TSTP Solution File: SEU598^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU598^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 03:28:27 EDT 2024
% Result : Theorem 0.77s 0.61s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 284
% Syntax : Number of formulae : 317 ( 5 unt; 169 typ; 0 def)
% Number of atoms : 1207 ( 193 equ; 0 cnn)
% Maximal formula atoms : 349 ( 8 avg)
% Number of connectives : 3885 ( 287 ~; 283 |; 229 &;2326 @)
% ( 172 <=>; 588 =>; 0 <=; 0 <~>)
% Maximal formula depth : 430 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 244 ( 244 >; 0 *; 0 +; 0 <<)
% Number of symbols : 172 ( 169 usr; 121 con; 0-4 aty)
% Number of variables : 1004 ( 59 ^ 880 !; 65 ?;1004 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
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,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
epred1_0: $o ).
thf(decl_154,type,
esk1_2: $i > $i > $i ).
thf(decl_155,type,
esk2_2: $i > $i > $i ).
thf(decl_156,type,
esk3_2: $i > $i > $i ).
thf(decl_157,type,
esk4_1: $i > $i ).
thf(decl_158,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_159,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_160,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_161,type,
esk8_1: $i > $i ).
thf(decl_162,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_163,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_164,type,
esk11_2: $i > $i > $i ).
thf(decl_165,type,
esk12_2: $i > $i > $i ).
thf(decl_166,type,
esk13_1: $i > $i ).
thf(decl_167,type,
esk14_1: $i > $i ).
thf(decl_168,type,
esk15_1: $i > $i ).
thf(decl_169,type,
esk16_2: $i > $i > $i ).
thf(decl_170,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_171,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_172,type,
esk19_1: $i > $i ).
thf(decl_173,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_174,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_175,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_176,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_177,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_178,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_179,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_180,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_181,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_182,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_183,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_184,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_185,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_186,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_187,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_188,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_189,type,
esk36_2: $i > $i > $i ).
thf(decl_190,type,
esk37_2: $i > $i > $i ).
thf(decl_191,type,
esk38_2: $i > $i > $i ).
thf(decl_192,type,
esk39_0: $i ).
thf(decl_193,type,
esk40_0: $i ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(binintersectSubset4,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
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_114,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_115,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_116,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_117,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_118,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_119,plain,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI1]) ).
thf(c_0_120,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_121,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_122,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_123,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_124,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_125,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_126,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_127,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_128,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_129,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_130,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_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,
( 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_133,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_134,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_135,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_136,plain,
( epred1_0
<=> ! [X352: $i] :
? [X353: $i] :
( ! [X354: $i] :
( ( in @ X354 @ X353 )
=> ! [X355: $i] :
( ( in @ X355 @ X354 )
=> ( in @ X355 @ X352 ) ) )
& ! [X356: $i,X357: $i] :
( ( ( in @ X356 @ X352 )
& ( in @ X357 @ X352 ) )
=> ( ! [X358: $i] :
( ( in @ X358 @ X353 )
=> ( ( in @ X356 @ X358 )
<=> ( in @ X357 @ X358 ) ) )
=> ( X356 = X357 ) ) )
& ! [X359: $i,X360: $i] :
( ( ( in @ X359 @ X353 )
& ( in @ X360 @ X353 ) )
=> ( ! [X361: $i] :
( ( in @ X361 @ X359 )
=> ( in @ X361 @ X360 ) )
| ! [X362: $i] :
( ( in @ X362 @ X360 )
=> ( in @ X362 @ X359 ) ) ) )
& ! [X363: $i] :
( ( ! [X364: $i] :
( ( in @ X364 @ X363 )
=> ( in @ X364 @ X352 ) )
& ? [X365: $i] : ( in @ X365 @ X363 ) )
=> ? [X366: $i,X367: $i] :
( ( in @ X366 @ X353 )
& ( in @ X367 @ X363 )
& ~ ? [X368: $i] :
( ( in @ X368 @ X366 )
& ( in @ X368 @ X363 ) )
& ! [X369: $i] :
( ( in @ X369 @ X353 )
=> ( ! [X370: $i] :
( ( in @ X370 @ X369 )
=> ( in @ X370 @ X366 ) )
| ( in @ X367 @ X369 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_137,negated_conjecture,
~ ( ! [X325: $i,X326: $i] :
( ! [X327: $i] :
( ( in @ X327 @ X325 )
<=> ( in @ X327 @ X326 ) )
=> ( X325 = X326 ) )
=> ( ! [X328: $i] :
~ ( in @ X328 @ emptyset )
=> ( ! [X329: $i,X330: $i,X331: $i] :
( ( in @ X331 @ ( setadjoin @ X329 @ X330 ) )
<=> ( ( X331 = X329 )
| ( in @ X331 @ X330 ) ) )
=> ( ! [X332: $i,X333: $i] :
( ( in @ X333 @ ( powerset @ X332 ) )
<=> ! [X334: $i] :
( ( in @ X334 @ X333 )
=> ( in @ X334 @ X332 ) ) )
=> ( ! [X335: $i,X336: $i] :
( ( in @ X336 @ ( setunion @ X335 ) )
<=> ? [X337: $i] :
( ( in @ X336 @ X337 )
& ( in @ X337 @ X335 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X338: $i] :
( ( in @ X338 @ omega )
=> ( in @ ( setadjoin @ X338 @ X338 ) @ omega ) )
=> ( ! [X339: $i] :
( ( ( in @ emptyset @ X339 )
& ! [X340: $i] :
( ( ( in @ X340 @ omega )
& ( in @ X340 @ X339 ) )
=> ( in @ ( setadjoin @ X340 @ X340 ) @ X339 ) ) )
=> ! [X341: $i] :
( ( in @ X341 @ omega )
=> ( in @ X341 @ X339 ) ) )
=> ( ! [X342: $i > $i > $o,X343: $i] :
( ! [X344: $i] :
( ( in @ X344 @ X343 )
=> ( exu @ ( X342 @ X344 ) ) )
=> ? [X345: $i] :
! [X346: $i] :
( ( in @ X346 @ X345 )
<=> ? [X347: $i] :
( ( in @ X347 @ X343 )
& ( X342 @ X347 @ X346 ) ) ) )
=> ( ! [X348: $i] :
( ? [X349: $i] : ( in @ X349 @ X348 )
=> ? [X350: $i] :
( ( in @ X350 @ X348 )
& ~ ? [X351: $i] :
( ( in @ X351 @ X350 )
& ( in @ X351 @ X348 ) ) ) )
=> ( epred1_0
=> ( ! [X371: $i > $o] :
( ( exu @ X371 )
=> ( X371
@ ( descr
@ ^ [Z0: $i] : ( X371 @ Z0 ) ) ) )
=> ( ! [X372: $i,X373: $i > $o,X374: $i] :
( ( in @ X374 @ X372 )
=> ( ( X373 @ X374 )
=> ( in @ X374 @ ( dsetconstr @ X372 @ X373 ) ) ) )
=> ( ! [X375: $i,X376: $i > $o,X377: $i] :
( ( in @ X377 @ ( dsetconstr @ X375 @ X376 ) )
=> ( in @ X377 @ X375 ) )
=> ( ! [X378: $i,X379: $i > $o,X380: $i] :
( ( in @ X380 @ ( dsetconstr @ X378 @ X379 ) )
=> ( X379 @ X380 ) )
=> ( ! [X381: $i > $o] :
( ( exu @ X381 )
=> ? [X382: $i] :
( ( X381 @ X382 )
& ! [X383: $i] :
( ( X381 @ X383 )
=> ( X382 = X383 ) ) ) )
=> ( ! [X384: $o,X385: $i] :
( ( in @ X385 @ ( prop2set @ X384 ) )
=> X384 )
=> ( ! [X386: $i] :
( ( in @ X386 @ emptyset )
=> ! [X387: $o] : X387 )
=> ( ! [X388: $i] :
( ( in @ X388 @ emptyset )
=> ~ $true )
=> ( ! [X389: $i] :
~ ( in @ X389 @ emptyset )
=> ( ! [X390: $i > $o] :
( ( exu @ X390 )
=> ? [X391: $i] : ( X390 @ X391 ) )
=> ( ! [X392: $i,X393: $i] :
( ! [X394: $i] :
( ( in @ X394 @ X392 )
=> ( in @ X394 @ X393 ) )
=> ( ! [X395: $i] :
( ( in @ X395 @ X393 )
=> ( in @ X395 @ X392 ) )
=> ( X392 = X393 ) ) )
=> ( ! [X396: $i] :
( ! [X397: $i] :
~ ( in @ X397 @ X396 )
=> ( X396 = emptyset ) )
=> ( ! [X398: $i] :
( ! [X399: $i] :
~ ( in @ X399 @ X398 )
=> ( X398 = emptyset ) )
=> ( ! [X400: $i,X401: $i > $o,X402: $i] :
( ( in @ X402 @ X400 )
=> ( ( in @ X402 @ ( dsetconstr @ X400 @ X401 ) )
<=> ( X401 @ X402 ) ) )
=> ( ! [X403: $i] :
( ( nonempty @ X403 )
=> ? [X404: $i] : ( in @ X404 @ X403 ) )
=> ( ! [X405: $i,X406: $i > $o,X407: $i] :
( ( in @ X407 @ X405 )
=> ( ( X406 @ X407 )
=> ( nonempty @ ( dsetconstr @ X405 @ X406 ) ) ) )
=> ( ! [X408: $i] :
( ? [X409: $i] : ( in @ X409 @ X408 )
=> ( nonempty @ X408 ) )
=> ( ! [X410: $i,X411: $i] : ( in @ X410 @ ( setadjoin @ X410 @ X411 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X412: $i,X413: $i,X414: $i] :
( ( in @ X414 @ X413 )
=> ( in @ X414 @ ( setadjoin @ X412 @ X413 ) ) )
=> ( ! [X415: $i,X416: $i,X417: $i] :
( ( in @ X417 @ ( setadjoin @ X415 @ X416 ) )
=> ! [X418: $o] :
( ( ( X417 = X415 )
=> X418 )
=> ( ( ( in @ X417 @ X416 )
=> X418 )
=> X418 ) ) )
=> ( ! [X419: $i,X420: $i,X421: $i] :
( ( in @ X421 @ ( setadjoin @ X419 @ X420 ) )
=> ( ( X421 = X419 )
| ( in @ X421 @ X420 ) ) )
=> ( ! [X422: $i] :
( ( dsetconstr @ X422
@ ^ [Z0: $i] : $true )
= X422 )
=> ( ! [X423: $i,X424: $i] :
( ! [X425: $i] :
( ( in @ X425 @ X424 )
=> ( in @ X425 @ X423 ) )
=> ( in @ X424 @ ( powerset @ X423 ) ) )
=> ( ! [X426: $i] : ( in @ emptyset @ ( powerset @ X426 ) )
=> ( ! [X427: $i] : ( in @ emptyset @ ( powerset @ X427 ) )
=> ( ! [X428: $i,X429: $i,X430: $i] :
( ( in @ X429 @ ( powerset @ X428 ) )
=> ( ( in @ X430 @ X429 )
=> ( in @ X430 @ X428 ) ) )
=> ( ! [X431: $i,X432: $i,X433: $i] :
( ( in @ X432 @ X433 )
=> ( ( in @ X433 @ X431 )
=> ( in @ X432 @ ( setunion @ X431 ) ) ) )
=> ( ! [X434: $i,X435: $i] :
( ( in @ X435 @ ( setunion @ X434 ) )
=> ! [X436: $o] :
( ! [X437: $i] :
( ( in @ X435 @ X437 )
=> ( ( in @ X437 @ X434 )
=> X436 ) )
=> X436 ) )
=> ( ! [X438: $i,X439: $i] :
( ( in @ X439 @ X438 )
=> ( in @ X439 @ ( powerset @ ( setunion @ X438 ) ) ) )
=> ( ! [X440: $i > $o] :
( ( exu @ X440 )
=> ? [X441: $i] :
! [X442: $i] :
( ( X440 @ X442 )
<=> ( X442 = X441 ) ) )
=> ( ! [X443: $i] :
( ( nonempty @ X443 )
=> ? [X444: $i] :
( ( in @ X444 @ X443 )
& $true ) )
=> ( ! [X445: $i,X446: $i] :
( ( in @ X445 @ ( setadjoin @ X446 @ emptyset ) )
=> ( X445 = X446 ) )
=> ( ! [X447: $i,X448: $i] :
( ( X447 != X448 )
=> ~ ( in @ X448 @ ( setadjoin @ X447 @ emptyset ) ) )
=> ( ! [X449: $i,X450: $i] :
( ( X449 = X450 )
=> ( in @ X449 @ ( setadjoin @ X450 @ emptyset ) ) )
=> ( ! [X451: $i,X452: $i] :
( ( in @ X451 @ ( setadjoin @ X452 @ emptyset ) )
=> ( in @ X452 @ ( setadjoin @ X451 @ emptyset ) ) )
=> ( ! [X453: $i,X454: $i,X455: $i] :
( ( in @ X455 @ ( setadjoin @ X453 @ ( setadjoin @ X454 @ emptyset ) ) )
=> ( ( X455 = X453 )
| ( X455 = X454 ) ) )
=> ( ! [X456: $i,X457: $i] : ( in @ X456 @ ( setadjoin @ X456 @ ( setadjoin @ X457 @ emptyset ) ) )
=> ( ! [X458: $i,X459: $i] : ( in @ X459 @ ( setadjoin @ X458 @ ( setadjoin @ X459 @ emptyset ) ) )
=> ( ! [X460: $i,X461: $i > $o] :
( ? [X462: $i] :
( ( in @ X462 @ X460 )
& ( X461 @ X462 ) )
=> ( ( ( dsetconstr @ X460 @ X461 )
= emptyset )
=> ~ $true ) )
=> ( ! [X463: $i > $o,X464: $i] :
( ( in @ X464 @ emptyset )
=> ( X463 @ X464 ) )
=> ( ! [X465: $i,X466: $i > $o] :
( ~ ! [X467: $i] :
( ( in @ X467 @ X465 )
=> ( X466 @ X467 ) )
=> ? [X468: $i] :
( ( in @ X468 @ X465 )
& ~ ( X466 @ X468 ) ) )
=> ( ! [X469: $i,X470: $i > $o] :
( ! [X471: $i] :
( ( in @ X471 @ X469 )
=> ~ ( X470 @ X471 ) )
=> ~ ? [X472: $i] :
( ( in @ X472 @ X469 )
& ( X470 @ X472 ) ) )
=> ( ! [X473: $i,X474: $i > $o] :
( ~ ? [X475: $i] :
( ( in @ X475 @ X473 )
& ( X474 @ X475 ) )
=> ! [X476: $i] :
( ( in @ X476 @ X473 )
=> ~ ( X474 @ X476 ) ) )
=> ( ! [X477: $i,X478: $i > $o] :
( ? [X479: $i] :
( ( in @ X479 @ X477 )
& ~ ( X478 @ X479 ) )
=> ~ ! [X480: $i] :
( ( in @ X480 @ X477 )
=> ( X478 @ X480 ) ) )
=> ( ! [X481: $o] :
( X481
=> ( in @ emptyset @ ( prop2set @ X481 ) ) )
=> ( prop2set2propI
=> ( ! [X482: $i,X483: $i > $o] :
( ~ ? [X484: $i] :
( ( in @ X484 @ X482 )
& ( X483 @ X484 ) )
=> ! [X485: $i] :
( ( in @ X485 @ X482 )
=> ~ ( X483 @ X485 ) ) )
=> ( ! [X486: $i,X487: $i > $o] :
( ~ ! [X488: $i] :
( ( in @ X488 @ X486 )
=> ( X487 @ X488 ) )
=> ? [X489: $i] :
( ( in @ X489 @ X486 )
& ~ ( X487 @ X489 ) ) )
=> ( ! [X490: $i > $o] :
( ? [X491: $i] :
( ( X490 @ X491 )
& ! [X492: $i] :
( ( X490 @ X492 )
=> ( X491 = X492 ) ) )
=> ( exu @ X490 ) )
=> ( ! [X493: $i > $o] :
( ? [X494: $i] : ( X493 @ X494 )
=> ( ! [X495: $i,X496: $i] :
( ( X493 @ X495 )
=> ( ( X493 @ X496 )
=> ( X495 = X496 ) ) )
=> ( exu @ X493 ) ) )
=> ( ! [X497: $i > $o] :
( ? [X498: $i] :
! [X499: $i] :
( ( X497 @ X499 )
<=> ( X499 = X498 ) )
=> ( exu @ X497 ) )
=> ( ! [X500: $i,X501: $i] :
( ( X500 = X501 )
=> ! [X502: $i,X503: $i] :
( ( X502 = X503 )
=> ( ( in @ X502 @ X500 )
=> ( in @ X503 @ X501 ) ) ) )
=> ( ! [X504: $i,X505: $i] :
( ( X504 = X505 )
=> ! [X506: $i,X507: $i] :
( ( X506 = X507 )
=> ( ( in @ X506 @ X504 )
<=> ( in @ X507 @ X505 ) ) ) )
=> ( ! [X508: $i > $o] :
( ( exu @ X508 )
=> ! [X509: $i,X510: $i] :
( ( X508 @ X509 )
=> ( ( X508 @ X510 )
=> ( X509 = X510 ) ) ) )
=> ( ! [X511: $i > $o,X512: $i > $o] :
( ! [X513: $i,X514: $i] :
( ( X513 = X514 )
=> ( ( X511 @ X513 )
<=> ( X512 @ X514 ) ) )
=> ( ( exu @ X511 )
<=> ( exu @ X512 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X515: $i,X516: $i] :
( ( X515 = X516 )
=> ! [X517: $i,X518: $i] :
( ( X517 = X518 )
=> ( ( setadjoin @ X515 @ X517 )
= ( setadjoin @ X516 @ X518 ) ) ) )
=> ( ! [X519: $i,X520: $i] :
( ( X519 = X520 )
=> ( ( powerset @ X519 )
= ( powerset @ X520 ) ) )
=> ( ! [X521: $i,X522: $i] :
( ( X521 = X522 )
=> ( ( setunion @ X521 )
= ( setunion @ X522 ) ) )
=> ( ( omega = omega )
=> ( ! [X523: $i > $o] :
( ( exu @ X523 )
=> ! [X524: $i,X525: $i] :
( ( X523 @ X524 )
=> ( ( X523 @ X525 )
=> ( X524 = X525 ) ) ) )
=> ( ! [X526: $i > $o,X527: $i > $o] :
( ! [X528: $i,X529: $i] :
( ( X528 = X529 )
=> ( ( X526 @ X528 )
<=> ( X527 @ X529 ) ) )
=> ( ( exu @ X526 )
=> ( ( exu @ X527 )
=> ( ( descr @ X526 )
= ( descr @ X527 ) ) ) ) )
=> ( ! [X530: $i,X531: $i] :
( ( X530 = X531 )
=> ! [X532: $i > $o,X533: $i > $o] :
( ! [X534: $i] :
( ( in @ X534 @ X530 )
=> ! [X535: $i] :
( ( in @ X535 @ X531 )
=> ( ( X534 = X535 )
=> ( ( X532 @ X534 )
<=> ( X533 @ X535 ) ) ) ) )
=> ( ( dsetconstr @ X530 @ X532 )
= ( dsetconstr @ X531 @ X533 ) ) ) )
=> ( ! [X536: $i,X537: $i] :
( ! [X538: $i] :
( ( in @ X538 @ X536 )
=> ( in @ X538 @ X537 ) )
=> ( subset @ X536 @ X537 ) )
=> ( ! [X539: $i,X540: $i] :
( ( X539 = X540 )
=> ( subset @ X540 @ X539 ) )
=> ( ! [X541: $i,X542: $i] :
( ( X541 = X542 )
=> ( subset @ X541 @ X542 ) )
=> ( ! [X543: $i,X544: $i] :
( ! [X545: $i] :
( ( in @ X545 @ X543 )
=> ( in @ X545 @ X544 ) )
=> ( subset @ X543 @ X544 ) )
=> ( ! [X546: $i] : ( subset @ emptyset @ X546 )
=> ( ! [X547: $i,X548: $i,X549: $i] :
( ( subset @ X547 @ X548 )
=> ( ( in @ X549 @ X547 )
=> ( in @ X549 @ X548 ) ) )
=> ( ! [X550: $i,X551: $i,X552: $i] :
( ( subset @ X550 @ X551 )
=> ( ~ ( in @ X552 @ X551 )
=> ~ ( in @ X552 @ X550 ) ) )
=> ( ! [X553: $i,X554: $i,X555: $i] :
( ( in @ X555 @ X553 )
=> ( ~ ( in @ X555 @ X554 )
=> ~ ( subset @ X553 @ X554 ) ) )
=> ( ! [X556: $i,X557: $i] :
( ~ ( subset @ X556 @ X557 )
=> ( X556 != X557 ) )
=> ( ! [X558: $i,X559: $i,X560: $i] :
( ( in @ X560 @ X558 )
=> ( ~ ( in @ X560 @ X559 )
=> ( X558 != X559 ) ) )
=> ( ! [X561: $i] : ( subset @ X561 @ X561 )
=> ( ! [X562: $i,X563: $i,X564: $i] :
( ( subset @ X562 @ X563 )
=> ( ( subset @ X563 @ X564 )
=> ( subset @ X562 @ X564 ) ) )
=> ( ! [X565: $i,X566: $i] : ( subset @ X566 @ ( setadjoin @ X565 @ X566 ) )
=> ( ! [X567: $i,X568: $i,X569: $i] :
( ( subset @ X567 @ X569 )
=> ( subset @ X567 @ ( setadjoin @ X568 @ X569 ) ) )
=> ( ! [X570: $i,X571: $i] :
( ( subset @ X570 @ X571 )
=> ( in @ X570 @ ( powerset @ X571 ) ) )
=> ( ! [X572: $i,X573: $i] :
( ( subset @ X572 @ X573 )
=> ( ( subset @ X573 @ X572 )
=> ( X572 = X573 ) ) )
=> ( ! [X574: $i] :
( ( subset @ X574 @ emptyset )
=> ( X574 = emptyset ) )
=> ( ! [X575: $i,X576: $i] :
( ( subset @ X576 @ X575 )
=> ( in @ X576 @ ( powerset @ X575 ) ) )
=> ( ! [X577: $i,X578: $i] :
( ( in @ X578 @ ( powerset @ X577 ) )
=> ( subset @ X578 @ X577 ) )
=> ( ! [X579: $i] : ( in @ X579 @ ( powerset @ X579 ) )
=> ( ! [X580: $i,X581: $i] :
( ( subset @ X580 @ X581 )
=> ( subset @ ( powerset @ X580 ) @ ( powerset @ X581 ) ) )
=> ( ! [X582: $i,X583: $i > $o] : ( in @ ( dsetconstr @ X582 @ X583 ) @ ( powerset @ X582 ) )
=> ( ! [X584: $i,X585: $i > $o] : ( subset @ ( dsetconstr @ X584 @ X585 ) @ X584 )
=> ( ! [X586: $i,X587: $i,X588: $i] :
( ( in @ X588 @ X586 )
=> ( in @ X588 @ ( binunion @ X586 @ X587 ) ) )
=> ( ! [X589: $i,X590: $i] : ( in @ X590 @ ( setadjoin @ X589 @ ( setadjoin @ X590 @ emptyset ) ) )
=> ( ! [X591: $i,X592: $i,X593: $i] :
( ( in @ X593 @ X592 )
=> ( in @ X593 @ ( binunion @ X591 @ X592 ) ) )
=> ( ! [X594: $i,X595: $i,X596: $i,X597: $o] :
( ( in @ X596 @ ( binunion @ X594 @ X595 ) )
=> ( ( ( in @ X596 @ X594 )
=> X597 )
=> ( ( ( in @ X596 @ X595 )
=> X597 )
=> X597 ) ) )
=> ( ! [X598: $i,X599: $i,X600: $i] :
( ( in @ X600 @ ( binunion @ X598 @ X599 ) )
=> ( ( in @ X600 @ X598 )
| ( in @ X600 @ X599 ) ) )
=> ( ! [X601: $i,X602: $i] : ( subset @ X601 @ ( binunion @ X601 @ X602 ) )
=> ( ! [X603: $i,X604: $i] : ( subset @ X604 @ ( binunion @ X603 @ X604 ) )
=> ( ! [X605: $i,X606: $i,X607: $i] :
( ( in @ X607 @ X605 )
=> ( ( in @ X607 @ X606 )
=> ( in @ X607 @ ( binintersect @ X605 @ X606 ) ) ) )
=> ( ! [X608: $i,X609: $i,X610: $i] :
( ( subset @ X610 @ X608 )
=> ( ( subset @ X610 @ X609 )
=> ( subset @ X610 @ ( binintersect @ X608 @ X609 ) ) ) )
=> ( ! [X611: $i,X612: $i,X613: $i] :
( ( in @ X613 @ ( binintersect @ X611 @ X612 ) )
=> ( in @ X613 @ X611 ) )
=> ( ! [X614: $i,X615: $i] : ( subset @ ( binintersect @ X614 @ X615 ) @ X614 )
=> ( ! [X616: $i,X617: $i] :
( ( subset @ X616 @ X617 )
=> ( ( binintersect @ X616 @ X617 )
= X616 ) )
=> ( ! [X618: $i,X619: $i] :
( ( ( binintersect @ X618 @ X619 )
= X619 )
=> ( subset @ X619 @ X618 ) )
=> ( ! [X620: $i,X621: $i,X622: $i] :
( ( in @ X622 @ ( binintersect @ X620 @ X621 ) )
=> ( in @ X622 @ X621 ) )
=> ( ! [X623: $i,X624: $i] :
( ~ ? [X625: $i] :
( ( in @ X625 @ X623 )
& ( in @ X625 @ X624 ) )
=> ( ( binintersect @ X623 @ X624 )
= emptyset ) )
=> ( ! [X626: $i,X627: $i] : ( subset @ ( binintersect @ X626 @ X627 ) @ X627 )
=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_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)],[binintersectSubset4]),binintersectRsub]),powersetI1]),emptyInPowerset]),powersetE1]),inPowerset]),powersetsubset]),powersetE]),c_0_114]),c_0_115]),setunionI]),binunionIL]),upairset2IR]),setunionE]),binunionIR]),binunionEcases]),subPowSU]),binunionE]),binunionLsub]),c_0_116]),binunionRsub]),binintersectI]),nonemptyImpWitness]),binintersectSubset5]),uniqinunit]),binintersectEL]),binintersectLsub]),binintersectSubset2]),notinsingleton]),binintersectSubset3]),binintersectER]),disjointsetsI1]),eqinunit]),c_0_117]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_118]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_119]),c_0_120]),c_0_121]),inCongP]),in__Cong]),c_0_122]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_123]),c_0_124]),c_0_125]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),powersetI]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),emptyinPowerset]),c_0_126]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_127]),nonemptyE1]),c_0_128]),noeltsimpempty]),emptyI]),setext]),c_0_129]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_130]),c_0_131]),c_0_132]),c_0_133]),c_0_134]),wellorderingAx]),foundationAx]),c_0_135]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_136]) ).
thf(c_0_138,negated_conjecture,
! [X628: $i,X629: $i,X631: $i,X632: $i,X633: $i,X634: $i,X635: $i,X636: $i,X637: $i,X638: $i,X639: $i,X641: $i,X642: $i,X644: $i,X645: $i,X646: $i,X647: $i,X648: $i,X650: $i,X651: $i > $i > $o,X652: $i,X655: $i,X657: $i,X658: $i,X659: $i,X660: $i,X662: $i,X663: $i > $o,X664: $i,X665: $i > $o,X666: $i,X667: $i,X668: $i > $o,X669: $i,X670: $i,X671: $i > $o,X672: $i,X673: $i > $o,X675: $i,X676: $o,X677: $i,X678: $i,X679: $o,X680: $i,X681: $i,X682: $i > $o,X684: $i,X685: $i,X688: $i,X690: $i,X692: $i,X693: $i > $o,X694: $i,X695: $i,X697: $i,X698: $i > $o,X699: $i,X700: $i,X701: $i,X702: $i,X703: $i,X704: $i,X705: $i,X706: $i,X707: $i,X708: $i,X709: $i,X710: $o,X711: $i,X712: $i,X713: $i,X714: $i,X715: $i,X716: $i,X718: $i,X719: $i,X720: $i,X721: $i,X722: $i,X723: $i,X724: $i,X725: $i,X726: $i,X727: $i,X728: $o,X730: $i,X731: $i,X732: $i > $o,X734: $i,X735: $i,X736: $i,X738: $i,X739: $i,X740: $i,X741: $i,X742: $i,X743: $i,X744: $i,X745: $i,X746: $i,X747: $i,X748: $i,X749: $i,X750: $i,X751: $i,X752: $i,X753: $i,X754: $i > $o,X755: $i,X756: $i > $o,X757: $i,X758: $i,X759: $i > $o,X760: $i,X762: $i,X763: $i > $o,X765: $i,X766: $i,X767: $i > $o,X769: $i,X770: $i,X771: $i > $o,X772: $i,X774: $o,X775: $i,X776: $i > $o,X778: $i,X779: $i,X780: $i > $o,X781: $i,X783: $i > $o,X784: $i,X786: $i > $o,X787: $i,X790: $i > $o,X791: $i,X793: $i,X794: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X800: $i,X801: $i > $o,X802: $i,X803: $i,X804: $i > $o,X805: $i > $o,X808: $i,X809: $i,X810: $i,X811: $i,X812: $i,X813: $i,X814: $i,X815: $i,X816: $i > $o,X817: $i,X818: $i,X819: $i > $o,X820: $i > $o,X823: $i,X824: $i,X825: $i > $o,X826: $i > $o,X829: $i,X830: $i,X832: $i,X833: $i,X834: $i,X835: $i,X836: $i,X837: $i,X839: $i,X840: $i,X841: $i,X842: $i,X843: $i,X844: $i,X845: $i,X846: $i,X847: $i,X848: $i,X849: $i,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $i,X859: $i,X860: $i,X861: $i,X862: $i,X863: $i,X864: $i,X865: $i,X866: $i,X867: $i,X868: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i > $o,X877: $i,X878: $i > $o,X879: $i,X880: $i,X881: $i,X882: $i,X883: $i,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X890: $o,X891: $i,X892: $i,X893: $i,X894: $i,X895: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X901: $i,X902: $i,X903: $i,X904: $i,X905: $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,X919: $i,X920: $i] :
( ( ~ ( in @ ( esk1_2 @ X628 @ X629 ) @ X628 )
| ~ ( in @ ( esk1_2 @ X628 @ X629 ) @ X629 )
| ( X628 = X629 ) )
& ( ( in @ ( esk1_2 @ X628 @ X629 ) @ X628 )
| ( in @ ( esk1_2 @ X628 @ X629 ) @ X629 )
| ( X628 = X629 ) )
& ~ ( in @ X631 @ emptyset )
& ( ~ ( in @ X634 @ ( setadjoin @ X632 @ X633 ) )
| ( X634 = X632 )
| ( in @ X634 @ X633 ) )
& ( ( X634 != X632 )
| ( in @ X634 @ ( setadjoin @ X632 @ X633 ) ) )
& ( ~ ( in @ X634 @ X633 )
| ( in @ X634 @ ( setadjoin @ X632 @ X633 ) ) )
& ( ~ ( in @ X636 @ ( powerset @ X635 ) )
| ~ ( in @ X637 @ X636 )
| ( in @ X637 @ X635 ) )
& ( ( in @ ( esk2_2 @ X638 @ X639 ) @ X639 )
| ( in @ X639 @ ( powerset @ X638 ) ) )
& ( ~ ( in @ ( esk2_2 @ X638 @ X639 ) @ X638 )
| ( in @ X639 @ ( powerset @ X638 ) ) )
& ( ( in @ X642 @ ( esk3_2 @ X641 @ X642 ) )
| ~ ( in @ X642 @ ( setunion @ X641 ) ) )
& ( ( in @ ( esk3_2 @ X641 @ X642 ) @ X641 )
| ~ ( in @ X642 @ ( setunion @ X641 ) ) )
& ( ~ ( in @ X645 @ X646 )
| ~ ( in @ X646 @ X644 )
| ( in @ X645 @ ( setunion @ X644 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X647 @ omega )
| ( in @ ( setadjoin @ X647 @ X647 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X648 ) @ omega )
| ~ ( in @ emptyset @ X648 )
| ~ ( in @ X650 @ omega )
| ( in @ X650 @ X648 ) )
& ( ( in @ ( esk4_1 @ X648 ) @ X648 )
| ~ ( in @ emptyset @ X648 )
| ~ ( in @ X650 @ omega )
| ( in @ X650 @ X648 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X648 ) @ ( esk4_1 @ X648 ) ) @ X648 )
| ~ ( in @ emptyset @ X648 )
| ~ ( in @ X650 @ omega )
| ( in @ X650 @ X648 ) )
& ( ( in @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X652 )
| ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
| ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
& ( ( X651 @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X655 )
| ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
| ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
& ( ~ ( in @ X658 @ X652 )
| ~ ( X651 @ X658 @ X657 )
| ( in @ X657 @ ( esk6_2 @ X651 @ X652 ) )
| ( in @ ( esk5_2 @ X651 @ X652 ) @ X652 ) )
& ( ( in @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X652 )
| ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
| ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
& ( ( X651 @ ( esk7_3 @ X651 @ X652 @ X655 ) @ X655 )
| ~ ( in @ X655 @ ( esk6_2 @ X651 @ X652 ) )
| ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
& ( ~ ( in @ X658 @ X652 )
| ~ ( X651 @ X658 @ X657 )
| ( in @ X657 @ ( esk6_2 @ X651 @ X652 ) )
| ~ ( exu @ ( X651 @ ( esk5_2 @ X651 @ X652 ) ) ) )
& ( ( in @ ( esk8_1 @ X659 ) @ X659 )
| ~ ( in @ X660 @ X659 ) )
& ( ~ ( in @ X662 @ ( esk8_1 @ X659 ) )
| ~ ( in @ X662 @ X659 )
| ~ ( in @ X660 @ X659 ) )
& epred1_0
& ( ~ ( exu @ X663 )
| ( X663 @ ( descr @ X663 ) ) )
& ( ~ ( in @ X666 @ X664 )
| ~ ( X665 @ X666 )
| ( in @ X666 @ ( dsetconstr @ X664 @ X665 ) ) )
& ( ~ ( in @ X669 @ ( dsetconstr @ X667 @ X668 ) )
| ( in @ X669 @ X667 ) )
& ( ~ ( in @ X672 @ ( dsetconstr @ X670 @ X671 ) )
| ( X671 @ X672 ) )
& ( ( X673 @ ( esk9_1 @ X673 ) )
| ~ ( exu @ X673 ) )
& ( ~ ( X673 @ X675 )
| ( ( esk9_1 @ X673 )
= X675 )
| ~ ( exu @ X673 ) )
& ( ~ ( in @ X677 @ ( prop2set @ X676 ) )
| X676 )
& ( ~ ( in @ X678 @ emptyset )
| X679 )
& ( ~ ( in @ X680 @ emptyset )
| ~ $true )
& ~ ( in @ X681 @ emptyset )
& ( ~ ( exu @ X682 )
| ( X682 @ ( esk10_1 @ X682 ) ) )
& ( ( in @ ( esk12_2 @ X684 @ X685 ) @ X685 )
| ( X684 = X685 )
| ( in @ ( esk11_2 @ X684 @ X685 ) @ X684 ) )
& ( ~ ( in @ ( esk12_2 @ X684 @ X685 ) @ X684 )
| ( X684 = X685 )
| ( in @ ( esk11_2 @ X684 @ X685 ) @ X684 ) )
& ( ( in @ ( esk12_2 @ X684 @ X685 ) @ X685 )
| ( X684 = X685 )
| ~ ( in @ ( esk11_2 @ X684 @ X685 ) @ X685 ) )
& ( ~ ( in @ ( esk12_2 @ X684 @ X685 ) @ X684 )
| ( X684 = X685 )
| ~ ( in @ ( esk11_2 @ X684 @ X685 ) @ X685 ) )
& ( ( in @ ( esk13_1 @ X688 ) @ X688 )
| ( X688 = emptyset ) )
& ( ( in @ ( esk14_1 @ X690 ) @ X690 )
| ( X690 = emptyset ) )
& ( ~ ( in @ X694 @ ( dsetconstr @ X692 @ X693 ) )
| ( X693 @ X694 )
| ~ ( in @ X694 @ X692 ) )
& ( ~ ( X693 @ X694 )
| ( in @ X694 @ ( dsetconstr @ X692 @ X693 ) )
| ~ ( in @ X694 @ X692 ) )
& ( ~ ( nonempty @ X695 )
| ( in @ ( esk15_1 @ X695 ) @ X695 ) )
& ( ~ ( in @ X699 @ X697 )
| ~ ( X698 @ X699 )
| ( nonempty @ ( dsetconstr @ X697 @ X698 ) ) )
& ( ~ ( in @ X701 @ X700 )
| ( nonempty @ X700 ) )
& ( in @ X702 @ ( setadjoin @ X702 @ X703 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X706 @ X705 )
| ( in @ X706 @ ( setadjoin @ X704 @ X705 ) ) )
& ( ( in @ X709 @ X708 )
| X710
| ( X709 = X707 )
| ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
& ( ~ X710
| X710
| ( X709 = X707 )
| ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
& ( ( in @ X709 @ X708 )
| X710
| ~ X710
| ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
& ( ~ X710
| X710
| ~ X710
| ~ ( in @ X709 @ ( setadjoin @ X707 @ X708 ) ) )
& ( ~ ( in @ X713 @ ( setadjoin @ X711 @ X712 ) )
| ( X713 = X711 )
| ( in @ X713 @ X712 ) )
& ( ( dsetconstr @ X714
@ ^ [Z0: $i] : $true )
= X714 )
& ( ( in @ ( esk16_2 @ X715 @ X716 ) @ X716 )
| ( in @ X716 @ ( powerset @ X715 ) ) )
& ( ~ ( in @ ( esk16_2 @ X715 @ X716 ) @ X715 )
| ( in @ X716 @ ( powerset @ X715 ) ) )
& ( in @ emptyset @ ( powerset @ X718 ) )
& ( in @ emptyset @ ( powerset @ X719 ) )
& ( ~ ( in @ X721 @ ( powerset @ X720 ) )
| ~ ( in @ X722 @ X721 )
| ( in @ X722 @ X720 ) )
& ( ~ ( in @ X724 @ X725 )
| ~ ( in @ X725 @ X723 )
| ( in @ X724 @ ( setunion @ X723 ) ) )
& ( ( in @ X727 @ ( esk17_3 @ X726 @ X727 @ X728 ) )
| X728
| ~ ( in @ X727 @ ( setunion @ X726 ) ) )
& ( ( in @ ( esk17_3 @ X726 @ X727 @ X728 ) @ X726 )
| X728
| ~ ( in @ X727 @ ( setunion @ X726 ) ) )
& ( ~ X728
| X728
| ~ ( in @ X727 @ ( setunion @ X726 ) ) )
& ( ~ ( in @ X731 @ X730 )
| ( in @ X731 @ ( powerset @ ( setunion @ X730 ) ) ) )
& ( ~ ( X732 @ X734 )
| ( X734
= ( esk18_1 @ X732 ) )
| ~ ( exu @ X732 ) )
& ( ( X735
!= ( esk18_1 @ X732 ) )
| ( X732 @ X735 )
| ~ ( exu @ X732 ) )
& ( ( in @ ( esk19_1 @ X736 ) @ X736 )
| ~ ( nonempty @ X736 ) )
& ( $true
| ~ ( nonempty @ X736 ) )
& ( ~ ( in @ X738 @ ( setadjoin @ X739 @ emptyset ) )
| ( X738 = X739 ) )
& ( ( X740 = X741 )
| ~ ( in @ X741 @ ( setadjoin @ X740 @ emptyset ) ) )
& ( ( X742 != X743 )
| ( in @ X742 @ ( setadjoin @ X743 @ emptyset ) ) )
& ( ~ ( in @ X744 @ ( setadjoin @ X745 @ emptyset ) )
| ( in @ X745 @ ( setadjoin @ X744 @ emptyset ) ) )
& ( ~ ( in @ X748 @ ( setadjoin @ X746 @ ( setadjoin @ X747 @ emptyset ) ) )
| ( X748 = X746 )
| ( X748 = X747 ) )
& ( in @ X749 @ ( setadjoin @ X749 @ ( setadjoin @ X750 @ emptyset ) ) )
& ( in @ X752 @ ( setadjoin @ X751 @ ( setadjoin @ X752 @ emptyset ) ) )
& ( ~ ( in @ X755 @ X753 )
| ~ ( X754 @ X755 )
| ( ( dsetconstr @ X753 @ X754 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X757 @ emptyset )
| ( X756 @ X757 ) )
& ( ( in @ ( esk20_2 @ X758 @ X759 ) @ X758 )
| ~ ( in @ X760 @ X758 )
| ( X759 @ X760 ) )
& ( ~ ( X759 @ ( esk20_2 @ X758 @ X759 ) )
| ~ ( in @ X760 @ X758 )
| ( X759 @ X760 ) )
& ( ( in @ ( esk21_2 @ X762 @ X763 ) @ X762 )
| ~ ( in @ X765 @ X762 )
| ~ ( X763 @ X765 ) )
& ( ( X763 @ ( esk21_2 @ X762 @ X763 ) )
| ~ ( in @ X765 @ X762 )
| ~ ( X763 @ X765 ) )
& ( ( in @ ( esk22_2 @ X766 @ X767 ) @ X766 )
| ~ ( in @ X769 @ X766 )
| ~ ( X767 @ X769 ) )
& ( ( X767 @ ( esk22_2 @ X766 @ X767 ) )
| ~ ( in @ X769 @ X766 )
| ~ ( X767 @ X769 ) )
& ( ( in @ ( esk23_2 @ X770 @ X771 ) @ X770 )
| ~ ( in @ X772 @ X770 )
| ( X771 @ X772 ) )
& ( ~ ( X771 @ ( esk23_2 @ X770 @ X771 ) )
| ~ ( in @ X772 @ X770 )
| ( X771 @ X772 ) )
& ( ~ X774
| ( in @ emptyset @ ( prop2set @ X774 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X775 @ X776 ) @ X775 )
| ~ ( in @ X778 @ X775 )
| ~ ( X776 @ X778 ) )
& ( ( X776 @ ( esk24_2 @ X775 @ X776 ) )
| ~ ( in @ X778 @ X775 )
| ~ ( X776 @ X778 ) )
& ( ( in @ ( esk25_2 @ X779 @ X780 ) @ X779 )
| ~ ( in @ X781 @ X779 )
| ( X780 @ X781 ) )
& ( ~ ( X780 @ ( esk25_2 @ X779 @ X780 ) )
| ~ ( in @ X781 @ X779 )
| ( X780 @ X781 ) )
& ( ( X783 @ ( esk26_2 @ X783 @ X784 ) )
| ~ ( X783 @ X784 )
| ( exu @ X783 ) )
& ( ( X784
!= ( esk26_2 @ X783 @ X784 ) )
| ~ ( X783 @ X784 )
| ( exu @ X783 ) )
& ( ( X786 @ ( esk27_1 @ X786 ) )
| ( exu @ X786 )
| ~ ( X786 @ X787 ) )
& ( ( X786 @ ( esk28_1 @ X786 ) )
| ( exu @ X786 )
| ~ ( X786 @ X787 ) )
& ( ( ( esk27_1 @ X786 )
!= ( esk28_1 @ X786 ) )
| ( exu @ X786 )
| ~ ( X786 @ X787 ) )
& ( ~ ( X790 @ ( esk29_2 @ X790 @ X791 ) )
| ( ( esk29_2 @ X790 @ X791 )
!= X791 )
| ( exu @ X790 ) )
& ( ( X790 @ ( esk29_2 @ X790 @ X791 ) )
| ( ( esk29_2 @ X790 @ X791 )
= X791 )
| ( exu @ X790 ) )
& ( ( X793 != X794 )
| ( X795 != X796 )
| ~ ( in @ X795 @ X793 )
| ( in @ X796 @ X794 ) )
& ( ~ ( in @ X799 @ X797 )
| ( in @ X800 @ X798 )
| ( X799 != X800 )
| ( X797 != X798 ) )
& ( ~ ( in @ X800 @ X798 )
| ( in @ X799 @ X797 )
| ( X799 != X800 )
| ( X797 != X798 ) )
& ( ~ ( exu @ X801 )
| ~ ( X801 @ X802 )
| ~ ( X801 @ X803 )
| ( X802 = X803 ) )
& ( ~ ( exu @ X804 )
| ( exu @ X805 )
| ( ( esk30_2 @ X804 @ X805 )
= ( esk31_2 @ X804 @ X805 ) ) )
& ( ~ ( exu @ X805 )
| ( exu @ X804 )
| ( ( esk30_2 @ X804 @ X805 )
= ( esk31_2 @ X804 @ X805 ) ) )
& ( ~ ( exu @ X804 )
| ( exu @ X805 )
| ~ ( X804 @ ( esk30_2 @ X804 @ X805 ) )
| ~ ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
& ( ~ ( exu @ X805 )
| ( exu @ X804 )
| ~ ( X804 @ ( esk30_2 @ X804 @ X805 ) )
| ~ ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
& ( ~ ( exu @ X804 )
| ( exu @ X805 )
| ( X804 @ ( esk30_2 @ X804 @ X805 ) )
| ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
& ( ~ ( exu @ X805 )
| ( exu @ X804 )
| ( X804 @ ( esk30_2 @ X804 @ X805 ) )
| ( X805 @ ( esk31_2 @ X804 @ X805 ) ) )
& ( emptyset = emptyset )
& ( ( X808 != X809 )
| ( X810 != X811 )
| ( ( setadjoin @ X808 @ X810 )
= ( setadjoin @ X809 @ X811 ) ) )
& ( ( X812 != X813 )
| ( ( powerset @ X812 )
= ( powerset @ X813 ) ) )
& ( ( X814 != X815 )
| ( ( setunion @ X814 )
= ( setunion @ X815 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X816 )
| ~ ( X816 @ X817 )
| ~ ( X816 @ X818 )
| ( X817 = X818 ) )
& ( ( ( esk32_2 @ X819 @ X820 )
= ( esk33_2 @ X819 @ X820 ) )
| ~ ( exu @ X819 )
| ~ ( exu @ X820 )
| ( ( descr @ X819 )
= ( descr @ X820 ) ) )
& ( ~ ( X819 @ ( esk32_2 @ X819 @ X820 ) )
| ~ ( X820 @ ( esk33_2 @ X819 @ X820 ) )
| ~ ( exu @ X819 )
| ~ ( exu @ X820 )
| ( ( descr @ X819 )
= ( descr @ X820 ) ) )
& ( ( X819 @ ( esk32_2 @ X819 @ X820 ) )
| ( X820 @ ( esk33_2 @ X819 @ X820 ) )
| ~ ( exu @ X819 )
| ~ ( exu @ X820 )
| ( ( descr @ X819 )
= ( descr @ X820 ) ) )
& ( ( in @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) @ X823 )
| ( ( dsetconstr @ X823 @ X825 )
= ( dsetconstr @ X824 @ X826 ) )
| ( X823 != X824 ) )
& ( ( in @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) @ X824 )
| ( ( dsetconstr @ X823 @ X825 )
= ( dsetconstr @ X824 @ X826 ) )
| ( X823 != X824 ) )
& ( ( ( esk34_4 @ X823 @ X824 @ X825 @ X826 )
= ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
| ( ( dsetconstr @ X823 @ X825 )
= ( dsetconstr @ X824 @ X826 ) )
| ( X823 != X824 ) )
& ( ~ ( X825 @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) )
| ~ ( X826 @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
| ( ( dsetconstr @ X823 @ X825 )
= ( dsetconstr @ X824 @ X826 ) )
| ( X823 != X824 ) )
& ( ( X825 @ ( esk34_4 @ X823 @ X824 @ X825 @ X826 ) )
| ( X826 @ ( esk35_4 @ X823 @ X824 @ X825 @ X826 ) )
| ( ( dsetconstr @ X823 @ X825 )
= ( dsetconstr @ X824 @ X826 ) )
| ( X823 != X824 ) )
& ( ( in @ ( esk36_2 @ X829 @ X830 ) @ X829 )
| ( subset @ X829 @ X830 ) )
& ( ~ ( in @ ( esk36_2 @ X829 @ X830 ) @ X830 )
| ( subset @ X829 @ X830 ) )
& ( ( X832 != X833 )
| ( subset @ X833 @ X832 ) )
& ( ( X834 != X835 )
| ( subset @ X834 @ X835 ) )
& ( ( in @ ( esk37_2 @ X836 @ X837 ) @ X836 )
| ( subset @ X836 @ X837 ) )
& ( ~ ( in @ ( esk37_2 @ X836 @ X837 ) @ X837 )
| ( subset @ X836 @ X837 ) )
& ( subset @ emptyset @ X839 )
& ( ~ ( subset @ X840 @ X841 )
| ~ ( in @ X842 @ X840 )
| ( in @ X842 @ X841 ) )
& ( ~ ( subset @ X843 @ X844 )
| ( in @ X845 @ X844 )
| ~ ( in @ X845 @ X843 ) )
& ( ~ ( in @ X848 @ X846 )
| ( in @ X848 @ X847 )
| ~ ( subset @ X846 @ X847 ) )
& ( ( subset @ X849 @ X850 )
| ( X849 != X850 ) )
& ( ~ ( in @ X853 @ X851 )
| ( in @ X853 @ X852 )
| ( X851 != X852 ) )
& ( subset @ X854 @ X854 )
& ( ~ ( subset @ X855 @ X856 )
| ~ ( subset @ X856 @ X857 )
| ( subset @ X855 @ X857 ) )
& ( subset @ X859 @ ( setadjoin @ X858 @ X859 ) )
& ( ~ ( subset @ X860 @ X862 )
| ( subset @ X860 @ ( setadjoin @ X861 @ X862 ) ) )
& ( ~ ( subset @ X863 @ X864 )
| ( in @ X863 @ ( powerset @ X864 ) ) )
& ( ~ ( subset @ X865 @ X866 )
| ~ ( subset @ X866 @ X865 )
| ( X865 = X866 ) )
& ( ~ ( subset @ X867 @ emptyset )
| ( X867 = emptyset ) )
& ( ~ ( subset @ X869 @ X868 )
| ( in @ X869 @ ( powerset @ X868 ) ) )
& ( ~ ( in @ X871 @ ( powerset @ X870 ) )
| ( subset @ X871 @ X870 ) )
& ( in @ X872 @ ( powerset @ X872 ) )
& ( ~ ( subset @ X873 @ X874 )
| ( subset @ ( powerset @ X873 ) @ ( powerset @ X874 ) ) )
& ( in @ ( dsetconstr @ X875 @ X876 ) @ ( powerset @ X875 ) )
& ( subset @ ( dsetconstr @ X877 @ X878 ) @ X877 )
& ( ~ ( in @ X881 @ X879 )
| ( in @ X881 @ ( binunion @ X879 @ X880 ) ) )
& ( in @ X883 @ ( setadjoin @ X882 @ ( setadjoin @ X883 @ emptyset ) ) )
& ( ~ ( in @ X886 @ X885 )
| ( in @ X886 @ ( binunion @ X884 @ X885 ) ) )
& ( ( in @ X889 @ X888 )
| X890
| ( in @ X889 @ X887 )
| ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
& ( ~ X890
| X890
| ( in @ X889 @ X887 )
| ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
& ( ( in @ X889 @ X888 )
| X890
| ~ X890
| ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
& ( ~ X890
| X890
| ~ X890
| ~ ( in @ X889 @ ( binunion @ X887 @ X888 ) ) )
& ( ~ ( in @ X893 @ ( binunion @ X891 @ X892 ) )
| ( in @ X893 @ X891 )
| ( in @ X893 @ X892 ) )
& ( subset @ X894 @ ( binunion @ X894 @ X895 ) )
& ( subset @ X897 @ ( binunion @ X896 @ X897 ) )
& ( ~ ( in @ X900 @ X898 )
| ~ ( in @ X900 @ X899 )
| ( in @ X900 @ ( binintersect @ X898 @ X899 ) ) )
& ( ~ ( subset @ X903 @ X901 )
| ~ ( subset @ X903 @ X902 )
| ( subset @ X903 @ ( binintersect @ X901 @ X902 ) ) )
& ( ~ ( in @ X906 @ ( binintersect @ X904 @ X905 ) )
| ( in @ X906 @ X904 ) )
& ( subset @ ( binintersect @ X907 @ X908 ) @ X907 )
& ( ~ ( subset @ X909 @ X910 )
| ( ( binintersect @ X909 @ X910 )
= X909 ) )
& ( ( ( binintersect @ X911 @ X912 )
!= X912 )
| ( subset @ X912 @ X911 ) )
& ( ~ ( in @ X915 @ ( binintersect @ X913 @ X914 ) )
| ( in @ X915 @ X914 ) )
& ( ( in @ ( esk38_2 @ X916 @ X917 ) @ X916 )
| ( ( binintersect @ X916 @ X917 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X916 @ X917 ) @ X917 )
| ( ( binintersect @ X916 @ X917 )
= emptyset ) )
& ( subset @ ( binintersect @ X919 @ X920 ) @ X920 )
& ( subset @ esk40_0 @ esk39_0 )
& ( ( binintersect @ esk39_0 @ esk40_0 )
!= esk40_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_137])])])])])])]) ).
thf(c_0_139,negated_conjecture,
! [X3: $i,X2: $i] :
( ( X2 = X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_140,negated_conjecture,
! [X2: $i,X3: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_141,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ~ ( subset @ X3 @ ( binintersect @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
thf(c_0_142,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( binintersect @ X3 @ X4 ) )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_143,negated_conjecture,
! [X2: $i] : ( subset @ X2 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_144,negated_conjecture,
( ( binintersect @ esk39_0 @ esk40_0 )
!= esk40_0 ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_145,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ~ ( subset @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143])]) ).
thf(c_0_146,negated_conjecture,
subset @ esk40_0 @ esk39_0,
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_147,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU598^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:12:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.61 # Version: 3.1.0-ho
% 0.77/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61 # Starting pre_casc_3 with 300s (1) cores
% 0.77/0.61 # Starting ho_unfolding_8 with 300s (1) cores
% 0.77/0.61 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.77/0.61 # Starting new_bool_3 with 300s (1) cores
% 0.77/0.61 # Starting new_ho_5 with 300s (1) cores
% 0.77/0.61 # new_ho_5 with pid 3244 completed with status 8
% 0.77/0.61 # new_bool_5 with pid 3239 completed with status 0
% 0.77/0.61 # Result found by new_bool_5
% 0.77/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.77/0.61 # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.77/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.61 # Starting ehoh_best3 with 163s (1) cores
% 0.77/0.61 # ehoh_best3 with pid 3248 completed with status 0
% 0.77/0.61 # Result found by ehoh_best3
% 0.77/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.77/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.77/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.77/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.77/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.77/0.61 # Search class: HGHSM-FSLM31-SHFMMSBN
% 0.77/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.77/0.61 # Starting ehoh_best3 with 163s (1) cores
% 0.77/0.61 # Preprocessing time : 0.002 s
% 0.77/0.61 # Presaturation interreduction done
% 0.77/0.61
% 0.77/0.61 # Proof found!
% 0.77/0.61 # SZS status Theorem
% 0.77/0.61 # SZS output start CNFRefutation
% See solution above
% 0.77/0.61 # Parsed axioms : 248
% 0.77/0.61 # Removed by relevancy pruning/SinE : 134
% 0.77/0.61 # Initial clauses : 187
% 0.77/0.61 # Removed in clause preprocessing : 18
% 0.77/0.61 # Initial clauses in saturation : 169
% 0.77/0.61 # Processed clauses : 1215
% 0.77/0.61 # ...of these trivial : 53
% 0.77/0.61 # ...subsumed : 486
% 0.77/0.61 # ...remaining for further processing : 676
% 0.77/0.61 # Other redundant clauses eliminated : 38
% 0.77/0.61 # Clauses deleted for lack of memory : 0
% 0.77/0.61 # Backward-subsumed : 3
% 0.77/0.61 # Backward-rewritten : 3
% 0.77/0.61 # Generated clauses : 8020
% 0.77/0.61 # ...of the previous two non-redundant : 5761
% 0.77/0.61 # ...aggressively subsumed : 0
% 0.77/0.61 # Contextual simplify-reflections : 3
% 0.77/0.61 # Paramodulations : 7979
% 0.77/0.61 # Factorizations : 2
% 0.77/0.61 # NegExts : 0
% 0.77/0.61 # Equation resolutions : 38
% 0.77/0.61 # Disequality decompositions : 0
% 0.77/0.61 # Total rewrite steps : 2795
% 0.77/0.61 # ...of those cached : 2524
% 0.77/0.61 # Propositional unsat checks : 0
% 0.77/0.61 # Propositional check models : 0
% 0.77/0.61 # Propositional check unsatisfiable : 0
% 0.77/0.61 # Propositional clauses : 0
% 0.77/0.61 # Propositional clauses after purity: 0
% 0.77/0.61 # Propositional unsat core size : 0
% 0.77/0.61 # Propositional preprocessing time : 0.000
% 0.77/0.61 # Propositional encoding time : 0.000
% 0.77/0.61 # Propositional solver time : 0.000
% 0.77/0.61 # Success case prop preproc time : 0.000
% 0.77/0.61 # Success case prop encoding time : 0.000
% 0.77/0.61 # Success case prop solver time : 0.000
% 0.77/0.61 # Current number of processed clauses : 516
% 0.77/0.61 # Positive orientable unit clauses : 150
% 0.77/0.61 # Positive unorientable unit clauses: 0
% 0.77/0.61 # Negative unit clauses : 6
% 0.77/0.61 # Non-unit-clauses : 360
% 0.77/0.61 # Current number of unprocessed clauses: 4785
% 0.77/0.61 # ...number of literals in the above : 13258
% 0.77/0.61 # Current number of archived formulas : 0
% 0.77/0.61 # Current number of archived clauses : 149
% 0.77/0.61 # Clause-clause subsumption calls (NU) : 15812
% 0.77/0.61 # Rec. Clause-clause subsumption calls : 9286
% 0.77/0.61 # Non-unit clause-clause subsumptions : 452
% 0.77/0.61 # Unit Clause-clause subsumption calls : 2724
% 0.77/0.61 # Rewrite failures with RHS unbound : 0
% 0.77/0.61 # BW rewrite match attempts : 389
% 0.77/0.61 # BW rewrite match successes : 4
% 0.77/0.61 # Condensation attempts : 0
% 0.77/0.61 # Condensation successes : 0
% 0.77/0.61 # Termbank termtop insertions : 114557
% 0.77/0.61 # Search garbage collected termcells : 10241
% 0.77/0.61
% 0.77/0.61 # -------------------------------------------------
% 0.77/0.61 # User time : 0.117 s
% 0.77/0.61 # System time : 0.005 s
% 0.77/0.61 # Total time : 0.122 s
% 0.77/0.61 # Maximum resident set size: 4396 pages
% 0.77/0.61
% 0.77/0.61 # -------------------------------------------------
% 0.77/0.61 # User time : 0.163 s
% 0.77/0.61 # System time : 0.046 s
% 0.77/0.61 # Total time : 0.209 s
% 0.77/0.61 # Maximum resident set size: 2020 pages
% 0.77/0.61 % E---3.1 exiting
% 0.77/0.62 % E exiting
%------------------------------------------------------------------------------