%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU641^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 03:28:46 EDT 2024
% Result : Theorem 0.21s 0.57s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 386
% Syntax : Number of formulae : 418 ( 4 unt; 228 typ; 0 def)
% Number of atoms : 1654 ( 234 equ; 0 cnn)
% Maximal formula atoms : 493 ( 8 avg)
% Number of connectives : 5724 ( 408 ~; 392 |; 309 &;3572 @)
% ( 219 <=>; 824 =>; 0 <=; 0 <~>)
% Maximal formula depth : 612 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 300 ( 300 >; 0 *; 0 +; 0 <<)
% Number of symbols : 231 ( 228 usr; 164 con; 0-4 aty)
% Number of variables : 1384 ( 67 ^1237 !; 80 ?;1384 :)
% 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_181,type,
cartprod: $i > $i > $i ).
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,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
epred1_0: $o ).
thf(decl_205,type,
esk1_2: $i > $i > $i ).
thf(decl_206,type,
esk2_2: $i > $i > $i ).
thf(decl_207,type,
esk3_2: $i > $i > $i ).
thf(decl_208,type,
esk4_1: $i > $i ).
thf(decl_209,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_210,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_211,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_212,type,
esk8_1: $i > $i ).
thf(decl_213,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_214,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_215,type,
esk11_2: $i > $i > $i ).
thf(decl_216,type,
esk12_2: $i > $i > $i ).
thf(decl_217,type,
esk13_1: $i > $i ).
thf(decl_218,type,
esk14_1: $i > $i ).
thf(decl_219,type,
esk15_1: $i > $i ).
thf(decl_220,type,
esk16_2: $i > $i > $i ).
thf(decl_221,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_222,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_223,type,
esk19_1: $i > $i ).
thf(decl_224,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_225,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_226,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_227,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_228,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_229,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_230,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_231,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_232,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_233,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_234,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_235,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_236,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_237,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_238,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_239,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_240,type,
esk36_2: $i > $i > $i ).
thf(decl_241,type,
esk37_2: $i > $i > $i ).
thf(decl_242,type,
esk38_2: $i > $i > $i ).
thf(decl_243,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_244,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_245,type,
esk41_2: $i > $i > $i ).
thf(decl_246,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_247,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_248,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_249,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_250,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_251,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_252,type,
esk48_0: $i ).
thf(decl_253,type,
esk49_0: $i ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
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(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
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(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
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(singletonsuniq,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
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
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(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(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(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
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(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(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(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(upairinpowunion,axiom,
( upairinpowunion
<=> ! [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(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
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(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
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(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(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(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(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(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(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
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(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
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(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
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(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(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
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(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(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(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(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(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(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(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_157,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_158,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_159,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_160,plain,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singletonprop]) ).
thf(c_0_161,plain,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E1]) ).
thf(c_0_162,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_163,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_172,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_173,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_174,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_175,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_176,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_177,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_178,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_179,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_180,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_181,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_182,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_183,plain,
( epred1_0
<=> ! [X479: $i] :
? [X480: $i] :
( ! [X481: $i] :
( ( in @ X481 @ X480 )
=> ! [X482: $i] :
( ( in @ X482 @ X481 )
=> ( in @ X482 @ X479 ) ) )
& ! [X483: $i,X484: $i] :
( ( ( in @ X483 @ X479 )
& ( in @ X484 @ X479 ) )
=> ( ! [X485: $i] :
( ( in @ X485 @ X480 )
=> ( ( in @ X483 @ X485 )
<=> ( in @ X484 @ X485 ) ) )
=> ( X483 = X484 ) ) )
& ! [X486: $i,X487: $i] :
( ( ( in @ X486 @ X480 )
& ( in @ X487 @ X480 ) )
=> ( ! [X488: $i] :
( ( in @ X488 @ X486 )
=> ( in @ X488 @ X487 ) )
| ! [X489: $i] :
( ( in @ X489 @ X487 )
=> ( in @ X489 @ X486 ) ) ) )
& ! [X490: $i] :
( ( ! [X491: $i] :
( ( in @ X491 @ X490 )
=> ( in @ X491 @ X479 ) )
& ? [X492: $i] : ( in @ X492 @ X490 ) )
=> ? [X493: $i,X494: $i] :
( ( in @ X493 @ X480 )
& ( in @ X494 @ X490 )
& ~ ? [X495: $i] :
( ( in @ X495 @ X493 )
& ( in @ X495 @ X490 ) )
& ! [X496: $i] :
( ( in @ X496 @ X480 )
=> ( ! [X497: $i] :
( ( in @ X497 @ X496 )
=> ( in @ X497 @ X493 ) )
| ( in @ X494 @ X496 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_184,negated_conjecture,
~ ( ! [X452: $i,X453: $i] :
( ! [X454: $i] :
( ( in @ X454 @ X452 )
<=> ( in @ X454 @ X453 ) )
=> ( X452 = X453 ) )
=> ( ! [X455: $i] :
~ ( in @ X455 @ emptyset )
=> ( ! [X456: $i,X457: $i,X458: $i] :
( ( in @ X458 @ ( setadjoin @ X456 @ X457 ) )
<=> ( ( X458 = X456 )
| ( in @ X458 @ X457 ) ) )
=> ( ! [X459: $i,X460: $i] :
( ( in @ X460 @ ( powerset @ X459 ) )
<=> ! [X461: $i] :
( ( in @ X461 @ X460 )
=> ( in @ X461 @ X459 ) ) )
=> ( ! [X462: $i,X463: $i] :
( ( in @ X463 @ ( setunion @ X462 ) )
<=> ? [X464: $i] :
( ( in @ X463 @ X464 )
& ( in @ X464 @ X462 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X465: $i] :
( ( in @ X465 @ omega )
=> ( in @ ( setadjoin @ X465 @ X465 ) @ omega ) )
=> ( ! [X466: $i] :
( ( ( in @ emptyset @ X466 )
& ! [X467: $i] :
( ( ( in @ X467 @ omega )
& ( in @ X467 @ X466 ) )
=> ( in @ ( setadjoin @ X467 @ X467 ) @ X466 ) ) )
=> ! [X468: $i] :
( ( in @ X468 @ omega )
=> ( in @ X468 @ X466 ) ) )
=> ( ! [X469: $i > $i > $o,X470: $i] :
( ! [X471: $i] :
( ( in @ X471 @ X470 )
=> ( exu @ ( X469 @ X471 ) ) )
=> ? [X472: $i] :
! [X473: $i] :
( ( in @ X473 @ X472 )
<=> ? [X474: $i] :
( ( in @ X474 @ X470 )
& ( X469 @ X474 @ X473 ) ) ) )
=> ( ! [X475: $i] :
( ? [X476: $i] : ( in @ X476 @ X475 )
=> ? [X477: $i] :
( ( in @ X477 @ X475 )
& ~ ? [X478: $i] :
( ( in @ X478 @ X477 )
& ( in @ X478 @ X475 ) ) ) )
=> ( epred1_0
=> ( ! [X498: $i > $o] :
( ( exu @ X498 )
=> ( X498
@ ( descr
@ ^ [Z0: $i] : ( X498 @ Z0 ) ) ) )
=> ( ! [X499: $i,X500: $i > $o,X501: $i] :
( ( in @ X501 @ X499 )
=> ( ( X500 @ X501 )
=> ( in @ X501 @ ( dsetconstr @ X499 @ X500 ) ) ) )
=> ( ! [X502: $i,X503: $i > $o,X504: $i] :
( ( in @ X504 @ ( dsetconstr @ X502 @ X503 ) )
=> ( in @ X504 @ X502 ) )
=> ( ! [X505: $i,X506: $i > $o,X507: $i] :
( ( in @ X507 @ ( dsetconstr @ X505 @ X506 ) )
=> ( X506 @ X507 ) )
=> ( ! [X508: $i > $o] :
( ( exu @ X508 )
=> ? [X509: $i] :
( ( X508 @ X509 )
& ! [X510: $i] :
( ( X508 @ X510 )
=> ( X509 = X510 ) ) ) )
=> ( ! [X511: $o,X512: $i] :
( ( in @ X512 @ ( prop2set @ X511 ) )
=> X511 )
=> ( ! [X513: $i] :
( ( in @ X513 @ emptyset )
=> ! [X514: $o] : X514 )
=> ( ! [X515: $i] :
( ( in @ X515 @ emptyset )
=> ~ $true )
=> ( ! [X516: $i] :
~ ( in @ X516 @ emptyset )
=> ( ! [X517: $i > $o] :
( ( exu @ X517 )
=> ? [X518: $i] : ( X517 @ X518 ) )
=> ( ! [X519: $i,X520: $i] :
( ! [X521: $i] :
( ( in @ X521 @ X519 )
=> ( in @ X521 @ X520 ) )
=> ( ! [X522: $i] :
( ( in @ X522 @ X520 )
=> ( in @ X522 @ X519 ) )
=> ( X519 = X520 ) ) )
=> ( ! [X523: $i] :
( ! [X524: $i] :
~ ( in @ X524 @ X523 )
=> ( X523 = emptyset ) )
=> ( ! [X525: $i] :
( ! [X526: $i] :
~ ( in @ X526 @ X525 )
=> ( X525 = emptyset ) )
=> ( ! [X527: $i,X528: $i > $o,X529: $i] :
( ( in @ X529 @ X527 )
=> ( ( in @ X529 @ ( dsetconstr @ X527 @ X528 ) )
<=> ( X528 @ X529 ) ) )
=> ( ! [X530: $i] :
( ( nonempty @ X530 )
=> ? [X531: $i] : ( in @ X531 @ X530 ) )
=> ( ! [X532: $i,X533: $i > $o,X534: $i] :
( ( in @ X534 @ X532 )
=> ( ( X533 @ X534 )
=> ( nonempty @ ( dsetconstr @ X532 @ X533 ) ) ) )
=> ( ! [X535: $i] :
( ? [X536: $i] : ( in @ X536 @ X535 )
=> ( nonempty @ X535 ) )
=> ( ! [X537: $i,X538: $i] : ( in @ X537 @ ( setadjoin @ X537 @ X538 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X539: $i,X540: $i,X541: $i] :
( ( in @ X541 @ X540 )
=> ( in @ X541 @ ( setadjoin @ X539 @ X540 ) ) )
=> ( ! [X542: $i,X543: $i,X544: $i] :
( ( in @ X544 @ ( setadjoin @ X542 @ X543 ) )
=> ! [X545: $o] :
( ( ( X544 = X542 )
=> X545 )
=> ( ( ( in @ X544 @ X543 )
=> X545 )
=> X545 ) ) )
=> ( ! [X546: $i,X547: $i,X548: $i] :
( ( in @ X548 @ ( setadjoin @ X546 @ X547 ) )
=> ( ( X548 = X546 )
| ( in @ X548 @ X547 ) ) )
=> ( ! [X549: $i] :
( ( dsetconstr @ X549
@ ^ [Z0: $i] : $true )
= X549 )
=> ( ! [X550: $i,X551: $i] :
( ! [X552: $i] :
( ( in @ X552 @ X551 )
=> ( in @ X552 @ X550 ) )
=> ( in @ X551 @ ( powerset @ X550 ) ) )
=> ( ! [X553: $i] : ( in @ emptyset @ ( powerset @ X553 ) )
=> ( ! [X554: $i] : ( in @ emptyset @ ( powerset @ X554 ) )
=> ( ! [X555: $i,X556: $i,X557: $i] :
( ( in @ X556 @ ( powerset @ X555 ) )
=> ( ( in @ X557 @ X556 )
=> ( in @ X557 @ X555 ) ) )
=> ( ! [X558: $i,X559: $i,X560: $i] :
( ( in @ X559 @ X560 )
=> ( ( in @ X560 @ X558 )
=> ( in @ X559 @ ( setunion @ X558 ) ) ) )
=> ( ! [X561: $i,X562: $i] :
( ( in @ X562 @ ( setunion @ X561 ) )
=> ! [X563: $o] :
( ! [X564: $i] :
( ( in @ X562 @ X564 )
=> ( ( in @ X564 @ X561 )
=> X563 ) )
=> X563 ) )
=> ( ! [X565: $i,X566: $i] :
( ( in @ X566 @ X565 )
=> ( in @ X566 @ ( powerset @ ( setunion @ X565 ) ) ) )
=> ( ! [X567: $i > $o] :
( ( exu @ X567 )
=> ? [X568: $i] :
! [X569: $i] :
( ( X567 @ X569 )
<=> ( X569 = X568 ) ) )
=> ( ! [X570: $i] :
( ( nonempty @ X570 )
=> ? [X571: $i] :
( ( in @ X571 @ X570 )
& $true ) )
=> ( ! [X572: $i,X573: $i] :
( ( in @ X572 @ ( setadjoin @ X573 @ emptyset ) )
=> ( X572 = X573 ) )
=> ( ! [X574: $i,X575: $i] :
( ( X574 != X575 )
=> ~ ( in @ X575 @ ( setadjoin @ X574 @ emptyset ) ) )
=> ( ! [X576: $i,X577: $i] :
( ( X576 = X577 )
=> ( in @ X576 @ ( setadjoin @ X577 @ emptyset ) ) )
=> ( ! [X578: $i,X579: $i] :
( ( in @ X578 @ ( setadjoin @ X579 @ emptyset ) )
=> ( in @ X579 @ ( setadjoin @ X578 @ emptyset ) ) )
=> ( ! [X580: $i,X581: $i,X582: $i] :
( ( in @ X582 @ ( setadjoin @ X580 @ ( setadjoin @ X581 @ emptyset ) ) )
=> ( ( X582 = X580 )
| ( X582 = X581 ) ) )
=> ( ! [X583: $i,X584: $i] : ( in @ X583 @ ( setadjoin @ X583 @ ( setadjoin @ X584 @ emptyset ) ) )
=> ( ! [X585: $i,X586: $i] : ( in @ X586 @ ( setadjoin @ X585 @ ( setadjoin @ X586 @ emptyset ) ) )
=> ( ! [X587: $i,X588: $i > $o] :
( ? [X589: $i] :
( ( in @ X589 @ X587 )
& ( X588 @ X589 ) )
=> ( ( ( dsetconstr @ X587 @ X588 )
= emptyset )
=> ~ $true ) )
=> ( ! [X590: $i > $o,X591: $i] :
( ( in @ X591 @ emptyset )
=> ( X590 @ X591 ) )
=> ( ! [X592: $i,X593: $i > $o] :
( ~ ! [X594: $i] :
( ( in @ X594 @ X592 )
=> ( X593 @ X594 ) )
=> ? [X595: $i] :
( ( in @ X595 @ X592 )
& ~ ( X593 @ X595 ) ) )
=> ( ! [X596: $i,X597: $i > $o] :
( ! [X598: $i] :
( ( in @ X598 @ X596 )
=> ~ ( X597 @ X598 ) )
=> ~ ? [X599: $i] :
( ( in @ X599 @ X596 )
& ( X597 @ X599 ) ) )
=> ( ! [X600: $i,X601: $i > $o] :
( ~ ? [X602: $i] :
( ( in @ X602 @ X600 )
& ( X601 @ X602 ) )
=> ! [X603: $i] :
( ( in @ X603 @ X600 )
=> ~ ( X601 @ X603 ) ) )
=> ( ! [X604: $i,X605: $i > $o] :
( ? [X606: $i] :
( ( in @ X606 @ X604 )
& ~ ( X605 @ X606 ) )
=> ~ ! [X607: $i] :
( ( in @ X607 @ X604 )
=> ( X605 @ X607 ) ) )
=> ( ! [X608: $o] :
( X608
=> ( in @ emptyset @ ( prop2set @ X608 ) ) )
=> ( prop2set2propI
=> ( ! [X609: $i,X610: $i > $o] :
( ~ ? [X611: $i] :
( ( in @ X611 @ X609 )
& ( X610 @ X611 ) )
=> ! [X612: $i] :
( ( in @ X612 @ X609 )
=> ~ ( X610 @ X612 ) ) )
=> ( ! [X613: $i,X614: $i > $o] :
( ~ ! [X615: $i] :
( ( in @ X615 @ X613 )
=> ( X614 @ X615 ) )
=> ? [X616: $i] :
( ( in @ X616 @ X613 )
& ~ ( X614 @ X616 ) ) )
=> ( ! [X617: $i > $o] :
( ? [X618: $i] :
( ( X617 @ X618 )
& ! [X619: $i] :
( ( X617 @ X619 )
=> ( X618 = X619 ) ) )
=> ( exu @ X617 ) )
=> ( ! [X620: $i > $o] :
( ? [X621: $i] : ( X620 @ X621 )
=> ( ! [X622: $i,X623: $i] :
( ( X620 @ X622 )
=> ( ( X620 @ X623 )
=> ( X622 = X623 ) ) )
=> ( exu @ X620 ) ) )
=> ( ! [X624: $i > $o] :
( ? [X625: $i] :
! [X626: $i] :
( ( X624 @ X626 )
<=> ( X626 = X625 ) )
=> ( exu @ X624 ) )
=> ( ! [X627: $i,X628: $i] :
( ( X627 = X628 )
=> ! [X629: $i,X630: $i] :
( ( X629 = X630 )
=> ( ( in @ X629 @ X627 )
=> ( in @ X630 @ X628 ) ) ) )
=> ( ! [X631: $i,X632: $i] :
( ( X631 = X632 )
=> ! [X633: $i,X634: $i] :
( ( X633 = X634 )
=> ( ( in @ X633 @ X631 )
<=> ( in @ X634 @ X632 ) ) ) )
=> ( ! [X635: $i > $o] :
( ( exu @ X635 )
=> ! [X636: $i,X637: $i] :
( ( X635 @ X636 )
=> ( ( X635 @ X637 )
=> ( X636 = X637 ) ) ) )
=> ( ! [X638: $i > $o,X639: $i > $o] :
( ! [X640: $i,X641: $i] :
( ( X640 = X641 )
=> ( ( X638 @ X640 )
<=> ( X639 @ X641 ) ) )
=> ( ( exu @ X638 )
<=> ( exu @ X639 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X642: $i,X643: $i] :
( ( X642 = X643 )
=> ! [X644: $i,X645: $i] :
( ( X644 = X645 )
=> ( ( setadjoin @ X642 @ X644 )
= ( setadjoin @ X643 @ X645 ) ) ) )
=> ( ! [X646: $i,X647: $i] :
( ( X646 = X647 )
=> ( ( powerset @ X646 )
= ( powerset @ X647 ) ) )
=> ( ! [X648: $i,X649: $i] :
( ( X648 = X649 )
=> ( ( setunion @ X648 )
= ( setunion @ X649 ) ) )
=> ( ( omega = omega )
=> ( ! [X650: $i > $o] :
( ( exu @ X650 )
=> ! [X651: $i,X652: $i] :
( ( X650 @ X651 )
=> ( ( X650 @ X652 )
=> ( X651 = X652 ) ) ) )
=> ( ! [X653: $i > $o,X654: $i > $o] :
( ! [X655: $i,X656: $i] :
( ( X655 = X656 )
=> ( ( X653 @ X655 )
<=> ( X654 @ X656 ) ) )
=> ( ( exu @ X653 )
=> ( ( exu @ X654 )
=> ( ( descr @ X653 )
= ( descr @ X654 ) ) ) ) )
=> ( ! [X657: $i,X658: $i] :
( ( X657 = X658 )
=> ! [X659: $i > $o,X660: $i > $o] :
( ! [X661: $i] :
( ( in @ X661 @ X657 )
=> ! [X662: $i] :
( ( in @ X662 @ X658 )
=> ( ( X661 = X662 )
=> ( ( X659 @ X661 )
<=> ( X660 @ X662 ) ) ) ) )
=> ( ( dsetconstr @ X657 @ X659 )
= ( dsetconstr @ X658 @ X660 ) ) ) )
=> ( ! [X663: $i,X664: $i] :
( ! [X665: $i] :
( ( in @ X665 @ X663 )
=> ( in @ X665 @ X664 ) )
=> ( subset @ X663 @ X664 ) )
=> ( ! [X666: $i,X667: $i] :
( ( X666 = X667 )
=> ( subset @ X667 @ X666 ) )
=> ( ! [X668: $i,X669: $i] :
( ( X668 = X669 )
=> ( subset @ X668 @ X669 ) )
=> ( ! [X670: $i,X671: $i] :
( ! [X672: $i] :
( ( in @ X672 @ X670 )
=> ( in @ X672 @ X671 ) )
=> ( subset @ X670 @ X671 ) )
=> ( ! [X673: $i] : ( subset @ emptyset @ X673 )
=> ( ! [X674: $i,X675: $i,X676: $i] :
( ( subset @ X674 @ X675 )
=> ( ( in @ X676 @ X674 )
=> ( in @ X676 @ X675 ) ) )
=> ( ! [X677: $i,X678: $i,X679: $i] :
( ( subset @ X677 @ X678 )
=> ( ~ ( in @ X679 @ X678 )
=> ~ ( in @ X679 @ X677 ) ) )
=> ( ! [X680: $i,X681: $i,X682: $i] :
( ( in @ X682 @ X680 )
=> ( ~ ( in @ X682 @ X681 )
=> ~ ( subset @ X680 @ X681 ) ) )
=> ( ! [X683: $i,X684: $i] :
( ~ ( subset @ X683 @ X684 )
=> ( X683 != X684 ) )
=> ( ! [X685: $i,X686: $i,X687: $i] :
( ( in @ X687 @ X685 )
=> ( ~ ( in @ X687 @ X686 )
=> ( X685 != X686 ) ) )
=> ( ! [X688: $i] : ( subset @ X688 @ X688 )
=> ( ! [X689: $i,X690: $i,X691: $i] :
( ( subset @ X689 @ X690 )
=> ( ( subset @ X690 @ X691 )
=> ( subset @ X689 @ X691 ) ) )
=> ( ! [X692: $i,X693: $i] : ( subset @ X693 @ ( setadjoin @ X692 @ X693 ) )
=> ( ! [X694: $i,X695: $i,X696: $i] :
( ( subset @ X694 @ X696 )
=> ( subset @ X694 @ ( setadjoin @ X695 @ X696 ) ) )
=> ( ! [X697: $i,X698: $i] :
( ( subset @ X697 @ X698 )
=> ( in @ X697 @ ( powerset @ X698 ) ) )
=> ( ! [X699: $i,X700: $i] :
( ( subset @ X699 @ X700 )
=> ( ( subset @ X700 @ X699 )
=> ( X699 = X700 ) ) )
=> ( ! [X701: $i] :
( ( subset @ X701 @ emptyset )
=> ( X701 = emptyset ) )
=> ( ! [X702: $i,X703: $i] :
( ( subset @ X703 @ X702 )
=> ( in @ X703 @ ( powerset @ X702 ) ) )
=> ( ! [X704: $i,X705: $i] :
( ( in @ X705 @ ( powerset @ X704 ) )
=> ( subset @ X705 @ X704 ) )
=> ( ! [X706: $i] : ( in @ X706 @ ( powerset @ X706 ) )
=> ( ! [X707: $i,X708: $i] :
( ( subset @ X707 @ X708 )
=> ( subset @ ( powerset @ X707 ) @ ( powerset @ X708 ) ) )
=> ( ! [X709: $i,X710: $i > $o] : ( in @ ( dsetconstr @ X709 @ X710 ) @ ( powerset @ X709 ) )
=> ( ! [X711: $i,X712: $i > $o] : ( subset @ ( dsetconstr @ X711 @ X712 ) @ X711 )
=> ( ! [X713: $i,X714: $i,X715: $i] :
( ( in @ X715 @ X713 )
=> ( in @ X715 @ ( binunion @ X713 @ X714 ) ) )
=> ( ! [X716: $i,X717: $i] : ( in @ X717 @ ( setadjoin @ X716 @ ( setadjoin @ X717 @ emptyset ) ) )
=> ( ! [X718: $i,X719: $i,X720: $i] :
( ( in @ X720 @ X719 )
=> ( in @ X720 @ ( binunion @ X718 @ X719 ) ) )
=> ( ! [X721: $i,X722: $i,X723: $i,X724: $o] :
( ( in @ X723 @ ( binunion @ X721 @ X722 ) )
=> ( ( ( in @ X723 @ X721 )
=> X724 )
=> ( ( ( in @ X723 @ X722 )
=> X724 )
=> X724 ) ) )
=> ( ! [X725: $i,X726: $i,X727: $i] :
( ( in @ X727 @ ( binunion @ X725 @ X726 ) )
=> ( ( in @ X727 @ X725 )
| ( in @ X727 @ X726 ) ) )
=> ( ! [X728: $i,X729: $i] : ( subset @ X728 @ ( binunion @ X728 @ X729 ) )
=> ( ! [X730: $i,X731: $i] : ( subset @ X731 @ ( binunion @ X730 @ X731 ) )
=> ( ! [X732: $i,X733: $i,X734: $i] :
( ( in @ X734 @ X732 )
=> ( ( in @ X734 @ X733 )
=> ( in @ X734 @ ( binintersect @ X732 @ X733 ) ) ) )
=> ( ! [X735: $i,X736: $i,X737: $i] :
( ( subset @ X737 @ X735 )
=> ( ( subset @ X737 @ X736 )
=> ( subset @ X737 @ ( binintersect @ X735 @ X736 ) ) ) )
=> ( ! [X738: $i,X739: $i,X740: $i] :
( ( in @ X740 @ ( binintersect @ X738 @ X739 ) )
=> ( in @ X740 @ X738 ) )
=> ( ! [X741: $i,X742: $i] : ( subset @ ( binintersect @ X741 @ X742 ) @ X741 )
=> ( ! [X743: $i,X744: $i] :
( ( subset @ X743 @ X744 )
=> ( ( binintersect @ X743 @ X744 )
= X743 ) )
=> ( ! [X745: $i,X746: $i] :
( ( ( binintersect @ X745 @ X746 )
= X746 )
=> ( subset @ X746 @ X745 ) )
=> ( ! [X747: $i,X748: $i,X749: $i] :
( ( in @ X749 @ ( binintersect @ X747 @ X748 ) )
=> ( in @ X749 @ X748 ) )
=> ( ! [X750: $i,X751: $i] :
( ~ ? [X752: $i] :
( ( in @ X752 @ X750 )
& ( in @ X752 @ X751 ) )
=> ( ( binintersect @ X750 @ X751 )
= emptyset ) )
=> ( ! [X753: $i,X754: $i] : ( subset @ ( binintersect @ X753 @ X754 ) @ X754 )
=> ( ! [X755: $i,X756: $i] :
( ( subset @ X756 @ X755 )
=> ( ( binintersect @ X755 @ X756 )
= X756 ) )
=> ( ! [X757: $i,X758: $i] :
( ( ( binintersect @ X757 @ X758 )
= X757 )
=> ( subset @ X757 @ X758 ) )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ( binintersect @ X759 @ ( binunion @ X760 @ X761 ) )
= ( binunion @ ( binintersect @ X759 @ X760 ) @ ( binintersect @ X759 @ X761 ) ) )
=> ( ! [X762: $i,X763: $i,X764: $i] :
( ( in @ X764 @ X762 )
=> ( ~ ( in @ X764 @ X763 )
=> ( in @ X764 @ ( setminus @ X762 @ X763 ) ) ) )
=> ( ! [X765: $i,X766: $i,X767: $i] :
( ( in @ X767 @ ( setminus @ X765 @ X766 ) )
=> ( in @ X767 @ X765 ) )
=> ( ! [X768: $i,X769: $i,X770: $i] :
( ( in @ X770 @ ( setminus @ X768 @ X769 ) )
=> ~ ( in @ X770 @ X769 ) )
=> ( ! [X771: $i,X772: $i] :
( ( subset @ X771 @ X772 )
=> ( ( setminus @ X771 @ X772 )
= emptyset ) )
=> ( ! [X773: $i,X774: $i,X775: $i] :
( ~ ( in @ X775 @ ( setminus @ X773 @ X774 ) )
=> ( ( in @ X775 @ X773 )
=> ( in @ X775 @ X774 ) ) )
=> ( ! [X776: $i,X777: $i,X778: $i] :
( ~ ( in @ X778 @ ( setminus @ X776 @ X777 ) )
=> ( ~ ( in @ X778 @ X777 )
=> ~ ( in @ X778 @ X776 ) ) )
=> ( ! [X779: $i,X780: $i,X781: $i] :
( ~ ( in @ X781 @ X779 )
=> ~ ( in @ X781 @ ( setminus @ X779 @ X780 ) ) )
=> ( ! [X782: $i,X783: $i,X784: $i] :
( ( in @ X784 @ X783 )
=> ~ ( in @ X784 @ ( setminus @ X782 @ X783 ) ) )
=> ( ! [X785: $i,X786: $i] : ( subset @ ( setminus @ X785 @ X786 ) @ X785 )
=> ( ! [X787: $i,X788: $i] :
( ( ( setminus @ X787 @ X788 )
= emptyset )
=> ( subset @ X787 @ X788 ) )
=> ( ! [X789: $i,X790: $i,X791: $i] :
( ( in @ X791 @ ( symdiff @ X789 @ X790 ) )
=> ! [X792: $o] :
( ( ( in @ X791 @ X789 )
=> ( ~ ( in @ X791 @ X790 )
=> X792 ) )
=> ( ( ~ ( in @ X791 @ X789 )
=> ( ( in @ X791 @ X790 )
=> X792 ) )
=> X792 ) ) )
=> ( ! [X793: $i,X794: $i,X795: $i] :
( ( in @ X795 @ X793 )
=> ( ~ ( in @ X795 @ X794 )
=> ( in @ X795 @ ( symdiff @ X793 @ X794 ) ) ) )
=> ( ! [X796: $i,X797: $i,X798: $i] :
( ~ ( in @ X798 @ X796 )
=> ( ( in @ X798 @ X797 )
=> ( in @ X798 @ ( symdiff @ X796 @ X797 ) ) ) )
=> ( ! [X799: $i,X800: $i,X801: $i] :
( ( in @ X801 @ X799 )
=> ( ( in @ X801 @ X800 )
=> ~ ( in @ X801 @ ( symdiff @ X799 @ X800 ) ) ) )
=> ( ! [X802: $i,X803: $i,X804: $i] :
( ~ ( in @ X804 @ X802 )
=> ( ~ ( in @ X804 @ X803 )
=> ~ ( in @ X804 @ ( symdiff @ X802 @ X803 ) ) ) )
=> ( ! [X805: $i,X806: $i] : ( in @ X806 @ ( setadjoin @ X805 @ ( setadjoin @ X806 @ emptyset ) ) )
=> ( ! [X807: $i,X808: $i] : ( in @ X807 @ ( setunion @ ( setadjoin @ ( setadjoin @ X807 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X807 @ ( setadjoin @ X808 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X809: $i,X810: $i] : ( in @ X810 @ ( setunion @ ( setadjoin @ ( setadjoin @ X809 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X809 @ ( setadjoin @ X810 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X811: $i,X812: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X811 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X811 @ ( setadjoin @ X812 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X813: $i,X814: $i] : ( iskpair @ ( kpair @ X813 @ X814 ) )
=> ( ! [X815: $i,X816: $i] :
( ( in @ X816 @ X815 )
=> ( subset @ ( setadjoin @ X816 @ emptyset ) @ X815 ) )
=> ( ! [X817: $i,X818: $i] :
( ( in @ X818 @ X817 )
=> ( in @ ( setadjoin @ X818 @ emptyset ) @ ( powerset @ X817 ) ) )
=> ( ! [X819: $i,X820: $i,X821: $i] :
( ( in @ X821 @ X819 )
=> ( in @ ( setadjoin @ X821 @ emptyset ) @ ( powerset @ ( binunion @ X819 @ X820 ) ) ) )
=> ( ! [X822: $i,X823: $i,X824: $i] :
( ( in @ X824 @ ( setadjoin @ X822 @ ( setadjoin @ X823 @ emptyset ) ) )
=> ( ( X824 = X822 )
| ( X824 = X823 ) ) )
=> ( ! [X825: $i,X826: $i,X827: $i] :
( ( in @ X827 @ X825 )
=> ! [X828: $i] :
( ( in @ X828 @ X826 )
=> ( subset @ ( setadjoin @ X827 @ ( setadjoin @ X828 @ emptyset ) ) @ ( binunion @ X825 @ X826 ) ) ) )
=> ( ! [X829: $i,X830: $i,X831: $i] :
( ( in @ X831 @ X829 )
=> ! [X832: $i] :
( ( in @ X832 @ X830 )
=> ( in @ ( setadjoin @ X831 @ ( setadjoin @ X832 @ emptyset ) ) @ ( powerset @ ( binunion @ X829 @ X830 ) ) ) ) )
=> ( ! [X833: $i,X834: $i,X835: $i] :
( ( in @ X835 @ X833 )
=> ! [X836: $i] :
( ( in @ X836 @ X834 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X835 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X835 @ ( setadjoin @ X836 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X833 @ X834 ) ) ) ) )
=> ( ! [X837: $i,X838: $i,X839: $i] :
( ( in @ X839 @ X837 )
=> ! [X840: $i] :
( ( in @ X840 @ X838 )
=> ( in @ ( setadjoin @ ( setadjoin @ X839 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X839 @ ( setadjoin @ X840 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X837 @ X838 ) ) ) ) ) )
=> ( ! [X841: $i,X842: $i,X843: $i] :
( ( in @ X843 @ X841 )
=> ! [X844: $i] :
( ( in @ X844 @ X842 )
=> ( in @ ( kpair @ X843 @ X844 ) @ ( powerset @ ( powerset @ ( binunion @ X841 @ X842 ) ) ) ) ) )
=> ( ! [X845: $i,X846: $i,X847: $i] :
( ( in @ X847 @ X845 )
=> ! [X848: $i] :
( ( in @ X848 @ X846 )
=> ( in @ ( kpair @ X847 @ X848 ) @ ( cartprod @ X845 @ X846 ) ) ) )
=> ( ! [X849: $i,X850: $i,X851: $i] :
( ( in @ X851 @ ( cartprod @ X849 @ X850 ) )
=> ? [X852: $i] :
( ( in @ X852 @ X849 )
& ? [X853: $i] :
( ( in @ X853 @ X850 )
& ( X851
= ( kpair @ X852 @ X853 ) ) ) ) )
=> ( ! [X854: $i,X855: $i,X856: $i] :
( ( in @ X856 @ ( cartprod @ X854 @ X855 ) )
=> ( iskpair @ X856 ) )
=> ( ! [X857: $i,X858: $i] :
( ( in @ X858 @ ( setunion @ X857 ) )
=> ? [X859: $i] :
( ( in @ X859 @ X857 )
& ( in @ X858 @ X859 ) ) )
=> ( ! [X860: $i] : ( subset @ ( setunion @ ( setadjoin @ X860 @ emptyset ) ) @ X860 )
=> ( ! [X861: $i] : ( subset @ X861 @ ( setunion @ ( setadjoin @ X861 @ emptyset ) ) )
=> ( ! [X862: $i] :
( ( setunion @ ( setadjoin @ X862 @ emptyset ) )
= X862 )
=> ( ! [X863: $i,X864: $i > $o] :
( ! [X865: $i] :
( ( in @ X865 @ X863 )
=> ! [X866: $i] :
( ( in @ X866 @ X863 )
=> ( ( X864 @ X865 )
=> ( ( X864 @ X866 )
=> ( X865 = X866 ) ) ) ) )
=> ( ? [X867: $i] :
( ( in @ X867 @ X863 )
& ( X864 @ X867 ) )
=> ( singleton @ ( dsetconstr @ X863 @ X864 ) ) ) )
=> ( ! [X868: $i,X869: $i > $o] :
( ( ex1 @ X868 @ X869 )
=> ? [X870: $i] :
( ( in @ X870 @ X868 )
& ( X869 @ X870 ) ) )
=> ( ! [X871: $i,X872: $i > $o,X873: $i] :
( ( in @ X873 @ X871 )
=> ( ( X872 @ X873 )
=> ( ! [X874: $i] :
( ( in @ X874 @ X871 )
=> ( ( X872 @ X874 )
=> ( X874 = X873 ) ) )
=> ( ex1 @ X871 @ X872 ) ) ) )
=> ( ! [X875: $i,X876: $i > $o] :
( ! [X877: $i] :
( ( in @ X877 @ X875 )
=> ! [X878: $i] :
( ( in @ X878 @ X875 )
=> ( ( X876 @ X877 )
=> ( ( X876 @ X878 )
=> ( X877 = X878 ) ) ) ) )
=> ( ? [X879: $i] :
( ( in @ X879 @ X875 )
& ( X876 @ X879 ) )
=> ( ex1 @ X875 @ X876 ) ) )
=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[singletonsuniq]),ubforcartprodlem2]),c_0_157]),setminusILneg]),upairsetE]),setminusIRneg]),setminusLsub]),setminusSubset1]),upairsetIL]),symdiffE]),symdiffI1]),upairsetIR]),symdiffI2]),symdiffIneg1]),c_0_158]),symdiffIneg2]),secondinupair]),vacuousDall]),setukpairIL]),setukpairIR]),quantDeMorgan1]),kpairiskpair]),kpairp]),quantDeMorgan2]),singletonsubset]),quantDeMorgan3]),singletoninpowerset]),singletoninpowunion]),upairset2E]),quantDeMorgan4]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),prop2setI]),eqimpsubset2]),ubforcartprodlem3]),cartprodpairin]),notdexE]),cartprodmempair1]),cartprodmempair]),notdallE]),setunionE2]),setunionsingleton1]),c_0_159]),setunionsingleton2]),setunionsingleton]),c_0_160]),c_0_161]),c_0_162]),c_0_163]),c_0_164]),inCongP]),in__Cong]),c_0_165]),c_0_166]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_167]),c_0_168]),c_0_169]),subsetI1]),disjointsetsI1]),binintersectRsub]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_170]),c_0_171]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),uniqinunit]),binintersectSubset5]),notinsingleton]),binintersectEL]),binintersectLsub]),eqinunit]),binintersectSubset2]),binintersectSubset3]),binintersectER]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),singletonsswitch]),nonemptyImpWitness]),c_0_172]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_173]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_174]),nonemptyE1]),c_0_175]),noeltsimpempty]),emptyI]),setext]),c_0_176]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_177]),c_0_178]),c_0_179]),c_0_180]),c_0_181]),wellorderingAx]),foundationAx]),c_0_182]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_183]) ).
thf(c_0_185,negated_conjecture,
! [X880: $i,X881: $i,X883: $i,X884: $i,X885: $i,X886: $i,X887: $i,X888: $i,X889: $i,X890: $i,X891: $i,X893: $i,X894: $i,X896: $i,X897: $i,X898: $i,X899: $i,X900: $i,X902: $i,X903: $i > $i > $o,X904: $i,X907: $i,X909: $i,X910: $i,X911: $i,X912: $i,X914: $i,X915: $i > $o,X916: $i,X917: $i > $o,X918: $i,X919: $i,X920: $i > $o,X921: $i,X922: $i,X923: $i > $o,X924: $i,X925: $i > $o,X927: $i,X928: $o,X929: $i,X930: $i,X931: $o,X932: $i,X933: $i,X934: $i > $o,X936: $i,X937: $i,X940: $i,X942: $i,X944: $i,X945: $i > $o,X946: $i,X947: $i,X949: $i,X950: $i > $o,X951: $i,X952: $i,X953: $i,X954: $i,X955: $i,X956: $i,X957: $i,X958: $i,X959: $i,X960: $i,X961: $i,X962: $o,X963: $i,X964: $i,X965: $i,X966: $i,X967: $i,X968: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X975: $i,X976: $i,X977: $i,X978: $i,X979: $i,X980: $o,X982: $i,X983: $i,X984: $i > $o,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 > $o,X1007: $i,X1008: $i > $o,X1009: $i,X1010: $i,X1011: $i > $o,X1012: $i,X1014: $i,X1015: $i > $o,X1017: $i,X1018: $i,X1019: $i > $o,X1021: $i,X1022: $i,X1023: $i > $o,X1024: $i,X1026: $o,X1027: $i,X1028: $i > $o,X1030: $i,X1031: $i,X1032: $i > $o,X1033: $i,X1035: $i > $o,X1036: $i,X1038: $i > $o,X1039: $i,X1042: $i > $o,X1043: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1053: $i > $o,X1054: $i,X1055: $i,X1056: $i > $o,X1057: $i > $o,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i > $o,X1069: $i,X1070: $i,X1071: $i > $o,X1072: $i > $o,X1075: $i,X1076: $i,X1077: $i > $o,X1078: $i > $o,X1081: $i,X1082: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,X1089: $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: $i,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 > $o,X1129: $i,X1130: $i > $o,X1131: $i,X1132: $i,X1133: $i,X1134: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $o,X1143: $i,X1144: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i,X1166: $i,X1167: $i,X1168: $i,X1169: $i,X1171: $i,X1172: $i,X1173: $i,X1174: $i,X1175: $i,X1176: $i,X1177: $i,X1178: $i,X1179: $i,X1180: $i,X1181: $i,X1182: $i,X1183: $i,X1184: $i,X1185: $i,X1186: $i,X1187: $i,X1188: $i,X1189: $i,X1190: $i,X1191: $i,X1192: $i,X1193: $i,X1194: $i,X1195: $i,X1196: $i,X1197: $i,X1198: $i,X1199: $i,X1200: $i,X1201: $i,X1202: $i,X1203: $i,X1204: $i,X1205: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $o,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $i,X1217: $i,X1218: $i,X1219: $i,X1220: $i,X1221: $i,X1222: $i,X1223: $i,X1224: $i,X1225: $i,X1226: $i,X1227: $i,X1228: $i,X1229: $i,X1230: $i,X1231: $i,X1232: $i,X1233: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1241: $i,X1242: $i,X1243: $i,X1244: $i,X1245: $i,X1246: $i,X1247: $i,X1248: $i,X1249: $i,X1250: $i,X1251: $i,X1252: $i,X1253: $i,X1254: $i,X1255: $i,X1256: $i,X1257: $i,X1258: $i,X1259: $i,X1260: $i,X1261: $i,X1262: $i,X1263: $i,X1264: $i,X1265: $i,X1266: $i,X1267: $i,X1268: $i,X1269: $i,X1272: $i,X1273: $i,X1274: $i,X1275: $i,X1276: $i,X1278: $i,X1279: $i,X1280: $i,X1281: $i,X1282: $i > $o,X1285: $i,X1286: $i,X1287: $i > $o,X1289: $i,X1290: $i > $o,X1291: $i,X1293: $i,X1294: $i > $o,X1297: $i] :
( ( ~ ( in @ ( esk1_2 @ X880 @ X881 ) @ X880 )
| ~ ( in @ ( esk1_2 @ X880 @ X881 ) @ X881 )
| ( X880 = X881 ) )
& ( ( in @ ( esk1_2 @ X880 @ X881 ) @ X880 )
| ( in @ ( esk1_2 @ X880 @ X881 ) @ X881 )
| ( X880 = X881 ) )
& ~ ( in @ X883 @ emptyset )
& ( ~ ( in @ X886 @ ( setadjoin @ X884 @ X885 ) )
| ( X886 = X884 )
| ( in @ X886 @ X885 ) )
& ( ( X886 != X884 )
| ( in @ X886 @ ( setadjoin @ X884 @ X885 ) ) )
& ( ~ ( in @ X886 @ X885 )
| ( in @ X886 @ ( setadjoin @ X884 @ X885 ) ) )
& ( ~ ( in @ X888 @ ( powerset @ X887 ) )
| ~ ( in @ X889 @ X888 )
| ( in @ X889 @ X887 ) )
& ( ( in @ ( esk2_2 @ X890 @ X891 ) @ X891 )
| ( in @ X891 @ ( powerset @ X890 ) ) )
& ( ~ ( in @ ( esk2_2 @ X890 @ X891 ) @ X890 )
| ( in @ X891 @ ( powerset @ X890 ) ) )
& ( ( in @ X894 @ ( esk3_2 @ X893 @ X894 ) )
| ~ ( in @ X894 @ ( setunion @ X893 ) ) )
& ( ( in @ ( esk3_2 @ X893 @ X894 ) @ X893 )
| ~ ( in @ X894 @ ( setunion @ X893 ) ) )
& ( ~ ( in @ X897 @ X898 )
| ~ ( in @ X898 @ X896 )
| ( in @ X897 @ ( setunion @ X896 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X899 @ omega )
| ( in @ ( setadjoin @ X899 @ X899 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X900 ) @ omega )
| ~ ( in @ emptyset @ X900 )
| ~ ( in @ X902 @ omega )
| ( in @ X902 @ X900 ) )
& ( ( in @ ( esk4_1 @ X900 ) @ X900 )
| ~ ( in @ emptyset @ X900 )
| ~ ( in @ X902 @ omega )
| ( in @ X902 @ X900 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X900 ) @ ( esk4_1 @ X900 ) ) @ X900 )
| ~ ( in @ emptyset @ X900 )
| ~ ( in @ X902 @ omega )
| ( in @ X902 @ X900 ) )
& ( ( in @ ( esk7_3 @ X903 @ X904 @ X907 ) @ X904 )
| ~ ( in @ X907 @ ( esk6_2 @ X903 @ X904 ) )
| ( in @ ( esk5_2 @ X903 @ X904 ) @ X904 ) )
& ( ( X903 @ ( esk7_3 @ X903 @ X904 @ X907 ) @ X907 )
| ~ ( in @ X907 @ ( esk6_2 @ X903 @ X904 ) )
| ( in @ ( esk5_2 @ X903 @ X904 ) @ X904 ) )
& ( ~ ( in @ X910 @ X904 )
| ~ ( X903 @ X910 @ X909 )
| ( in @ X909 @ ( esk6_2 @ X903 @ X904 ) )
| ( in @ ( esk5_2 @ X903 @ X904 ) @ X904 ) )
& ( ( in @ ( esk7_3 @ X903 @ X904 @ X907 ) @ X904 )
| ~ ( in @ X907 @ ( esk6_2 @ X903 @ X904 ) )
| ~ ( exu @ ( X903 @ ( esk5_2 @ X903 @ X904 ) ) ) )
& ( ( X903 @ ( esk7_3 @ X903 @ X904 @ X907 ) @ X907 )
| ~ ( in @ X907 @ ( esk6_2 @ X903 @ X904 ) )
| ~ ( exu @ ( X903 @ ( esk5_2 @ X903 @ X904 ) ) ) )
& ( ~ ( in @ X910 @ X904 )
| ~ ( X903 @ X910 @ X909 )
| ( in @ X909 @ ( esk6_2 @ X903 @ X904 ) )
| ~ ( exu @ ( X903 @ ( esk5_2 @ X903 @ X904 ) ) ) )
& ( ( in @ ( esk8_1 @ X911 ) @ X911 )
| ~ ( in @ X912 @ X911 ) )
& ( ~ ( in @ X914 @ ( esk8_1 @ X911 ) )
| ~ ( in @ X914 @ X911 )
| ~ ( in @ X912 @ X911 ) )
& epred1_0
& ( ~ ( exu @ X915 )
| ( X915 @ ( descr @ X915 ) ) )
& ( ~ ( in @ X918 @ X916 )
| ~ ( X917 @ X918 )
| ( in @ X918 @ ( dsetconstr @ X916 @ X917 ) ) )
& ( ~ ( in @ X921 @ ( dsetconstr @ X919 @ X920 ) )
| ( in @ X921 @ X919 ) )
& ( ~ ( in @ X924 @ ( dsetconstr @ X922 @ X923 ) )
| ( X923 @ X924 ) )
& ( ( X925 @ ( esk9_1 @ X925 ) )
| ~ ( exu @ X925 ) )
& ( ~ ( X925 @ X927 )
| ( ( esk9_1 @ X925 )
= X927 )
| ~ ( exu @ X925 ) )
& ( ~ ( in @ X929 @ ( prop2set @ X928 ) )
| X928 )
& ( ~ ( in @ X930 @ emptyset )
| X931 )
& ( ~ ( in @ X932 @ emptyset )
| ~ $true )
& ~ ( in @ X933 @ emptyset )
& ( ~ ( exu @ X934 )
| ( X934 @ ( esk10_1 @ X934 ) ) )
& ( ( in @ ( esk12_2 @ X936 @ X937 ) @ X937 )
| ( X936 = X937 )
| ( in @ ( esk11_2 @ X936 @ X937 ) @ X936 ) )
& ( ~ ( in @ ( esk12_2 @ X936 @ X937 ) @ X936 )
| ( X936 = X937 )
| ( in @ ( esk11_2 @ X936 @ X937 ) @ X936 ) )
& ( ( in @ ( esk12_2 @ X936 @ X937 ) @ X937 )
| ( X936 = X937 )
| ~ ( in @ ( esk11_2 @ X936 @ X937 ) @ X937 ) )
& ( ~ ( in @ ( esk12_2 @ X936 @ X937 ) @ X936 )
| ( X936 = X937 )
| ~ ( in @ ( esk11_2 @ X936 @ X937 ) @ X937 ) )
& ( ( in @ ( esk13_1 @ X940 ) @ X940 )
| ( X940 = emptyset ) )
& ( ( in @ ( esk14_1 @ X942 ) @ X942 )
| ( X942 = emptyset ) )
& ( ~ ( in @ X946 @ ( dsetconstr @ X944 @ X945 ) )
| ( X945 @ X946 )
| ~ ( in @ X946 @ X944 ) )
& ( ~ ( X945 @ X946 )
| ( in @ X946 @ ( dsetconstr @ X944 @ X945 ) )
| ~ ( in @ X946 @ X944 ) )
& ( ~ ( nonempty @ X947 )
| ( in @ ( esk15_1 @ X947 ) @ X947 ) )
& ( ~ ( in @ X951 @ X949 )
| ~ ( X950 @ X951 )
| ( nonempty @ ( dsetconstr @ X949 @ X950 ) ) )
& ( ~ ( in @ X953 @ X952 )
| ( nonempty @ X952 ) )
& ( in @ X954 @ ( setadjoin @ X954 @ X955 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X958 @ X957 )
| ( in @ X958 @ ( setadjoin @ X956 @ X957 ) ) )
& ( ( in @ X961 @ X960 )
| X962
| ( X961 = X959 )
| ~ ( in @ X961 @ ( setadjoin @ X959 @ X960 ) ) )
& ( ~ X962
| X962
| ( X961 = X959 )
| ~ ( in @ X961 @ ( setadjoin @ X959 @ X960 ) ) )
& ( ( in @ X961 @ X960 )
| X962
| ~ X962
| ~ ( in @ X961 @ ( setadjoin @ X959 @ X960 ) ) )
& ( ~ X962
| X962
| ~ X962
| ~ ( in @ X961 @ ( setadjoin @ X959 @ X960 ) ) )
& ( ~ ( in @ X965 @ ( setadjoin @ X963 @ X964 ) )
| ( X965 = X963 )
| ( in @ X965 @ X964 ) )
& ( ( dsetconstr @ X966
@ ^ [Z0: $i] : $true )
= X966 )
& ( ( in @ ( esk16_2 @ X967 @ X968 ) @ X968 )
| ( in @ X968 @ ( powerset @ X967 ) ) )
& ( ~ ( in @ ( esk16_2 @ X967 @ X968 ) @ X967 )
| ( in @ X968 @ ( powerset @ X967 ) ) )
& ( in @ emptyset @ ( powerset @ X970 ) )
& ( in @ emptyset @ ( powerset @ X971 ) )
& ( ~ ( in @ X973 @ ( powerset @ X972 ) )
| ~ ( in @ X974 @ X973 )
| ( in @ X974 @ X972 ) )
& ( ~ ( in @ X976 @ X977 )
| ~ ( in @ X977 @ X975 )
| ( in @ X976 @ ( setunion @ X975 ) ) )
& ( ( in @ X979 @ ( esk17_3 @ X978 @ X979 @ X980 ) )
| X980
| ~ ( in @ X979 @ ( setunion @ X978 ) ) )
& ( ( in @ ( esk17_3 @ X978 @ X979 @ X980 ) @ X978 )
| X980
| ~ ( in @ X979 @ ( setunion @ X978 ) ) )
& ( ~ X980
| X980
| ~ ( in @ X979 @ ( setunion @ X978 ) ) )
& ( ~ ( in @ X983 @ X982 )
| ( in @ X983 @ ( powerset @ ( setunion @ X982 ) ) ) )
& ( ~ ( X984 @ X986 )
| ( X986
= ( esk18_1 @ X984 ) )
| ~ ( exu @ X984 ) )
& ( ( X987
!= ( esk18_1 @ X984 ) )
| ( X984 @ X987 )
| ~ ( exu @ X984 ) )
& ( ( in @ ( esk19_1 @ X988 ) @ X988 )
| ~ ( nonempty @ X988 ) )
& ( $true
| ~ ( nonempty @ X988 ) )
& ( ~ ( in @ X990 @ ( setadjoin @ X991 @ emptyset ) )
| ( X990 = X991 ) )
& ( ( X992 = X993 )
| ~ ( in @ X993 @ ( setadjoin @ X992 @ emptyset ) ) )
& ( ( X994 != X995 )
| ( in @ X994 @ ( setadjoin @ X995 @ emptyset ) ) )
& ( ~ ( in @ X996 @ ( setadjoin @ X997 @ emptyset ) )
| ( in @ X997 @ ( setadjoin @ X996 @ emptyset ) ) )
& ( ~ ( in @ X1000 @ ( setadjoin @ X998 @ ( setadjoin @ X999 @ emptyset ) ) )
| ( X1000 = X998 )
| ( X1000 = X999 ) )
& ( in @ X1001 @ ( setadjoin @ X1001 @ ( setadjoin @ X1002 @ emptyset ) ) )
& ( in @ X1004 @ ( setadjoin @ X1003 @ ( setadjoin @ X1004 @ emptyset ) ) )
& ( ~ ( in @ X1007 @ X1005 )
| ~ ( X1006 @ X1007 )
| ( ( dsetconstr @ X1005 @ X1006 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1009 @ emptyset )
| ( X1008 @ X1009 ) )
& ( ( in @ ( esk20_2 @ X1010 @ X1011 ) @ X1010 )
| ~ ( in @ X1012 @ X1010 )
| ( X1011 @ X1012 ) )
& ( ~ ( X1011 @ ( esk20_2 @ X1010 @ X1011 ) )
| ~ ( in @ X1012 @ X1010 )
| ( X1011 @ X1012 ) )
& ( ( in @ ( esk21_2 @ X1014 @ X1015 ) @ X1014 )
| ~ ( in @ X1017 @ X1014 )
| ~ ( X1015 @ X1017 ) )
& ( ( X1015 @ ( esk21_2 @ X1014 @ X1015 ) )
| ~ ( in @ X1017 @ X1014 )
| ~ ( X1015 @ X1017 ) )
& ( ( in @ ( esk22_2 @ X1018 @ X1019 ) @ X1018 )
| ~ ( in @ X1021 @ X1018 )
| ~ ( X1019 @ X1021 ) )
& ( ( X1019 @ ( esk22_2 @ X1018 @ X1019 ) )
| ~ ( in @ X1021 @ X1018 )
| ~ ( X1019 @ X1021 ) )
& ( ( in @ ( esk23_2 @ X1022 @ X1023 ) @ X1022 )
| ~ ( in @ X1024 @ X1022 )
| ( X1023 @ X1024 ) )
& ( ~ ( X1023 @ ( esk23_2 @ X1022 @ X1023 ) )
| ~ ( in @ X1024 @ X1022 )
| ( X1023 @ X1024 ) )
& ( ~ X1026
| ( in @ emptyset @ ( prop2set @ X1026 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1027 @ X1028 ) @ X1027 )
| ~ ( in @ X1030 @ X1027 )
| ~ ( X1028 @ X1030 ) )
& ( ( X1028 @ ( esk24_2 @ X1027 @ X1028 ) )
| ~ ( in @ X1030 @ X1027 )
| ~ ( X1028 @ X1030 ) )
& ( ( in @ ( esk25_2 @ X1031 @ X1032 ) @ X1031 )
| ~ ( in @ X1033 @ X1031 )
| ( X1032 @ X1033 ) )
& ( ~ ( X1032 @ ( esk25_2 @ X1031 @ X1032 ) )
| ~ ( in @ X1033 @ X1031 )
| ( X1032 @ X1033 ) )
& ( ( X1035 @ ( esk26_2 @ X1035 @ X1036 ) )
| ~ ( X1035 @ X1036 )
| ( exu @ X1035 ) )
& ( ( X1036
!= ( esk26_2 @ X1035 @ X1036 ) )
| ~ ( X1035 @ X1036 )
| ( exu @ X1035 ) )
& ( ( X1038 @ ( esk27_1 @ X1038 ) )
| ( exu @ X1038 )
| ~ ( X1038 @ X1039 ) )
& ( ( X1038 @ ( esk28_1 @ X1038 ) )
| ( exu @ X1038 )
| ~ ( X1038 @ X1039 ) )
& ( ( ( esk27_1 @ X1038 )
!= ( esk28_1 @ X1038 ) )
| ( exu @ X1038 )
| ~ ( X1038 @ X1039 ) )
& ( ~ ( X1042 @ ( esk29_2 @ X1042 @ X1043 ) )
| ( ( esk29_2 @ X1042 @ X1043 )
!= X1043 )
| ( exu @ X1042 ) )
& ( ( X1042 @ ( esk29_2 @ X1042 @ X1043 ) )
| ( ( esk29_2 @ X1042 @ X1043 )
= X1043 )
| ( exu @ X1042 ) )
& ( ( X1045 != X1046 )
| ( X1047 != X1048 )
| ~ ( in @ X1047 @ X1045 )
| ( in @ X1048 @ X1046 ) )
& ( ~ ( in @ X1051 @ X1049 )
| ( in @ X1052 @ X1050 )
| ( X1051 != X1052 )
| ( X1049 != X1050 ) )
& ( ~ ( in @ X1052 @ X1050 )
| ( in @ X1051 @ X1049 )
| ( X1051 != X1052 )
| ( X1049 != X1050 ) )
& ( ~ ( exu @ X1053 )
| ~ ( X1053 @ X1054 )
| ~ ( X1053 @ X1055 )
| ( X1054 = X1055 ) )
& ( ~ ( exu @ X1056 )
| ( exu @ X1057 )
| ( ( esk30_2 @ X1056 @ X1057 )
= ( esk31_2 @ X1056 @ X1057 ) ) )
& ( ~ ( exu @ X1057 )
| ( exu @ X1056 )
| ( ( esk30_2 @ X1056 @ X1057 )
= ( esk31_2 @ X1056 @ X1057 ) ) )
& ( ~ ( exu @ X1056 )
| ( exu @ X1057 )
| ~ ( X1056 @ ( esk30_2 @ X1056 @ X1057 ) )
| ~ ( X1057 @ ( esk31_2 @ X1056 @ X1057 ) ) )
& ( ~ ( exu @ X1057 )
| ( exu @ X1056 )
| ~ ( X1056 @ ( esk30_2 @ X1056 @ X1057 ) )
| ~ ( X1057 @ ( esk31_2 @ X1056 @ X1057 ) ) )
& ( ~ ( exu @ X1056 )
| ( exu @ X1057 )
| ( X1056 @ ( esk30_2 @ X1056 @ X1057 ) )
| ( X1057 @ ( esk31_2 @ X1056 @ X1057 ) ) )
& ( ~ ( exu @ X1057 )
| ( exu @ X1056 )
| ( X1056 @ ( esk30_2 @ X1056 @ X1057 ) )
| ( X1057 @ ( esk31_2 @ X1056 @ X1057 ) ) )
& ( emptyset = emptyset )
& ( ( X1060 != X1061 )
| ( X1062 != X1063 )
| ( ( setadjoin @ X1060 @ X1062 )
= ( setadjoin @ X1061 @ X1063 ) ) )
& ( ( X1064 != X1065 )
| ( ( powerset @ X1064 )
= ( powerset @ X1065 ) ) )
& ( ( X1066 != X1067 )
| ( ( setunion @ X1066 )
= ( setunion @ X1067 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1068 )
| ~ ( X1068 @ X1069 )
| ~ ( X1068 @ X1070 )
| ( X1069 = X1070 ) )
& ( ( ( esk32_2 @ X1071 @ X1072 )
= ( esk33_2 @ X1071 @ X1072 ) )
| ~ ( exu @ X1071 )
| ~ ( exu @ X1072 )
| ( ( descr @ X1071 )
= ( descr @ X1072 ) ) )
& ( ~ ( X1071 @ ( esk32_2 @ X1071 @ X1072 ) )
| ~ ( X1072 @ ( esk33_2 @ X1071 @ X1072 ) )
| ~ ( exu @ X1071 )
| ~ ( exu @ X1072 )
| ( ( descr @ X1071 )
= ( descr @ X1072 ) ) )
& ( ( X1071 @ ( esk32_2 @ X1071 @ X1072 ) )
| ( X1072 @ ( esk33_2 @ X1071 @ X1072 ) )
| ~ ( exu @ X1071 )
| ~ ( exu @ X1072 )
| ( ( descr @ X1071 )
= ( descr @ X1072 ) ) )
& ( ( in @ ( esk34_4 @ X1075 @ X1076 @ X1077 @ X1078 ) @ X1075 )
| ( ( dsetconstr @ X1075 @ X1077 )
= ( dsetconstr @ X1076 @ X1078 ) )
| ( X1075 != X1076 ) )
& ( ( in @ ( esk35_4 @ X1075 @ X1076 @ X1077 @ X1078 ) @ X1076 )
| ( ( dsetconstr @ X1075 @ X1077 )
= ( dsetconstr @ X1076 @ X1078 ) )
| ( X1075 != X1076 ) )
& ( ( ( esk34_4 @ X1075 @ X1076 @ X1077 @ X1078 )
= ( esk35_4 @ X1075 @ X1076 @ X1077 @ X1078 ) )
| ( ( dsetconstr @ X1075 @ X1077 )
= ( dsetconstr @ X1076 @ X1078 ) )
| ( X1075 != X1076 ) )
& ( ~ ( X1077 @ ( esk34_4 @ X1075 @ X1076 @ X1077 @ X1078 ) )
| ~ ( X1078 @ ( esk35_4 @ X1075 @ X1076 @ X1077 @ X1078 ) )
| ( ( dsetconstr @ X1075 @ X1077 )
= ( dsetconstr @ X1076 @ X1078 ) )
| ( X1075 != X1076 ) )
& ( ( X1077 @ ( esk34_4 @ X1075 @ X1076 @ X1077 @ X1078 ) )
| ( X1078 @ ( esk35_4 @ X1075 @ X1076 @ X1077 @ X1078 ) )
| ( ( dsetconstr @ X1075 @ X1077 )
= ( dsetconstr @ X1076 @ X1078 ) )
| ( X1075 != X1076 ) )
& ( ( in @ ( esk36_2 @ X1081 @ X1082 ) @ X1081 )
| ( subset @ X1081 @ X1082 ) )
& ( ~ ( in @ ( esk36_2 @ X1081 @ X1082 ) @ X1082 )
| ( subset @ X1081 @ X1082 ) )
& ( ( X1084 != X1085 )
| ( subset @ X1085 @ X1084 ) )
& ( ( X1086 != X1087 )
| ( subset @ X1086 @ X1087 ) )
& ( ( in @ ( esk37_2 @ X1088 @ X1089 ) @ X1088 )
| ( subset @ X1088 @ X1089 ) )
& ( ~ ( in @ ( esk37_2 @ X1088 @ X1089 ) @ X1089 )
| ( subset @ X1088 @ X1089 ) )
& ( subset @ emptyset @ X1091 )
& ( ~ ( subset @ X1092 @ X1093 )
| ~ ( in @ X1094 @ X1092 )
| ( in @ X1094 @ X1093 ) )
& ( ~ ( subset @ X1095 @ X1096 )
| ( in @ X1097 @ X1096 )
| ~ ( in @ X1097 @ X1095 ) )
& ( ~ ( in @ X1100 @ X1098 )
| ( in @ X1100 @ X1099 )
| ~ ( subset @ X1098 @ X1099 ) )
& ( ( subset @ X1101 @ X1102 )
| ( X1101 != X1102 ) )
& ( ~ ( in @ X1105 @ X1103 )
| ( in @ X1105 @ X1104 )
| ( X1103 != X1104 ) )
& ( subset @ X1106 @ X1106 )
& ( ~ ( subset @ X1107 @ X1108 )
| ~ ( subset @ X1108 @ X1109 )
| ( subset @ X1107 @ X1109 ) )
& ( subset @ X1111 @ ( setadjoin @ X1110 @ X1111 ) )
& ( ~ ( subset @ X1112 @ X1114 )
| ( subset @ X1112 @ ( setadjoin @ X1113 @ X1114 ) ) )
& ( ~ ( subset @ X1115 @ X1116 )
| ( in @ X1115 @ ( powerset @ X1116 ) ) )
& ( ~ ( subset @ X1117 @ X1118 )
| ~ ( subset @ X1118 @ X1117 )
| ( X1117 = X1118 ) )
& ( ~ ( subset @ X1119 @ emptyset )
| ( X1119 = emptyset ) )
& ( ~ ( subset @ X1121 @ X1120 )
| ( in @ X1121 @ ( powerset @ X1120 ) ) )
& ( ~ ( in @ X1123 @ ( powerset @ X1122 ) )
| ( subset @ X1123 @ X1122 ) )
& ( in @ X1124 @ ( powerset @ X1124 ) )
& ( ~ ( subset @ X1125 @ X1126 )
| ( subset @ ( powerset @ X1125 ) @ ( powerset @ X1126 ) ) )
& ( in @ ( dsetconstr @ X1127 @ X1128 ) @ ( powerset @ X1127 ) )
& ( subset @ ( dsetconstr @ X1129 @ X1130 ) @ X1129 )
& ( ~ ( in @ X1133 @ X1131 )
| ( in @ X1133 @ ( binunion @ X1131 @ X1132 ) ) )
& ( in @ X1135 @ ( setadjoin @ X1134 @ ( setadjoin @ X1135 @ emptyset ) ) )
& ( ~ ( in @ X1138 @ X1137 )
| ( in @ X1138 @ ( binunion @ X1136 @ X1137 ) ) )
& ( ( in @ X1141 @ X1140 )
| X1142
| ( in @ X1141 @ X1139 )
| ~ ( in @ X1141 @ ( binunion @ X1139 @ X1140 ) ) )
& ( ~ X1142
| X1142
| ( in @ X1141 @ X1139 )
| ~ ( in @ X1141 @ ( binunion @ X1139 @ X1140 ) ) )
& ( ( in @ X1141 @ X1140 )
| X1142
| ~ X1142
| ~ ( in @ X1141 @ ( binunion @ X1139 @ X1140 ) ) )
& ( ~ X1142
| X1142
| ~ X1142
| ~ ( in @ X1141 @ ( binunion @ X1139 @ X1140 ) ) )
& ( ~ ( in @ X1145 @ ( binunion @ X1143 @ X1144 ) )
| ( in @ X1145 @ X1143 )
| ( in @ X1145 @ X1144 ) )
& ( subset @ X1146 @ ( binunion @ X1146 @ X1147 ) )
& ( subset @ X1149 @ ( binunion @ X1148 @ X1149 ) )
& ( ~ ( in @ X1152 @ X1150 )
| ~ ( in @ X1152 @ X1151 )
| ( in @ X1152 @ ( binintersect @ X1150 @ X1151 ) ) )
& ( ~ ( subset @ X1155 @ X1153 )
| ~ ( subset @ X1155 @ X1154 )
| ( subset @ X1155 @ ( binintersect @ X1153 @ X1154 ) ) )
& ( ~ ( in @ X1158 @ ( binintersect @ X1156 @ X1157 ) )
| ( in @ X1158 @ X1156 ) )
& ( subset @ ( binintersect @ X1159 @ X1160 ) @ X1159 )
& ( ~ ( subset @ X1161 @ X1162 )
| ( ( binintersect @ X1161 @ X1162 )
= X1161 ) )
& ( ( ( binintersect @ X1163 @ X1164 )
!= X1164 )
| ( subset @ X1164 @ X1163 ) )
& ( ~ ( in @ X1167 @ ( binintersect @ X1165 @ X1166 ) )
| ( in @ X1167 @ X1166 ) )
& ( ( in @ ( esk38_2 @ X1168 @ X1169 ) @ X1168 )
| ( ( binintersect @ X1168 @ X1169 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1168 @ X1169 ) @ X1169 )
| ( ( binintersect @ X1168 @ X1169 )
= emptyset ) )
& ( subset @ ( binintersect @ X1171 @ X1172 ) @ X1172 )
& ( ~ ( subset @ X1174 @ X1173 )
| ( ( binintersect @ X1173 @ X1174 )
= X1174 ) )
& ( ( ( binintersect @ X1175 @ X1176 )
!= X1175 )
| ( subset @ X1175 @ X1176 ) )
& ( ( binintersect @ X1177 @ ( binunion @ X1178 @ X1179 ) )
= ( binunion @ ( binintersect @ X1177 @ X1178 ) @ ( binintersect @ X1177 @ X1179 ) ) )
& ( ~ ( in @ X1182 @ X1180 )
| ( in @ X1182 @ X1181 )
| ( in @ X1182 @ ( setminus @ X1180 @ X1181 ) ) )
& ( ~ ( in @ X1185 @ ( setminus @ X1183 @ X1184 ) )
| ( in @ X1185 @ X1183 ) )
& ( ~ ( in @ X1188 @ ( setminus @ X1186 @ X1187 ) )
| ~ ( in @ X1188 @ X1187 ) )
& ( ~ ( subset @ X1189 @ X1190 )
| ( ( setminus @ X1189 @ X1190 )
= emptyset ) )
& ( ( in @ X1193 @ ( setminus @ X1191 @ X1192 ) )
| ~ ( in @ X1193 @ X1191 )
| ( in @ X1193 @ X1192 ) )
& ( ( in @ X1196 @ ( setminus @ X1194 @ X1195 ) )
| ( in @ X1196 @ X1195 )
| ~ ( in @ X1196 @ X1194 ) )
& ( ( in @ X1199 @ X1197 )
| ~ ( in @ X1199 @ ( setminus @ X1197 @ X1198 ) ) )
& ( ~ ( in @ X1202 @ X1201 )
| ~ ( in @ X1202 @ ( setminus @ X1200 @ X1201 ) ) )
& ( subset @ ( setminus @ X1203 @ X1204 ) @ X1203 )
& ( ( ( setminus @ X1205 @ X1206 )
!= emptyset )
| ( subset @ X1205 @ X1206 ) )
& ( ~ ( in @ X1209 @ X1207 )
| X1210
| ( in @ X1209 @ X1207 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ( in @ X1209 @ X1208 )
| X1210
| ( in @ X1209 @ X1207 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ X1210
| X1210
| ( in @ X1209 @ X1207 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ ( in @ X1209 @ X1207 )
| X1210
| ~ ( in @ X1209 @ X1208 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ( in @ X1209 @ X1208 )
| X1210
| ~ ( in @ X1209 @ X1208 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ X1210
| X1210
| ~ ( in @ X1209 @ X1208 )
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ ( in @ X1209 @ X1207 )
| X1210
| ~ X1210
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ( in @ X1209 @ X1208 )
| X1210
| ~ X1210
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ X1210
| X1210
| ~ X1210
| ~ ( in @ X1209 @ ( symdiff @ X1207 @ X1208 ) ) )
& ( ~ ( in @ X1213 @ X1211 )
| ( in @ X1213 @ X1212 )
| ( in @ X1213 @ ( symdiff @ X1211 @ X1212 ) ) )
& ( ( in @ X1216 @ X1214 )
| ~ ( in @ X1216 @ X1215 )
| ( in @ X1216 @ ( symdiff @ X1214 @ X1215 ) ) )
& ( ~ ( in @ X1219 @ X1217 )
| ~ ( in @ X1219 @ X1218 )
| ~ ( in @ X1219 @ ( symdiff @ X1217 @ X1218 ) ) )
& ( ( in @ X1222 @ X1220 )
| ( in @ X1222 @ X1221 )
| ~ ( in @ X1222 @ ( symdiff @ X1220 @ X1221 ) ) )
& ( in @ X1224 @ ( setadjoin @ X1223 @ ( setadjoin @ X1224 @ emptyset ) ) )
& ( in @ X1225 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1225 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1225 @ ( setadjoin @ X1226 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1228 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1227 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1227 @ ( setadjoin @ X1228 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1229 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1229 @ ( setadjoin @ X1230 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1231 @ X1232 ) )
& ( ~ ( in @ X1234 @ X1233 )
| ( subset @ ( setadjoin @ X1234 @ emptyset ) @ X1233 ) )
& ( ~ ( in @ X1236 @ X1235 )
| ( in @ ( setadjoin @ X1236 @ emptyset ) @ ( powerset @ X1235 ) ) )
& ( ~ ( in @ X1239 @ X1237 )
| ( in @ ( setadjoin @ X1239 @ emptyset ) @ ( powerset @ ( binunion @ X1237 @ X1238 ) ) ) )
& ( ~ ( in @ X1242 @ ( setadjoin @ X1240 @ ( setadjoin @ X1241 @ emptyset ) ) )
| ( X1242 = X1240 )
| ( X1242 = X1241 ) )
& ( ~ ( in @ X1245 @ X1243 )
| ~ ( in @ X1246 @ X1244 )
| ( subset @ ( setadjoin @ X1245 @ ( setadjoin @ X1246 @ emptyset ) ) @ ( binunion @ X1243 @ X1244 ) ) )
& ( ~ ( in @ X1249 @ X1247 )
| ~ ( in @ X1250 @ X1248 )
| ( in @ ( setadjoin @ X1249 @ ( setadjoin @ X1250 @ emptyset ) ) @ ( powerset @ ( binunion @ X1247 @ X1248 ) ) ) )
& ( ~ ( in @ X1253 @ X1251 )
| ~ ( in @ X1254 @ X1252 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1253 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1253 @ ( setadjoin @ X1254 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1251 @ X1252 ) ) ) )
& ( ~ ( in @ X1257 @ X1255 )
| ~ ( in @ X1258 @ X1256 )
| ( in @ ( setadjoin @ ( setadjoin @ X1257 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1257 @ ( setadjoin @ X1258 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1255 @ X1256 ) ) ) ) )
& ( ~ ( in @ X1261 @ X1259 )
| ~ ( in @ X1262 @ X1260 )
| ( in @ ( kpair @ X1261 @ X1262 ) @ ( powerset @ ( powerset @ ( binunion @ X1259 @ X1260 ) ) ) ) )
& ( ~ ( in @ X1265 @ X1263 )
| ~ ( in @ X1266 @ X1264 )
| ( in @ ( kpair @ X1265 @ X1266 ) @ ( cartprod @ X1263 @ X1264 ) ) )
& ( ( in @ ( esk39_3 @ X1267 @ X1268 @ X1269 ) @ X1267 )
| ~ ( in @ X1269 @ ( cartprod @ X1267 @ X1268 ) ) )
& ( ( in @ ( esk40_3 @ X1267 @ X1268 @ X1269 ) @ X1268 )
| ~ ( in @ X1269 @ ( cartprod @ X1267 @ X1268 ) ) )
& ( ( X1269
= ( kpair @ ( esk39_3 @ X1267 @ X1268 @ X1269 ) @ ( esk40_3 @ X1267 @ X1268 @ X1269 ) ) )
| ~ ( in @ X1269 @ ( cartprod @ X1267 @ X1268 ) ) )
& ( ~ ( in @ X1274 @ ( cartprod @ X1272 @ X1273 ) )
| ( iskpair @ X1274 ) )
& ( ( in @ ( esk41_2 @ X1275 @ X1276 ) @ X1275 )
| ~ ( in @ X1276 @ ( setunion @ X1275 ) ) )
& ( ( in @ X1276 @ ( esk41_2 @ X1275 @ X1276 ) )
| ~ ( in @ X1276 @ ( setunion @ X1275 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1278 @ emptyset ) ) @ X1278 )
& ( subset @ X1279 @ ( setunion @ ( setadjoin @ X1279 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1280 @ emptyset ) )
= X1280 )
& ( ( in @ ( esk42_2 @ X1281 @ X1282 ) @ X1281 )
| ~ ( in @ X1285 @ X1281 )
| ~ ( X1282 @ X1285 )
| ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) )
& ( ( in @ ( esk43_2 @ X1281 @ X1282 ) @ X1281 )
| ~ ( in @ X1285 @ X1281 )
| ~ ( X1282 @ X1285 )
| ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) )
& ( ( X1282 @ ( esk42_2 @ X1281 @ X1282 ) )
| ~ ( in @ X1285 @ X1281 )
| ~ ( X1282 @ X1285 )
| ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) )
& ( ( X1282 @ ( esk43_2 @ X1281 @ X1282 ) )
| ~ ( in @ X1285 @ X1281 )
| ~ ( X1282 @ X1285 )
| ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) )
& ( ( ( esk42_2 @ X1281 @ X1282 )
!= ( esk43_2 @ X1281 @ X1282 ) )
| ~ ( in @ X1285 @ X1281 )
| ~ ( X1282 @ X1285 )
| ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) )
& ( ( in @ ( esk44_2 @ X1286 @ X1287 ) @ X1286 )
| ~ ( ex1 @ X1286 @ X1287 ) )
& ( ( X1287 @ ( esk44_2 @ X1286 @ X1287 ) )
| ~ ( ex1 @ X1286 @ X1287 ) )
& ( ( in @ ( esk45_3 @ X1289 @ X1290 @ X1291 ) @ X1289 )
| ( ex1 @ X1289 @ X1290 )
| ~ ( X1290 @ X1291 )
| ~ ( in @ X1291 @ X1289 ) )
& ( ( X1290 @ ( esk45_3 @ X1289 @ X1290 @ X1291 ) )
| ( ex1 @ X1289 @ X1290 )
| ~ ( X1290 @ X1291 )
| ~ ( in @ X1291 @ X1289 ) )
& ( ( ( esk45_3 @ X1289 @ X1290 @ X1291 )
!= X1291 )
| ( ex1 @ X1289 @ X1290 )
| ~ ( X1290 @ X1291 )
| ~ ( in @ X1291 @ X1289 ) )
& ( ( in @ ( esk46_2 @ X1293 @ X1294 ) @ X1293 )
| ~ ( in @ X1297 @ X1293 )
| ~ ( X1294 @ X1297 )
| ( ex1 @ X1293 @ X1294 ) )
& ( ( in @ ( esk47_2 @ X1293 @ X1294 ) @ X1293 )
| ~ ( in @ X1297 @ X1293 )
| ~ ( X1294 @ X1297 )
| ( ex1 @ X1293 @ X1294 ) )
& ( ( X1294 @ ( esk46_2 @ X1293 @ X1294 ) )
| ~ ( in @ X1297 @ X1293 )
| ~ ( X1294 @ X1297 )
| ( ex1 @ X1293 @ X1294 ) )
& ( ( X1294 @ ( esk47_2 @ X1293 @ X1294 ) )
| ~ ( in @ X1297 @ X1293 )
| ~ ( X1294 @ X1297 )
| ( ex1 @ X1293 @ X1294 ) )
& ( ( ( esk46_2 @ X1293 @ X1294 )
!= ( esk47_2 @ X1293 @ X1294 ) )
| ~ ( in @ X1297 @ X1293 )
| ~ ( X1294 @ X1297 )
| ( ex1 @ X1293 @ X1294 ) )
& ( ( setadjoin @ esk48_0 @ emptyset )
= ( setadjoin @ esk49_0 @ emptyset ) )
& ( esk48_0 != esk49_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_184])])])])])])]) ).
thf(c_0_186,negated_conjecture,
! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
thf(c_0_187,negated_conjecture,
( ( setadjoin @ esk48_0 @ emptyset )
= ( setadjoin @ esk49_0 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
thf(c_0_188,negated_conjecture,
esk48_0 != esk49_0,
inference(split_conjunct,[status(thm)],[c_0_185]) ).
thf(c_0_189,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_186]),c_0_188]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU641^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:16:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running higher-order theorem proving
% 0.21/0.47 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
% 0.21/0.57 # Version: 3.1.0-ho
% 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.57 # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.57 # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.57 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.57 # Starting new_ho_5 with 300s (1) cores
% 0.21/0.57 # new_bool_5 with pid 23612 completed with status 0
% 0.21/0.57 # Result found by new_bool_5
% 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.21/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.21/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.21/0.57 # new_ho_10_cnf2 with pid 23624 completed with status 0
% 0.21/0.57 # Result found by new_ho_10_cnf2
% 0.21/0.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.57 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.57 # Starting new_bool_5 with 300s (1) cores
% 0.21/0.57 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.21/0.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.21/0.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.21/0.57 # Preprocessing time : 0.005 s
% 0.21/0.57 # Presaturation interreduction done
% 0.21/0.57
% 0.21/0.57 # Proof found!
% 0.21/0.57 # SZS status Theorem
% 0.21/0.57 # SZS output start CNFRefutation
% See solution above
% 0.21/0.57 # Parsed axioms : 346
% 0.21/0.57 # Removed by relevancy pruning/SinE : 189
% 0.21/0.57 # Initial clauses : 252
% 0.21/0.57 # Removed in clause preprocessing : 25
% 0.21/0.57 # Initial clauses in saturation : 227
% 0.21/0.57 # Processed clauses : 247
% 0.21/0.57 # ...of these trivial : 6
% 0.21/0.57 # ...subsumed : 24
% 0.21/0.57 # ...remaining for further processing : 217
% 0.21/0.57 # Other redundant clauses eliminated : 11
% 0.21/0.57 # Clauses deleted for lack of memory : 0
% 0.21/0.57 # Backward-subsumed : 0
% 0.21/0.57 # Backward-rewritten : 1
% 0.21/0.57 # Generated clauses : 12
% 0.21/0.57 # ...of the previous two non-redundant : 6
% 0.21/0.57 # ...aggressively subsumed : 0
% 0.21/0.57 # Contextual simplify-reflections : 0
% 0.21/0.57 # Paramodulations : 1
% 0.21/0.57 # Factorizations : 0
% 0.21/0.57 # NegExts : 0
% 0.21/0.57 # Equation resolutions : 11
% 0.21/0.57 # Disequality decompositions : 0
% 0.21/0.57 # Total rewrite steps : 28
% 0.21/0.57 # ...of those cached : 18
% 0.21/0.57 # Propositional unsat checks : 0
% 0.21/0.57 # Propositional check models : 0
% 0.21/0.57 # Propositional check unsatisfiable : 0
% 0.21/0.57 # Propositional clauses : 0
% 0.21/0.57 # Propositional clauses after purity: 0
% 0.21/0.57 # Propositional unsat core size : 0
% 0.21/0.57 # Propositional preprocessing time : 0.000
% 0.21/0.57 # Propositional encoding time : 0.000
% 0.21/0.57 # Propositional solver time : 0.000
% 0.21/0.57 # Success case prop preproc time : 0.000
% 0.21/0.57 # Success case prop encoding time : 0.000
% 0.21/0.57 # Success case prop solver time : 0.000
% 0.21/0.57 # Current number of processed clauses : 14
% 0.21/0.57 # Positive orientable unit clauses : 10
% 0.21/0.57 # Positive unorientable unit clauses: 0
% 0.21/0.57 # Negative unit clauses : 3
% 0.21/0.57 # Non-unit-clauses : 1
% 0.21/0.57 # Current number of unprocessed clauses: 177
% 0.21/0.57 # ...number of literals in the above : 477
% 0.21/0.57 # Current number of archived formulas : 0
% 0.21/0.57 # Current number of archived clauses : 192
% 0.21/0.57 # Clause-clause subsumption calls (NU) : 4537
% 0.21/0.57 # Rec. Clause-clause subsumption calls : 2796
% 0.21/0.57 # Non-unit clause-clause subsumptions : 23
% 0.21/0.57 # Unit Clause-clause subsumption calls : 6
% 0.21/0.57 # Rewrite failures with RHS unbound : 0
% 0.21/0.57 # BW rewrite match attempts : 8
% 0.21/0.57 # BW rewrite match successes : 1
% 0.21/0.57 # Condensation attempts : 247
% 0.21/0.57 # Condensation successes : 3
% 0.21/0.57 # Termbank termtop insertions : 36514
% 0.21/0.57 # Search garbage collected termcells : 14048
% 0.21/0.57
% 0.21/0.57 # -------------------------------------------------
% 0.21/0.57 # User time : 0.060 s
% 0.21/0.57 # System time : 0.011 s
% 0.21/0.57 # Total time : 0.071 s
% 0.21/0.57 # Maximum resident set size: 5300 pages
% 0.21/0.57
% 0.21/0.57 # -------------------------------------------------
% 0.21/0.57 # User time : 0.066 s
% 0.21/0.57 # System time : 0.017 s
% 0.21/0.57 # Total time : 0.083 s
% 0.21/0.57 # Maximum resident set size: 2136 pages
% 0.21/0.57 % E---3.1 exiting
% 0.21/0.57 % E exiting
%------------------------------------------------------------------------------