%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU626^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 03:28:40 EDT 2024
% Result : Timeout 0.91s 300.03s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 346
% Syntax : Number of formulae : 377 ( 5 unt; 203 typ; 0 def)
% Number of atoms : 1460 ( 207 equ; 0 cnn)
% Maximal formula atoms : 427 ( 8 avg)
% Number of connectives : 4916 ( 365 ~; 338 |; 266 &;3031 @)
% ( 200 <=>; 716 =>; 0 <=; 0 <~>)
% Maximal formula depth : 544 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 251 ( 251 >; 0 *; 0 +; 0 <<)
% Number of symbols : 206 ( 203 usr; 151 con; 0-4 aty)
% Number of variables : 1224 ( 59 ^1100 !; 65 ?;1224 :)
% 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,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
epred1_0: $o ).
thf(decl_188,type,
esk1_2: $i > $i > $i ).
thf(decl_189,type,
esk2_2: $i > $i > $i ).
thf(decl_190,type,
esk3_2: $i > $i > $i ).
thf(decl_191,type,
esk4_1: $i > $i ).
thf(decl_192,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_193,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_194,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_195,type,
esk8_1: $i > $i ).
thf(decl_196,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_197,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_198,type,
esk11_2: $i > $i > $i ).
thf(decl_199,type,
esk12_2: $i > $i > $i ).
thf(decl_200,type,
esk13_1: $i > $i ).
thf(decl_201,type,
esk14_1: $i > $i ).
thf(decl_202,type,
esk15_1: $i > $i ).
thf(decl_203,type,
esk16_2: $i > $i > $i ).
thf(decl_204,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_205,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_206,type,
esk19_1: $i > $i ).
thf(decl_207,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_208,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_209,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_210,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_211,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_212,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_213,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_214,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_215,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_216,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_217,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_218,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_219,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_220,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_221,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_222,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_223,type,
esk36_2: $i > $i > $i ).
thf(decl_224,type,
esk37_2: $i > $i > $i ).
thf(decl_225,type,
esk38_2: $i > $i > $i ).
thf(decl_226,type,
esk39_0: $i ).
thf(decl_227,type,
esk40_0: $i ).
thf(decl_228,type,
esk41_0: $i ).
thf(decl_229,type,
esk42_0: $i ).
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(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(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(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(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(upairinpowunion,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
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
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(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
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(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
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(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
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(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
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(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
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(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(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(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(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
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(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(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(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(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(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(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(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
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(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
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(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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_152,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_153,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_154,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_155,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_156,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_157,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_158,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_159,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_160,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_161,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_162,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_163,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_164,plain,
( epred1_0
<=> ! [X429: $i] :
? [X430: $i] :
( ! [X431: $i] :
( ( in @ X431 @ X430 )
=> ! [X432: $i] :
( ( in @ X432 @ X431 )
=> ( in @ X432 @ X429 ) ) )
& ! [X433: $i,X434: $i] :
( ( ( in @ X433 @ X429 )
& ( in @ X434 @ X429 ) )
=> ( ! [X435: $i] :
( ( in @ X435 @ X430 )
=> ( ( in @ X433 @ X435 )
<=> ( in @ X434 @ X435 ) ) )
=> ( X433 = X434 ) ) )
& ! [X436: $i,X437: $i] :
( ( ( in @ X436 @ X430 )
& ( in @ X437 @ X430 ) )
=> ( ! [X438: $i] :
( ( in @ X438 @ X436 )
=> ( in @ X438 @ X437 ) )
| ! [X439: $i] :
( ( in @ X439 @ X437 )
=> ( in @ X439 @ X436 ) ) ) )
& ! [X440: $i] :
( ( ! [X441: $i] :
( ( in @ X441 @ X440 )
=> ( in @ X441 @ X429 ) )
& ? [X442: $i] : ( in @ X442 @ X440 ) )
=> ? [X443: $i,X444: $i] :
( ( in @ X443 @ X430 )
& ( in @ X444 @ X440 )
& ~ ? [X445: $i] :
( ( in @ X445 @ X443 )
& ( in @ X445 @ X440 ) )
& ! [X446: $i] :
( ( in @ X446 @ X430 )
=> ( ! [X447: $i] :
( ( in @ X447 @ X446 )
=> ( in @ X447 @ X443 ) )
| ( in @ X444 @ X446 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_165,negated_conjecture,
~ ( ! [X402: $i,X403: $i] :
( ! [X404: $i] :
( ( in @ X404 @ X402 )
<=> ( in @ X404 @ X403 ) )
=> ( X402 = X403 ) )
=> ( ! [X405: $i] :
~ ( in @ X405 @ emptyset )
=> ( ! [X406: $i,X407: $i,X408: $i] :
( ( in @ X408 @ ( setadjoin @ X406 @ X407 ) )
<=> ( ( X408 = X406 )
| ( in @ X408 @ X407 ) ) )
=> ( ! [X409: $i,X410: $i] :
( ( in @ X410 @ ( powerset @ X409 ) )
<=> ! [X411: $i] :
( ( in @ X411 @ X410 )
=> ( in @ X411 @ X409 ) ) )
=> ( ! [X412: $i,X413: $i] :
( ( in @ X413 @ ( setunion @ X412 ) )
<=> ? [X414: $i] :
( ( in @ X413 @ X414 )
& ( in @ X414 @ X412 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X415: $i] :
( ( in @ X415 @ omega )
=> ( in @ ( setadjoin @ X415 @ X415 ) @ omega ) )
=> ( ! [X416: $i] :
( ( ( in @ emptyset @ X416 )
& ! [X417: $i] :
( ( ( in @ X417 @ omega )
& ( in @ X417 @ X416 ) )
=> ( in @ ( setadjoin @ X417 @ X417 ) @ X416 ) ) )
=> ! [X418: $i] :
( ( in @ X418 @ omega )
=> ( in @ X418 @ X416 ) ) )
=> ( ! [X419: $i > $i > $o,X420: $i] :
( ! [X421: $i] :
( ( in @ X421 @ X420 )
=> ( exu @ ( X419 @ X421 ) ) )
=> ? [X422: $i] :
! [X423: $i] :
( ( in @ X423 @ X422 )
<=> ? [X424: $i] :
( ( in @ X424 @ X420 )
& ( X419 @ X424 @ X423 ) ) ) )
=> ( ! [X425: $i] :
( ? [X426: $i] : ( in @ X426 @ X425 )
=> ? [X427: $i] :
( ( in @ X427 @ X425 )
& ~ ? [X428: $i] :
( ( in @ X428 @ X427 )
& ( in @ X428 @ X425 ) ) ) )
=> ( epred1_0
=> ( ! [X448: $i > $o] :
( ( exu @ X448 )
=> ( X448
@ ( descr
@ ^ [Z0: $i] : ( X448 @ Z0 ) ) ) )
=> ( ! [X449: $i,X450: $i > $o,X451: $i] :
( ( in @ X451 @ X449 )
=> ( ( X450 @ X451 )
=> ( in @ X451 @ ( dsetconstr @ X449 @ X450 ) ) ) )
=> ( ! [X452: $i,X453: $i > $o,X454: $i] :
( ( in @ X454 @ ( dsetconstr @ X452 @ X453 ) )
=> ( in @ X454 @ X452 ) )
=> ( ! [X455: $i,X456: $i > $o,X457: $i] :
( ( in @ X457 @ ( dsetconstr @ X455 @ X456 ) )
=> ( X456 @ X457 ) )
=> ( ! [X458: $i > $o] :
( ( exu @ X458 )
=> ? [X459: $i] :
( ( X458 @ X459 )
& ! [X460: $i] :
( ( X458 @ X460 )
=> ( X459 = X460 ) ) ) )
=> ( ! [X461: $o,X462: $i] :
( ( in @ X462 @ ( prop2set @ X461 ) )
=> X461 )
=> ( ! [X463: $i] :
( ( in @ X463 @ emptyset )
=> ! [X464: $o] : X464 )
=> ( ! [X465: $i] :
( ( in @ X465 @ emptyset )
=> ~ $true )
=> ( ! [X466: $i] :
~ ( in @ X466 @ emptyset )
=> ( ! [X467: $i > $o] :
( ( exu @ X467 )
=> ? [X468: $i] : ( X467 @ X468 ) )
=> ( ! [X469: $i,X470: $i] :
( ! [X471: $i] :
( ( in @ X471 @ X469 )
=> ( in @ X471 @ X470 ) )
=> ( ! [X472: $i] :
( ( in @ X472 @ X470 )
=> ( in @ X472 @ X469 ) )
=> ( X469 = X470 ) ) )
=> ( ! [X473: $i] :
( ! [X474: $i] :
~ ( in @ X474 @ X473 )
=> ( X473 = emptyset ) )
=> ( ! [X475: $i] :
( ! [X476: $i] :
~ ( in @ X476 @ X475 )
=> ( X475 = emptyset ) )
=> ( ! [X477: $i,X478: $i > $o,X479: $i] :
( ( in @ X479 @ X477 )
=> ( ( in @ X479 @ ( dsetconstr @ X477 @ X478 ) )
<=> ( X478 @ X479 ) ) )
=> ( ! [X480: $i] :
( ( nonempty @ X480 )
=> ? [X481: $i] : ( in @ X481 @ X480 ) )
=> ( ! [X482: $i,X483: $i > $o,X484: $i] :
( ( in @ X484 @ X482 )
=> ( ( X483 @ X484 )
=> ( nonempty @ ( dsetconstr @ X482 @ X483 ) ) ) )
=> ( ! [X485: $i] :
( ? [X486: $i] : ( in @ X486 @ X485 )
=> ( nonempty @ X485 ) )
=> ( ! [X487: $i,X488: $i] : ( in @ X487 @ ( setadjoin @ X487 @ X488 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X489: $i,X490: $i,X491: $i] :
( ( in @ X491 @ X490 )
=> ( in @ X491 @ ( setadjoin @ X489 @ X490 ) ) )
=> ( ! [X492: $i,X493: $i,X494: $i] :
( ( in @ X494 @ ( setadjoin @ X492 @ X493 ) )
=> ! [X495: $o] :
( ( ( X494 = X492 )
=> X495 )
=> ( ( ( in @ X494 @ X493 )
=> X495 )
=> X495 ) ) )
=> ( ! [X496: $i,X497: $i,X498: $i] :
( ( in @ X498 @ ( setadjoin @ X496 @ X497 ) )
=> ( ( X498 = X496 )
| ( in @ X498 @ X497 ) ) )
=> ( ! [X499: $i] :
( ( dsetconstr @ X499
@ ^ [Z0: $i] : $true )
= X499 )
=> ( ! [X500: $i,X501: $i] :
( ! [X502: $i] :
( ( in @ X502 @ X501 )
=> ( in @ X502 @ X500 ) )
=> ( in @ X501 @ ( powerset @ X500 ) ) )
=> ( ! [X503: $i] : ( in @ emptyset @ ( powerset @ X503 ) )
=> ( ! [X504: $i] : ( in @ emptyset @ ( powerset @ X504 ) )
=> ( ! [X505: $i,X506: $i,X507: $i] :
( ( in @ X506 @ ( powerset @ X505 ) )
=> ( ( in @ X507 @ X506 )
=> ( in @ X507 @ X505 ) ) )
=> ( ! [X508: $i,X509: $i,X510: $i] :
( ( in @ X509 @ X510 )
=> ( ( in @ X510 @ X508 )
=> ( in @ X509 @ ( setunion @ X508 ) ) ) )
=> ( ! [X511: $i,X512: $i] :
( ( in @ X512 @ ( setunion @ X511 ) )
=> ! [X513: $o] :
( ! [X514: $i] :
( ( in @ X512 @ X514 )
=> ( ( in @ X514 @ X511 )
=> X513 ) )
=> X513 ) )
=> ( ! [X515: $i,X516: $i] :
( ( in @ X516 @ X515 )
=> ( in @ X516 @ ( powerset @ ( setunion @ X515 ) ) ) )
=> ( ! [X517: $i > $o] :
( ( exu @ X517 )
=> ? [X518: $i] :
! [X519: $i] :
( ( X517 @ X519 )
<=> ( X519 = X518 ) ) )
=> ( ! [X520: $i] :
( ( nonempty @ X520 )
=> ? [X521: $i] :
( ( in @ X521 @ X520 )
& $true ) )
=> ( ! [X522: $i,X523: $i] :
( ( in @ X522 @ ( setadjoin @ X523 @ emptyset ) )
=> ( X522 = X523 ) )
=> ( ! [X524: $i,X525: $i] :
( ( X524 != X525 )
=> ~ ( in @ X525 @ ( setadjoin @ X524 @ emptyset ) ) )
=> ( ! [X526: $i,X527: $i] :
( ( X526 = X527 )
=> ( in @ X526 @ ( setadjoin @ X527 @ emptyset ) ) )
=> ( ! [X528: $i,X529: $i] :
( ( in @ X528 @ ( setadjoin @ X529 @ emptyset ) )
=> ( in @ X529 @ ( setadjoin @ X528 @ emptyset ) ) )
=> ( ! [X530: $i,X531: $i,X532: $i] :
( ( in @ X532 @ ( setadjoin @ X530 @ ( setadjoin @ X531 @ emptyset ) ) )
=> ( ( X532 = X530 )
| ( X532 = X531 ) ) )
=> ( ! [X533: $i,X534: $i] : ( in @ X533 @ ( setadjoin @ X533 @ ( setadjoin @ X534 @ emptyset ) ) )
=> ( ! [X535: $i,X536: $i] : ( in @ X536 @ ( setadjoin @ X535 @ ( setadjoin @ X536 @ emptyset ) ) )
=> ( ! [X537: $i,X538: $i > $o] :
( ? [X539: $i] :
( ( in @ X539 @ X537 )
& ( X538 @ X539 ) )
=> ( ( ( dsetconstr @ X537 @ X538 )
= emptyset )
=> ~ $true ) )
=> ( ! [X540: $i > $o,X541: $i] :
( ( in @ X541 @ emptyset )
=> ( X540 @ X541 ) )
=> ( ! [X542: $i,X543: $i > $o] :
( ~ ! [X544: $i] :
( ( in @ X544 @ X542 )
=> ( X543 @ X544 ) )
=> ? [X545: $i] :
( ( in @ X545 @ X542 )
& ~ ( X543 @ X545 ) ) )
=> ( ! [X546: $i,X547: $i > $o] :
( ! [X548: $i] :
( ( in @ X548 @ X546 )
=> ~ ( X547 @ X548 ) )
=> ~ ? [X549: $i] :
( ( in @ X549 @ X546 )
& ( X547 @ X549 ) ) )
=> ( ! [X550: $i,X551: $i > $o] :
( ~ ? [X552: $i] :
( ( in @ X552 @ X550 )
& ( X551 @ X552 ) )
=> ! [X553: $i] :
( ( in @ X553 @ X550 )
=> ~ ( X551 @ X553 ) ) )
=> ( ! [X554: $i,X555: $i > $o] :
( ? [X556: $i] :
( ( in @ X556 @ X554 )
& ~ ( X555 @ X556 ) )
=> ~ ! [X557: $i] :
( ( in @ X557 @ X554 )
=> ( X555 @ X557 ) ) )
=> ( ! [X558: $o] :
( X558
=> ( in @ emptyset @ ( prop2set @ X558 ) ) )
=> ( prop2set2propI
=> ( ! [X559: $i,X560: $i > $o] :
( ~ ? [X561: $i] :
( ( in @ X561 @ X559 )
& ( X560 @ X561 ) )
=> ! [X562: $i] :
( ( in @ X562 @ X559 )
=> ~ ( X560 @ X562 ) ) )
=> ( ! [X563: $i,X564: $i > $o] :
( ~ ! [X565: $i] :
( ( in @ X565 @ X563 )
=> ( X564 @ X565 ) )
=> ? [X566: $i] :
( ( in @ X566 @ X563 )
& ~ ( X564 @ X566 ) ) )
=> ( ! [X567: $i > $o] :
( ? [X568: $i] :
( ( X567 @ X568 )
& ! [X569: $i] :
( ( X567 @ X569 )
=> ( X568 = X569 ) ) )
=> ( exu @ X567 ) )
=> ( ! [X570: $i > $o] :
( ? [X571: $i] : ( X570 @ X571 )
=> ( ! [X572: $i,X573: $i] :
( ( X570 @ X572 )
=> ( ( X570 @ X573 )
=> ( X572 = X573 ) ) )
=> ( exu @ X570 ) ) )
=> ( ! [X574: $i > $o] :
( ? [X575: $i] :
! [X576: $i] :
( ( X574 @ X576 )
<=> ( X576 = X575 ) )
=> ( exu @ X574 ) )
=> ( ! [X577: $i,X578: $i] :
( ( X577 = X578 )
=> ! [X579: $i,X580: $i] :
( ( X579 = X580 )
=> ( ( in @ X579 @ X577 )
=> ( in @ X580 @ X578 ) ) ) )
=> ( ! [X581: $i,X582: $i] :
( ( X581 = X582 )
=> ! [X583: $i,X584: $i] :
( ( X583 = X584 )
=> ( ( in @ X583 @ X581 )
<=> ( in @ X584 @ X582 ) ) ) )
=> ( ! [X585: $i > $o] :
( ( exu @ X585 )
=> ! [X586: $i,X587: $i] :
( ( X585 @ X586 )
=> ( ( X585 @ X587 )
=> ( X586 = X587 ) ) ) )
=> ( ! [X588: $i > $o,X589: $i > $o] :
( ! [X590: $i,X591: $i] :
( ( X590 = X591 )
=> ( ( X588 @ X590 )
<=> ( X589 @ X591 ) ) )
=> ( ( exu @ X588 )
<=> ( exu @ X589 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X592: $i,X593: $i] :
( ( X592 = X593 )
=> ! [X594: $i,X595: $i] :
( ( X594 = X595 )
=> ( ( setadjoin @ X592 @ X594 )
= ( setadjoin @ X593 @ X595 ) ) ) )
=> ( ! [X596: $i,X597: $i] :
( ( X596 = X597 )
=> ( ( powerset @ X596 )
= ( powerset @ X597 ) ) )
=> ( ! [X598: $i,X599: $i] :
( ( X598 = X599 )
=> ( ( setunion @ X598 )
= ( setunion @ X599 ) ) )
=> ( ( omega = omega )
=> ( ! [X600: $i > $o] :
( ( exu @ X600 )
=> ! [X601: $i,X602: $i] :
( ( X600 @ X601 )
=> ( ( X600 @ X602 )
=> ( X601 = X602 ) ) ) )
=> ( ! [X603: $i > $o,X604: $i > $o] :
( ! [X605: $i,X606: $i] :
( ( X605 = X606 )
=> ( ( X603 @ X605 )
<=> ( X604 @ X606 ) ) )
=> ( ( exu @ X603 )
=> ( ( exu @ X604 )
=> ( ( descr @ X603 )
= ( descr @ X604 ) ) ) ) )
=> ( ! [X607: $i,X608: $i] :
( ( X607 = X608 )
=> ! [X609: $i > $o,X610: $i > $o] :
( ! [X611: $i] :
( ( in @ X611 @ X607 )
=> ! [X612: $i] :
( ( in @ X612 @ X608 )
=> ( ( X611 = X612 )
=> ( ( X609 @ X611 )
<=> ( X610 @ X612 ) ) ) ) )
=> ( ( dsetconstr @ X607 @ X609 )
= ( dsetconstr @ X608 @ X610 ) ) ) )
=> ( ! [X613: $i,X614: $i] :
( ! [X615: $i] :
( ( in @ X615 @ X613 )
=> ( in @ X615 @ X614 ) )
=> ( subset @ X613 @ X614 ) )
=> ( ! [X616: $i,X617: $i] :
( ( X616 = X617 )
=> ( subset @ X617 @ X616 ) )
=> ( ! [X618: $i,X619: $i] :
( ( X618 = X619 )
=> ( subset @ X618 @ X619 ) )
=> ( ! [X620: $i,X621: $i] :
( ! [X622: $i] :
( ( in @ X622 @ X620 )
=> ( in @ X622 @ X621 ) )
=> ( subset @ X620 @ X621 ) )
=> ( ! [X623: $i] : ( subset @ emptyset @ X623 )
=> ( ! [X624: $i,X625: $i,X626: $i] :
( ( subset @ X624 @ X625 )
=> ( ( in @ X626 @ X624 )
=> ( in @ X626 @ X625 ) ) )
=> ( ! [X627: $i,X628: $i,X629: $i] :
( ( subset @ X627 @ X628 )
=> ( ~ ( in @ X629 @ X628 )
=> ~ ( in @ X629 @ X627 ) ) )
=> ( ! [X630: $i,X631: $i,X632: $i] :
( ( in @ X632 @ X630 )
=> ( ~ ( in @ X632 @ X631 )
=> ~ ( subset @ X630 @ X631 ) ) )
=> ( ! [X633: $i,X634: $i] :
( ~ ( subset @ X633 @ X634 )
=> ( X633 != X634 ) )
=> ( ! [X635: $i,X636: $i,X637: $i] :
( ( in @ X637 @ X635 )
=> ( ~ ( in @ X637 @ X636 )
=> ( X635 != X636 ) ) )
=> ( ! [X638: $i] : ( subset @ X638 @ X638 )
=> ( ! [X639: $i,X640: $i,X641: $i] :
( ( subset @ X639 @ X640 )
=> ( ( subset @ X640 @ X641 )
=> ( subset @ X639 @ X641 ) ) )
=> ( ! [X642: $i,X643: $i] : ( subset @ X643 @ ( setadjoin @ X642 @ X643 ) )
=> ( ! [X644: $i,X645: $i,X646: $i] :
( ( subset @ X644 @ X646 )
=> ( subset @ X644 @ ( setadjoin @ X645 @ X646 ) ) )
=> ( ! [X647: $i,X648: $i] :
( ( subset @ X647 @ X648 )
=> ( in @ X647 @ ( powerset @ X648 ) ) )
=> ( ! [X649: $i,X650: $i] :
( ( subset @ X649 @ X650 )
=> ( ( subset @ X650 @ X649 )
=> ( X649 = X650 ) ) )
=> ( ! [X651: $i] :
( ( subset @ X651 @ emptyset )
=> ( X651 = emptyset ) )
=> ( ! [X652: $i,X653: $i] :
( ( subset @ X653 @ X652 )
=> ( in @ X653 @ ( powerset @ X652 ) ) )
=> ( ! [X654: $i,X655: $i] :
( ( in @ X655 @ ( powerset @ X654 ) )
=> ( subset @ X655 @ X654 ) )
=> ( ! [X656: $i] : ( in @ X656 @ ( powerset @ X656 ) )
=> ( ! [X657: $i,X658: $i] :
( ( subset @ X657 @ X658 )
=> ( subset @ ( powerset @ X657 ) @ ( powerset @ X658 ) ) )
=> ( ! [X659: $i,X660: $i > $o] : ( in @ ( dsetconstr @ X659 @ X660 ) @ ( powerset @ X659 ) )
=> ( ! [X661: $i,X662: $i > $o] : ( subset @ ( dsetconstr @ X661 @ X662 ) @ X661 )
=> ( ! [X663: $i,X664: $i,X665: $i] :
( ( in @ X665 @ X663 )
=> ( in @ X665 @ ( binunion @ X663 @ X664 ) ) )
=> ( ! [X666: $i,X667: $i] : ( in @ X667 @ ( setadjoin @ X666 @ ( setadjoin @ X667 @ emptyset ) ) )
=> ( ! [X668: $i,X669: $i,X670: $i] :
( ( in @ X670 @ X669 )
=> ( in @ X670 @ ( binunion @ X668 @ X669 ) ) )
=> ( ! [X671: $i,X672: $i,X673: $i,X674: $o] :
( ( in @ X673 @ ( binunion @ X671 @ X672 ) )
=> ( ( ( in @ X673 @ X671 )
=> X674 )
=> ( ( ( in @ X673 @ X672 )
=> X674 )
=> X674 ) ) )
=> ( ! [X675: $i,X676: $i,X677: $i] :
( ( in @ X677 @ ( binunion @ X675 @ X676 ) )
=> ( ( in @ X677 @ X675 )
| ( in @ X677 @ X676 ) ) )
=> ( ! [X678: $i,X679: $i] : ( subset @ X678 @ ( binunion @ X678 @ X679 ) )
=> ( ! [X680: $i,X681: $i] : ( subset @ X681 @ ( binunion @ X680 @ X681 ) )
=> ( ! [X682: $i,X683: $i,X684: $i] :
( ( in @ X684 @ X682 )
=> ( ( in @ X684 @ X683 )
=> ( in @ X684 @ ( binintersect @ X682 @ X683 ) ) ) )
=> ( ! [X685: $i,X686: $i,X687: $i] :
( ( subset @ X687 @ X685 )
=> ( ( subset @ X687 @ X686 )
=> ( subset @ X687 @ ( binintersect @ X685 @ X686 ) ) ) )
=> ( ! [X688: $i,X689: $i,X690: $i] :
( ( in @ X690 @ ( binintersect @ X688 @ X689 ) )
=> ( in @ X690 @ X688 ) )
=> ( ! [X691: $i,X692: $i] : ( subset @ ( binintersect @ X691 @ X692 ) @ X691 )
=> ( ! [X693: $i,X694: $i] :
( ( subset @ X693 @ X694 )
=> ( ( binintersect @ X693 @ X694 )
= X693 ) )
=> ( ! [X695: $i,X696: $i] :
( ( ( binintersect @ X695 @ X696 )
= X696 )
=> ( subset @ X696 @ X695 ) )
=> ( ! [X697: $i,X698: $i,X699: $i] :
( ( in @ X699 @ ( binintersect @ X697 @ X698 ) )
=> ( in @ X699 @ X698 ) )
=> ( ! [X700: $i,X701: $i] :
( ~ ? [X702: $i] :
( ( in @ X702 @ X700 )
& ( in @ X702 @ X701 ) )
=> ( ( binintersect @ X700 @ X701 )
= emptyset ) )
=> ( ! [X703: $i,X704: $i] : ( subset @ ( binintersect @ X703 @ X704 ) @ X704 )
=> ( ! [X705: $i,X706: $i] :
( ( subset @ X706 @ X705 )
=> ( ( binintersect @ X705 @ X706 )
= X706 ) )
=> ( ! [X707: $i,X708: $i] :
( ( ( binintersect @ X707 @ X708 )
= X707 )
=> ( subset @ X707 @ X708 ) )
=> ( ! [X709: $i,X710: $i,X711: $i] :
( ( binintersect @ X709 @ ( binunion @ X710 @ X711 ) )
= ( binunion @ ( binintersect @ X709 @ X710 ) @ ( binintersect @ X709 @ X711 ) ) )
=> ( ! [X712: $i,X713: $i,X714: $i] :
( ( in @ X714 @ X712 )
=> ( ~ ( in @ X714 @ X713 )
=> ( in @ X714 @ ( setminus @ X712 @ X713 ) ) ) )
=> ( ! [X715: $i,X716: $i,X717: $i] :
( ( in @ X717 @ ( setminus @ X715 @ X716 ) )
=> ( in @ X717 @ X715 ) )
=> ( ! [X718: $i,X719: $i,X720: $i] :
( ( in @ X720 @ ( setminus @ X718 @ X719 ) )
=> ~ ( in @ X720 @ X719 ) )
=> ( ! [X721: $i,X722: $i] :
( ( subset @ X721 @ X722 )
=> ( ( setminus @ X721 @ X722 )
= emptyset ) )
=> ( ! [X723: $i,X724: $i,X725: $i] :
( ~ ( in @ X725 @ ( setminus @ X723 @ X724 ) )
=> ( ( in @ X725 @ X723 )
=> ( in @ X725 @ X724 ) ) )
=> ( ! [X726: $i,X727: $i,X728: $i] :
( ~ ( in @ X728 @ ( setminus @ X726 @ X727 ) )
=> ( ~ ( in @ X728 @ X727 )
=> ~ ( in @ X728 @ X726 ) ) )
=> ( ! [X729: $i,X730: $i,X731: $i] :
( ~ ( in @ X731 @ X729 )
=> ~ ( in @ X731 @ ( setminus @ X729 @ X730 ) ) )
=> ( ! [X732: $i,X733: $i,X734: $i] :
( ( in @ X734 @ X733 )
=> ~ ( in @ X734 @ ( setminus @ X732 @ X733 ) ) )
=> ( ! [X735: $i,X736: $i] : ( subset @ ( setminus @ X735 @ X736 ) @ X735 )
=> ( ! [X737: $i,X738: $i] :
( ( ( setminus @ X737 @ X738 )
= emptyset )
=> ( subset @ X737 @ X738 ) )
=> ( ! [X739: $i,X740: $i,X741: $i] :
( ( in @ X741 @ ( symdiff @ X739 @ X740 ) )
=> ! [X742: $o] :
( ( ( in @ X741 @ X739 )
=> ( ~ ( in @ X741 @ X740 )
=> X742 ) )
=> ( ( ~ ( in @ X741 @ X739 )
=> ( ( in @ X741 @ X740 )
=> X742 ) )
=> X742 ) ) )
=> ( ! [X743: $i,X744: $i,X745: $i] :
( ( in @ X745 @ X743 )
=> ( ~ ( in @ X745 @ X744 )
=> ( in @ X745 @ ( symdiff @ X743 @ X744 ) ) ) )
=> ( ! [X746: $i,X747: $i,X748: $i] :
( ~ ( in @ X748 @ X746 )
=> ( ( in @ X748 @ X747 )
=> ( in @ X748 @ ( symdiff @ X746 @ X747 ) ) ) )
=> ( ! [X749: $i,X750: $i,X751: $i] :
( ( in @ X751 @ X749 )
=> ( ( in @ X751 @ X750 )
=> ~ ( in @ X751 @ ( symdiff @ X749 @ X750 ) ) ) )
=> ( ! [X752: $i,X753: $i,X754: $i] :
( ~ ( in @ X754 @ X752 )
=> ( ~ ( in @ X754 @ X753 )
=> ~ ( in @ X754 @ ( symdiff @ X752 @ X753 ) ) ) )
=> ( ! [X755: $i,X756: $i] : ( in @ X756 @ ( setadjoin @ X755 @ ( setadjoin @ X756 @ emptyset ) ) )
=> ( ! [X757: $i,X758: $i] : ( in @ X757 @ ( setunion @ ( setadjoin @ ( setadjoin @ X757 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X757 @ ( setadjoin @ X758 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X759: $i,X760: $i] : ( in @ X760 @ ( setunion @ ( setadjoin @ ( setadjoin @ X759 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X759 @ ( setadjoin @ X760 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X761: $i,X762: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X761 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X761 @ ( setadjoin @ X762 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X763: $i,X764: $i] : ( iskpair @ ( kpair @ X763 @ X764 ) )
=> ( ! [X765: $i,X766: $i] :
( ( in @ X766 @ X765 )
=> ( subset @ ( setadjoin @ X766 @ emptyset ) @ X765 ) )
=> ( ! [X767: $i,X768: $i] :
( ( in @ X768 @ X767 )
=> ( in @ ( setadjoin @ X768 @ emptyset ) @ ( powerset @ X767 ) ) )
=> ( ! [X769: $i,X770: $i,X771: $i] :
( ( in @ X771 @ X769 )
=> ( in @ ( setadjoin @ X771 @ emptyset ) @ ( powerset @ ( binunion @ X769 @ X770 ) ) ) )
=> ( ! [X772: $i,X773: $i,X774: $i] :
( ( in @ X774 @ ( setadjoin @ X772 @ ( setadjoin @ X773 @ emptyset ) ) )
=> ( ( X774 = X772 )
| ( X774 = X773 ) ) )
=> ( ! [X775: $i,X776: $i,X777: $i] :
( ( in @ X777 @ X775 )
=> ! [X778: $i] :
( ( in @ X778 @ X776 )
=> ( subset @ ( setadjoin @ X777 @ ( setadjoin @ X778 @ emptyset ) ) @ ( binunion @ X775 @ X776 ) ) ) )
=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[upairinpowunion]),secondinupair]),upairsubunion]),binintersectER]),nonemptyImpWitness]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),uniqinunit]),binintersectSubset1]),bs114d]),notinsingleton]),setminusI]),setminusEL]),eqinunit]),setminusER]),setminusSubset2]),singletonsswitch]),setminusERneg]),setminusELneg]),upairsetE]),setminusILneg]),setminusIRneg]),upairsetIL]),setminusLsub]),upairsetIR]),setminusSubset1]),symdiffE]),symdiffI1]),c_0_142]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),vacuousDall]),omega__Cong]),setukpairIL]),setukpairIR]),quantDeMorgan1]),kpairiskpair]),kpairp]),quantDeMorgan2]),singletonsubset]),singletoninpowerset]),quantDeMorgan3]),singletoninpowunion]),upairset2E]),quantDeMorgan4]),prop2setI]),notdexE]),notdallE]),c_0_143]),c_0_144]),c_0_145]),inCongP]),in__Cong]),c_0_146]),c_0_147]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),binintersectEL]),binintersectLsub]),c_0_148]),c_0_149]),c_0_150]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),setunionI]),inPowerset]),powersetsubset]),c_0_151]),c_0_152]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),setunionE]),subPowSU]),binunionE]),binunionLsub]),c_0_153]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectSubset2]),binintersectSubset3]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_154]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_155]),nonemptyE1]),c_0_156]),noeltsimpempty]),emptyI]),setext]),c_0_157]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_158]),c_0_159]),c_0_160]),c_0_161]),c_0_162]),wellorderingAx]),foundationAx]),c_0_163]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_164]) ).
thf(c_0_166,negated_conjecture,
! [X779: $i,X780: $i,X782: $i,X783: $i,X784: $i,X785: $i,X786: $i,X787: $i,X788: $i,X789: $i,X790: $i,X792: $i,X793: $i,X795: $i,X796: $i,X797: $i,X798: $i,X799: $i,X801: $i,X802: $i > $i > $o,X803: $i,X806: $i,X808: $i,X809: $i,X810: $i,X811: $i,X813: $i,X814: $i > $o,X815: $i,X816: $i > $o,X817: $i,X818: $i,X819: $i > $o,X820: $i,X821: $i,X822: $i > $o,X823: $i,X824: $i > $o,X826: $i,X827: $o,X828: $i,X829: $i,X830: $o,X831: $i,X832: $i,X833: $i > $o,X835: $i,X836: $i,X839: $i,X841: $i,X843: $i,X844: $i > $o,X845: $i,X846: $i,X848: $i,X849: $i > $o,X850: $i,X851: $i,X852: $i,X853: $i,X854: $i,X855: $i,X856: $i,X857: $i,X858: $i,X859: $i,X860: $i,X861: $o,X862: $i,X863: $i,X864: $i,X865: $i,X866: $i,X867: $i,X869: $i,X870: $i,X871: $i,X872: $i,X873: $i,X874: $i,X875: $i,X876: $i,X877: $i,X878: $i,X879: $o,X881: $i,X882: $i,X883: $i > $o,X885: $i,X886: $i,X887: $i,X889: $i,X890: $i,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 > $o,X906: $i,X907: $i > $o,X908: $i,X909: $i,X910: $i > $o,X911: $i,X913: $i,X914: $i > $o,X916: $i,X917: $i,X918: $i > $o,X920: $i,X921: $i,X922: $i > $o,X923: $i,X925: $o,X926: $i,X927: $i > $o,X929: $i,X930: $i,X931: $i > $o,X932: $i,X934: $i > $o,X935: $i,X937: $i > $o,X938: $i,X941: $i > $o,X942: $i,X944: $i,X945: $i,X946: $i,X947: $i,X948: $i,X949: $i,X950: $i,X951: $i,X952: $i > $o,X953: $i,X954: $i,X955: $i > $o,X956: $i > $o,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i > $o,X968: $i,X969: $i,X970: $i > $o,X971: $i > $o,X974: $i,X975: $i,X976: $i > $o,X977: $i > $o,X980: $i,X981: $i,X983: $i,X984: $i,X985: $i,X986: $i,X987: $i,X988: $i,X990: $i,X991: $i,X992: $i,X993: $i,X994: $i,X995: $i,X996: $i,X997: $i,X998: $i,X999: $i,X1000: $i,X1001: $i,X1002: $i,X1003: $i,X1004: $i,X1005: $i,X1006: $i,X1007: $i,X1008: $i,X1009: $i,X1010: $i,X1011: $i,X1012: $i,X1013: $i,X1014: $i,X1015: $i,X1016: $i,X1017: $i,X1018: $i,X1019: $i,X1020: $i,X1021: $i,X1022: $i,X1023: $i,X1024: $i,X1025: $i,X1026: $i,X1027: $i > $o,X1028: $i,X1029: $i > $o,X1030: $i,X1031: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $o,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1053: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1059: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i,X1081: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i,X1099: $i,X1100: $i,X1101: $i,X1102: $i,X1103: $i,X1104: $i,X1105: $i,X1106: $i,X1107: $i,X1108: $i,X1109: $o,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i,X1115: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,X1133: $i,X1134: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $i,X1143: $i,X1144: $i,X1145: $i] :
( ( ~ ( in @ ( esk1_2 @ X779 @ X780 ) @ X779 )
| ~ ( in @ ( esk1_2 @ X779 @ X780 ) @ X780 )
| ( X779 = X780 ) )
& ( ( in @ ( esk1_2 @ X779 @ X780 ) @ X779 )
| ( in @ ( esk1_2 @ X779 @ X780 ) @ X780 )
| ( X779 = X780 ) )
& ~ ( in @ X782 @ emptyset )
& ( ~ ( in @ X785 @ ( setadjoin @ X783 @ X784 ) )
| ( X785 = X783 )
| ( in @ X785 @ X784 ) )
& ( ( X785 != X783 )
| ( in @ X785 @ ( setadjoin @ X783 @ X784 ) ) )
& ( ~ ( in @ X785 @ X784 )
| ( in @ X785 @ ( setadjoin @ X783 @ X784 ) ) )
& ( ~ ( in @ X787 @ ( powerset @ X786 ) )
| ~ ( in @ X788 @ X787 )
| ( in @ X788 @ X786 ) )
& ( ( in @ ( esk2_2 @ X789 @ X790 ) @ X790 )
| ( in @ X790 @ ( powerset @ X789 ) ) )
& ( ~ ( in @ ( esk2_2 @ X789 @ X790 ) @ X789 )
| ( in @ X790 @ ( powerset @ X789 ) ) )
& ( ( in @ X793 @ ( esk3_2 @ X792 @ X793 ) )
| ~ ( in @ X793 @ ( setunion @ X792 ) ) )
& ( ( in @ ( esk3_2 @ X792 @ X793 ) @ X792 )
| ~ ( in @ X793 @ ( setunion @ X792 ) ) )
& ( ~ ( in @ X796 @ X797 )
| ~ ( in @ X797 @ X795 )
| ( in @ X796 @ ( setunion @ X795 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X798 @ omega )
| ( in @ ( setadjoin @ X798 @ X798 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X799 ) @ omega )
| ~ ( in @ emptyset @ X799 )
| ~ ( in @ X801 @ omega )
| ( in @ X801 @ X799 ) )
& ( ( in @ ( esk4_1 @ X799 ) @ X799 )
| ~ ( in @ emptyset @ X799 )
| ~ ( in @ X801 @ omega )
| ( in @ X801 @ X799 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X799 ) @ ( esk4_1 @ X799 ) ) @ X799 )
| ~ ( in @ emptyset @ X799 )
| ~ ( in @ X801 @ omega )
| ( in @ X801 @ X799 ) )
& ( ( in @ ( esk7_3 @ X802 @ X803 @ X806 ) @ X803 )
| ~ ( in @ X806 @ ( esk6_2 @ X802 @ X803 ) )
| ( in @ ( esk5_2 @ X802 @ X803 ) @ X803 ) )
& ( ( X802 @ ( esk7_3 @ X802 @ X803 @ X806 ) @ X806 )
| ~ ( in @ X806 @ ( esk6_2 @ X802 @ X803 ) )
| ( in @ ( esk5_2 @ X802 @ X803 ) @ X803 ) )
& ( ~ ( in @ X809 @ X803 )
| ~ ( X802 @ X809 @ X808 )
| ( in @ X808 @ ( esk6_2 @ X802 @ X803 ) )
| ( in @ ( esk5_2 @ X802 @ X803 ) @ X803 ) )
& ( ( in @ ( esk7_3 @ X802 @ X803 @ X806 ) @ X803 )
| ~ ( in @ X806 @ ( esk6_2 @ X802 @ X803 ) )
| ~ ( exu @ ( X802 @ ( esk5_2 @ X802 @ X803 ) ) ) )
& ( ( X802 @ ( esk7_3 @ X802 @ X803 @ X806 ) @ X806 )
| ~ ( in @ X806 @ ( esk6_2 @ X802 @ X803 ) )
| ~ ( exu @ ( X802 @ ( esk5_2 @ X802 @ X803 ) ) ) )
& ( ~ ( in @ X809 @ X803 )
| ~ ( X802 @ X809 @ X808 )
| ( in @ X808 @ ( esk6_2 @ X802 @ X803 ) )
| ~ ( exu @ ( X802 @ ( esk5_2 @ X802 @ X803 ) ) ) )
& ( ( in @ ( esk8_1 @ X810 ) @ X810 )
| ~ ( in @ X811 @ X810 ) )
& ( ~ ( in @ X813 @ ( esk8_1 @ X810 ) )
| ~ ( in @ X813 @ X810 )
| ~ ( in @ X811 @ X810 ) )
& epred1_0
& ( ~ ( exu @ X814 )
| ( X814 @ ( descr @ X814 ) ) )
& ( ~ ( in @ X817 @ X815 )
| ~ ( X816 @ X817 )
| ( in @ X817 @ ( dsetconstr @ X815 @ X816 ) ) )
& ( ~ ( in @ X820 @ ( dsetconstr @ X818 @ X819 ) )
| ( in @ X820 @ X818 ) )
& ( ~ ( in @ X823 @ ( dsetconstr @ X821 @ X822 ) )
| ( X822 @ X823 ) )
& ( ( X824 @ ( esk9_1 @ X824 ) )
| ~ ( exu @ X824 ) )
& ( ~ ( X824 @ X826 )
| ( ( esk9_1 @ X824 )
= X826 )
| ~ ( exu @ X824 ) )
& ( ~ ( in @ X828 @ ( prop2set @ X827 ) )
| X827 )
& ( ~ ( in @ X829 @ emptyset )
| X830 )
& ( ~ ( in @ X831 @ emptyset )
| ~ $true )
& ~ ( in @ X832 @ emptyset )
& ( ~ ( exu @ X833 )
| ( X833 @ ( esk10_1 @ X833 ) ) )
& ( ( in @ ( esk12_2 @ X835 @ X836 ) @ X836 )
| ( X835 = X836 )
| ( in @ ( esk11_2 @ X835 @ X836 ) @ X835 ) )
& ( ~ ( in @ ( esk12_2 @ X835 @ X836 ) @ X835 )
| ( X835 = X836 )
| ( in @ ( esk11_2 @ X835 @ X836 ) @ X835 ) )
& ( ( in @ ( esk12_2 @ X835 @ X836 ) @ X836 )
| ( X835 = X836 )
| ~ ( in @ ( esk11_2 @ X835 @ X836 ) @ X836 ) )
& ( ~ ( in @ ( esk12_2 @ X835 @ X836 ) @ X835 )
| ( X835 = X836 )
| ~ ( in @ ( esk11_2 @ X835 @ X836 ) @ X836 ) )
& ( ( in @ ( esk13_1 @ X839 ) @ X839 )
| ( X839 = emptyset ) )
& ( ( in @ ( esk14_1 @ X841 ) @ X841 )
| ( X841 = emptyset ) )
& ( ~ ( in @ X845 @ ( dsetconstr @ X843 @ X844 ) )
| ( X844 @ X845 )
| ~ ( in @ X845 @ X843 ) )
& ( ~ ( X844 @ X845 )
| ( in @ X845 @ ( dsetconstr @ X843 @ X844 ) )
| ~ ( in @ X845 @ X843 ) )
& ( ~ ( nonempty @ X846 )
| ( in @ ( esk15_1 @ X846 ) @ X846 ) )
& ( ~ ( in @ X850 @ X848 )
| ~ ( X849 @ X850 )
| ( nonempty @ ( dsetconstr @ X848 @ X849 ) ) )
& ( ~ ( in @ X852 @ X851 )
| ( nonempty @ X851 ) )
& ( in @ X853 @ ( setadjoin @ X853 @ X854 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X857 @ X856 )
| ( in @ X857 @ ( setadjoin @ X855 @ X856 ) ) )
& ( ( in @ X860 @ X859 )
| X861
| ( X860 = X858 )
| ~ ( in @ X860 @ ( setadjoin @ X858 @ X859 ) ) )
& ( ~ X861
| X861
| ( X860 = X858 )
| ~ ( in @ X860 @ ( setadjoin @ X858 @ X859 ) ) )
& ( ( in @ X860 @ X859 )
| X861
| ~ X861
| ~ ( in @ X860 @ ( setadjoin @ X858 @ X859 ) ) )
& ( ~ X861
| X861
| ~ X861
| ~ ( in @ X860 @ ( setadjoin @ X858 @ X859 ) ) )
& ( ~ ( in @ X864 @ ( setadjoin @ X862 @ X863 ) )
| ( X864 = X862 )
| ( in @ X864 @ X863 ) )
& ( ( dsetconstr @ X865
@ ^ [Z0: $i] : $true )
= X865 )
& ( ( in @ ( esk16_2 @ X866 @ X867 ) @ X867 )
| ( in @ X867 @ ( powerset @ X866 ) ) )
& ( ~ ( in @ ( esk16_2 @ X866 @ X867 ) @ X866 )
| ( in @ X867 @ ( powerset @ X866 ) ) )
& ( in @ emptyset @ ( powerset @ X869 ) )
& ( in @ emptyset @ ( powerset @ X870 ) )
& ( ~ ( in @ X872 @ ( powerset @ X871 ) )
| ~ ( in @ X873 @ X872 )
| ( in @ X873 @ X871 ) )
& ( ~ ( in @ X875 @ X876 )
| ~ ( in @ X876 @ X874 )
| ( in @ X875 @ ( setunion @ X874 ) ) )
& ( ( in @ X878 @ ( esk17_3 @ X877 @ X878 @ X879 ) )
| X879
| ~ ( in @ X878 @ ( setunion @ X877 ) ) )
& ( ( in @ ( esk17_3 @ X877 @ X878 @ X879 ) @ X877 )
| X879
| ~ ( in @ X878 @ ( setunion @ X877 ) ) )
& ( ~ X879
| X879
| ~ ( in @ X878 @ ( setunion @ X877 ) ) )
& ( ~ ( in @ X882 @ X881 )
| ( in @ X882 @ ( powerset @ ( setunion @ X881 ) ) ) )
& ( ~ ( X883 @ X885 )
| ( X885
= ( esk18_1 @ X883 ) )
| ~ ( exu @ X883 ) )
& ( ( X886
!= ( esk18_1 @ X883 ) )
| ( X883 @ X886 )
| ~ ( exu @ X883 ) )
& ( ( in @ ( esk19_1 @ X887 ) @ X887 )
| ~ ( nonempty @ X887 ) )
& ( $true
| ~ ( nonempty @ X887 ) )
& ( ~ ( in @ X889 @ ( setadjoin @ X890 @ emptyset ) )
| ( X889 = X890 ) )
& ( ( X891 = X892 )
| ~ ( in @ X892 @ ( setadjoin @ X891 @ emptyset ) ) )
& ( ( X893 != X894 )
| ( in @ X893 @ ( setadjoin @ X894 @ emptyset ) ) )
& ( ~ ( in @ X895 @ ( setadjoin @ X896 @ emptyset ) )
| ( in @ X896 @ ( setadjoin @ X895 @ emptyset ) ) )
& ( ~ ( in @ X899 @ ( setadjoin @ X897 @ ( setadjoin @ X898 @ emptyset ) ) )
| ( X899 = X897 )
| ( X899 = X898 ) )
& ( in @ X900 @ ( setadjoin @ X900 @ ( setadjoin @ X901 @ emptyset ) ) )
& ( in @ X903 @ ( setadjoin @ X902 @ ( setadjoin @ X903 @ emptyset ) ) )
& ( ~ ( in @ X906 @ X904 )
| ~ ( X905 @ X906 )
| ( ( dsetconstr @ X904 @ X905 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X908 @ emptyset )
| ( X907 @ X908 ) )
& ( ( in @ ( esk20_2 @ X909 @ X910 ) @ X909 )
| ~ ( in @ X911 @ X909 )
| ( X910 @ X911 ) )
& ( ~ ( X910 @ ( esk20_2 @ X909 @ X910 ) )
| ~ ( in @ X911 @ X909 )
| ( X910 @ X911 ) )
& ( ( in @ ( esk21_2 @ X913 @ X914 ) @ X913 )
| ~ ( in @ X916 @ X913 )
| ~ ( X914 @ X916 ) )
& ( ( X914 @ ( esk21_2 @ X913 @ X914 ) )
| ~ ( in @ X916 @ X913 )
| ~ ( X914 @ X916 ) )
& ( ( in @ ( esk22_2 @ X917 @ X918 ) @ X917 )
| ~ ( in @ X920 @ X917 )
| ~ ( X918 @ X920 ) )
& ( ( X918 @ ( esk22_2 @ X917 @ X918 ) )
| ~ ( in @ X920 @ X917 )
| ~ ( X918 @ X920 ) )
& ( ( in @ ( esk23_2 @ X921 @ X922 ) @ X921 )
| ~ ( in @ X923 @ X921 )
| ( X922 @ X923 ) )
& ( ~ ( X922 @ ( esk23_2 @ X921 @ X922 ) )
| ~ ( in @ X923 @ X921 )
| ( X922 @ X923 ) )
& ( ~ X925
| ( in @ emptyset @ ( prop2set @ X925 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X926 @ X927 ) @ X926 )
| ~ ( in @ X929 @ X926 )
| ~ ( X927 @ X929 ) )
& ( ( X927 @ ( esk24_2 @ X926 @ X927 ) )
| ~ ( in @ X929 @ X926 )
| ~ ( X927 @ X929 ) )
& ( ( in @ ( esk25_2 @ X930 @ X931 ) @ X930 )
| ~ ( in @ X932 @ X930 )
| ( X931 @ X932 ) )
& ( ~ ( X931 @ ( esk25_2 @ X930 @ X931 ) )
| ~ ( in @ X932 @ X930 )
| ( X931 @ X932 ) )
& ( ( X934 @ ( esk26_2 @ X934 @ X935 ) )
| ~ ( X934 @ X935 )
| ( exu @ X934 ) )
& ( ( X935
!= ( esk26_2 @ X934 @ X935 ) )
| ~ ( X934 @ X935 )
| ( exu @ X934 ) )
& ( ( X937 @ ( esk27_1 @ X937 ) )
| ( exu @ X937 )
| ~ ( X937 @ X938 ) )
& ( ( X937 @ ( esk28_1 @ X937 ) )
| ( exu @ X937 )
| ~ ( X937 @ X938 ) )
& ( ( ( esk27_1 @ X937 )
!= ( esk28_1 @ X937 ) )
| ( exu @ X937 )
| ~ ( X937 @ X938 ) )
& ( ~ ( X941 @ ( esk29_2 @ X941 @ X942 ) )
| ( ( esk29_2 @ X941 @ X942 )
!= X942 )
| ( exu @ X941 ) )
& ( ( X941 @ ( esk29_2 @ X941 @ X942 ) )
| ( ( esk29_2 @ X941 @ X942 )
= X942 )
| ( exu @ X941 ) )
& ( ( X944 != X945 )
| ( X946 != X947 )
| ~ ( in @ X946 @ X944 )
| ( in @ X947 @ X945 ) )
& ( ~ ( in @ X950 @ X948 )
| ( in @ X951 @ X949 )
| ( X950 != X951 )
| ( X948 != X949 ) )
& ( ~ ( in @ X951 @ X949 )
| ( in @ X950 @ X948 )
| ( X950 != X951 )
| ( X948 != X949 ) )
& ( ~ ( exu @ X952 )
| ~ ( X952 @ X953 )
| ~ ( X952 @ X954 )
| ( X953 = X954 ) )
& ( ~ ( exu @ X955 )
| ( exu @ X956 )
| ( ( esk30_2 @ X955 @ X956 )
= ( esk31_2 @ X955 @ X956 ) ) )
& ( ~ ( exu @ X956 )
| ( exu @ X955 )
| ( ( esk30_2 @ X955 @ X956 )
= ( esk31_2 @ X955 @ X956 ) ) )
& ( ~ ( exu @ X955 )
| ( exu @ X956 )
| ~ ( X955 @ ( esk30_2 @ X955 @ X956 ) )
| ~ ( X956 @ ( esk31_2 @ X955 @ X956 ) ) )
& ( ~ ( exu @ X956 )
| ( exu @ X955 )
| ~ ( X955 @ ( esk30_2 @ X955 @ X956 ) )
| ~ ( X956 @ ( esk31_2 @ X955 @ X956 ) ) )
& ( ~ ( exu @ X955 )
| ( exu @ X956 )
| ( X955 @ ( esk30_2 @ X955 @ X956 ) )
| ( X956 @ ( esk31_2 @ X955 @ X956 ) ) )
& ( ~ ( exu @ X956 )
| ( exu @ X955 )
| ( X955 @ ( esk30_2 @ X955 @ X956 ) )
| ( X956 @ ( esk31_2 @ X955 @ X956 ) ) )
& ( emptyset = emptyset )
& ( ( X959 != X960 )
| ( X961 != X962 )
| ( ( setadjoin @ X959 @ X961 )
= ( setadjoin @ X960 @ X962 ) ) )
& ( ( X963 != X964 )
| ( ( powerset @ X963 )
= ( powerset @ X964 ) ) )
& ( ( X965 != X966 )
| ( ( setunion @ X965 )
= ( setunion @ X966 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X967 )
| ~ ( X967 @ X968 )
| ~ ( X967 @ X969 )
| ( X968 = X969 ) )
& ( ( ( esk32_2 @ X970 @ X971 )
= ( esk33_2 @ X970 @ X971 ) )
| ~ ( exu @ X970 )
| ~ ( exu @ X971 )
| ( ( descr @ X970 )
= ( descr @ X971 ) ) )
& ( ~ ( X970 @ ( esk32_2 @ X970 @ X971 ) )
| ~ ( X971 @ ( esk33_2 @ X970 @ X971 ) )
| ~ ( exu @ X970 )
| ~ ( exu @ X971 )
| ( ( descr @ X970 )
= ( descr @ X971 ) ) )
& ( ( X970 @ ( esk32_2 @ X970 @ X971 ) )
| ( X971 @ ( esk33_2 @ X970 @ X971 ) )
| ~ ( exu @ X970 )
| ~ ( exu @ X971 )
| ( ( descr @ X970 )
= ( descr @ X971 ) ) )
& ( ( in @ ( esk34_4 @ X974 @ X975 @ X976 @ X977 ) @ X974 )
| ( ( dsetconstr @ X974 @ X976 )
= ( dsetconstr @ X975 @ X977 ) )
| ( X974 != X975 ) )
& ( ( in @ ( esk35_4 @ X974 @ X975 @ X976 @ X977 ) @ X975 )
| ( ( dsetconstr @ X974 @ X976 )
= ( dsetconstr @ X975 @ X977 ) )
| ( X974 != X975 ) )
& ( ( ( esk34_4 @ X974 @ X975 @ X976 @ X977 )
= ( esk35_4 @ X974 @ X975 @ X976 @ X977 ) )
| ( ( dsetconstr @ X974 @ X976 )
= ( dsetconstr @ X975 @ X977 ) )
| ( X974 != X975 ) )
& ( ~ ( X976 @ ( esk34_4 @ X974 @ X975 @ X976 @ X977 ) )
| ~ ( X977 @ ( esk35_4 @ X974 @ X975 @ X976 @ X977 ) )
| ( ( dsetconstr @ X974 @ X976 )
= ( dsetconstr @ X975 @ X977 ) )
| ( X974 != X975 ) )
& ( ( X976 @ ( esk34_4 @ X974 @ X975 @ X976 @ X977 ) )
| ( X977 @ ( esk35_4 @ X974 @ X975 @ X976 @ X977 ) )
| ( ( dsetconstr @ X974 @ X976 )
= ( dsetconstr @ X975 @ X977 ) )
| ( X974 != X975 ) )
& ( ( in @ ( esk36_2 @ X980 @ X981 ) @ X980 )
| ( subset @ X980 @ X981 ) )
& ( ~ ( in @ ( esk36_2 @ X980 @ X981 ) @ X981 )
| ( subset @ X980 @ X981 ) )
& ( ( X983 != X984 )
| ( subset @ X984 @ X983 ) )
& ( ( X985 != X986 )
| ( subset @ X985 @ X986 ) )
& ( ( in @ ( esk37_2 @ X987 @ X988 ) @ X987 )
| ( subset @ X987 @ X988 ) )
& ( ~ ( in @ ( esk37_2 @ X987 @ X988 ) @ X988 )
| ( subset @ X987 @ X988 ) )
& ( subset @ emptyset @ X990 )
& ( ~ ( subset @ X991 @ X992 )
| ~ ( in @ X993 @ X991 )
| ( in @ X993 @ X992 ) )
& ( ~ ( subset @ X994 @ X995 )
| ( in @ X996 @ X995 )
| ~ ( in @ X996 @ X994 ) )
& ( ~ ( in @ X999 @ X997 )
| ( in @ X999 @ X998 )
| ~ ( subset @ X997 @ X998 ) )
& ( ( subset @ X1000 @ X1001 )
| ( X1000 != X1001 ) )
& ( ~ ( in @ X1004 @ X1002 )
| ( in @ X1004 @ X1003 )
| ( X1002 != X1003 ) )
& ( subset @ X1005 @ X1005 )
& ( ~ ( subset @ X1006 @ X1007 )
| ~ ( subset @ X1007 @ X1008 )
| ( subset @ X1006 @ X1008 ) )
& ( subset @ X1010 @ ( setadjoin @ X1009 @ X1010 ) )
& ( ~ ( subset @ X1011 @ X1013 )
| ( subset @ X1011 @ ( setadjoin @ X1012 @ X1013 ) ) )
& ( ~ ( subset @ X1014 @ X1015 )
| ( in @ X1014 @ ( powerset @ X1015 ) ) )
& ( ~ ( subset @ X1016 @ X1017 )
| ~ ( subset @ X1017 @ X1016 )
| ( X1016 = X1017 ) )
& ( ~ ( subset @ X1018 @ emptyset )
| ( X1018 = emptyset ) )
& ( ~ ( subset @ X1020 @ X1019 )
| ( in @ X1020 @ ( powerset @ X1019 ) ) )
& ( ~ ( in @ X1022 @ ( powerset @ X1021 ) )
| ( subset @ X1022 @ X1021 ) )
& ( in @ X1023 @ ( powerset @ X1023 ) )
& ( ~ ( subset @ X1024 @ X1025 )
| ( subset @ ( powerset @ X1024 ) @ ( powerset @ X1025 ) ) )
& ( in @ ( dsetconstr @ X1026 @ X1027 ) @ ( powerset @ X1026 ) )
& ( subset @ ( dsetconstr @ X1028 @ X1029 ) @ X1028 )
& ( ~ ( in @ X1032 @ X1030 )
| ( in @ X1032 @ ( binunion @ X1030 @ X1031 ) ) )
& ( in @ X1034 @ ( setadjoin @ X1033 @ ( setadjoin @ X1034 @ emptyset ) ) )
& ( ~ ( in @ X1037 @ X1036 )
| ( in @ X1037 @ ( binunion @ X1035 @ X1036 ) ) )
& ( ( in @ X1040 @ X1039 )
| X1041
| ( in @ X1040 @ X1038 )
| ~ ( in @ X1040 @ ( binunion @ X1038 @ X1039 ) ) )
& ( ~ X1041
| X1041
| ( in @ X1040 @ X1038 )
| ~ ( in @ X1040 @ ( binunion @ X1038 @ X1039 ) ) )
& ( ( in @ X1040 @ X1039 )
| X1041
| ~ X1041
| ~ ( in @ X1040 @ ( binunion @ X1038 @ X1039 ) ) )
& ( ~ X1041
| X1041
| ~ X1041
| ~ ( in @ X1040 @ ( binunion @ X1038 @ X1039 ) ) )
& ( ~ ( in @ X1044 @ ( binunion @ X1042 @ X1043 ) )
| ( in @ X1044 @ X1042 )
| ( in @ X1044 @ X1043 ) )
& ( subset @ X1045 @ ( binunion @ X1045 @ X1046 ) )
& ( subset @ X1048 @ ( binunion @ X1047 @ X1048 ) )
& ( ~ ( in @ X1051 @ X1049 )
| ~ ( in @ X1051 @ X1050 )
| ( in @ X1051 @ ( binintersect @ X1049 @ X1050 ) ) )
& ( ~ ( subset @ X1054 @ X1052 )
| ~ ( subset @ X1054 @ X1053 )
| ( subset @ X1054 @ ( binintersect @ X1052 @ X1053 ) ) )
& ( ~ ( in @ X1057 @ ( binintersect @ X1055 @ X1056 ) )
| ( in @ X1057 @ X1055 ) )
& ( subset @ ( binintersect @ X1058 @ X1059 ) @ X1058 )
& ( ~ ( subset @ X1060 @ X1061 )
| ( ( binintersect @ X1060 @ X1061 )
= X1060 ) )
& ( ( ( binintersect @ X1062 @ X1063 )
!= X1063 )
| ( subset @ X1063 @ X1062 ) )
& ( ~ ( in @ X1066 @ ( binintersect @ X1064 @ X1065 ) )
| ( in @ X1066 @ X1065 ) )
& ( ( in @ ( esk38_2 @ X1067 @ X1068 ) @ X1067 )
| ( ( binintersect @ X1067 @ X1068 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1067 @ X1068 ) @ X1068 )
| ( ( binintersect @ X1067 @ X1068 )
= emptyset ) )
& ( subset @ ( binintersect @ X1070 @ X1071 ) @ X1071 )
& ( ~ ( subset @ X1073 @ X1072 )
| ( ( binintersect @ X1072 @ X1073 )
= X1073 ) )
& ( ( ( binintersect @ X1074 @ X1075 )
!= X1074 )
| ( subset @ X1074 @ X1075 ) )
& ( ( binintersect @ X1076 @ ( binunion @ X1077 @ X1078 ) )
= ( binunion @ ( binintersect @ X1076 @ X1077 ) @ ( binintersect @ X1076 @ X1078 ) ) )
& ( ~ ( in @ X1081 @ X1079 )
| ( in @ X1081 @ X1080 )
| ( in @ X1081 @ ( setminus @ X1079 @ X1080 ) ) )
& ( ~ ( in @ X1084 @ ( setminus @ X1082 @ X1083 ) )
| ( in @ X1084 @ X1082 ) )
& ( ~ ( in @ X1087 @ ( setminus @ X1085 @ X1086 ) )
| ~ ( in @ X1087 @ X1086 ) )
& ( ~ ( subset @ X1088 @ X1089 )
| ( ( setminus @ X1088 @ X1089 )
= emptyset ) )
& ( ( in @ X1092 @ ( setminus @ X1090 @ X1091 ) )
| ~ ( in @ X1092 @ X1090 )
| ( in @ X1092 @ X1091 ) )
& ( ( in @ X1095 @ ( setminus @ X1093 @ X1094 ) )
| ( in @ X1095 @ X1094 )
| ~ ( in @ X1095 @ X1093 ) )
& ( ( in @ X1098 @ X1096 )
| ~ ( in @ X1098 @ ( setminus @ X1096 @ X1097 ) ) )
& ( ~ ( in @ X1101 @ X1100 )
| ~ ( in @ X1101 @ ( setminus @ X1099 @ X1100 ) ) )
& ( subset @ ( setminus @ X1102 @ X1103 ) @ X1102 )
& ( ( ( setminus @ X1104 @ X1105 )
!= emptyset )
| ( subset @ X1104 @ X1105 ) )
& ( ~ ( in @ X1108 @ X1106 )
| X1109
| ( in @ X1108 @ X1106 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ( in @ X1108 @ X1107 )
| X1109
| ( in @ X1108 @ X1106 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ X1109
| X1109
| ( in @ X1108 @ X1106 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ ( in @ X1108 @ X1106 )
| X1109
| ~ ( in @ X1108 @ X1107 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ( in @ X1108 @ X1107 )
| X1109
| ~ ( in @ X1108 @ X1107 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ X1109
| X1109
| ~ ( in @ X1108 @ X1107 )
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ ( in @ X1108 @ X1106 )
| X1109
| ~ X1109
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ( in @ X1108 @ X1107 )
| X1109
| ~ X1109
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ X1109
| X1109
| ~ X1109
| ~ ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) )
& ( ~ ( in @ X1112 @ X1110 )
| ( in @ X1112 @ X1111 )
| ( in @ X1112 @ ( symdiff @ X1110 @ X1111 ) ) )
& ( ( in @ X1115 @ X1113 )
| ~ ( in @ X1115 @ X1114 )
| ( in @ X1115 @ ( symdiff @ X1113 @ X1114 ) ) )
& ( ~ ( in @ X1118 @ X1116 )
| ~ ( in @ X1118 @ X1117 )
| ~ ( in @ X1118 @ ( symdiff @ X1116 @ X1117 ) ) )
& ( ( in @ X1121 @ X1119 )
| ( in @ X1121 @ X1120 )
| ~ ( in @ X1121 @ ( symdiff @ X1119 @ X1120 ) ) )
& ( in @ X1123 @ ( setadjoin @ X1122 @ ( setadjoin @ X1123 @ emptyset ) ) )
& ( in @ X1124 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1124 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1124 @ ( setadjoin @ X1125 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1127 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1126 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1126 @ ( setadjoin @ X1127 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1128 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1128 @ ( setadjoin @ X1129 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1130 @ X1131 ) )
& ( ~ ( in @ X1133 @ X1132 )
| ( subset @ ( setadjoin @ X1133 @ emptyset ) @ X1132 ) )
& ( ~ ( in @ X1135 @ X1134 )
| ( in @ ( setadjoin @ X1135 @ emptyset ) @ ( powerset @ X1134 ) ) )
& ( ~ ( in @ X1138 @ X1136 )
| ( in @ ( setadjoin @ X1138 @ emptyset ) @ ( powerset @ ( binunion @ X1136 @ X1137 ) ) ) )
& ( ~ ( in @ X1141 @ ( setadjoin @ X1139 @ ( setadjoin @ X1140 @ emptyset ) ) )
| ( X1141 = X1139 )
| ( X1141 = X1140 ) )
& ( ~ ( in @ X1144 @ X1142 )
| ~ ( in @ X1145 @ X1143 )
| ( subset @ ( setadjoin @ X1144 @ ( setadjoin @ X1145 @ emptyset ) ) @ ( binunion @ X1142 @ X1143 ) ) )
& ( in @ esk41_0 @ esk39_0 )
& ( in @ esk42_0 @ esk40_0 )
& ~ ( in @ ( setadjoin @ esk41_0 @ ( setadjoin @ esk42_0 @ emptyset ) ) @ ( powerset @ ( binunion @ esk39_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_165])])])])])])]) ).
thf(c_0_167,negated_conjecture,
~ ( in @ ( setadjoin @ esk41_0 @ ( setadjoin @ esk42_0 @ emptyset ) ) @ ( powerset @ ( binunion @ esk39_0 @ esk40_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
thf(c_0_168,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
thf(c_0_169,negated_conjecture,
~ ( subset @ ( setadjoin @ esk41_0 @ ( setadjoin @ esk42_0 @ emptyset ) ) @ ( binunion @ esk39_0 @ esk40_0 ) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
thf(c_0_170,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i] :
( ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X3 @ X5 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_166]) ).
thf(c_0_171,negated_conjecture,
in @ esk42_0 @ esk40_0,
inference(split_conjunct,[status(thm)],[c_0_166]) ).
thf(c_0_172,negated_conjecture,
in @ esk41_0 @ esk39_0,
inference(split_conjunct,[status(thm)],[c_0_166]) ).
thf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]),c_0_172])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU626^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 17:49:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 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
% 0.91/300.03 # Version: 3.1.0-ho
% 0.91/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.91/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.91/300.03 # Starting ehoh_best5 with 300s (1) cores
% 0.91/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 0.91/300.03 # Starting new_bool_5 with 300s (1) cores
% 0.91/300.03 # Starting pre_casc_3 with 300s (1) cores
% 0.91/300.03 # Starting ho_unfolding_8 with 300s (1) cores
% 0.91/300.03 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.91/300.03 # Starting new_bool_3 with 300s (1) cores
% 0.91/300.03 # Starting new_ho_5 with 300s (1) cores
% 0.91/300.03 # new_ho_5 with pid 32167 completed with status 8
% 0.91/300.03 # new_bool_5 with pid 32162 completed with status 0
% 0.91/300.03 # Result found by new_bool_5
% 0.91/300.03 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.91/300.03 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.91/300.03 # Starting ehoh_best5 with 300s (1) cores
% 0.91/300.03 # Starting almost_fo_3_lam with 300s (1) cores
% 0.91/300.03 # Starting new_bool_5 with 300s (1) cores
% 0.91/300.03 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.91/300.03 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.91/300.03 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.91/300.03 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.91/300.04 # new_ho_10_cnf2 with pid 32177 completed with status 0
% 0.91/300.04 # Result found by new_ho_10_cnf2
% 0.91/300.04 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.91/300.04 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.91/300.04 # Starting ehoh_best5 with 300s (1) cores
% 0.91/300.04 # Starting almost_fo_3_lam with 300s (1) cores
% 0.91/300.04 # Starting new_bool_5 with 300s (1) cores
% 0.91/300.04 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.91/300.04 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.91/300.04 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.91/300.04 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.91/300.04 # Preprocessing time : 0.004 s
% 0.91/300.04 # Presaturation interreduction done
% 0.91/300.04
% 0.91/300.04 # Proof found!
% 0.91/300.04 # SZS status Theorem
% 0.91/300.04 # SZS output start CNFRefutation
% See solution above
% 0.91/300.04 # Parsed axioms : 313
% 0.91/300.04 # Removed by relevancy pruning/SinE : 171
% 0.91/300.04 # Initial clauses : 224
% 0.91/300.04 # Removed in clause preprocessing : 25
% 0.91/300.04 # Initial clauses in saturation : 199
% 0.91/300.04 # Processed clauses : 416
% 0.91/300.04 # ...of these trivial : 6
% 0.91/300.04 # ...subsumed : 53
% 0.91/300.04 # ...remaining for further processing : 357
% 0.91/300.04 # Other redundant clauses eliminated : 16
% 0.91/300.04 # Clauses deleted for lack of memory : 0
% 0.91/300.04 # Backward-subsumed : 0
% 0.91/300.04 # Backward-rewritten : 5
% 0.91/300.04 # Generated clauses : 1597
% 0.91/300.04 # ...of the previous two non-redundant : 1460
% 0.91/300.04 # ...aggressively subsumed : 0
% 0.91/300.04 # Contextual simplify-reflections : 0
% 0.91/300.04 # Paramodulations : 1581
% 0.91/300.04 # Factorizations : 0
% 0.91/300.04 # NegExts : 0
% 0.91/300.04 # Equation resolutions : 16
% 0.91/300.04 # Disequality decompositions : 0
% 0.91/300.04 # Total rewrite steps : 121
% 0.91/300.04 # ...of those cached : 75
% 0.91/300.04 # Propositional unsat checks : 0
% 0.91/300.04 # Propositional check models : 0
% 0.91/300.04 # Propositional check unsatisfiable : 0
% 0.91/300.04 # Propositional clauses : 0
% 0.91/300.04 # Propositional clauses after purity: 0
% 0.91/300.04 # Propositional unsat core size : 0
% 0.91/300.04 # Propositional preprocessing time : 0.000
% 0.91/300.04 # Propositional encoding time : 0.000
% 0.91/300.04 # Propositional solver time : 0.000
% 0.91/300.04 # Success case prop preproc time : 0.000
% 0.91/300.04 # Success case prop encoding time : 0.000
% 0.91/300.04 # Success case prop solver time : 0.000
% 0.91/300.04 # Current number of processed clauses : 176
% 0.91/300.04 # Positive orientable unit clauses : 43
% 0.91/300.04 # Positive unorientable unit clauses: 0
% 0.91/300.04 # Negative unit clauses : 4
% 0.91/300.04 # Non-unit-clauses : 129
% 0.91/300.04 # Current number of unprocessed clauses: 1395
% 0.91/300.04 # ...number of literals in the above : 3825
% 0.91/300.04 # Current number of archived formulas : 0
% 0.91/300.04 # Current number of archived clauses : 170
% 0.91/300.04 # Clause-clause subsumption calls (NU) : 4430
% 0.91/300.04 # Rec. Clause-clause subsumption calls : 2843
% 0.91/300.04 # Non-unit clause-clause subsumptions : 30
% 0.91/300.04 # Unit Clause-clause subsumption calls : 42
% 0.91/300.04 # Rewrite failures with RHS unbound : 0
% 0.91/300.04 # BW rewrite match attempts : 18
% 0.91/300.04 # BW rewrite match successes : 3
% 0.91/300.04 # Condensation attempts : 416
% 0.91/300.04 # Condensation successes : 4
% 0.91/300.04 # Termbank termtop insertions : 50350
% 0.91/300.04 # Search garbage collected termcells : 12320
% 0.91/300.04
% 0.91/300.04 # -------------------------------------------------
% 0.91/300.04 # User time : 0.066 s
% 0.91/300.04 # System time : 0.012 s
% 0.91/300.04 # Total time : 0.077 s
% 0.91/300.04 # Maximum resident set size: 4988 pages
% 0.91/300.04
% 0.91/300.04 # -------------------------------------------------
% 0.91/300.04 # User time : 0.129 s
% 0.91/300.04 # System time : 0.033 s
% 0.91/300.04 # Total time : 0.162 s
% 0.91/300.04 # Maximum resident set size: 2080 pages
% 0.91/300.04 % E---3.1 exiting
% 0.91/300.04 % E exiting
%------------------------------------------------------------------------------