TSTP Solution File: SEU571^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU571^1 : 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 03:28:16 EDT 2024
% Result : Theorem 0.46s 0.90s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 245
% Syntax : Number of formulae : 292 ( 23 unt; 155 typ; 0 def)
% Number of atoms : 1113 ( 326 equ; 0 cnn)
% Maximal formula atoms : 341 ( 8 avg)
% Number of connectives : 4388 ( 403 ~; 451 |; 274 &;2568 @)
% ( 149 <=>; 543 =>; 0 <=; 0 <~>)
% Maximal formula depth : 399 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 305 ( 305 >; 0 *; 0 +; 0 <<)
% Number of symbols : 158 ( 155 usr; 94 con; 0-4 aty)
% Number of variables : 940 ( 63 ^ 773 !; 104 ?; 940 :)
% 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,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
epred1_0: $o ).
thf(decl_125,type,
esk1_2: $i > $i > $i ).
thf(decl_126,type,
esk2_2: $i > $i > $i ).
thf(decl_127,type,
esk3_2: $i > $i > $i ).
thf(decl_128,type,
esk4_1: $i > $i ).
thf(decl_129,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_130,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_131,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_132,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_133,type,
esk9_1: $i > $i ).
thf(decl_134,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_135,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_136,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_137,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_138,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_139,type,
esk15_2: $i > $i > $i ).
thf(decl_140,type,
esk16_2: $i > $i > $i ).
thf(decl_141,type,
esk17_1: $i > $i ).
thf(decl_142,type,
esk18_1: $i > $i ).
thf(decl_143,type,
esk19_1: $i > $i ).
thf(decl_144,type,
esk20_2: $i > $i > $i ).
thf(decl_145,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_146,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_147,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_148,type,
esk24_1: $i > $i ).
thf(decl_149,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_150,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_151,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_152,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_153,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_154,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_155,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_156,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_157,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_158,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_159,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_160,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_161,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_162,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_163,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_164,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_165,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_166,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_167,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_168,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_169,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_170,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_171,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_172,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_173,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_174,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_175,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_176,type,
esk52_2: $i > $i > $i ).
thf(decl_177,type,
esk53_2: $i > $i > $i ).
thf(decl_178,type,
esk54_0: $i ).
thf(decl_179,type,
esk55_0: $i ).
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(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(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(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
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(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
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(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(setadjoinSub,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/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(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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
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(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(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
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(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
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(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
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(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(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_89,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_90,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_91,plain,
( 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_92,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_93,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_94,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_95,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_96,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_97,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_98,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_99,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_100,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_101,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_102,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_103,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_104,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X283: $i] :
( ( X1 @ X283 )
& ! [X284: $i] :
( ( X1 @ X284 )
=> ( X283 = X284 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_89,c_0_90]) ).
thf(c_0_105,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X285: $i] :
( ( X1 @ X285 )
& ! [X286: $i] :
( ( X1 @ X286 )
=> ( X285 = X286 ) ) )
=> ( ? [X287: $i] :
( ( X17 @ X287 )
& ! [X288: $i] :
( ( X17 @ X288 )
=> ( X287 = X288 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_91,c_0_90]) ).
thf(c_0_106,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_92]) ).
thf(c_0_107,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_108,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_93,c_0_92]) ).
thf(c_0_109,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_92]) ).
thf(c_0_110,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_111,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X269: $i] :
( ( X1 @ X269 )
& ! [X270: $i] :
( ( X1 @ X270 )
=> ( X269 = X270 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_94,c_0_90]) ).
thf(c_0_112,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_92]) ).
thf(c_0_113,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_114,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X271: $i] :
( ( X1 @ X271 )
& ! [X272: $i] :
( ( X1 @ X272 )
=> ( X271 = X272 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_95,c_0_90]) ).
thf(c_0_115,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X273: $i] :
( ( X1 @ X273 )
& ! [X274: $i] :
( ( X1 @ X274 )
=> ( X273 = X274 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_96,c_0_90]) ).
thf(c_0_116,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X275: $i] :
( ( X1 @ X275 )
& ! [X276: $i] :
( ( X1 @ X276 )
=> ( X275 = X276 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_97,c_0_90]) ).
thf(c_0_117,plain,
( exuE3u
= ( ! [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_98,c_0_90]) ).
thf(c_0_118,plain,
( exu__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 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_99,c_0_90]) ).
thf(c_0_119,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_120,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X267: $i] :
( ( X1 @ X267 )
& ! [X268: $i] :
( ( X1 @ X268 )
=> ( X267 = X268 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_100,c_0_90]) ).
thf(c_0_121,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X265: $i] :
( ( X1 @ X265 )
& ! [X266: $i] :
( ( X1 @ X266 )
=> ( X265 = X266 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_101,c_0_90]) ).
thf(c_0_122,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_123,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_124,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_125,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X263: $i] :
( ( X1 @ X263 )
& ! [X264: $i] :
( ( X1 @ X264 )
=> ( X263 = X264 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_102,c_0_90]) ).
thf(c_0_126,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X261: $i] :
( ( X6 @ X2 @ X261 )
& ! [X262: $i] :
( ( X6 @ X2 @ X262 )
=> ( X261 = X262 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_103,c_0_90]) ).
thf(c_0_127,plain,
( epred1_0
<=> ! [X318: $i] :
? [X319: $i] :
( ! [X320: $i] :
( ( in @ X320 @ X319 )
=> ! [X321: $i] :
( ( in @ X321 @ X320 )
=> ( in @ X321 @ X318 ) ) )
& ! [X322: $i,X323: $i] :
( ( ( in @ X322 @ X318 )
& ( in @ X323 @ X318 ) )
=> ( ! [X324: $i] :
( ( in @ X324 @ X319 )
=> ( ( in @ X322 @ X324 )
<=> ( in @ X323 @ X324 ) ) )
=> ( X322 = X323 ) ) )
& ! [X325: $i,X326: $i] :
( ( ( in @ X325 @ X319 )
& ( in @ X326 @ X319 ) )
=> ( ! [X327: $i] :
( ( in @ X327 @ X325 )
=> ( in @ X327 @ X326 ) )
| ! [X328: $i] :
( ( in @ X328 @ X326 )
=> ( in @ X328 @ X325 ) ) ) )
& ! [X329: $i] :
( ( ! [X330: $i] :
( ( in @ X330 @ X329 )
=> ( in @ X330 @ X318 ) )
& ? [X331: $i] : ( in @ X331 @ X329 ) )
=> ? [X332: $i,X333: $i] :
( ( in @ X332 @ X319 )
& ( in @ X333 @ X329 )
& ~ ? [X334: $i] :
( ( in @ X334 @ X332 )
& ( in @ X334 @ X329 ) )
& ! [X335: $i] :
( ( in @ X335 @ X319 )
=> ( ! [X336: $i] :
( ( in @ X336 @ X335 )
=> ( in @ X336 @ X332 ) )
| ( in @ X333 @ X335 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_128,negated_conjecture,
~ ( ! [X289: $i,X290: $i] :
( ! [X291: $i] :
( ( in @ X291 @ X289 )
<=> ( in @ X291 @ X290 ) )
=> ( X289 = X290 ) )
=> ( ! [X292: $i] :
~ ( in @ X292 @ emptyset )
=> ( ! [X293: $i,X294: $i,X295: $i] :
( ( in @ X295 @ ( setadjoin @ X293 @ X294 ) )
<=> ( ( X295 = X293 )
| ( in @ X295 @ X294 ) ) )
=> ( ! [X296: $i,X297: $i] :
( ( in @ X297 @ ( powerset @ X296 ) )
<=> ! [X298: $i] :
( ( in @ X298 @ X297 )
=> ( in @ X298 @ X296 ) ) )
=> ( ! [X299: $i,X300: $i] :
( ( in @ X300 @ ( setunion @ X299 ) )
<=> ? [X301: $i] :
( ( in @ X300 @ X301 )
& ( in @ X301 @ X299 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X302: $i] :
( ( in @ X302 @ omega )
=> ( in @ ( setadjoin @ X302 @ X302 ) @ omega ) )
=> ( ! [X303: $i] :
( ( ( in @ emptyset @ X303 )
& ! [X304: $i] :
( ( ( in @ X304 @ omega )
& ( in @ X304 @ X303 ) )
=> ( in @ ( setadjoin @ X304 @ X304 ) @ X303 ) ) )
=> ! [X305: $i] :
( ( in @ X305 @ omega )
=> ( in @ X305 @ X303 ) ) )
=> ( ! [X306: $i > $i > $o,X307: $i] :
( ! [X308: $i] :
( ( in @ X308 @ X307 )
=> ? [X309: $i] :
( ( X306 @ X308 @ X309 )
& ! [X310: $i] :
( ( X306 @ X308 @ X310 )
=> ( X309 = X310 ) ) ) )
=> ? [X311: $i] :
! [X312: $i] :
( ( in @ X312 @ X311 )
<=> ? [X313: $i] :
( ( in @ X313 @ X307 )
& ( X306 @ X313 @ X312 ) ) ) )
=> ( ! [X314: $i] :
( ? [X315: $i] : ( in @ X315 @ X314 )
=> ? [X316: $i] :
( ( in @ X316 @ X314 )
& ~ ? [X317: $i] :
( ( in @ X317 @ X316 )
& ( in @ X317 @ X314 ) ) ) )
=> ( epred1_0
=> ( ! [X337: $i > $o] :
( ? [X338: $i] :
( ( X337 @ X338 )
& ! [X339: $i] :
( ( X337 @ X339 )
=> ( X338 = X339 ) ) )
=> ( X337
@ ( descr
@ ^ [Z0: $i] : ( X337 @ Z0 ) ) ) )
=> ( ! [X340: $i,X341: $i > $o,X342: $i] :
( ( in @ X342 @ X340 )
=> ( ( X341 @ X342 )
=> ( in @ X342 @ ( dsetconstr @ X340 @ X341 ) ) ) )
=> ( ! [X343: $i,X344: $i > $o,X345: $i] :
( ( in @ X345 @ ( dsetconstr @ X343 @ X344 ) )
=> ( in @ X345 @ X343 ) )
=> ( ! [X346: $i,X347: $i > $o,X348: $i] :
( ( in @ X348 @ ( dsetconstr @ X346 @ X347 ) )
=> ( X347 @ X348 ) )
=> ( ! [X349: $i > $o] :
( ? [X350: $i] :
( ( X349 @ X350 )
& ! [X351: $i] :
( ( X349 @ X351 )
=> ( X350 = X351 ) ) )
=> ? [X352: $i] :
( ( X349 @ X352 )
& ! [X353: $i] :
( ( X349 @ X353 )
=> ( X352 = X353 ) ) ) )
=> ( ! [X354: $o,X355: $i] :
( ( in @ X355 @ ( prop2set @ X354 ) )
=> X354 )
=> ( ! [X356: $i] :
( ( in @ X356 @ emptyset )
=> ! [X357: $o] : X357 )
=> ( ! [X358: $i] :
( ( in @ X358 @ emptyset )
=> ~ $true )
=> ( ! [X359: $i] :
~ ( in @ X359 @ emptyset )
=> ( ! [X360: $i > $o] :
( ? [X361: $i] :
( ( X360 @ X361 )
& ! [X362: $i] :
( ( X360 @ X362 )
=> ( X361 = X362 ) ) )
=> ? [X363: $i] : ( X360 @ X363 ) )
=> ( ! [X364: $i,X365: $i] :
( ! [X366: $i] :
( ( in @ X366 @ X364 )
=> ( in @ X366 @ X365 ) )
=> ( ! [X367: $i] :
( ( in @ X367 @ X365 )
=> ( in @ X367 @ X364 ) )
=> ( X364 = X365 ) ) )
=> ( ! [X368: $i] :
( ! [X369: $i] :
~ ( in @ X369 @ X368 )
=> ( X368 = emptyset ) )
=> ( ! [X370: $i] :
( ! [X371: $i] :
~ ( in @ X371 @ X370 )
=> ( X370 = emptyset ) )
=> ( ! [X372: $i,X373: $i > $o,X374: $i] :
( ( in @ X374 @ X372 )
=> ( ( in @ X374 @ ( dsetconstr @ X372 @ X373 ) )
<=> ( X373 @ X374 ) ) )
=> ( ! [X375: $i] :
( ( X375 != emptyset )
=> ? [X376: $i] : ( in @ X376 @ X375 ) )
=> ( ! [X377: $i,X378: $i > $o,X379: $i] :
( ( in @ X379 @ X377 )
=> ( ( X378 @ X379 )
=> ( ( dsetconstr @ X377 @ X378 )
!= emptyset ) ) )
=> ( ! [X380: $i] :
( ? [X381: $i] : ( in @ X381 @ X380 )
=> ( X380 != emptyset ) )
=> ( ! [X382: $i,X383: $i] : ( in @ X382 @ ( setadjoin @ X382 @ X383 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X384: $i,X385: $i,X386: $i] :
( ( in @ X386 @ X385 )
=> ( in @ X386 @ ( setadjoin @ X384 @ X385 ) ) )
=> ( ! [X387: $i,X388: $i,X389: $i] :
( ( in @ X389 @ ( setadjoin @ X387 @ X388 ) )
=> ! [X390: $o] :
( ( ( X389 = X387 )
=> X390 )
=> ( ( ( in @ X389 @ X388 )
=> X390 )
=> X390 ) ) )
=> ( ! [X391: $i,X392: $i,X393: $i] :
( ( in @ X393 @ ( setadjoin @ X391 @ X392 ) )
=> ( ( X393 = X391 )
| ( in @ X393 @ X392 ) ) )
=> ( ! [X394: $i] :
( ( dsetconstr @ X394
@ ^ [Z0: $i] : $true )
= X394 )
=> ( ! [X395: $i,X396: $i] :
( ! [X397: $i] :
( ( in @ X397 @ X396 )
=> ( in @ X397 @ X395 ) )
=> ( in @ X396 @ ( powerset @ X395 ) ) )
=> ( ! [X398: $i] : ( in @ emptyset @ ( powerset @ X398 ) )
=> ( ! [X399: $i] : ( in @ emptyset @ ( powerset @ X399 ) )
=> ( ! [X400: $i,X401: $i,X402: $i] :
( ( in @ X401 @ ( powerset @ X400 ) )
=> ( ( in @ X402 @ X401 )
=> ( in @ X402 @ X400 ) ) )
=> ( ! [X403: $i,X404: $i,X405: $i] :
( ( in @ X404 @ X405 )
=> ( ( in @ X405 @ X403 )
=> ( in @ X404 @ ( setunion @ X403 ) ) ) )
=> ( ! [X406: $i,X407: $i] :
( ( in @ X407 @ ( setunion @ X406 ) )
=> ! [X408: $o] :
( ! [X409: $i] :
( ( in @ X407 @ X409 )
=> ( ( in @ X409 @ X406 )
=> X408 ) )
=> X408 ) )
=> ( ! [X410: $i,X411: $i] :
( ( in @ X411 @ X410 )
=> ( in @ X411 @ ( powerset @ ( setunion @ X410 ) ) ) )
=> ( ! [X412: $i > $o] :
( ? [X413: $i] :
( ( X412 @ X413 )
& ! [X414: $i] :
( ( X412 @ X414 )
=> ( X413 = X414 ) ) )
=> ? [X415: $i] :
! [X416: $i] :
( ( X412 @ X416 )
<=> ( X416 = X415 ) ) )
=> ( ! [X417: $i] :
( ( X417 != emptyset )
=> ? [X418: $i] :
( ( in @ X418 @ X417 )
& $true ) )
=> ( ! [X419: $i,X420: $i] :
( ( in @ X419 @ ( setadjoin @ X420 @ emptyset ) )
=> ( X419 = X420 ) )
=> ( ! [X421: $i,X422: $i] :
( ( X421 != X422 )
=> ~ ( in @ X422 @ ( setadjoin @ X421 @ emptyset ) ) )
=> ( ! [X423: $i,X424: $i] :
( ( X423 = X424 )
=> ( in @ X423 @ ( setadjoin @ X424 @ emptyset ) ) )
=> ( ! [X425: $i,X426: $i] :
( ( in @ X425 @ ( setadjoin @ X426 @ emptyset ) )
=> ( in @ X426 @ ( setadjoin @ X425 @ emptyset ) ) )
=> ( ! [X427: $i,X428: $i,X429: $i] :
( ( in @ X429 @ ( setadjoin @ X427 @ ( setadjoin @ X428 @ emptyset ) ) )
=> ( ( X429 = X427 )
| ( X429 = X428 ) ) )
=> ( ! [X430: $i,X431: $i] : ( in @ X430 @ ( setadjoin @ X430 @ ( setadjoin @ X431 @ emptyset ) ) )
=> ( ! [X432: $i,X433: $i] : ( in @ X433 @ ( setadjoin @ X432 @ ( setadjoin @ X433 @ emptyset ) ) )
=> ( ! [X434: $i,X435: $i > $o] :
( ? [X436: $i] :
( ( in @ X436 @ X434 )
& ( X435 @ X436 ) )
=> ( ( ( dsetconstr @ X434 @ X435 )
= emptyset )
=> ~ $true ) )
=> ( ! [X437: $i > $o,X438: $i] :
( ( in @ X438 @ emptyset )
=> ( X437 @ X438 ) )
=> ( ! [X439: $i,X440: $i > $o] :
( ~ ! [X441: $i] :
( ( in @ X441 @ X439 )
=> ( X440 @ X441 ) )
=> ? [X442: $i] :
( ( in @ X442 @ X439 )
& ~ ( X440 @ X442 ) ) )
=> ( ! [X443: $i,X444: $i > $o] :
( ! [X445: $i] :
( ( in @ X445 @ X443 )
=> ~ ( X444 @ X445 ) )
=> ~ ? [X446: $i] :
( ( in @ X446 @ X443 )
& ( X444 @ X446 ) ) )
=> ( ! [X447: $i,X448: $i > $o] :
( ~ ? [X449: $i] :
( ( in @ X449 @ X447 )
& ( X448 @ X449 ) )
=> ! [X450: $i] :
( ( in @ X450 @ X447 )
=> ~ ( X448 @ X450 ) ) )
=> ( ! [X451: $i,X452: $i > $o] :
( ? [X453: $i] :
( ( in @ X453 @ X451 )
& ~ ( X452 @ X453 ) )
=> ~ ! [X454: $i] :
( ( in @ X454 @ X451 )
=> ( X452 @ X454 ) ) )
=> ( ! [X455: $o] :
( X455
=> ( in @ emptyset @ ( prop2set @ X455 ) ) )
=> ( prop2set2propI
=> ( ! [X456: $i,X457: $i > $o] :
( ~ ? [X458: $i] :
( ( in @ X458 @ X456 )
& ( X457 @ X458 ) )
=> ! [X459: $i] :
( ( in @ X459 @ X456 )
=> ~ ( X457 @ X459 ) ) )
=> ( ! [X460: $i,X461: $i > $o] :
( ~ ! [X462: $i] :
( ( in @ X462 @ X460 )
=> ( X461 @ X462 ) )
=> ? [X463: $i] :
( ( in @ X463 @ X460 )
& ~ ( X461 @ X463 ) ) )
=> ( ! [X464: $i > $o] :
( ? [X465: $i] :
( ( X464 @ X465 )
& ! [X466: $i] :
( ( X464 @ X466 )
=> ( X465 = X466 ) ) )
=> ? [X467: $i] :
( ( X464 @ X467 )
& ! [X468: $i] :
( ( X464 @ X468 )
=> ( X467 = X468 ) ) ) )
=> ( ! [X469: $i > $o] :
( ? [X470: $i] : ( X469 @ X470 )
=> ( ! [X471: $i,X472: $i] :
( ( X469 @ X471 )
=> ( ( X469 @ X472 )
=> ( X471 = X472 ) ) )
=> ? [X473: $i] :
( ( X469 @ X473 )
& ! [X474: $i] :
( ( X469 @ X474 )
=> ( X473 = X474 ) ) ) ) )
=> ( ! [X475: $i > $o] :
( ? [X476: $i] :
! [X477: $i] :
( ( X475 @ X477 )
<=> ( X477 = X476 ) )
=> ? [X478: $i] :
( ( X475 @ X478 )
& ! [X479: $i] :
( ( X475 @ X479 )
=> ( X478 = X479 ) ) ) )
=> ( ! [X480: $i,X481: $i] :
( ( X480 = X481 )
=> ! [X482: $i,X483: $i] :
( ( X482 = X483 )
=> ( ( in @ X482 @ X480 )
=> ( in @ X483 @ X481 ) ) ) )
=> ( ! [X484: $i,X485: $i] :
( ( X484 = X485 )
=> ! [X486: $i,X487: $i] :
( ( X486 = X487 )
=> ( ( in @ X486 @ X484 )
<=> ( in @ X487 @ X485 ) ) ) )
=> ( ! [X488: $i > $o] :
( ? [X489: $i] :
( ( X488 @ X489 )
& ! [X490: $i] :
( ( X488 @ X490 )
=> ( X489 = X490 ) ) )
=> ! [X491: $i,X492: $i] :
( ( X488 @ X491 )
=> ( ( X488 @ X492 )
=> ( X491 = X492 ) ) ) )
=> ( ! [X493: $i > $o,X494: $i > $o] :
( ! [X495: $i,X496: $i] :
( ( X495 = X496 )
=> ( ( X493 @ X495 )
<=> ( X494 @ X496 ) ) )
=> ( ? [X497: $i] :
( ( X493 @ X497 )
& ! [X498: $i] :
( ( X493 @ X498 )
=> ( X497 = X498 ) ) )
<=> ? [X499: $i] :
( ( X494 @ X499 )
& ! [X500: $i] :
( ( X494 @ X500 )
=> ( X499 = X500 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X501: $i,X502: $i] :
( ( X501 = X502 )
=> ! [X503: $i,X504: $i] :
( ( X503 = X504 )
=> ( ( setadjoin @ X501 @ X503 )
= ( setadjoin @ X502 @ X504 ) ) ) )
=> ( ! [X505: $i,X506: $i] :
( ( X505 = X506 )
=> ( ( powerset @ X505 )
= ( powerset @ X506 ) ) )
=> ( ! [X507: $i,X508: $i] :
( ( X507 = X508 )
=> ( ( setunion @ X507 )
= ( setunion @ X508 ) ) )
=> ( ( omega = omega )
=> ( ! [X509: $i > $o] :
( ? [X510: $i] :
( ( X509 @ X510 )
& ! [X511: $i] :
( ( X509 @ X511 )
=> ( X510 = X511 ) ) )
=> ! [X512: $i,X513: $i] :
( ( X509 @ X512 )
=> ( ( X509 @ X513 )
=> ( X512 = X513 ) ) ) )
=> ( ! [X514: $i > $o,X515: $i > $o] :
( ! [X516: $i,X517: $i] :
( ( X516 = X517 )
=> ( ( X514 @ X516 )
<=> ( X515 @ X517 ) ) )
=> ( ? [X518: $i] :
( ( X514 @ X518 )
& ! [X519: $i] :
( ( X514 @ X519 )
=> ( X518 = X519 ) ) )
=> ( ? [X520: $i] :
( ( X515 @ X520 )
& ! [X521: $i] :
( ( X515 @ X521 )
=> ( X520 = X521 ) ) )
=> ( ( descr @ X514 )
= ( descr @ X515 ) ) ) ) )
=> ( ! [X522: $i,X523: $i] :
( ( X522 = X523 )
=> ! [X524: $i > $o,X525: $i > $o] :
( ! [X526: $i] :
( ( in @ X526 @ X522 )
=> ! [X527: $i] :
( ( in @ X527 @ X523 )
=> ( ( X526 = X527 )
=> ( ( X524 @ X526 )
<=> ( X525 @ X527 ) ) ) ) )
=> ( ( dsetconstr @ X522 @ X524 )
= ( dsetconstr @ X523 @ X525 ) ) ) )
=> ( ! [X528: $i,X529: $i] :
( ! [X530: $i] :
( ( in @ X530 @ X528 )
=> ( in @ X530 @ X529 ) )
=> ( subset @ X528 @ X529 ) )
=> ( ! [X531: $i,X532: $i] :
( ( X531 = X532 )
=> ( subset @ X532 @ X531 ) )
=> ( ! [X533: $i,X534: $i] :
( ( X533 = X534 )
=> ( subset @ X533 @ X534 ) )
=> ( ! [X535: $i,X536: $i] :
( ! [X537: $i] :
( ( in @ X537 @ X535 )
=> ( in @ X537 @ X536 ) )
=> ( subset @ X535 @ X536 ) )
=> ( ! [X538: $i] : ( subset @ emptyset @ X538 )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( subset @ X539 @ X540 )
=> ( ( in @ X541 @ X539 )
=> ( in @ X541 @ X540 ) ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( subset @ X542 @ X543 )
=> ( ~ ( in @ X544 @ X543 )
=> ~ ( in @ X544 @ X542 ) ) )
=> ( ! [X545: $i,X546: $i,X547: $i] :
( ( in @ X547 @ X545 )
=> ( ~ ( in @ X547 @ X546 )
=> ~ ( subset @ X545 @ X546 ) ) )
=> ( ! [X548: $i,X549: $i] :
( ~ ( subset @ X548 @ X549 )
=> ( X548 != X549 ) )
=> ( ! [X550: $i,X551: $i,X552: $i] :
( ( in @ X552 @ X550 )
=> ( ~ ( in @ X552 @ X551 )
=> ( X550 != X551 ) ) )
=> ( ! [X553: $i] : ( subset @ X553 @ X553 )
=> ( ! [X554: $i,X555: $i,X556: $i] :
( ( subset @ X554 @ X555 )
=> ( ( subset @ X555 @ X556 )
=> ( subset @ X554 @ X556 ) ) )
=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setadjoinSub]),subsetTrans]),omega__Cong]),c_0_104]),c_0_105]),c_0_106]),c_0_107]),subsetI1]),c_0_108]),eqimpsubset2]),eqimpsubset1]),c_0_109]),subsetI2]),emptysetsubset]),setadjoinIL]),subsetE]),subsetE2]),emptyinunitempty]),notsubsetI]),notequalI1]),setadjoinIR]),notequalI2]),setadjoinE]),subsetRefl]),setadjoinOr]),c_0_110]),vacuousDall]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_111]),c_0_112]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_113]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_114]),c_0_115]),c_0_116]),inCongP]),in__Cong]),c_0_117]),c_0_118]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),c_0_119]),noeltsimpempty]),emptyI]),setext]),c_0_120]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_121]),c_0_122]),c_0_123]),c_0_124]),c_0_125]),wellorderingAx]),foundationAx]),c_0_126]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_127]) ).
thf(c_0_129,negated_conjecture,
! [X557: $i,X558: $i,X560: $i,X561: $i,X562: $i,X563: $i,X564: $i,X565: $i,X566: $i,X567: $i,X568: $i,X570: $i,X571: $i,X573: $i,X574: $i,X575: $i,X576: $i,X577: $i,X579: $i,X580: $i > $i > $o,X581: $i,X583: $i,X586: $i,X588: $i,X589: $i,X590: $i,X591: $i,X593: $i,X594: $i > $o,X595: $i,X597: $i,X598: $i > $o,X599: $i,X600: $i,X601: $i > $o,X602: $i,X603: $i,X604: $i > $o,X605: $i,X606: $i > $o,X607: $i,X610: $i,X611: $o,X612: $i,X613: $i,X614: $o,X615: $i,X616: $i,X617: $i > $o,X618: $i,X621: $i,X622: $i,X625: $i,X627: $i,X629: $i,X630: $i > $o,X631: $i,X632: $i,X634: $i,X635: $i > $o,X636: $i,X637: $i,X638: $i,X639: $i,X640: $i,X641: $i,X642: $i,X643: $i,X644: $i,X645: $i,X646: $i,X647: $o,X648: $i,X649: $i,X650: $i,X651: $i,X652: $i,X653: $i,X655: $i,X656: $i,X657: $i,X658: $i,X659: $i,X660: $i,X661: $i,X662: $i,X663: $i,X664: $i,X665: $o,X667: $i,X668: $i,X669: $i > $o,X670: $i,X673: $i,X674: $i,X675: $i,X677: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X683: $i,X684: $i,X685: $i,X686: $i,X687: $i,X688: $i,X689: $i,X690: $i,X691: $i,X692: $i,X693: $i > $o,X694: $i,X695: $i > $o,X696: $i,X697: $i,X698: $i > $o,X699: $i,X701: $i,X702: $i > $o,X704: $i,X705: $i,X706: $i > $o,X708: $i,X709: $i,X710: $i > $o,X711: $i,X713: $o,X714: $i,X715: $i > $o,X717: $i,X718: $i,X719: $i > $o,X720: $i,X722: $i > $o,X723: $i,X726: $i,X727: $i > $o,X728: $i,X732: $i,X733: $i > $o,X734: $i,X737: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $i,X743: $i,X744: $i,X745: $i,X746: $i > $o,X747: $i,X749: $i,X750: $i,X751: $i > $o,X752: $i > $o,X755: $i,X758: $i,X759: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X770: $i,X771: $i > $o,X772: $i,X774: $i,X775: $i,X776: $i > $o,X777: $i > $o,X780: $i,X782: $i,X784: $i,X785: $i,X786: $i > $o,X787: $i > $o,X790: $i,X791: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X800: $i,X801: $i,X802: $i,X803: $i,X804: $i,X805: $i,X806: $i,X807: $i,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X814: $i,X815: $i,X816: $i,X817: $i,X818: $i] :
( ( ~ ( in @ ( esk1_2 @ X557 @ X558 ) @ X557 )
| ~ ( in @ ( esk1_2 @ X557 @ X558 ) @ X558 )
| ( X557 = X558 ) )
& ( ( in @ ( esk1_2 @ X557 @ X558 ) @ X557 )
| ( in @ ( esk1_2 @ X557 @ X558 ) @ X558 )
| ( X557 = X558 ) )
& ~ ( in @ X560 @ emptyset )
& ( ~ ( in @ X563 @ ( setadjoin @ X561 @ X562 ) )
| ( X563 = X561 )
| ( in @ X563 @ X562 ) )
& ( ( X563 != X561 )
| ( in @ X563 @ ( setadjoin @ X561 @ X562 ) ) )
& ( ~ ( in @ X563 @ X562 )
| ( in @ X563 @ ( setadjoin @ X561 @ X562 ) ) )
& ( ~ ( in @ X565 @ ( powerset @ X564 ) )
| ~ ( in @ X566 @ X565 )
| ( in @ X566 @ X564 ) )
& ( ( in @ ( esk2_2 @ X567 @ X568 ) @ X568 )
| ( in @ X568 @ ( powerset @ X567 ) ) )
& ( ~ ( in @ ( esk2_2 @ X567 @ X568 ) @ X567 )
| ( in @ X568 @ ( powerset @ X567 ) ) )
& ( ( in @ X571 @ ( esk3_2 @ X570 @ X571 ) )
| ~ ( in @ X571 @ ( setunion @ X570 ) ) )
& ( ( in @ ( esk3_2 @ X570 @ X571 ) @ X570 )
| ~ ( in @ X571 @ ( setunion @ X570 ) ) )
& ( ~ ( in @ X574 @ X575 )
| ~ ( in @ X575 @ X573 )
| ( in @ X574 @ ( setunion @ X573 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X576 @ omega )
| ( in @ ( setadjoin @ X576 @ X576 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X577 ) @ omega )
| ~ ( in @ emptyset @ X577 )
| ~ ( in @ X579 @ omega )
| ( in @ X579 @ X577 ) )
& ( ( in @ ( esk4_1 @ X577 ) @ X577 )
| ~ ( in @ emptyset @ X577 )
| ~ ( in @ X579 @ omega )
| ( in @ X579 @ X577 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X577 ) @ ( esk4_1 @ X577 ) ) @ X577 )
| ~ ( in @ emptyset @ X577 )
| ~ ( in @ X579 @ omega )
| ( in @ X579 @ X577 ) )
& ( ( in @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X581 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( in @ ( esk5_2 @ X580 @ X581 ) @ X581 ) )
& ( ( X580 @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X586 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( in @ ( esk5_2 @ X580 @ X581 ) @ X581 ) )
& ( ~ ( in @ X589 @ X581 )
| ~ ( X580 @ X589 @ X588 )
| ( in @ X588 @ ( esk7_2 @ X580 @ X581 ) )
| ( in @ ( esk5_2 @ X580 @ X581 ) @ X581 ) )
& ( ( in @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X581 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( X580 @ ( esk5_2 @ X580 @ X581 ) @ ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ( X580 @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X586 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( X580 @ ( esk5_2 @ X580 @ X581 ) @ ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ~ ( in @ X589 @ X581 )
| ~ ( X580 @ X589 @ X588 )
| ( in @ X588 @ ( esk7_2 @ X580 @ X581 ) )
| ( X580 @ ( esk5_2 @ X580 @ X581 ) @ ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ( in @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X581 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( X583
!= ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ( X580 @ ( esk8_3 @ X580 @ X581 @ X586 ) @ X586 )
| ~ ( in @ X586 @ ( esk7_2 @ X580 @ X581 ) )
| ( X583
!= ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ~ ( in @ X589 @ X581 )
| ~ ( X580 @ X589 @ X588 )
| ( in @ X588 @ ( esk7_2 @ X580 @ X581 ) )
| ( X583
!= ( esk6_3 @ X580 @ X581 @ X583 ) )
| ~ ( X580 @ ( esk5_2 @ X580 @ X581 ) @ X583 ) )
& ( ( in @ ( esk9_1 @ X590 ) @ X590 )
| ~ ( in @ X591 @ X590 ) )
& ( ~ ( in @ X593 @ ( esk9_1 @ X590 ) )
| ~ ( in @ X593 @ X590 )
| ~ ( in @ X591 @ X590 ) )
& epred1_0
& ( ( X594 @ ( esk10_2 @ X594 @ X595 ) )
| ~ ( X594 @ X595 )
| ( X594 @ ( descr @ X594 ) ) )
& ( ( X595
!= ( esk10_2 @ X594 @ X595 ) )
| ~ ( X594 @ X595 )
| ( X594 @ ( descr @ X594 ) ) )
& ( ~ ( in @ X599 @ X597 )
| ~ ( X598 @ X599 )
| ( in @ X599 @ ( dsetconstr @ X597 @ X598 ) ) )
& ( ~ ( in @ X602 @ ( dsetconstr @ X600 @ X601 ) )
| ( in @ X602 @ X600 ) )
& ( ~ ( in @ X605 @ ( dsetconstr @ X603 @ X604 ) )
| ( X604 @ X605 ) )
& ( ( X606 @ ( esk12_1 @ X606 ) )
| ( X606 @ ( esk11_2 @ X606 @ X607 ) )
| ~ ( X606 @ X607 ) )
& ( ~ ( X606 @ X610 )
| ( ( esk12_1 @ X606 )
= X610 )
| ( X606 @ ( esk11_2 @ X606 @ X607 ) )
| ~ ( X606 @ X607 ) )
& ( ( X606 @ ( esk12_1 @ X606 ) )
| ( X607
!= ( esk11_2 @ X606 @ X607 ) )
| ~ ( X606 @ X607 ) )
& ( ~ ( X606 @ X610 )
| ( ( esk12_1 @ X606 )
= X610 )
| ( X607
!= ( esk11_2 @ X606 @ X607 ) )
| ~ ( X606 @ X607 ) )
& ( ~ ( in @ X612 @ ( prop2set @ X611 ) )
| X611 )
& ( ~ ( in @ X613 @ emptyset )
| X614 )
& ( ~ ( in @ X615 @ emptyset )
| ~ $true )
& ~ ( in @ X616 @ emptyset )
& ( ( X617 @ ( esk13_2 @ X617 @ X618 ) )
| ~ ( X617 @ X618 )
| ( X617 @ ( esk14_1 @ X617 ) ) )
& ( ( X618
!= ( esk13_2 @ X617 @ X618 ) )
| ~ ( X617 @ X618 )
| ( X617 @ ( esk14_1 @ X617 ) ) )
& ( ( in @ ( esk16_2 @ X621 @ X622 ) @ X622 )
| ( X621 = X622 )
| ( in @ ( esk15_2 @ X621 @ X622 ) @ X621 ) )
& ( ~ ( in @ ( esk16_2 @ X621 @ X622 ) @ X621 )
| ( X621 = X622 )
| ( in @ ( esk15_2 @ X621 @ X622 ) @ X621 ) )
& ( ( in @ ( esk16_2 @ X621 @ X622 ) @ X622 )
| ( X621 = X622 )
| ~ ( in @ ( esk15_2 @ X621 @ X622 ) @ X622 ) )
& ( ~ ( in @ ( esk16_2 @ X621 @ X622 ) @ X621 )
| ( X621 = X622 )
| ~ ( in @ ( esk15_2 @ X621 @ X622 ) @ X622 ) )
& ( ( in @ ( esk17_1 @ X625 ) @ X625 )
| ( X625 = emptyset ) )
& ( ( in @ ( esk18_1 @ X627 ) @ X627 )
| ( X627 = emptyset ) )
& ( ~ ( in @ X631 @ ( dsetconstr @ X629 @ X630 ) )
| ( X630 @ X631 )
| ~ ( in @ X631 @ X629 ) )
& ( ~ ( X630 @ X631 )
| ( in @ X631 @ ( dsetconstr @ X629 @ X630 ) )
| ~ ( in @ X631 @ X629 ) )
& ( ( X632 = emptyset )
| ( in @ ( esk19_1 @ X632 ) @ X632 ) )
& ( ~ ( in @ X636 @ X634 )
| ~ ( X635 @ X636 )
| ( ( dsetconstr @ X634 @ X635 )
!= emptyset ) )
& ( ~ ( in @ X638 @ X637 )
| ( X637 != emptyset ) )
& ( in @ X639 @ ( setadjoin @ X639 @ X640 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X643 @ X642 )
| ( in @ X643 @ ( setadjoin @ X641 @ X642 ) ) )
& ( ( in @ X646 @ X645 )
| X647
| ( X646 = X644 )
| ~ ( in @ X646 @ ( setadjoin @ X644 @ X645 ) ) )
& ( ~ X647
| X647
| ( X646 = X644 )
| ~ ( in @ X646 @ ( setadjoin @ X644 @ X645 ) ) )
& ( ( in @ X646 @ X645 )
| X647
| ~ X647
| ~ ( in @ X646 @ ( setadjoin @ X644 @ X645 ) ) )
& ( ~ X647
| X647
| ~ X647
| ~ ( in @ X646 @ ( setadjoin @ X644 @ X645 ) ) )
& ( ~ ( in @ X650 @ ( setadjoin @ X648 @ X649 ) )
| ( X650 = X648 )
| ( in @ X650 @ X649 ) )
& ( ( dsetconstr @ X651
@ ^ [Z0: $i] : $true )
= X651 )
& ( ( in @ ( esk20_2 @ X652 @ X653 ) @ X653 )
| ( in @ X653 @ ( powerset @ X652 ) ) )
& ( ~ ( in @ ( esk20_2 @ X652 @ X653 ) @ X652 )
| ( in @ X653 @ ( powerset @ X652 ) ) )
& ( in @ emptyset @ ( powerset @ X655 ) )
& ( in @ emptyset @ ( powerset @ X656 ) )
& ( ~ ( in @ X658 @ ( powerset @ X657 ) )
| ~ ( in @ X659 @ X658 )
| ( in @ X659 @ X657 ) )
& ( ~ ( in @ X661 @ X662 )
| ~ ( in @ X662 @ X660 )
| ( in @ X661 @ ( setunion @ X660 ) ) )
& ( ( in @ X664 @ ( esk21_3 @ X663 @ X664 @ X665 ) )
| X665
| ~ ( in @ X664 @ ( setunion @ X663 ) ) )
& ( ( in @ ( esk21_3 @ X663 @ X664 @ X665 ) @ X663 )
| X665
| ~ ( in @ X664 @ ( setunion @ X663 ) ) )
& ( ~ X665
| X665
| ~ ( in @ X664 @ ( setunion @ X663 ) ) )
& ( ~ ( in @ X668 @ X667 )
| ( in @ X668 @ ( powerset @ ( setunion @ X667 ) ) ) )
& ( ~ ( X669 @ X673 )
| ( X673
= ( esk23_1 @ X669 ) )
| ( X669 @ ( esk22_2 @ X669 @ X670 ) )
| ~ ( X669 @ X670 ) )
& ( ( X674
!= ( esk23_1 @ X669 ) )
| ( X669 @ X674 )
| ( X669 @ ( esk22_2 @ X669 @ X670 ) )
| ~ ( X669 @ X670 ) )
& ( ~ ( X669 @ X673 )
| ( X673
= ( esk23_1 @ X669 ) )
| ( X670
!= ( esk22_2 @ X669 @ X670 ) )
| ~ ( X669 @ X670 ) )
& ( ( X674
!= ( esk23_1 @ X669 ) )
| ( X669 @ X674 )
| ( X670
!= ( esk22_2 @ X669 @ X670 ) )
| ~ ( X669 @ X670 ) )
& ( ( in @ ( esk24_1 @ X675 ) @ X675 )
| ( X675 = emptyset ) )
& ( $true
| ( X675 = emptyset ) )
& ( ~ ( in @ X677 @ ( setadjoin @ X678 @ emptyset ) )
| ( X677 = X678 ) )
& ( ( X679 = X680 )
| ~ ( in @ X680 @ ( setadjoin @ X679 @ emptyset ) ) )
& ( ( X681 != X682 )
| ( in @ X681 @ ( setadjoin @ X682 @ emptyset ) ) )
& ( ~ ( in @ X683 @ ( setadjoin @ X684 @ emptyset ) )
| ( in @ X684 @ ( setadjoin @ X683 @ emptyset ) ) )
& ( ~ ( in @ X687 @ ( setadjoin @ X685 @ ( setadjoin @ X686 @ emptyset ) ) )
| ( X687 = X685 )
| ( X687 = X686 ) )
& ( in @ X688 @ ( setadjoin @ X688 @ ( setadjoin @ X689 @ emptyset ) ) )
& ( in @ X691 @ ( setadjoin @ X690 @ ( setadjoin @ X691 @ emptyset ) ) )
& ( ~ ( in @ X694 @ X692 )
| ~ ( X693 @ X694 )
| ( ( dsetconstr @ X692 @ X693 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X696 @ emptyset )
| ( X695 @ X696 ) )
& ( ( in @ ( esk25_2 @ X697 @ X698 ) @ X697 )
| ~ ( in @ X699 @ X697 )
| ( X698 @ X699 ) )
& ( ~ ( X698 @ ( esk25_2 @ X697 @ X698 ) )
| ~ ( in @ X699 @ X697 )
| ( X698 @ X699 ) )
& ( ( in @ ( esk26_2 @ X701 @ X702 ) @ X701 )
| ~ ( in @ X704 @ X701 )
| ~ ( X702 @ X704 ) )
& ( ( X702 @ ( esk26_2 @ X701 @ X702 ) )
| ~ ( in @ X704 @ X701 )
| ~ ( X702 @ X704 ) )
& ( ( in @ ( esk27_2 @ X705 @ X706 ) @ X705 )
| ~ ( in @ X708 @ X705 )
| ~ ( X706 @ X708 ) )
& ( ( X706 @ ( esk27_2 @ X705 @ X706 ) )
| ~ ( in @ X708 @ X705 )
| ~ ( X706 @ X708 ) )
& ( ( in @ ( esk28_2 @ X709 @ X710 ) @ X709 )
| ~ ( in @ X711 @ X709 )
| ( X710 @ X711 ) )
& ( ~ ( X710 @ ( esk28_2 @ X709 @ X710 ) )
| ~ ( in @ X711 @ X709 )
| ( X710 @ X711 ) )
& ( ~ X713
| ( in @ emptyset @ ( prop2set @ X713 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X714 @ X715 ) @ X714 )
| ~ ( in @ X717 @ X714 )
| ~ ( X715 @ X717 ) )
& ( ( X715 @ ( esk29_2 @ X714 @ X715 ) )
| ~ ( in @ X717 @ X714 )
| ~ ( X715 @ X717 ) )
& ( ( in @ ( esk30_2 @ X718 @ X719 ) @ X718 )
| ~ ( in @ X720 @ X718 )
| ( X719 @ X720 ) )
& ( ~ ( X719 @ ( esk30_2 @ X718 @ X719 ) )
| ~ ( in @ X720 @ X718 )
| ( X719 @ X720 ) )
& ( ( X722 @ ( esk32_1 @ X722 ) )
| ( X722 @ ( esk31_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 ) )
& ( ~ ( X722 @ X726 )
| ( ( esk32_1 @ X722 )
= X726 )
| ( X722 @ ( esk31_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 ) )
& ( ( X722 @ ( esk32_1 @ X722 ) )
| ( X723
!= ( esk31_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 ) )
& ( ~ ( X722 @ X726 )
| ( ( esk32_1 @ X722 )
= X726 )
| ( X723
!= ( esk31_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 ) )
& ( ( X727 @ ( esk35_1 @ X727 ) )
| ( X727 @ ( esk33_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ~ ( X727 @ X732 )
| ( ( esk35_1 @ X727 )
= X732 )
| ( X727 @ ( esk33_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ( X727 @ ( esk35_1 @ X727 ) )
| ( X727 @ ( esk34_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ~ ( X727 @ X732 )
| ( ( esk35_1 @ X727 )
= X732 )
| ( X727 @ ( esk34_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ( X727 @ ( esk35_1 @ X727 ) )
| ( ( esk33_1 @ X727 )
!= ( esk34_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ~ ( X727 @ X732 )
| ( ( esk35_1 @ X727 )
= X732 )
| ( ( esk33_1 @ X727 )
!= ( esk34_1 @ X727 ) )
| ~ ( X727 @ X728 ) )
& ( ( X733 @ ( esk37_1 @ X733 ) )
| ~ ( X733 @ ( esk36_2 @ X733 @ X734 ) )
| ( ( esk36_2 @ X733 @ X734 )
!= X734 ) )
& ( ~ ( X733 @ X737 )
| ( ( esk37_1 @ X733 )
= X737 )
| ~ ( X733 @ ( esk36_2 @ X733 @ X734 ) )
| ( ( esk36_2 @ X733 @ X734 )
!= X734 ) )
& ( ( X733 @ ( esk37_1 @ X733 ) )
| ( X733 @ ( esk36_2 @ X733 @ X734 ) )
| ( ( esk36_2 @ X733 @ X734 )
= X734 ) )
& ( ~ ( X733 @ X737 )
| ( ( esk37_1 @ X733 )
= X737 )
| ( X733 @ ( esk36_2 @ X733 @ X734 ) )
| ( ( esk36_2 @ X733 @ X734 )
= X734 ) )
& ( ( X738 != X739 )
| ( X740 != X741 )
| ~ ( in @ X740 @ X738 )
| ( in @ X741 @ X739 ) )
& ( ~ ( in @ X744 @ X742 )
| ( in @ X745 @ X743 )
| ( X744 != X745 )
| ( X742 != X743 ) )
& ( ~ ( in @ X745 @ X743 )
| ( in @ X744 @ X742 )
| ( X744 != X745 )
| ( X742 != X743 ) )
& ( ( X746 @ ( esk38_2 @ X746 @ X747 ) )
| ~ ( X746 @ X747 )
| ~ ( X746 @ X749 )
| ~ ( X746 @ X750 )
| ( X749 = X750 ) )
& ( ( X747
!= ( esk38_2 @ X746 @ X747 ) )
| ~ ( X746 @ X747 )
| ~ ( X746 @ X749 )
| ~ ( X746 @ X750 )
| ( X749 = X750 ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( ( esk39_2 @ X751 @ X752 )
= ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ~ ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ~ ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X751 @ ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X752 @ ( esk42_2 @ X751 @ X752 ) )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X752 @ X758 )
| ( ( esk42_2 @ X751 @ X752 )
= X758 )
| ( X755
!= ( esk41_3 @ X751 @ X752 @ X755 ) )
| ~ ( X751 @ X755 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X752 @ ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ( X751 @ ( esk44_2 @ X751 @ X752 ) )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( ~ ( X751 @ X762 )
| ( ( esk44_2 @ X751 @ X752 )
= X762 )
| ( X759
!= ( esk43_3 @ X751 @ X752 @ X759 ) )
| ~ ( X752 @ X759 )
| ( X751 @ ( esk39_2 @ X751 @ X752 ) )
| ( X752 @ ( esk40_2 @ X751 @ X752 ) ) )
& ( emptyset = emptyset )
& ( ( X763 != X764 )
| ( X765 != X766 )
| ( ( setadjoin @ X763 @ X765 )
= ( setadjoin @ X764 @ X766 ) ) )
& ( ( X767 != X768 )
| ( ( powerset @ X767 )
= ( powerset @ X768 ) ) )
& ( ( X769 != X770 )
| ( ( setunion @ X769 )
= ( setunion @ X770 ) ) )
& ( omega = omega )
& ( ( X771 @ ( esk45_2 @ X771 @ X772 ) )
| ~ ( X771 @ X772 )
| ~ ( X771 @ X774 )
| ~ ( X771 @ X775 )
| ( X774 = X775 ) )
& ( ( X772
!= ( esk45_2 @ X771 @ X772 ) )
| ~ ( X771 @ X772 )
| ~ ( X771 @ X774 )
| ~ ( X771 @ X775 )
| ( X774 = X775 ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( ( esk46_2 @ X776 @ X777 )
= ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( ( esk46_2 @ X776 @ X777 )
= ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( ( esk46_2 @ X776 @ X777 )
= ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( ( esk46_2 @ X776 @ X777 )
= ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ~ ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ~ ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ~ ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ~ ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ~ ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ~ ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ~ ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ~ ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X776 @ ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X777 @ ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( X782
!= ( esk49_3 @ X776 @ X777 @ X782 ) )
| ~ ( X777 @ X782 )
| ( ( descr @ X776 )
= ( descr @ X777 ) )
| ( X780
!= ( esk48_3 @ X776 @ X777 @ X780 ) )
| ~ ( X776 @ X780 )
| ( X776 @ ( esk46_2 @ X776 @ X777 ) )
| ( X777 @ ( esk47_2 @ X776 @ X777 ) ) )
& ( ( in @ ( esk50_4 @ X784 @ X785 @ X786 @ X787 ) @ X784 )
| ( ( dsetconstr @ X784 @ X786 )
= ( dsetconstr @ X785 @ X787 ) )
| ( X784 != X785 ) )
& ( ( in @ ( esk51_4 @ X784 @ X785 @ X786 @ X787 ) @ X785 )
| ( ( dsetconstr @ X784 @ X786 )
= ( dsetconstr @ X785 @ X787 ) )
| ( X784 != X785 ) )
& ( ( ( esk50_4 @ X784 @ X785 @ X786 @ X787 )
= ( esk51_4 @ X784 @ X785 @ X786 @ X787 ) )
| ( ( dsetconstr @ X784 @ X786 )
= ( dsetconstr @ X785 @ X787 ) )
| ( X784 != X785 ) )
& ( ~ ( X786 @ ( esk50_4 @ X784 @ X785 @ X786 @ X787 ) )
| ~ ( X787 @ ( esk51_4 @ X784 @ X785 @ X786 @ X787 ) )
| ( ( dsetconstr @ X784 @ X786 )
= ( dsetconstr @ X785 @ X787 ) )
| ( X784 != X785 ) )
& ( ( X786 @ ( esk50_4 @ X784 @ X785 @ X786 @ X787 ) )
| ( X787 @ ( esk51_4 @ X784 @ X785 @ X786 @ X787 ) )
| ( ( dsetconstr @ X784 @ X786 )
= ( dsetconstr @ X785 @ X787 ) )
| ( X784 != X785 ) )
& ( ( in @ ( esk52_2 @ X790 @ X791 ) @ X790 )
| ( subset @ X790 @ X791 ) )
& ( ~ ( in @ ( esk52_2 @ X790 @ X791 ) @ X791 )
| ( subset @ X790 @ X791 ) )
& ( ( X793 != X794 )
| ( subset @ X794 @ X793 ) )
& ( ( X795 != X796 )
| ( subset @ X795 @ X796 ) )
& ( ( in @ ( esk53_2 @ X797 @ X798 ) @ X797 )
| ( subset @ X797 @ X798 ) )
& ( ~ ( in @ ( esk53_2 @ X797 @ X798 ) @ X798 )
| ( subset @ X797 @ X798 ) )
& ( subset @ emptyset @ X800 )
& ( ~ ( subset @ X801 @ X802 )
| ~ ( in @ X803 @ X801 )
| ( in @ X803 @ X802 ) )
& ( ~ ( subset @ X804 @ X805 )
| ( in @ X806 @ X805 )
| ~ ( in @ X806 @ X804 ) )
& ( ~ ( in @ X809 @ X807 )
| ( in @ X809 @ X808 )
| ~ ( subset @ X807 @ X808 ) )
& ( ( subset @ X810 @ X811 )
| ( X810 != X811 ) )
& ( ~ ( in @ X814 @ X812 )
| ( in @ X814 @ X813 )
| ( X812 != X813 ) )
& ( subset @ X815 @ X815 )
& ( ~ ( subset @ X816 @ X817 )
| ~ ( subset @ X817 @ X818 )
| ( subset @ X816 @ X818 ) )
& ~ ( subset @ esk55_0 @ ( setadjoin @ esk54_0 @ esk55_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_128])])])])])])]) ).
thf(c_0_130,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk53_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_131,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X4 @ X3 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_132,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( setadjoin @ X3 @ X4 ) )
| ~ ( in @ ( esk53_2 @ X2 @ ( setadjoin @ X3 @ X4 ) ) @ X4 ) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
thf(c_0_133,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk53_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_134,negated_conjecture,
~ ( subset @ esk55_0 @ ( setadjoin @ esk54_0 @ esk55_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_135,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
thf(c_0_136,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU571^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 16:47:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.53 Running higher-order theorem proving
% 0.20/0.53 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
% 0.46/0.90 # Version: 3.1.0-ho
% 0.46/0.90 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.46/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.90 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.46/0.90 # Starting ehoh_best3_rw with 300s (1) cores
% 0.46/0.90 # Starting almost_fo_3 with 300s (1) cores
% 0.46/0.90 # Starting new_ho_13 with 300s (1) cores
% 0.46/0.90 # ehoh_best3_rw with pid 7811 completed with status 0
% 0.46/0.90 # Result found by ehoh_best3_rw
% 0.46/0.90 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.46/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.90 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.46/0.90 # Starting ehoh_best3_rw with 300s (1) cores
% 0.46/0.90 # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.46/0.90 # Search class: HGHSM-FSLS31-SHFMMMBN
% 0.46/0.90 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.46/0.90 # Starting new_ho_10 with 163s (1) cores
% 0.46/0.90 # new_ho_10 with pid 7814 completed with status 0
% 0.46/0.90 # Result found by new_ho_10
% 0.46/0.90 # Preprocessing class: HSMMSLSSLLLCHFA.
% 0.46/0.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.90 # Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.46/0.90 # Starting ehoh_best3_rw with 300s (1) cores
% 0.46/0.90 # SinE strategy is gf120_gu_RUU_F100_L01000
% 0.46/0.90 # Search class: HGHSM-FSLS31-SHFMMMBN
% 0.46/0.90 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.46/0.90 # Starting new_ho_10 with 163s (1) cores
% 0.46/0.90 # Preprocessing time : 0.005 s
% 0.46/0.90 # Presaturation interreduction done
% 0.46/0.90
% 0.46/0.90 # Proof found!
% 0.46/0.90 # SZS status Theorem
% 0.46/0.90 # SZS output start CNFRefutation
% See solution above
% 0.46/0.90 # Parsed axioms : 192
% 0.46/0.90 # Removed by relevancy pruning/SinE : 103
% 0.46/0.90 # Initial clauses : 198
% 0.46/0.90 # Removed in clause preprocessing : 14
% 0.46/0.90 # Initial clauses in saturation : 184
% 0.46/0.90 # Processed clauses : 778
% 0.46/0.90 # ...of these trivial : 17
% 0.46/0.90 # ...subsumed : 155
% 0.46/0.90 # ...remaining for further processing : 606
% 0.46/0.90 # Other redundant clauses eliminated : 14
% 0.46/0.90 # Clauses deleted for lack of memory : 0
% 0.46/0.90 # Backward-subsumed : 7
% 0.46/0.90 # Backward-rewritten : 9
% 0.46/0.90 # Generated clauses : 10138
% 0.46/0.90 # ...of the previous two non-redundant : 9944
% 0.46/0.90 # ...aggressively subsumed : 0
% 0.46/0.90 # Contextual simplify-reflections : 0
% 0.46/0.90 # Paramodulations : 10121
% 0.46/0.90 # Factorizations : 3
% 0.46/0.90 # NegExts : 0
% 0.46/0.90 # Equation resolutions : 14
% 0.46/0.90 # Disequality decompositions : 0
% 0.46/0.90 # Total rewrite steps : 316
% 0.46/0.90 # ...of those cached : 256
% 0.46/0.90 # Propositional unsat checks : 0
% 0.46/0.90 # Propositional check models : 0
% 0.46/0.90 # Propositional check unsatisfiable : 0
% 0.46/0.90 # Propositional clauses : 0
% 0.46/0.90 # Propositional clauses after purity: 0
% 0.46/0.90 # Propositional unsat core size : 0
% 0.46/0.90 # Propositional preprocessing time : 0.000
% 0.46/0.90 # Propositional encoding time : 0.000
% 0.46/0.90 # Propositional solver time : 0.000
% 0.46/0.90 # Success case prop preproc time : 0.000
% 0.46/0.90 # Success case prop encoding time : 0.000
% 0.46/0.90 # Success case prop solver time : 0.000
% 0.46/0.90 # Current number of processed clauses : 417
% 0.46/0.90 # Positive orientable unit clauses : 23
% 0.46/0.90 # Positive unorientable unit clauses: 0
% 0.46/0.90 # Negative unit clauses : 8
% 0.46/0.90 # Non-unit-clauses : 386
% 0.46/0.90 # Current number of unprocessed clauses: 9464
% 0.46/0.90 # ...number of literals in the above : 37559
% 0.46/0.90 # Current number of archived formulas : 0
% 0.46/0.90 # Current number of archived clauses : 176
% 0.46/0.90 # Clause-clause subsumption calls (NU) : 24325
% 0.46/0.90 # Rec. Clause-clause subsumption calls : 12039
% 0.46/0.90 # Non-unit clause-clause subsumptions : 98
% 0.46/0.90 # Unit Clause-clause subsumption calls : 965
% 0.46/0.90 # Rewrite failures with RHS unbound : 0
% 0.46/0.90 # BW rewrite match attempts : 23
% 0.46/0.90 # BW rewrite match successes : 9
% 0.46/0.90 # Condensation attempts : 778
% 0.46/0.90 # Condensation successes : 6
% 0.46/0.90 # Termbank termtop insertions : 225408
% 0.46/0.90 # Search garbage collected termcells : 9924
% 0.46/0.90
% 0.46/0.90 # -------------------------------------------------
% 0.46/0.90 # User time : 0.338 s
% 0.46/0.90 # System time : 0.010 s
% 0.46/0.90 # Total time : 0.348 s
% 0.46/0.90 # Maximum resident set size: 4540 pages
% 0.46/0.90
% 0.46/0.90 # -------------------------------------------------
% 0.46/0.90 # User time : 0.343 s
% 0.46/0.90 # System time : 0.013 s
% 0.46/0.90 # Total time : 0.356 s
% 0.46/0.90 # Maximum resident set size: 1920 pages
% 0.46/0.90 % E---3.1 exiting
% 0.46/0.91 % E exiting
%------------------------------------------------------------------------------