TSTP Solution File: SEU592^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU592^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 03:28:25 EDT 2024
% Result : Timeout 0.82s 300.03s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 292
% Syntax : Number of formulae : 341 ( 28 unt; 179 typ; 0 def)
% Number of atoms : 1287 ( 336 equ; 0 cnn)
% Maximal formula atoms : 386 ( 7 avg)
% Number of connectives : 4944 ( 425 ~; 479 |; 298 &;2940 @)
% ( 173 <=>; 629 =>; 0 <=; 0 <~>)
% Maximal formula depth : 473 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 319 ( 319 >; 0 *; 0 +; 0 <<)
% Number of symbols : 182 ( 179 usr; 115 con; 0-4 aty)
% Number of variables : 1102 ( 73 ^ 925 !; 104 ?;1102 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
epred1_0: $o ).
thf(decl_148,type,
esk1_2: $i > $i > $i ).
thf(decl_149,type,
esk2_2: $i > $i > $i ).
thf(decl_150,type,
esk3_2: $i > $i > $i ).
thf(decl_151,type,
esk4_1: $i > $i ).
thf(decl_152,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_153,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_154,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_155,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_156,type,
esk9_1: $i > $i ).
thf(decl_157,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_158,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_159,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_160,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_161,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_162,type,
esk15_2: $i > $i > $i ).
thf(decl_163,type,
esk16_2: $i > $i > $i ).
thf(decl_164,type,
esk17_1: $i > $i ).
thf(decl_165,type,
esk18_1: $i > $i ).
thf(decl_166,type,
esk19_1: $i > $i ).
thf(decl_167,type,
esk20_2: $i > $i > $i ).
thf(decl_168,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_169,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_170,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_171,type,
esk24_1: $i > $i ).
thf(decl_172,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_173,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_174,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_175,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_176,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_177,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_178,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_179,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_180,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_181,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_182,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_183,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_184,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_185,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_186,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_187,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_188,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_189,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_190,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_191,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_192,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_193,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_194,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_195,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_196,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_197,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_198,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_199,type,
esk52_2: $i > $i > $i ).
thf(decl_200,type,
esk53_2: $i > $i > $i ).
thf(decl_201,type,
esk54_0: $i ).
thf(decl_202,type,
esk55_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
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(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(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(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
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(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(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(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(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(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(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(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(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(binintersectLsub,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
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
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(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
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(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(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(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/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(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(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(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(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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
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(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersect,axiom,
( binintersect
= ( ^ [X4: $i,X5: $i] :
( dsetconstr @ X4
@ ^ [X2: $i] : ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(c_0_112,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_113,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_114,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_115,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_116,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_117,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X312: $i] :
( ( X6 @ X2 @ X312 )
& ! [X313: $i] :
( ( X6 @ X2 @ X313 )
=> ( X312 = X313 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_112,c_0_113]) ).
thf(c_0_128,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X314: $i] :
( ( X1 @ X314 )
& ! [X315: $i] :
( ( X1 @ X315 )
=> ( X314 = X315 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_114,c_0_113]) ).
thf(c_0_129,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_130,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_131,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_132,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X316: $i] :
( ( X1 @ X316 )
& ! [X317: $i] :
( ( X1 @ X317 )
=> ( X316 = X317 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_115,c_0_113]) ).
thf(c_0_133,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X318: $i] :
( ( X1 @ X318 )
& ! [X319: $i] :
( ( X1 @ X319 )
=> ( X318 = X319 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_116,c_0_113]) ).
thf(c_0_134,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_135,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_117]) ).
thf(c_0_136,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_118,c_0_117]) ).
thf(c_0_137,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_117]) ).
thf(c_0_138,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_139,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X320: $i] :
( ( X1 @ X320 )
& ! [X321: $i] :
( ( X1 @ X321 )
=> ( X320 = X321 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_119,c_0_113]) ).
thf(c_0_140,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_117]) ).
thf(c_0_141,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_142,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X322: $i] :
( ( X1 @ X322 )
& ! [X323: $i] :
( ( X1 @ X323 )
=> ( X322 = X323 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_120,c_0_113]) ).
thf(c_0_143,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X324: $i] :
( ( X1 @ X324 )
& ! [X325: $i] :
( ( X1 @ X325 )
=> ( X324 = X325 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_121,c_0_113]) ).
thf(c_0_144,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X326: $i] :
( ( X1 @ X326 )
& ! [X327: $i] :
( ( X1 @ X327 )
=> ( X326 = X327 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_122,c_0_113]) ).
thf(c_0_145,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X328: $i] :
( ( X1 @ X328 )
& ! [X329: $i] :
( ( X1 @ X329 )
=> ( X328 = X329 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_123,c_0_113]) ).
thf(c_0_146,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X330: $i] :
( ( X1 @ X330 )
& ! [X331: $i] :
( ( X1 @ X331 )
=> ( X330 = X331 ) ) )
<=> ? [X332: $i] :
( ( X17 @ X332 )
& ! [X333: $i] :
( ( X17 @ X333 )
=> ( X332 = X333 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_124,c_0_113]) ).
thf(c_0_147,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X334: $i] :
( ( X1 @ X334 )
& ! [X335: $i] :
( ( X1 @ X335 )
=> ( X334 = X335 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_125,c_0_113]) ).
thf(c_0_148,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X336: $i] :
( ( X1 @ X336 )
& ! [X337: $i] :
( ( X1 @ X337 )
=> ( X336 = X337 ) ) )
=> ( ? [X338: $i] :
( ( X17 @ X338 )
& ! [X339: $i] :
( ( X17 @ X339 )
=> ( X338 = X339 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_126,c_0_113]) ).
thf(c_0_149,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_150,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_151,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_152,plain,
( epred1_0
<=> ! [X369: $i] :
? [X370: $i] :
( ! [X371: $i] :
( ( in @ X371 @ X370 )
=> ! [X372: $i] :
( ( in @ X372 @ X371 )
=> ( in @ X372 @ X369 ) ) )
& ! [X373: $i,X374: $i] :
( ( ( in @ X373 @ X369 )
& ( in @ X374 @ X369 ) )
=> ( ! [X375: $i] :
( ( in @ X375 @ X370 )
=> ( ( in @ X373 @ X375 )
<=> ( in @ X374 @ X375 ) ) )
=> ( X373 = X374 ) ) )
& ! [X376: $i,X377: $i] :
( ( ( in @ X376 @ X370 )
& ( in @ X377 @ X370 ) )
=> ( ! [X378: $i] :
( ( in @ X378 @ X376 )
=> ( in @ X378 @ X377 ) )
| ! [X379: $i] :
( ( in @ X379 @ X377 )
=> ( in @ X379 @ X376 ) ) ) )
& ! [X380: $i] :
( ( ! [X381: $i] :
( ( in @ X381 @ X380 )
=> ( in @ X381 @ X369 ) )
& ? [X382: $i] : ( in @ X382 @ X380 ) )
=> ? [X383: $i,X384: $i] :
( ( in @ X383 @ X370 )
& ( in @ X384 @ X380 )
& ~ ? [X385: $i] :
( ( in @ X385 @ X383 )
& ( in @ X385 @ X380 ) )
& ! [X386: $i] :
( ( in @ X386 @ X370 )
=> ( ! [X387: $i] :
( ( in @ X387 @ X386 )
=> ( in @ X387 @ X383 ) )
| ( in @ X384 @ X386 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_153,negated_conjecture,
~ ( ! [X340: $i,X341: $i] :
( ! [X342: $i] :
( ( in @ X342 @ X340 )
<=> ( in @ X342 @ X341 ) )
=> ( X340 = X341 ) )
=> ( ! [X343: $i] :
~ ( in @ X343 @ emptyset )
=> ( ! [X344: $i,X345: $i,X346: $i] :
( ( in @ X346 @ ( setadjoin @ X344 @ X345 ) )
<=> ( ( X346 = X344 )
| ( in @ X346 @ X345 ) ) )
=> ( ! [X347: $i,X348: $i] :
( ( in @ X348 @ ( powerset @ X347 ) )
<=> ! [X349: $i] :
( ( in @ X349 @ X348 )
=> ( in @ X349 @ X347 ) ) )
=> ( ! [X350: $i,X351: $i] :
( ( in @ X351 @ ( setunion @ X350 ) )
<=> ? [X352: $i] :
( ( in @ X351 @ X352 )
& ( in @ X352 @ X350 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X353: $i] :
( ( in @ X353 @ omega )
=> ( in @ ( setadjoin @ X353 @ X353 ) @ omega ) )
=> ( ! [X354: $i] :
( ( ( in @ emptyset @ X354 )
& ! [X355: $i] :
( ( ( in @ X355 @ omega )
& ( in @ X355 @ X354 ) )
=> ( in @ ( setadjoin @ X355 @ X355 ) @ X354 ) ) )
=> ! [X356: $i] :
( ( in @ X356 @ omega )
=> ( in @ X356 @ X354 ) ) )
=> ( ! [X357: $i > $i > $o,X358: $i] :
( ! [X359: $i] :
( ( in @ X359 @ X358 )
=> ? [X360: $i] :
( ( X357 @ X359 @ X360 )
& ! [X361: $i] :
( ( X357 @ X359 @ X361 )
=> ( X360 = X361 ) ) ) )
=> ? [X362: $i] :
! [X363: $i] :
( ( in @ X363 @ X362 )
<=> ? [X364: $i] :
( ( in @ X364 @ X358 )
& ( X357 @ X364 @ X363 ) ) ) )
=> ( ! [X365: $i] :
( ? [X366: $i] : ( in @ X366 @ X365 )
=> ? [X367: $i] :
( ( in @ X367 @ X365 )
& ~ ? [X368: $i] :
( ( in @ X368 @ X367 )
& ( in @ X368 @ X365 ) ) ) )
=> ( epred1_0
=> ( ! [X388: $i > $o] :
( ? [X389: $i] :
( ( X388 @ X389 )
& ! [X390: $i] :
( ( X388 @ X390 )
=> ( X389 = X390 ) ) )
=> ( X388
@ ( descr
@ ^ [Z0: $i] : ( X388 @ Z0 ) ) ) )
=> ( ! [X391: $i,X392: $i > $o,X393: $i] :
( ( in @ X393 @ X391 )
=> ( ( X392 @ X393 )
=> ( in @ X393 @ ( dsetconstr @ X391 @ X392 ) ) ) )
=> ( ! [X394: $i,X395: $i > $o,X396: $i] :
( ( in @ X396 @ ( dsetconstr @ X394 @ X395 ) )
=> ( in @ X396 @ X394 ) )
=> ( ! [X397: $i,X398: $i > $o,X399: $i] :
( ( in @ X399 @ ( dsetconstr @ X397 @ X398 ) )
=> ( X398 @ X399 ) )
=> ( ! [X400: $i > $o] :
( ? [X401: $i] :
( ( X400 @ X401 )
& ! [X402: $i] :
( ( X400 @ X402 )
=> ( X401 = X402 ) ) )
=> ? [X403: $i] :
( ( X400 @ X403 )
& ! [X404: $i] :
( ( X400 @ X404 )
=> ( X403 = X404 ) ) ) )
=> ( ! [X405: $o,X406: $i] :
( ( in @ X406 @ ( prop2set @ X405 ) )
=> X405 )
=> ( ! [X407: $i] :
( ( in @ X407 @ emptyset )
=> ! [X408: $o] : X408 )
=> ( ! [X409: $i] :
( ( in @ X409 @ emptyset )
=> ~ $true )
=> ( ! [X410: $i] :
~ ( in @ X410 @ emptyset )
=> ( ! [X411: $i > $o] :
( ? [X412: $i] :
( ( X411 @ X412 )
& ! [X413: $i] :
( ( X411 @ X413 )
=> ( X412 = X413 ) ) )
=> ? [X414: $i] : ( X411 @ X414 ) )
=> ( ! [X415: $i,X416: $i] :
( ! [X417: $i] :
( ( in @ X417 @ X415 )
=> ( in @ X417 @ X416 ) )
=> ( ! [X418: $i] :
( ( in @ X418 @ X416 )
=> ( in @ X418 @ X415 ) )
=> ( X415 = X416 ) ) )
=> ( ! [X419: $i] :
( ! [X420: $i] :
~ ( in @ X420 @ X419 )
=> ( X419 = emptyset ) )
=> ( ! [X421: $i] :
( ! [X422: $i] :
~ ( in @ X422 @ X421 )
=> ( X421 = emptyset ) )
=> ( ! [X423: $i,X424: $i > $o,X425: $i] :
( ( in @ X425 @ X423 )
=> ( ( in @ X425 @ ( dsetconstr @ X423 @ X424 ) )
<=> ( X424 @ X425 ) ) )
=> ( ! [X426: $i] :
( ( X426 != emptyset )
=> ? [X427: $i] : ( in @ X427 @ X426 ) )
=> ( ! [X428: $i,X429: $i > $o,X430: $i] :
( ( in @ X430 @ X428 )
=> ( ( X429 @ X430 )
=> ( ( dsetconstr @ X428 @ X429 )
!= emptyset ) ) )
=> ( ! [X431: $i] :
( ? [X432: $i] : ( in @ X432 @ X431 )
=> ( X431 != emptyset ) )
=> ( ! [X433: $i,X434: $i] : ( in @ X433 @ ( setadjoin @ X433 @ X434 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X435: $i,X436: $i,X437: $i] :
( ( in @ X437 @ X436 )
=> ( in @ X437 @ ( setadjoin @ X435 @ X436 ) ) )
=> ( ! [X438: $i,X439: $i,X440: $i] :
( ( in @ X440 @ ( setadjoin @ X438 @ X439 ) )
=> ! [X441: $o] :
( ( ( X440 = X438 )
=> X441 )
=> ( ( ( in @ X440 @ X439 )
=> X441 )
=> X441 ) ) )
=> ( ! [X442: $i,X443: $i,X444: $i] :
( ( in @ X444 @ ( setadjoin @ X442 @ X443 ) )
=> ( ( X444 = X442 )
| ( in @ X444 @ X443 ) ) )
=> ( ! [X445: $i] :
( ( dsetconstr @ X445
@ ^ [Z0: $i] : $true )
= X445 )
=> ( ! [X446: $i,X447: $i] :
( ! [X448: $i] :
( ( in @ X448 @ X447 )
=> ( in @ X448 @ X446 ) )
=> ( in @ X447 @ ( powerset @ X446 ) ) )
=> ( ! [X449: $i] : ( in @ emptyset @ ( powerset @ X449 ) )
=> ( ! [X450: $i] : ( in @ emptyset @ ( powerset @ X450 ) )
=> ( ! [X451: $i,X452: $i,X453: $i] :
( ( in @ X452 @ ( powerset @ X451 ) )
=> ( ( in @ X453 @ X452 )
=> ( in @ X453 @ X451 ) ) )
=> ( ! [X454: $i,X455: $i,X456: $i] :
( ( in @ X455 @ X456 )
=> ( ( in @ X456 @ X454 )
=> ( in @ X455 @ ( setunion @ X454 ) ) ) )
=> ( ! [X457: $i,X458: $i] :
( ( in @ X458 @ ( setunion @ X457 ) )
=> ! [X459: $o] :
( ! [X460: $i] :
( ( in @ X458 @ X460 )
=> ( ( in @ X460 @ X457 )
=> X459 ) )
=> X459 ) )
=> ( ! [X461: $i,X462: $i] :
( ( in @ X462 @ X461 )
=> ( in @ X462 @ ( powerset @ ( setunion @ X461 ) ) ) )
=> ( ! [X463: $i > $o] :
( ? [X464: $i] :
( ( X463 @ X464 )
& ! [X465: $i] :
( ( X463 @ X465 )
=> ( X464 = X465 ) ) )
=> ? [X466: $i] :
! [X467: $i] :
( ( X463 @ X467 )
<=> ( X467 = X466 ) ) )
=> ( ! [X468: $i] :
( ( X468 != emptyset )
=> ? [X469: $i] :
( ( in @ X469 @ X468 )
& $true ) )
=> ( ! [X470: $i,X471: $i] :
( ( in @ X470 @ ( setadjoin @ X471 @ emptyset ) )
=> ( X470 = X471 ) )
=> ( ! [X472: $i,X473: $i] :
( ( X472 != X473 )
=> ~ ( in @ X473 @ ( setadjoin @ X472 @ emptyset ) ) )
=> ( ! [X474: $i,X475: $i] :
( ( X474 = X475 )
=> ( in @ X474 @ ( setadjoin @ X475 @ emptyset ) ) )
=> ( ! [X476: $i,X477: $i] :
( ( in @ X476 @ ( setadjoin @ X477 @ emptyset ) )
=> ( in @ X477 @ ( setadjoin @ X476 @ emptyset ) ) )
=> ( ! [X478: $i,X479: $i,X480: $i] :
( ( in @ X480 @ ( setadjoin @ X478 @ ( setadjoin @ X479 @ emptyset ) ) )
=> ( ( X480 = X478 )
| ( X480 = X479 ) ) )
=> ( ! [X481: $i,X482: $i] : ( in @ X481 @ ( setadjoin @ X481 @ ( setadjoin @ X482 @ emptyset ) ) )
=> ( ! [X483: $i,X484: $i] : ( in @ X484 @ ( setadjoin @ X483 @ ( setadjoin @ X484 @ emptyset ) ) )
=> ( ! [X485: $i,X486: $i > $o] :
( ? [X487: $i] :
( ( in @ X487 @ X485 )
& ( X486 @ X487 ) )
=> ( ( ( dsetconstr @ X485 @ X486 )
= emptyset )
=> ~ $true ) )
=> ( ! [X488: $i > $o,X489: $i] :
( ( in @ X489 @ emptyset )
=> ( X488 @ X489 ) )
=> ( ! [X490: $i,X491: $i > $o] :
( ~ ! [X492: $i] :
( ( in @ X492 @ X490 )
=> ( X491 @ X492 ) )
=> ? [X493: $i] :
( ( in @ X493 @ X490 )
& ~ ( X491 @ X493 ) ) )
=> ( ! [X494: $i,X495: $i > $o] :
( ! [X496: $i] :
( ( in @ X496 @ X494 )
=> ~ ( X495 @ X496 ) )
=> ~ ? [X497: $i] :
( ( in @ X497 @ X494 )
& ( X495 @ X497 ) ) )
=> ( ! [X498: $i,X499: $i > $o] :
( ~ ? [X500: $i] :
( ( in @ X500 @ X498 )
& ( X499 @ X500 ) )
=> ! [X501: $i] :
( ( in @ X501 @ X498 )
=> ~ ( X499 @ X501 ) ) )
=> ( ! [X502: $i,X503: $i > $o] :
( ? [X504: $i] :
( ( in @ X504 @ X502 )
& ~ ( X503 @ X504 ) )
=> ~ ! [X505: $i] :
( ( in @ X505 @ X502 )
=> ( X503 @ X505 ) ) )
=> ( ! [X506: $o] :
( X506
=> ( in @ emptyset @ ( prop2set @ X506 ) ) )
=> ( ! [X507: $o] :
( X507
=> ( set2prop @ ( prop2set @ X507 ) ) )
=> ( ! [X508: $i,X509: $i > $o] :
( ~ ? [X510: $i] :
( ( in @ X510 @ X508 )
& ( X509 @ X510 ) )
=> ! [X511: $i] :
( ( in @ X511 @ X508 )
=> ~ ( X509 @ X511 ) ) )
=> ( ! [X512: $i,X513: $i > $o] :
( ~ ! [X514: $i] :
( ( in @ X514 @ X512 )
=> ( X513 @ X514 ) )
=> ? [X515: $i] :
( ( in @ X515 @ X512 )
& ~ ( X513 @ X515 ) ) )
=> ( ! [X516: $i > $o] :
( ? [X517: $i] :
( ( X516 @ X517 )
& ! [X518: $i] :
( ( X516 @ X518 )
=> ( X517 = X518 ) ) )
=> ? [X519: $i] :
( ( X516 @ X519 )
& ! [X520: $i] :
( ( X516 @ X520 )
=> ( X519 = X520 ) ) ) )
=> ( ! [X521: $i > $o] :
( ? [X522: $i] : ( X521 @ X522 )
=> ( ! [X523: $i,X524: $i] :
( ( X521 @ X523 )
=> ( ( X521 @ X524 )
=> ( X523 = X524 ) ) )
=> ? [X525: $i] :
( ( X521 @ X525 )
& ! [X526: $i] :
( ( X521 @ X526 )
=> ( X525 = X526 ) ) ) ) )
=> ( ! [X527: $i > $o] :
( ? [X528: $i] :
! [X529: $i] :
( ( X527 @ X529 )
<=> ( X529 = X528 ) )
=> ? [X530: $i] :
( ( X527 @ X530 )
& ! [X531: $i] :
( ( X527 @ X531 )
=> ( X530 = X531 ) ) ) )
=> ( ! [X532: $i,X533: $i] :
( ( X532 = X533 )
=> ! [X534: $i,X535: $i] :
( ( X534 = X535 )
=> ( ( in @ X534 @ X532 )
=> ( in @ X535 @ X533 ) ) ) )
=> ( ! [X536: $i,X537: $i] :
( ( X536 = X537 )
=> ! [X538: $i,X539: $i] :
( ( X538 = X539 )
=> ( ( in @ X538 @ X536 )
<=> ( in @ X539 @ X537 ) ) ) )
=> ( ! [X540: $i > $o] :
( ? [X541: $i] :
( ( X540 @ X541 )
& ! [X542: $i] :
( ( X540 @ X542 )
=> ( X541 = X542 ) ) )
=> ! [X543: $i,X544: $i] :
( ( X540 @ X543 )
=> ( ( X540 @ X544 )
=> ( X543 = X544 ) ) ) )
=> ( ! [X545: $i > $o,X546: $i > $o] :
( ! [X547: $i,X548: $i] :
( ( X547 = X548 )
=> ( ( X545 @ X547 )
<=> ( X546 @ X548 ) ) )
=> ( ? [X549: $i] :
( ( X545 @ X549 )
& ! [X550: $i] :
( ( X545 @ X550 )
=> ( X549 = X550 ) ) )
<=> ? [X551: $i] :
( ( X546 @ X551 )
& ! [X552: $i] :
( ( X546 @ X552 )
=> ( X551 = X552 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X553: $i,X554: $i] :
( ( X553 = X554 )
=> ! [X555: $i,X556: $i] :
( ( X555 = X556 )
=> ( ( setadjoin @ X553 @ X555 )
= ( setadjoin @ X554 @ X556 ) ) ) )
=> ( ! [X557: $i,X558: $i] :
( ( X557 = X558 )
=> ( ( powerset @ X557 )
= ( powerset @ X558 ) ) )
=> ( ! [X559: $i,X560: $i] :
( ( X559 = X560 )
=> ( ( setunion @ X559 )
= ( setunion @ X560 ) ) )
=> ( ( omega = omega )
=> ( ! [X561: $i > $o] :
( ? [X562: $i] :
( ( X561 @ X562 )
& ! [X563: $i] :
( ( X561 @ X563 )
=> ( X562 = X563 ) ) )
=> ! [X564: $i,X565: $i] :
( ( X561 @ X564 )
=> ( ( X561 @ X565 )
=> ( X564 = X565 ) ) ) )
=> ( ! [X566: $i > $o,X567: $i > $o] :
( ! [X568: $i,X569: $i] :
( ( X568 = X569 )
=> ( ( X566 @ X568 )
<=> ( X567 @ X569 ) ) )
=> ( ? [X570: $i] :
( ( X566 @ X570 )
& ! [X571: $i] :
( ( X566 @ X571 )
=> ( X570 = X571 ) ) )
=> ( ? [X572: $i] :
( ( X567 @ X572 )
& ! [X573: $i] :
( ( X567 @ X573 )
=> ( X572 = X573 ) ) )
=> ( ( descr @ X566 )
= ( descr @ X567 ) ) ) ) )
=> ( ! [X574: $i,X575: $i] :
( ( X574 = X575 )
=> ! [X576: $i > $o,X577: $i > $o] :
( ! [X578: $i] :
( ( in @ X578 @ X574 )
=> ! [X579: $i] :
( ( in @ X579 @ X575 )
=> ( ( X578 = X579 )
=> ( ( X576 @ X578 )
<=> ( X577 @ X579 ) ) ) ) )
=> ( ( dsetconstr @ X574 @ X576 )
= ( dsetconstr @ X575 @ X577 ) ) ) )
=> ( ! [X580: $i,X581: $i] :
( ! [X582: $i] :
( ( in @ X582 @ X580 )
=> ( in @ X582 @ X581 ) )
=> ( subset @ X580 @ X581 ) )
=> ( ! [X583: $i,X584: $i] :
( ( X583 = X584 )
=> ( subset @ X584 @ X583 ) )
=> ( ! [X585: $i,X586: $i] :
( ( X585 = X586 )
=> ( subset @ X585 @ X586 ) )
=> ( ! [X587: $i,X588: $i] :
( ! [X589: $i] :
( ( in @ X589 @ X587 )
=> ( in @ X589 @ X588 ) )
=> ( subset @ X587 @ X588 ) )
=> ( ! [X590: $i] : ( subset @ emptyset @ X590 )
=> ( ! [X591: $i,X592: $i,X593: $i] :
( ( subset @ X591 @ X592 )
=> ( ( in @ X593 @ X591 )
=> ( in @ X593 @ X592 ) ) )
=> ( ! [X594: $i,X595: $i,X596: $i] :
( ( subset @ X594 @ X595 )
=> ( ~ ( in @ X596 @ X595 )
=> ~ ( in @ X596 @ X594 ) ) )
=> ( ! [X597: $i,X598: $i,X599: $i] :
( ( in @ X599 @ X597 )
=> ( ~ ( in @ X599 @ X598 )
=> ~ ( subset @ X597 @ X598 ) ) )
=> ( ! [X600: $i,X601: $i] :
( ~ ( subset @ X600 @ X601 )
=> ( X600 != X601 ) )
=> ( ! [X602: $i,X603: $i,X604: $i] :
( ( in @ X604 @ X602 )
=> ( ~ ( in @ X604 @ X603 )
=> ( X602 != X603 ) ) )
=> ( ! [X605: $i] : ( subset @ X605 @ X605 )
=> ( ! [X606: $i,X607: $i,X608: $i] :
( ( subset @ X606 @ X607 )
=> ( ( subset @ X607 @ X608 )
=> ( subset @ X606 @ X608 ) ) )
=> ( ! [X609: $i,X610: $i] : ( subset @ X610 @ ( setadjoin @ X609 @ X610 ) )
=> ( ! [X611: $i,X612: $i,X613: $i] :
( ( subset @ X611 @ X613 )
=> ( subset @ X611 @ ( setadjoin @ X612 @ X613 ) ) )
=> ( ! [X614: $i,X615: $i] :
( ( subset @ X614 @ X615 )
=> ( in @ X614 @ ( powerset @ X615 ) ) )
=> ( ! [X616: $i,X617: $i] :
( ( subset @ X616 @ X617 )
=> ( ( subset @ X617 @ X616 )
=> ( X616 = X617 ) ) )
=> ( ! [X618: $i] :
( ( subset @ X618 @ emptyset )
=> ( X618 = emptyset ) )
=> ( ! [X619: $i,X620: $i] :
( ( subset @ X620 @ X619 )
=> ( in @ X620 @ ( powerset @ X619 ) ) )
=> ( ! [X621: $i,X622: $i] :
( ( in @ X622 @ ( powerset @ X621 ) )
=> ( subset @ X622 @ X621 ) )
=> ( ! [X623: $i] : ( in @ X623 @ ( powerset @ X623 ) )
=> ( ! [X624: $i,X625: $i] :
( ( subset @ X624 @ X625 )
=> ( subset @ ( powerset @ X624 ) @ ( powerset @ X625 ) ) )
=> ( ! [X626: $i,X627: $i > $o] : ( in @ ( dsetconstr @ X626 @ X627 ) @ ( powerset @ X626 ) )
=> ( ! [X628: $i,X629: $i > $o] : ( subset @ ( dsetconstr @ X628 @ X629 ) @ X628 )
=> ( ! [X630: $i,X631: $i,X632: $i] :
( ( in @ X632 @ X630 )
=> ( in @ X632 @ ( binunion @ X630 @ X631 ) ) )
=> ( ! [X633: $i,X634: $i] : ( in @ X634 @ ( setadjoin @ X633 @ ( setadjoin @ X634 @ emptyset ) ) )
=> ( ! [X635: $i,X636: $i,X637: $i] :
( ( in @ X637 @ X636 )
=> ( in @ X637 @ ( binunion @ X635 @ X636 ) ) )
=> ( ! [X638: $i,X639: $i,X640: $i,X641: $o] :
( ( in @ X640 @ ( binunion @ X638 @ X639 ) )
=> ( ( ( in @ X640 @ X638 )
=> X641 )
=> ( ( ( in @ X640 @ X639 )
=> X641 )
=> X641 ) ) )
=> ( ! [X642: $i,X643: $i,X644: $i] :
( ( in @ X644 @ ( binunion @ X642 @ X643 ) )
=> ( ( in @ X644 @ X642 )
| ( in @ X644 @ X643 ) ) )
=> ( ! [X645: $i,X646: $i] : ( subset @ X645 @ ( binunion @ X645 @ X646 ) )
=> ( ! [X647: $i,X648: $i] : ( subset @ X648 @ ( binunion @ X647 @ X648 ) )
=> ( ! [X649: $i,X650: $i,X651: $i] :
( ( in @ X651 @ X649 )
=> ( ( in @ X651 @ X650 )
=> ( in @ X651 @ ( binintersect @ X649 @ X650 ) ) ) )
=> ( ! [X652: $i,X653: $i,X654: $i] :
( ( subset @ X654 @ X652 )
=> ( ( subset @ X654 @ X653 )
=> ( subset @ X654 @ ( binintersect @ X652 @ X653 ) ) ) )
=> ( ! [X655: $i,X656: $i,X657: $i] :
( ( in @ X657 @ ( binintersect @ X655 @ X656 ) )
=> ( in @ X657 @ X655 ) )
=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[binintersectLsub]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_127]),foundationAx]),wellorderingAx]),c_0_128]),c_0_129]),c_0_130]),c_0_131]),c_0_132]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_133]),setext]),emptyI]),noeltsimpempty]),c_0_134]),c_0_135]),c_0_136]),c_0_137]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_138]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_139]),c_0_140]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_141]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_142]),c_0_143]),c_0_144]),inCongP]),in__Cong]),c_0_145]),c_0_146]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_147]),c_0_148]),c_0_149]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_150]),c_0_151]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL])])]),c_0_152]) ).
thf(c_0_154,plain,
! [X658: $i,X659: $i] :
( ( binintersect @ X658 @ X659 )
= ( dsetconstr @ X658
@ ^ [Z0: $i] : ( in @ Z0 @ X659 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binintersect])]) ).
thf(c_0_155,negated_conjecture,
! [X662: $i,X663: $i,X665: $i,X666: $i,X667: $i,X668: $i,X669: $i,X670: $i,X671: $i,X672: $i,X673: $i,X675: $i,X676: $i,X678: $i,X679: $i,X680: $i,X681: $i,X682: $i,X684: $i,X685: $i > $i > $o,X686: $i,X688: $i,X691: $i,X693: $i,X694: $i,X695: $i,X696: $i,X698: $i,X699: $i > $o,X700: $i,X702: $i,X703: $i > $o,X704: $i,X705: $i,X706: $i > $o,X707: $i,X708: $i,X709: $i > $o,X710: $i,X711: $i > $o,X712: $i,X715: $i,X716: $o,X717: $i,X718: $i,X719: $o,X720: $i,X721: $i,X722: $i > $o,X723: $i,X726: $i,X727: $i,X730: $i,X732: $i,X734: $i,X735: $i > $o,X736: $i,X737: $i,X739: $i,X740: $i > $o,X741: $i,X742: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i,X752: $o,X753: $i,X754: $i,X755: $i,X756: $i,X757: $i,X758: $i,X760: $i,X761: $i,X762: $i,X763: $i,X764: $i,X765: $i,X766: $i,X767: $i,X768: $i,X769: $i,X770: $o,X772: $i,X773: $i,X774: $i > $o,X775: $i,X778: $i,X779: $i,X780: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i,X787: $i,X788: $i,X789: $i,X790: $i,X791: $i,X792: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i > $o,X799: $i,X800: $i > $o,X801: $i,X802: $i,X803: $i > $o,X804: $i,X806: $i,X807: $i > $o,X809: $i,X810: $i,X811: $i > $o,X813: $i,X814: $i,X815: $i > $o,X816: $i,X818: $o,X819: $o,X820: $i,X821: $i > $o,X823: $i,X824: $i,X825: $i > $o,X826: $i,X828: $i > $o,X829: $i,X832: $i,X833: $i > $o,X834: $i,X838: $i,X839: $i > $o,X840: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i > $o,X853: $i,X855: $i,X856: $i,X857: $i > $o,X858: $i > $o,X861: $i,X864: $i,X865: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i > $o,X878: $i,X880: $i,X881: $i,X882: $i > $o,X883: $i > $o,X886: $i,X888: $i,X890: $i,X891: $i,X892: $i > $o,X893: $i > $o,X896: $i,X897: $i,X899: $i,X900: $i,X901: $i,X902: $i,X903: $i,X904: $i,X906: $i,X907: $i,X908: $i,X909: $i,X910: $i,X911: $i,X912: $i,X913: $i,X914: $i,X915: $i,X916: $i,X917: $i,X918: $i,X919: $i,X920: $i,X921: $i,X922: $i,X923: $i,X924: $i,X925: $i,X926: $i,X927: $i,X928: $i,X929: $i,X930: $i,X931: $i,X932: $i,X933: $i,X934: $i,X935: $i,X936: $i,X937: $i,X938: $i,X939: $i,X940: $i,X941: $i,X942: $i,X943: $i > $o,X944: $i,X945: $i > $o,X946: $i,X947: $i,X948: $i,X949: $i,X950: $i,X951: $i,X952: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $o,X958: $i,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i] :
( ( ~ ( in @ ( esk1_2 @ X662 @ X663 ) @ X662 )
| ~ ( in @ ( esk1_2 @ X662 @ X663 ) @ X663 )
| ( X662 = X663 ) )
& ( ( in @ ( esk1_2 @ X662 @ X663 ) @ X662 )
| ( in @ ( esk1_2 @ X662 @ X663 ) @ X663 )
| ( X662 = X663 ) )
& ~ ( in @ X665 @ emptyset )
& ( ~ ( in @ X668 @ ( setadjoin @ X666 @ X667 ) )
| ( X668 = X666 )
| ( in @ X668 @ X667 ) )
& ( ( X668 != X666 )
| ( in @ X668 @ ( setadjoin @ X666 @ X667 ) ) )
& ( ~ ( in @ X668 @ X667 )
| ( in @ X668 @ ( setadjoin @ X666 @ X667 ) ) )
& ( ~ ( in @ X670 @ ( powerset @ X669 ) )
| ~ ( in @ X671 @ X670 )
| ( in @ X671 @ X669 ) )
& ( ( in @ ( esk2_2 @ X672 @ X673 ) @ X673 )
| ( in @ X673 @ ( powerset @ X672 ) ) )
& ( ~ ( in @ ( esk2_2 @ X672 @ X673 ) @ X672 )
| ( in @ X673 @ ( powerset @ X672 ) ) )
& ( ( in @ X676 @ ( esk3_2 @ X675 @ X676 ) )
| ~ ( in @ X676 @ ( setunion @ X675 ) ) )
& ( ( in @ ( esk3_2 @ X675 @ X676 ) @ X675 )
| ~ ( in @ X676 @ ( setunion @ X675 ) ) )
& ( ~ ( in @ X679 @ X680 )
| ~ ( in @ X680 @ X678 )
| ( in @ X679 @ ( setunion @ X678 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X681 @ omega )
| ( in @ ( setadjoin @ X681 @ X681 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X682 ) @ omega )
| ~ ( in @ emptyset @ X682 )
| ~ ( in @ X684 @ omega )
| ( in @ X684 @ X682 ) )
& ( ( in @ ( esk4_1 @ X682 ) @ X682 )
| ~ ( in @ emptyset @ X682 )
| ~ ( in @ X684 @ omega )
| ( in @ X684 @ X682 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X682 ) @ ( esk4_1 @ X682 ) ) @ X682 )
| ~ ( in @ emptyset @ X682 )
| ~ ( in @ X684 @ omega )
| ( in @ X684 @ X682 ) )
& ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
& ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
& ( ~ ( in @ X694 @ X686 )
| ~ ( X685 @ X694 @ X693 )
| ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
| ( in @ ( esk5_2 @ X685 @ X686 ) @ X686 ) )
& ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ~ ( in @ X694 @ X686 )
| ~ ( X685 @ X694 @ X693 )
| ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
| ( X685 @ ( esk5_2 @ X685 @ X686 ) @ ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ( in @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X686 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( X688
!= ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ( X685 @ ( esk8_3 @ X685 @ X686 @ X691 ) @ X691 )
| ~ ( in @ X691 @ ( esk7_2 @ X685 @ X686 ) )
| ( X688
!= ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ~ ( in @ X694 @ X686 )
| ~ ( X685 @ X694 @ X693 )
| ( in @ X693 @ ( esk7_2 @ X685 @ X686 ) )
| ( X688
!= ( esk6_3 @ X685 @ X686 @ X688 ) )
| ~ ( X685 @ ( esk5_2 @ X685 @ X686 ) @ X688 ) )
& ( ( in @ ( esk9_1 @ X695 ) @ X695 )
| ~ ( in @ X696 @ X695 ) )
& ( ~ ( in @ X698 @ ( esk9_1 @ X695 ) )
| ~ ( in @ X698 @ X695 )
| ~ ( in @ X696 @ X695 ) )
& epred1_0
& ( ( X699 @ ( esk10_2 @ X699 @ X700 ) )
| ~ ( X699 @ X700 )
| ( X699 @ ( descr @ X699 ) ) )
& ( ( X700
!= ( esk10_2 @ X699 @ X700 ) )
| ~ ( X699 @ X700 )
| ( X699 @ ( descr @ X699 ) ) )
& ( ~ ( in @ X704 @ X702 )
| ~ ( X703 @ X704 )
| ( in @ X704 @ ( dsetconstr @ X702 @ X703 ) ) )
& ( ~ ( in @ X707 @ ( dsetconstr @ X705 @ X706 ) )
| ( in @ X707 @ X705 ) )
& ( ~ ( in @ X710 @ ( dsetconstr @ X708 @ X709 ) )
| ( X709 @ X710 ) )
& ( ( X711 @ ( esk12_1 @ X711 ) )
| ( X711 @ ( esk11_2 @ X711 @ X712 ) )
| ~ ( X711 @ X712 ) )
& ( ~ ( X711 @ X715 )
| ( ( esk12_1 @ X711 )
= X715 )
| ( X711 @ ( esk11_2 @ X711 @ X712 ) )
| ~ ( X711 @ X712 ) )
& ( ( X711 @ ( esk12_1 @ X711 ) )
| ( X712
!= ( esk11_2 @ X711 @ X712 ) )
| ~ ( X711 @ X712 ) )
& ( ~ ( X711 @ X715 )
| ( ( esk12_1 @ X711 )
= X715 )
| ( X712
!= ( esk11_2 @ X711 @ X712 ) )
| ~ ( X711 @ X712 ) )
& ( ~ ( in @ X717 @ ( prop2set @ X716 ) )
| X716 )
& ( ~ ( in @ X718 @ emptyset )
| X719 )
& ( ~ ( in @ X720 @ emptyset )
| ~ $true )
& ~ ( in @ X721 @ emptyset )
& ( ( X722 @ ( esk13_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 )
| ( X722 @ ( esk14_1 @ X722 ) ) )
& ( ( X723
!= ( esk13_2 @ X722 @ X723 ) )
| ~ ( X722 @ X723 )
| ( X722 @ ( esk14_1 @ X722 ) ) )
& ( ( in @ ( esk16_2 @ X726 @ X727 ) @ X727 )
| ( X726 = X727 )
| ( in @ ( esk15_2 @ X726 @ X727 ) @ X726 ) )
& ( ~ ( in @ ( esk16_2 @ X726 @ X727 ) @ X726 )
| ( X726 = X727 )
| ( in @ ( esk15_2 @ X726 @ X727 ) @ X726 ) )
& ( ( in @ ( esk16_2 @ X726 @ X727 ) @ X727 )
| ( X726 = X727 )
| ~ ( in @ ( esk15_2 @ X726 @ X727 ) @ X727 ) )
& ( ~ ( in @ ( esk16_2 @ X726 @ X727 ) @ X726 )
| ( X726 = X727 )
| ~ ( in @ ( esk15_2 @ X726 @ X727 ) @ X727 ) )
& ( ( in @ ( esk17_1 @ X730 ) @ X730 )
| ( X730 = emptyset ) )
& ( ( in @ ( esk18_1 @ X732 ) @ X732 )
| ( X732 = emptyset ) )
& ( ~ ( in @ X736 @ ( dsetconstr @ X734 @ X735 ) )
| ( X735 @ X736 )
| ~ ( in @ X736 @ X734 ) )
& ( ~ ( X735 @ X736 )
| ( in @ X736 @ ( dsetconstr @ X734 @ X735 ) )
| ~ ( in @ X736 @ X734 ) )
& ( ( X737 = emptyset )
| ( in @ ( esk19_1 @ X737 ) @ X737 ) )
& ( ~ ( in @ X741 @ X739 )
| ~ ( X740 @ X741 )
| ( ( dsetconstr @ X739 @ X740 )
!= emptyset ) )
& ( ~ ( in @ X743 @ X742 )
| ( X742 != emptyset ) )
& ( in @ X744 @ ( setadjoin @ X744 @ X745 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X748 @ X747 )
| ( in @ X748 @ ( setadjoin @ X746 @ X747 ) ) )
& ( ( in @ X751 @ X750 )
| X752
| ( X751 = X749 )
| ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
& ( ~ X752
| X752
| ( X751 = X749 )
| ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
& ( ( in @ X751 @ X750 )
| X752
| ~ X752
| ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
& ( ~ X752
| X752
| ~ X752
| ~ ( in @ X751 @ ( setadjoin @ X749 @ X750 ) ) )
& ( ~ ( in @ X755 @ ( setadjoin @ X753 @ X754 ) )
| ( X755 = X753 )
| ( in @ X755 @ X754 ) )
& ( ( dsetconstr @ X756
@ ^ [Z0: $i] : $true )
= X756 )
& ( ( in @ ( esk20_2 @ X757 @ X758 ) @ X758 )
| ( in @ X758 @ ( powerset @ X757 ) ) )
& ( ~ ( in @ ( esk20_2 @ X757 @ X758 ) @ X757 )
| ( in @ X758 @ ( powerset @ X757 ) ) )
& ( in @ emptyset @ ( powerset @ X760 ) )
& ( in @ emptyset @ ( powerset @ X761 ) )
& ( ~ ( in @ X763 @ ( powerset @ X762 ) )
| ~ ( in @ X764 @ X763 )
| ( in @ X764 @ X762 ) )
& ( ~ ( in @ X766 @ X767 )
| ~ ( in @ X767 @ X765 )
| ( in @ X766 @ ( setunion @ X765 ) ) )
& ( ( in @ X769 @ ( esk21_3 @ X768 @ X769 @ X770 ) )
| X770
| ~ ( in @ X769 @ ( setunion @ X768 ) ) )
& ( ( in @ ( esk21_3 @ X768 @ X769 @ X770 ) @ X768 )
| X770
| ~ ( in @ X769 @ ( setunion @ X768 ) ) )
& ( ~ X770
| X770
| ~ ( in @ X769 @ ( setunion @ X768 ) ) )
& ( ~ ( in @ X773 @ X772 )
| ( in @ X773 @ ( powerset @ ( setunion @ X772 ) ) ) )
& ( ~ ( X774 @ X778 )
| ( X778
= ( esk23_1 @ X774 ) )
| ( X774 @ ( esk22_2 @ X774 @ X775 ) )
| ~ ( X774 @ X775 ) )
& ( ( X779
!= ( esk23_1 @ X774 ) )
| ( X774 @ X779 )
| ( X774 @ ( esk22_2 @ X774 @ X775 ) )
| ~ ( X774 @ X775 ) )
& ( ~ ( X774 @ X778 )
| ( X778
= ( esk23_1 @ X774 ) )
| ( X775
!= ( esk22_2 @ X774 @ X775 ) )
| ~ ( X774 @ X775 ) )
& ( ( X779
!= ( esk23_1 @ X774 ) )
| ( X774 @ X779 )
| ( X775
!= ( esk22_2 @ X774 @ X775 ) )
| ~ ( X774 @ X775 ) )
& ( ( in @ ( esk24_1 @ X780 ) @ X780 )
| ( X780 = emptyset ) )
& ( $true
| ( X780 = emptyset ) )
& ( ~ ( in @ X782 @ ( setadjoin @ X783 @ emptyset ) )
| ( X782 = X783 ) )
& ( ( X784 = X785 )
| ~ ( in @ X785 @ ( setadjoin @ X784 @ emptyset ) ) )
& ( ( X786 != X787 )
| ( in @ X786 @ ( setadjoin @ X787 @ emptyset ) ) )
& ( ~ ( in @ X788 @ ( setadjoin @ X789 @ emptyset ) )
| ( in @ X789 @ ( setadjoin @ X788 @ emptyset ) ) )
& ( ~ ( in @ X792 @ ( setadjoin @ X790 @ ( setadjoin @ X791 @ emptyset ) ) )
| ( X792 = X790 )
| ( X792 = X791 ) )
& ( in @ X793 @ ( setadjoin @ X793 @ ( setadjoin @ X794 @ emptyset ) ) )
& ( in @ X796 @ ( setadjoin @ X795 @ ( setadjoin @ X796 @ emptyset ) ) )
& ( ~ ( in @ X799 @ X797 )
| ~ ( X798 @ X799 )
| ( ( dsetconstr @ X797 @ X798 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X801 @ emptyset )
| ( X800 @ X801 ) )
& ( ( in @ ( esk25_2 @ X802 @ X803 ) @ X802 )
| ~ ( in @ X804 @ X802 )
| ( X803 @ X804 ) )
& ( ~ ( X803 @ ( esk25_2 @ X802 @ X803 ) )
| ~ ( in @ X804 @ X802 )
| ( X803 @ X804 ) )
& ( ( in @ ( esk26_2 @ X806 @ X807 ) @ X806 )
| ~ ( in @ X809 @ X806 )
| ~ ( X807 @ X809 ) )
& ( ( X807 @ ( esk26_2 @ X806 @ X807 ) )
| ~ ( in @ X809 @ X806 )
| ~ ( X807 @ X809 ) )
& ( ( in @ ( esk27_2 @ X810 @ X811 ) @ X810 )
| ~ ( in @ X813 @ X810 )
| ~ ( X811 @ X813 ) )
& ( ( X811 @ ( esk27_2 @ X810 @ X811 ) )
| ~ ( in @ X813 @ X810 )
| ~ ( X811 @ X813 ) )
& ( ( in @ ( esk28_2 @ X814 @ X815 ) @ X814 )
| ~ ( in @ X816 @ X814 )
| ( X815 @ X816 ) )
& ( ~ ( X815 @ ( esk28_2 @ X814 @ X815 ) )
| ~ ( in @ X816 @ X814 )
| ( X815 @ X816 ) )
& ( ~ X818
| ( in @ emptyset @ ( prop2set @ X818 ) ) )
& ( ~ X819
| ( set2prop @ ( prop2set @ X819 ) ) )
& ( ( in @ ( esk29_2 @ X820 @ X821 ) @ X820 )
| ~ ( in @ X823 @ X820 )
| ~ ( X821 @ X823 ) )
& ( ( X821 @ ( esk29_2 @ X820 @ X821 ) )
| ~ ( in @ X823 @ X820 )
| ~ ( X821 @ X823 ) )
& ( ( in @ ( esk30_2 @ X824 @ X825 ) @ X824 )
| ~ ( in @ X826 @ X824 )
| ( X825 @ X826 ) )
& ( ~ ( X825 @ ( esk30_2 @ X824 @ X825 ) )
| ~ ( in @ X826 @ X824 )
| ( X825 @ X826 ) )
& ( ( X828 @ ( esk32_1 @ X828 ) )
| ( X828 @ ( esk31_2 @ X828 @ X829 ) )
| ~ ( X828 @ X829 ) )
& ( ~ ( X828 @ X832 )
| ( ( esk32_1 @ X828 )
= X832 )
| ( X828 @ ( esk31_2 @ X828 @ X829 ) )
| ~ ( X828 @ X829 ) )
& ( ( X828 @ ( esk32_1 @ X828 ) )
| ( X829
!= ( esk31_2 @ X828 @ X829 ) )
| ~ ( X828 @ X829 ) )
& ( ~ ( X828 @ X832 )
| ( ( esk32_1 @ X828 )
= X832 )
| ( X829
!= ( esk31_2 @ X828 @ X829 ) )
| ~ ( X828 @ X829 ) )
& ( ( X833 @ ( esk35_1 @ X833 ) )
| ( X833 @ ( esk33_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ~ ( X833 @ X838 )
| ( ( esk35_1 @ X833 )
= X838 )
| ( X833 @ ( esk33_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ( X833 @ ( esk35_1 @ X833 ) )
| ( X833 @ ( esk34_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ~ ( X833 @ X838 )
| ( ( esk35_1 @ X833 )
= X838 )
| ( X833 @ ( esk34_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ( X833 @ ( esk35_1 @ X833 ) )
| ( ( esk33_1 @ X833 )
!= ( esk34_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ~ ( X833 @ X838 )
| ( ( esk35_1 @ X833 )
= X838 )
| ( ( esk33_1 @ X833 )
!= ( esk34_1 @ X833 ) )
| ~ ( X833 @ X834 ) )
& ( ( X839 @ ( esk37_1 @ X839 ) )
| ~ ( X839 @ ( esk36_2 @ X839 @ X840 ) )
| ( ( esk36_2 @ X839 @ X840 )
!= X840 ) )
& ( ~ ( X839 @ X843 )
| ( ( esk37_1 @ X839 )
= X843 )
| ~ ( X839 @ ( esk36_2 @ X839 @ X840 ) )
| ( ( esk36_2 @ X839 @ X840 )
!= X840 ) )
& ( ( X839 @ ( esk37_1 @ X839 ) )
| ( X839 @ ( esk36_2 @ X839 @ X840 ) )
| ( ( esk36_2 @ X839 @ X840 )
= X840 ) )
& ( ~ ( X839 @ X843 )
| ( ( esk37_1 @ X839 )
= X843 )
| ( X839 @ ( esk36_2 @ X839 @ X840 ) )
| ( ( esk36_2 @ X839 @ X840 )
= X840 ) )
& ( ( X844 != X845 )
| ( X846 != X847 )
| ~ ( in @ X846 @ X844 )
| ( in @ X847 @ X845 ) )
& ( ~ ( in @ X850 @ X848 )
| ( in @ X851 @ X849 )
| ( X850 != X851 )
| ( X848 != X849 ) )
& ( ~ ( in @ X851 @ X849 )
| ( in @ X850 @ X848 )
| ( X850 != X851 )
| ( X848 != X849 ) )
& ( ( X852 @ ( esk38_2 @ X852 @ X853 ) )
| ~ ( X852 @ X853 )
| ~ ( X852 @ X855 )
| ~ ( X852 @ X856 )
| ( X855 = X856 ) )
& ( ( X853
!= ( esk38_2 @ X852 @ X853 ) )
| ~ ( X852 @ X853 )
| ~ ( X852 @ X855 )
| ~ ( X852 @ X856 )
| ( X855 = X856 ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( ( esk39_2 @ X857 @ X858 )
= ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ~ ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ~ ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X857 @ ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X858 @ ( esk42_2 @ X857 @ X858 ) )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X858 @ X864 )
| ( ( esk42_2 @ X857 @ X858 )
= X864 )
| ( X861
!= ( esk41_3 @ X857 @ X858 @ X861 ) )
| ~ ( X857 @ X861 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X858 @ ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ( X857 @ ( esk44_2 @ X857 @ X858 ) )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( ~ ( X857 @ X868 )
| ( ( esk44_2 @ X857 @ X858 )
= X868 )
| ( X865
!= ( esk43_3 @ X857 @ X858 @ X865 ) )
| ~ ( X858 @ X865 )
| ( X857 @ ( esk39_2 @ X857 @ X858 ) )
| ( X858 @ ( esk40_2 @ X857 @ X858 ) ) )
& ( emptyset = emptyset )
& ( ( X869 != X870 )
| ( X871 != X872 )
| ( ( setadjoin @ X869 @ X871 )
= ( setadjoin @ X870 @ X872 ) ) )
& ( ( X873 != X874 )
| ( ( powerset @ X873 )
= ( powerset @ X874 ) ) )
& ( ( X875 != X876 )
| ( ( setunion @ X875 )
= ( setunion @ X876 ) ) )
& ( omega = omega )
& ( ( X877 @ ( esk45_2 @ X877 @ X878 ) )
| ~ ( X877 @ X878 )
| ~ ( X877 @ X880 )
| ~ ( X877 @ X881 )
| ( X880 = X881 ) )
& ( ( X878
!= ( esk45_2 @ X877 @ X878 ) )
| ~ ( X877 @ X878 )
| ~ ( X877 @ X880 )
| ~ ( X877 @ X881 )
| ( X880 = X881 ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( ( esk46_2 @ X882 @ X883 )
= ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( ( esk46_2 @ X882 @ X883 )
= ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( ( esk46_2 @ X882 @ X883 )
= ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( ( esk46_2 @ X882 @ X883 )
= ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ~ ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ~ ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X882 @ ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X883 @ ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( X888
!= ( esk49_3 @ X882 @ X883 @ X888 ) )
| ~ ( X883 @ X888 )
| ( ( descr @ X882 )
= ( descr @ X883 ) )
| ( X886
!= ( esk48_3 @ X882 @ X883 @ X886 ) )
| ~ ( X882 @ X886 )
| ( X882 @ ( esk46_2 @ X882 @ X883 ) )
| ( X883 @ ( esk47_2 @ X882 @ X883 ) ) )
& ( ( in @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) @ X890 )
| ( ( dsetconstr @ X890 @ X892 )
= ( dsetconstr @ X891 @ X893 ) )
| ( X890 != X891 ) )
& ( ( in @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) @ X891 )
| ( ( dsetconstr @ X890 @ X892 )
= ( dsetconstr @ X891 @ X893 ) )
| ( X890 != X891 ) )
& ( ( ( esk50_4 @ X890 @ X891 @ X892 @ X893 )
= ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
| ( ( dsetconstr @ X890 @ X892 )
= ( dsetconstr @ X891 @ X893 ) )
| ( X890 != X891 ) )
& ( ~ ( X892 @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) )
| ~ ( X893 @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
| ( ( dsetconstr @ X890 @ X892 )
= ( dsetconstr @ X891 @ X893 ) )
| ( X890 != X891 ) )
& ( ( X892 @ ( esk50_4 @ X890 @ X891 @ X892 @ X893 ) )
| ( X893 @ ( esk51_4 @ X890 @ X891 @ X892 @ X893 ) )
| ( ( dsetconstr @ X890 @ X892 )
= ( dsetconstr @ X891 @ X893 ) )
| ( X890 != X891 ) )
& ( ( in @ ( esk52_2 @ X896 @ X897 ) @ X896 )
| ( subset @ X896 @ X897 ) )
& ( ~ ( in @ ( esk52_2 @ X896 @ X897 ) @ X897 )
| ( subset @ X896 @ X897 ) )
& ( ( X899 != X900 )
| ( subset @ X900 @ X899 ) )
& ( ( X901 != X902 )
| ( subset @ X901 @ X902 ) )
& ( ( in @ ( esk53_2 @ X903 @ X904 ) @ X903 )
| ( subset @ X903 @ X904 ) )
& ( ~ ( in @ ( esk53_2 @ X903 @ X904 ) @ X904 )
| ( subset @ X903 @ X904 ) )
& ( subset @ emptyset @ X906 )
& ( ~ ( subset @ X907 @ X908 )
| ~ ( in @ X909 @ X907 )
| ( in @ X909 @ X908 ) )
& ( ~ ( subset @ X910 @ X911 )
| ( in @ X912 @ X911 )
| ~ ( in @ X912 @ X910 ) )
& ( ~ ( in @ X915 @ X913 )
| ( in @ X915 @ X914 )
| ~ ( subset @ X913 @ X914 ) )
& ( ( subset @ X916 @ X917 )
| ( X916 != X917 ) )
& ( ~ ( in @ X920 @ X918 )
| ( in @ X920 @ X919 )
| ( X918 != X919 ) )
& ( subset @ X921 @ X921 )
& ( ~ ( subset @ X922 @ X923 )
| ~ ( subset @ X923 @ X924 )
| ( subset @ X922 @ X924 ) )
& ( subset @ X926 @ ( setadjoin @ X925 @ X926 ) )
& ( ~ ( subset @ X927 @ X929 )
| ( subset @ X927 @ ( setadjoin @ X928 @ X929 ) ) )
& ( ~ ( subset @ X930 @ X931 )
| ( in @ X930 @ ( powerset @ X931 ) ) )
& ( ~ ( subset @ X932 @ X933 )
| ~ ( subset @ X933 @ X932 )
| ( X932 = X933 ) )
& ( ~ ( subset @ X934 @ emptyset )
| ( X934 = emptyset ) )
& ( ~ ( subset @ X936 @ X935 )
| ( in @ X936 @ ( powerset @ X935 ) ) )
& ( ~ ( in @ X938 @ ( powerset @ X937 ) )
| ( subset @ X938 @ X937 ) )
& ( in @ X939 @ ( powerset @ X939 ) )
& ( ~ ( subset @ X940 @ X941 )
| ( subset @ ( powerset @ X940 ) @ ( powerset @ X941 ) ) )
& ( in @ ( dsetconstr @ X942 @ X943 ) @ ( powerset @ X942 ) )
& ( subset @ ( dsetconstr @ X944 @ X945 ) @ X944 )
& ( ~ ( in @ X948 @ X946 )
| ( in @ X948 @ ( binunion @ X946 @ X947 ) ) )
& ( in @ X950 @ ( setadjoin @ X949 @ ( setadjoin @ X950 @ emptyset ) ) )
& ( ~ ( in @ X953 @ X952 )
| ( in @ X953 @ ( binunion @ X951 @ X952 ) ) )
& ( ( in @ X956 @ X955 )
| X957
| ( in @ X956 @ X954 )
| ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
& ( ~ X957
| X957
| ( in @ X956 @ X954 )
| ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
& ( ( in @ X956 @ X955 )
| X957
| ~ X957
| ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
& ( ~ X957
| X957
| ~ X957
| ~ ( in @ X956 @ ( binunion @ X954 @ X955 ) ) )
& ( ~ ( in @ X960 @ ( binunion @ X958 @ X959 ) )
| ( in @ X960 @ X958 )
| ( in @ X960 @ X959 ) )
& ( subset @ X961 @ ( binunion @ X961 @ X962 ) )
& ( subset @ X964 @ ( binunion @ X963 @ X964 ) )
& ( ~ ( in @ X967 @ X965 )
| ~ ( in @ X967 @ X966 )
| ( in @ X967 @ ( binintersect @ X965 @ X966 ) ) )
& ( ~ ( subset @ X970 @ X968 )
| ~ ( subset @ X970 @ X969 )
| ( subset @ X970 @ ( binintersect @ X968 @ X969 ) ) )
& ( ~ ( in @ X973 @ ( binintersect @ X971 @ X972 ) )
| ( in @ X973 @ X971 ) )
& ~ ( subset @ ( binintersect @ esk54_0 @ esk55_0 ) @ esk54_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_153])])])])])])]) ).
thf(c_0_156,plain,
! [X660: $i,X661: $i] :
( ( binintersect @ X660 @ X661 )
= ( dsetconstr @ X660
@ ^ [Z0: $i] : ( in @ Z0 @ X661 ) ) ),
inference(variable_rename,[status(thm)],[c_0_154]) ).
thf(c_0_157,negated_conjecture,
! [X1: $i > $o,X2: $i] : ( subset @ ( dsetconstr @ X2 @ X1 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
thf(c_0_158,plain,
! [X2: $i,X3: $i] :
( ( binintersect @ X2 @ X3 )
= ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ Z0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
thf(c_0_159,negated_conjecture,
~ ( subset @ ( binintersect @ esk54_0 @ esk55_0 ) @ esk54_0 ),
inference(split_conjunct,[status(thm)],[c_0_155]) ).
thf(c_0_160,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
thf(c_0_161,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU592^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:12:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.51 Running higher-order theorem proving
% 0.21/0.51 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
% 0.82/300.03 # Version: 3.1.0-ho
% 0.82/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03 # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03 # Starting new_bool_5 with 300s (1) cores
% 0.82/300.03 # Starting pre_casc_3 with 300s (1) cores
% 0.82/300.03 # Starting ho_unfolding_8 with 300s (1) cores
% 0.82/300.03 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.82/300.03 # Starting new_bool_3 with 300s (1) cores
% 0.82/300.03 # Starting new_ho_5 with 300s (1) cores
% 0.82/300.03 # almost_fo_3_lam with pid 23097 completed with status 0
% 0.82/300.03 # Result found by almost_fo_3_lam
% 0.82/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03 # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03 # No SInE strategy applied
% 0.82/300.03 # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.82/300.03 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.82/300.03 # Starting pre_casc_7 with 163s (1) cores
% 0.82/300.03 # pre_casc_7 with pid 23114 completed with status 0
% 0.82/300.03 # Result found by pre_casc_7
% 0.82/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.82/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.82/300.03 # Starting ehoh_best5 with 300s (1) cores
% 0.82/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 0.82/300.03 # No SInE strategy applied
% 0.82/300.03 # Search class: HGHSM-FSLS31-MHFMMSBN
% 0.82/300.03 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.82/300.03 # Starting pre_casc_7 with 163s (1) cores
% 0.82/300.03 # Preprocessing time : 0.004 s
% 0.82/300.03
% 0.82/300.03 # Proof found!
% 0.82/300.03 # SZS status Theorem
% 0.82/300.03 # SZS output start CNFRefutation
% See solution above
% 0.82/300.03 # Parsed axioms : 237
% 0.82/300.03 # Removed by relevancy pruning/SinE : 0
% 0.82/300.03 # Initial clauses : 348
% 0.82/300.03 # Removed in clause preprocessing : 142
% 0.82/300.03 # Initial clauses in saturation : 206
% 0.82/300.03 # Processed clauses : 53
% 0.82/300.03 # ...of these trivial : 3
% 0.82/300.03 # ...subsumed : 8
% 0.82/300.03 # ...remaining for further processing : 42
% 0.82/300.03 # Other redundant clauses eliminated : 7
% 0.82/300.03 # Clauses deleted for lack of memory : 0
% 0.82/300.03 # Backward-subsumed : 0
% 0.82/300.03 # Backward-rewritten : 3
% 0.82/300.03 # Generated clauses : 36
% 0.82/300.03 # ...of the previous two non-redundant : 20
% 0.82/300.03 # ...aggressively subsumed : 0
% 0.82/300.03 # Contextual simplify-reflections : 0
% 0.82/300.03 # Paramodulations : 26
% 0.82/300.03 # Factorizations : 0
% 0.82/300.03 # NegExts : 0
% 0.82/300.03 # Equation resolutions : 7
% 0.82/300.03 # Disequality decompositions : 0
% 0.82/300.03 # Total rewrite steps : 17
% 0.82/300.03 # ...of those cached : 6
% 0.82/300.03 # Propositional unsat checks : 0
% 0.82/300.03 # Propositional check models : 0
% 0.82/300.03 # Propositional check unsatisfiable : 0
% 0.82/300.03 # Propositional clauses : 0
% 0.82/300.03 # Propositional clauses after purity: 0
% 0.82/300.03 # Propositional unsat core size : 0
% 0.82/300.03 # Propositional preprocessing time : 0.000
% 0.82/300.03 # Propositional encoding time : 0.000
% 0.82/300.03 # Propositional solver time : 0.000
% 0.82/300.03 # Success case prop preproc time : 0.000
% 0.82/300.03 # Success case prop encoding time : 0.000
% 0.82/300.03 # Success case prop solver time : 0.000
% 0.82/300.03 # Current number of processed clauses : 35
% 0.82/300.03 # Positive orientable unit clauses : 21
% 0.82/300.03 # Positive unorientable unit clauses: 0
% 0.82/300.03 # Negative unit clauses : 1
% 0.82/300.03 # Non-unit-clauses : 13
% 0.82/300.03 # Current number of unprocessed clauses: 173
% 0.82/300.03 # ...number of literals in the above : 641
% 0.82/300.03 # Current number of archived formulas : 0
% 0.82/300.03 # Current number of archived clauses : 3
% 0.82/300.03 # Clause-clause subsumption calls (NU) : 18
% 0.82/300.03 # Rec. Clause-clause subsumption calls : 17
% 0.82/300.03 # Non-unit clause-clause subsumptions : 1
% 0.82/300.03 # Unit Clause-clause subsumption calls : 3
% 0.82/300.03 # Rewrite failures with RHS unbound : 0
% 0.82/300.03 # BW rewrite match attempts : 7
% 0.82/300.03 # BW rewrite match successes : 3
% 0.82/300.03 # Condensation attempts : 53
% 0.82/300.03 # Condensation successes : 1
% 0.82/300.03 # Termbank termtop insertions : 28316
% 0.82/300.03 # Search garbage collected termcells : 11270
% 0.82/300.03
% 0.82/300.03 # -------------------------------------------------
% 0.82/300.03 # User time : 0.035 s
% 0.82/300.03 # System time : 0.009 s
% 0.82/300.03 # Total time : 0.044 s
% 0.82/300.03 # Maximum resident set size: 4664 pages
% 0.82/300.03
% 0.82/300.03 # -------------------------------------------------
% 0.82/300.03 # User time : 0.041 s
% 0.82/300.03 # System time : 0.012 s
% 0.82/300.03 # Total time : 0.053 s
% 0.82/300.03 # Maximum resident set size: 2044 pages
% 0.82/300.03 % E---3.1 exiting
% 0.82/300.03 % E exiting
%------------------------------------------------------------------------------