_1 @ X673 ) )
| ( X673 @ ( esk31_2 @ X673 @ X674 ) )
| ~ ( X673 @ X674 ) )
& ( ~ ( X673 @ X677 )
| ( ( esk32_1 @ X673 )
= X677 )
| ( X673 @ ( esk31_2 @ X673 @ X674 ) )
| ~ ( X673 @ X674 ) )
& ( ( X673 @ ( esk32_1 @ X673 ) )
| ( X674
!= ( esk31_2 @ X673 @ X674 ) )
| ~ ( X673 @ X674 ) )
& ( ~ ( X673 @ X677 )
| ( ( esk32_1 @ X673 )
= X677 )
| ( X674
!= ( esk31_2 @ X673 @ X674 ) )
| ~ ( X673 @ X674 ) )
& ( ( X678 @ ( esk35_1 @ X678 ) )
| ( X678 @ ( esk33_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ~ ( X678 @ X683 )
| ( ( esk35_1 @ X678 )
= X683 )
| ( X678 @ ( esk33_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ( X678 @ ( esk35_1 @ X678 ) )
| ( X678 @ ( esk34_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ~ ( X678 @ X683 )
| ( ( esk35_1 @ X678 )
= X683 )
| ( X678 @ ( esk34_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ( X678 @ ( esk35_1 @ X678 ) )
| ( ( esk33_1 @ X678 )
!= ( esk34_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ~ ( X678 @ X683 )
| ( ( esk35_1 @ X678 )
= X683 )
| ( ( esk33_1 @ X678 )
!= ( esk34_1 @ X678 ) )
| ~ ( X678 @ X679 ) )
& ( ( X684 @ ( esk37_1 @ X684 ) )
| ~ ( X684 @ ( esk36_2 @ X684 @ X685 ) )
| ( ( esk36_2 @ X684 @ X685 )
!= X685 ) )
& ( ~ ( X684 @ X688 )
| ( ( esk37_1 @ X684 )
= X688 )
| ~ ( X684 @ ( esk36_2 @ X684 @ X685 ) )
| ( ( esk36_2 @ X684 @ X685 )
!= X685 ) )
& ( ( X684 @ ( esk37_1 @ X684 ) )
| ( X684 @ ( esk36_2 @ X684 @ X685 ) )
| ( ( esk36_2 @ X684 @ X685 )
= X685 ) )
& ( ~ ( X684 @ X688 )
| ( ( esk37_1 @ X684 )
= X688 )
| ( X684 @ ( esk36_2 @ X684 @ X685 ) )
| ( ( esk36_2 @ X684 @ X685 )
= X685 ) )
& ( ( X689 != X690 )
| ( X691 != X692 )
| ~ ( in @ X691 @ X689 )
| ( in @ X692 @ X690 ) )
& ( ~ ( in @ X695 @ X693 )
| ( in @ X696 @ X694 )
| ( X695 != X696 )
| ( X693 != X694 ) )
& ( ~ ( in @ X696 @ X694 )
| ( in @ X695 @ X693 )
| ( X695 != X696 )
| ( X693 != X694 ) )
& ( ( X697 @ ( esk38_2 @ X697 @ X698 ) )
| ~ ( X697 @ X698 )
| ~ ( X697 @ X700 )
| ~ ( X697 @ X701 )
| ( X700 = X701 ) )
& ( ( X698
!= ( esk38_2 @ X697 @ X698 ) )
| ~ ( X697 @ X698 )
| ~ ( X697 @ X700 )
| ~ ( X697 @ X701 )
| ( X700 = X701 ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( ( esk39_2 @ X702 @ X703 )
= ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ~ ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ~ ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X702 @ ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X703 @ ( esk42_2 @ X702 @ X703 ) )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X703 @ X709 )
| ( ( esk42_2 @ X702 @ X703 )
= X709 )
| ( X706
!= ( esk41_3 @ X702 @ X703 @ X706 ) )
| ~ ( X702 @ X706 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X703 @ ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ( X702 @ ( esk44_2 @ X702 @ X703 ) )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( ~ ( X702 @ X713 )
| ( ( esk44_2 @ X702 @ X703 )
= X713 )
| ( X710
!= ( esk43_3 @ X702 @ X703 @ X710 ) )
| ~ ( X703 @ X710 )
| ( X702 @ ( esk39_2 @ X702 @ X703 ) )
| ( X703 @ ( esk40_2 @ X702 @ X703 ) ) )
& ( emptyset = emptyset )
& ( ( X714 != X715 )
| ( X716 != X717 )
| ( ( setadjoin @ X714 @ X716 )
= ( setadjoin @ X715 @ X717 ) ) )
& ( ( X718 != X719 )
| ( ( powerset @ X718 )
= ( powerset @ X719 ) ) )
& ( ( X720 != X721 )
| ( ( setunion @ X720 )
= ( setunion @ X721 ) ) )
& ( omega = omega )
& ( ( X722 @ ( esk45_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 )
| ~ ( X722 @ X725 )
| ~ ( X722 @ X726 )
| ( X725 = X726 ) )
& ( ( X723
!= ( esk45_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 )
| ~ ( X722 @ X725 )
| ~ ( X722 @ X726 )
| ( X725 = X726 ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( ( esk46_2 @ X727 @ X728 )
= ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( ( esk46_2 @ X727 @ X728 )
= ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( ( esk46_2 @ X727 @ X728 )
= ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( ( esk46_2 @ X727 @ X728 )
= ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ~ ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ~ ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X727 @ ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X728 @ ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( X733
!= ( esk49_3 @ X727 @ X728 @ X733 ) )
| ~ ( X728 @ X733 )
| ( ( descr
@ ^ [Z0: $i] : ( X727 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X728 @ Z0 ) ) )
| ( X731
!= ( esk48_3 @ X727 @ X728 @ X731 ) )
| ~ ( X727 @ X731 )
| ( X727 @ ( esk46_2 @ X727 @ X728 ) )
| ( X728 @ ( esk47_2 @ X727 @ X728 ) ) )
& ( ( in @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) @ X735 )
| ( ( dsetconstr @ X735
@ ^ [Z0: $i] : ( X737 @ Z0 ) )
= ( dsetconstr @ X736
@ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
| ( X735 != X736 ) )
& ( ( in @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) @ X736 )
| ( ( dsetconstr @ X735
@ ^ [Z0: $i] : ( X737 @ Z0 ) )
= ( dsetconstr @ X736
@ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
| ( X735 != X736 ) )
& ( ( ( esk50_4 @ X735 @ X736 @ X737 @ X738 )
= ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
| ( ( dsetconstr @ X735
@ ^ [Z0: $i] : ( X737 @ Z0 ) )
= ( dsetconstr @ X736
@ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
| ( X735 != X736 ) )
& ( ~ ( X737 @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) )
| ~ ( X738 @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
| ( ( dsetconstr @ X735
@ ^ [Z0: $i] : ( X737 @ Z0 ) )
= ( dsetconstr @ X736
@ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
| ( X735 != X736 ) )
& ( ( X737 @ ( esk50_4 @ X735 @ X736 @ X737 @ X738 ) )
| ( X738 @ ( esk51_4 @ X735 @ X736 @ X737 @ X738 ) )
| ( ( dsetconstr @ X735
@ ^ [Z0: $i] : ( X737 @ Z0 ) )
= ( dsetconstr @ X736
@ ^ [Z0: $i] : ( X738 @ Z0 ) ) )
| ( X735 != X736 ) )
& ( ( in @ ( esk52_2 @ X741 @ X742 ) @ X741 )
| ~ ( in @ X744 @ X741 )
| ( in @ X744 @ X742 ) )
& ( ~ ( in @ ( esk52_2 @ X741 @ X742 ) @ X742 )
| ~ ( in @ X744 @ X741 )
| ( in @ X744 @ X742 ) )
& ( esk53_0 = esk54_0 )
& ( in @ esk55_0 @ esk54_0 )
& ~ ( in @ esk55_0 @ esk53_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])])])])]) ).
thf(c_0_122,negated_conjecture,
in @ esk55_0 @ esk54_0,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
thf(c_0_123,negated_conjecture,
esk53_0 = esk54_0,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
thf(c_0_124,negated_conjecture,
~ ( in @ esk55_0 @ esk53_0 ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
thf(c_0_125,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_124]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU560^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun May 19 17:41:37 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.17/0.45 Running higher-order theorem proving
% 0.17/0.45 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
% 0.35/300.10 # Version: 3.1.0-ho
% 0.35/300.10 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10 # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10 # Starting sh5l with 300s (1) cores
% 0.35/300.10 # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10 # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10 # new_bool_2 with pid 16939 completed with status 0
% 0.35/300.10 # Result found by new_bool_2
% 0.35/300.10 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10 # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10 # Starting sh5l with 300s (1) cores
% 0.35/300.10 # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10 # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.35/300.10 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.35/300.10 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/300.10 # Starting ho_unfolding_3 with 163s (1) cores
% 0.35/300.10 # ho_unfolding_3 with pid 16940 completed with status 0
% 0.35/300.10 # Result found by ho_unfolding_3
% 0.35/300.10 # Preprocessing class: HSMSSLSSLLLCHFA.
% 0.35/300.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/300.10 # Starting new_ho_10 with 1500s (5) cores
% 0.35/300.10 # Starting sh5l with 300s (1) cores
% 0.35/300.10 # Starting new_bool_1 with 300s (1) cores
% 0.35/300.10 # Starting new_bool_2 with 300s (1) cores
% 0.35/300.10 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.35/300.10 # Search class: HGHSM-FSLM31-SHFMMMBN
% 0.35/300.10 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.35/300.10 # Starting ho_unfolding_3 with 163s (1) cores
% 0.35/300.10 # Preprocessing time : 0.005 s
% 0.35/300.10 # Presaturation interreduction done
% 0.35/300.10
% 0.35/300.10 # Proof found!
% 0.35/300.10 # SZS status Theorem
% 0.35/300.10 # SZS output start CNFRefutation
% See solution above
% 0.35/300.10 # Parsed axioms : 171
% 0.35/300.10 # Removed by relevancy pruning/SinE : 92
% 0.35/300.10 # Initial clauses : 187
% 0.35/300.10 # Removed in clause preprocessing : 12
% 0.35/300.10 # Initial clauses in saturation : 175
% 0.35/300.10 # Processed clauses : 6
% 0.35/300.10 # ...of these trivial : 0
% 0.35/300.10 # ...subsumed : 0
% 0.35/300.10 # ...remaining for further processing : 5
% 0.35/300.10 # Other redundant clauses eliminated : 0
% 0.35/300.10 # Clauses deleted for lack of memory : 0
% 0.35/300.10 # Backward-subsumed : 0
% 0.35/300.10 # Backward-rewritten : 0
% 0.35/300.10 # Generated clauses : 0
% 0.35/300.10 # ...of the previous two non-redundant : 0
% 0.35/300.10 # ...aggressively subsumed : 0
% 0.35/300.10 # Contextual simplify-reflections : 0
% 0.35/300.10 # Paramodulations : 0
% 0.35/300.10 # Factorizations : 0
% 0.35/300.10 # NegExts : 0
% 0.35/300.10 # Equation resolutions : 0
% 0.35/300.10 # Disequality decompositions : 0
% 0.35/300.10 # Total rewrite steps : 1
% 0.35/300.10 # ...of those cached : 0
% 0.35/300.10 # Propositional unsat checks : 0
% 0.35/300.10 # Propositional check models : 0
% 0.35/300.10 # Propositional check unsatisfiable : 0
% 0.35/300.10 # Propositional clauses : 0
% 0.35/300.10 # Propositional clauses after purity: 0
% 0.35/300.10 # Propositional unsat core size : 0
% 0.35/300.10 # Propositional preprocessing time : 0.000
% 0.35/300.10 # Propositional encoding time : 0.000
% 0.35/300.10 # Propositional solver time : 0.000
% 0.35/300.10 # Success case prop preproc time : 0.000
% 0.35/300.10 # Success case prop encoding time : 0.000
% 0.35/300.10 # Success case prop solver time : 0.000
% 0.35/300.10 # Current number of processed clauses : 5
% 0.35/300.10 # Positive orientable unit clauses : 4
% 0.35/300.10 # Positive unorientable unit clauses: 0
% 0.35/300.10 # Negative unit clauses : 1
% 0.35/300.10 # Non-unit-clauses : 0
% 0.35/300.10 # Current number of unprocessed clauses: 169
% 0.35/300.10 # ...number of literals in the above : 615
% 0.35/300.10 # Current number of archived formulas : 0
% 0.35/300.10 # Current number of archived clauses : 0
% 0.35/300.10 # Clause-clause subsumption calls (NU) : 0
% 0.35/300.10 # Rec. Clause-clause subsumption calls : 0
% 0.35/300.10 # Non-unit clause-clause subsumptions : 0
% 0.35/300.10 # Unit Clause-clause subsumption calls : 0
% 0.35/300.10 # Rewrite failures with RHS unbound : 0
% 0.35/300.10 # BW rewrite match attempts : 0
% 0.35/300.10 # BW rewrite match successes : 0
% 0.35/300.10 # Condensation attempts : 6
% 0.35/300.10 # Condensation successes : 0
% 0.35/300.10 # Termbank termtop insertions : 21365
% 0.35/300.10 # Search garbage collected termcells : 7642
% 0.35/300.10
% 0.35/300.10 # -------------------------------------------------
% 0.35/300.10 # User time : 0.013 s
% 0.35/300.10 # System time : 0.010 s
% 0.35/300.10 # Total time : 0.023 s
% 0.35/300.10 # Maximum resident set size: 4288 pages
% 0.35/300.10
% 0.35/300.10 # -------------------------------------------------
% 0.35/300.10 # User time : 0.017 s
% 0.35/300.10 # System time : 0.013 s
% 0.35/300.10 # Total time : 0.030 s
% 0.35/300.10 # Maximum resident set size: 1920 pages
% 0.35/300.10 % E---3.1 exiting
% 0.35/300.10 % E exiting
%------------------------------------------------------------------------------