%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU654^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 03:28:53 EDT 2024
% Result : Theorem 0.63s 0.69s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 416
% Syntax : Number of formulae : 457 ( 10 unt; 244 typ; 0 def)
% Number of atoms : 1777 ( 303 equ; 0 cnn)
% Maximal formula atoms : 520 ( 8 avg)
% Number of connectives : 6316 ( 424 ~; 408 |; 322 &;4052 @)
% ( 233 <=>; 877 =>; 0 <=; 0 <~>)
% Maximal formula depth : 657 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 301 >; 0 *; 0 +; 0 <<)
% Number of symbols : 247 ( 244 usr; 179 con; 0-4 aty)
% Number of variables : 1517 ( 73 ^1364 !; 80 ?;1517 :)
% 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,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
epred1_0: $o ).
thf(decl_223,type,
esk1_2: $i > $i > $i ).
thf(decl_224,type,
esk2_2: $i > $i > $i ).
thf(decl_225,type,
esk3_2: $i > $i > $i ).
thf(decl_226,type,
esk4_1: $i > $i ).
thf(decl_227,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_228,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_229,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_230,type,
esk8_1: $i > $i ).
thf(decl_231,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_232,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_233,type,
esk11_2: $i > $i > $i ).
thf(decl_234,type,
esk12_2: $i > $i > $i ).
thf(decl_235,type,
esk13_1: $i > $i ).
thf(decl_236,type,
esk14_1: $i > $i ).
thf(decl_237,type,
esk15_1: $i > $i ).
thf(decl_238,type,
esk16_2: $i > $i > $i ).
thf(decl_239,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_240,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_241,type,
esk19_1: $i > $i ).
thf(decl_242,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_243,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_244,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_245,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_246,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_247,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_248,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_249,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_250,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_251,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_252,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_253,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_254,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_255,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_256,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_257,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_258,type,
esk36_2: $i > $i > $i ).
thf(decl_259,type,
esk37_2: $i > $i > $i ).
thf(decl_260,type,
esk38_2: $i > $i > $i ).
thf(decl_261,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_262,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_263,type,
esk41_2: $i > $i > $i ).
thf(decl_264,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_265,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_266,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_267,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_268,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_269,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_270,type,
esk48_0: $i ).
thf(decl_271,type,
esk49_0: $i ).
thf(decl_272,type,
esk50_0: $i ).
thf(decl_273,type,
esk51_0: $i ).
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(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(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(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(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(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
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(setukpairinjR,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
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).
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(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
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(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(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
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(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(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(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(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(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(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(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(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(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(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
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(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(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(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(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(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(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
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(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
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(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(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(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(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(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(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(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(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(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(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(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(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(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(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
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(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(c_0_171,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_172,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_173,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_174,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_175,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_176,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_177,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_178,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_179,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_180,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_181,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_182,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_183,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_184,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_185,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_186,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_187,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_188,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_189,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_190,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_191,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_192,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_193,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_194,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_195,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_196,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_197,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_198,plain,
( epred1_0
<=> ! [X516: $i] :
? [X517: $i] :
( ! [X518: $i] :
( ( in @ X518 @ X517 )
=> ! [X519: $i] :
( ( in @ X519 @ X518 )
=> ( in @ X519 @ X516 ) ) )
& ! [X520: $i,X521: $i] :
( ( ( in @ X520 @ X516 )
& ( in @ X521 @ X516 ) )
=> ( ! [X522: $i] :
( ( in @ X522 @ X517 )
=> ( ( in @ X520 @ X522 )
<=> ( in @ X521 @ X522 ) ) )
=> ( X520 = X521 ) ) )
& ! [X523: $i,X524: $i] :
( ( ( in @ X523 @ X517 )
& ( in @ X524 @ X517 ) )
=> ( ! [X525: $i] :
( ( in @ X525 @ X523 )
=> ( in @ X525 @ X524 ) )
| ! [X526: $i] :
( ( in @ X526 @ X524 )
=> ( in @ X526 @ X523 ) ) ) )
& ! [X527: $i] :
( ( ! [X528: $i] :
( ( in @ X528 @ X527 )
=> ( in @ X528 @ X516 ) )
& ? [X529: $i] : ( in @ X529 @ X527 ) )
=> ? [X530: $i,X531: $i] :
( ( in @ X530 @ X517 )
& ( in @ X531 @ X527 )
& ~ ? [X532: $i] :
( ( in @ X532 @ X530 )
& ( in @ X532 @ X527 ) )
& ! [X533: $i] :
( ( in @ X533 @ X517 )
=> ( ! [X534: $i] :
( ( in @ X534 @ X533 )
=> ( in @ X534 @ X530 ) )
| ( in @ X531 @ X533 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_199,negated_conjecture,
~ ( ! [X489: $i,X490: $i] :
( ! [X491: $i] :
( ( in @ X491 @ X489 )
<=> ( in @ X491 @ X490 ) )
=> ( X489 = X490 ) )
=> ( ! [X492: $i] :
~ ( in @ X492 @ emptyset )
=> ( ! [X493: $i,X494: $i,X495: $i] :
( ( in @ X495 @ ( setadjoin @ X493 @ X494 ) )
<=> ( ( X495 = X493 )
| ( in @ X495 @ X494 ) ) )
=> ( ! [X496: $i,X497: $i] :
( ( in @ X497 @ ( powerset @ X496 ) )
<=> ! [X498: $i] :
( ( in @ X498 @ X497 )
=> ( in @ X498 @ X496 ) ) )
=> ( ! [X499: $i,X500: $i] :
( ( in @ X500 @ ( setunion @ X499 ) )
<=> ? [X501: $i] :
( ( in @ X500 @ X501 )
& ( in @ X501 @ X499 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X502: $i] :
( ( in @ X502 @ omega )
=> ( in @ ( setadjoin @ X502 @ X502 ) @ omega ) )
=> ( ! [X503: $i] :
( ( ( in @ emptyset @ X503 )
& ! [X504: $i] :
( ( ( in @ X504 @ omega )
& ( in @ X504 @ X503 ) )
=> ( in @ ( setadjoin @ X504 @ X504 ) @ X503 ) ) )
=> ! [X505: $i] :
( ( in @ X505 @ omega )
=> ( in @ X505 @ X503 ) ) )
=> ( ! [X506: $i > $i > $o,X507: $i] :
( ! [X508: $i] :
( ( in @ X508 @ X507 )
=> ( exu @ ( X506 @ X508 ) ) )
=> ? [X509: $i] :
! [X510: $i] :
( ( in @ X510 @ X509 )
<=> ? [X511: $i] :
( ( in @ X511 @ X507 )
& ( X506 @ X511 @ X510 ) ) ) )
=> ( ! [X512: $i] :
( ? [X513: $i] : ( in @ X513 @ X512 )
=> ? [X514: $i] :
( ( in @ X514 @ X512 )
& ~ ? [X515: $i] :
( ( in @ X515 @ X514 )
& ( in @ X515 @ X512 ) ) ) )
=> ( epred1_0
=> ( ! [X535: $i > $o] :
( ( exu @ X535 )
=> ( X535
@ ( descr
@ ^ [Z0: $i] : ( X535 @ Z0 ) ) ) )
=> ( ! [X536: $i,X537: $i > $o,X538: $i] :
( ( in @ X538 @ X536 )
=> ( ( X537 @ X538 )
=> ( in @ X538 @ ( dsetconstr @ X536 @ X537 ) ) ) )
=> ( ! [X539: $i,X540: $i > $o,X541: $i] :
( ( in @ X541 @ ( dsetconstr @ X539 @ X540 ) )
=> ( in @ X541 @ X539 ) )
=> ( ! [X542: $i,X543: $i > $o,X544: $i] :
( ( in @ X544 @ ( dsetconstr @ X542 @ X543 ) )
=> ( X543 @ X544 ) )
=> ( ! [X545: $i > $o] :
( ( exu @ X545 )
=> ? [X546: $i] :
( ( X545 @ X546 )
& ! [X547: $i] :
( ( X545 @ X547 )
=> ( X546 = X547 ) ) ) )
=> ( ! [X548: $o,X549: $i] :
( ( in @ X549 @ ( prop2set @ X548 ) )
=> X548 )
=> ( ! [X550: $i] :
( ( in @ X550 @ emptyset )
=> ! [X551: $o] : X551 )
=> ( ! [X552: $i] :
( ( in @ X552 @ emptyset )
=> ~ $true )
=> ( ! [X553: $i] :
~ ( in @ X553 @ emptyset )
=> ( ! [X554: $i > $o] :
( ( exu @ X554 )
=> ? [X555: $i] : ( X554 @ X555 ) )
=> ( ! [X556: $i,X557: $i] :
( ! [X558: $i] :
( ( in @ X558 @ X556 )
=> ( in @ X558 @ X557 ) )
=> ( ! [X559: $i] :
( ( in @ X559 @ X557 )
=> ( in @ X559 @ X556 ) )
=> ( X556 = X557 ) ) )
=> ( ! [X560: $i] :
( ! [X561: $i] :
~ ( in @ X561 @ X560 )
=> ( X560 = emptyset ) )
=> ( ! [X562: $i] :
( ! [X563: $i] :
~ ( in @ X563 @ X562 )
=> ( X562 = emptyset ) )
=> ( ! [X564: $i,X565: $i > $o,X566: $i] :
( ( in @ X566 @ X564 )
=> ( ( in @ X566 @ ( dsetconstr @ X564 @ X565 ) )
<=> ( X565 @ X566 ) ) )
=> ( ! [X567: $i] :
( ( nonempty @ X567 )
=> ? [X568: $i] : ( in @ X568 @ X567 ) )
=> ( ! [X569: $i,X570: $i > $o,X571: $i] :
( ( in @ X571 @ X569 )
=> ( ( X570 @ X571 )
=> ( nonempty @ ( dsetconstr @ X569 @ X570 ) ) ) )
=> ( ! [X572: $i] :
( ? [X573: $i] : ( in @ X573 @ X572 )
=> ( nonempty @ X572 ) )
=> ( ! [X574: $i,X575: $i] : ( in @ X574 @ ( setadjoin @ X574 @ X575 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X576: $i,X577: $i,X578: $i] :
( ( in @ X578 @ X577 )
=> ( in @ X578 @ ( setadjoin @ X576 @ X577 ) ) )
=> ( ! [X579: $i,X580: $i,X581: $i] :
( ( in @ X581 @ ( setadjoin @ X579 @ X580 ) )
=> ! [X582: $o] :
( ( ( X581 = X579 )
=> X582 )
=> ( ( ( in @ X581 @ X580 )
=> X582 )
=> X582 ) ) )
=> ( ! [X583: $i,X584: $i,X585: $i] :
( ( in @ X585 @ ( setadjoin @ X583 @ X584 ) )
=> ( ( X585 = X583 )
| ( in @ X585 @ X584 ) ) )
=> ( ! [X586: $i] :
( ( dsetconstr @ X586
@ ^ [Z0: $i] : $true )
= X586 )
=> ( ! [X587: $i,X588: $i] :
( ! [X589: $i] :
( ( in @ X589 @ X588 )
=> ( in @ X589 @ X587 ) )
=> ( in @ X588 @ ( powerset @ X587 ) ) )
=> ( ! [X590: $i] : ( in @ emptyset @ ( powerset @ X590 ) )
=> ( ! [X591: $i] : ( in @ emptyset @ ( powerset @ X591 ) )
=> ( ! [X592: $i,X593: $i,X594: $i] :
( ( in @ X593 @ ( powerset @ X592 ) )
=> ( ( in @ X594 @ X593 )
=> ( in @ X594 @ X592 ) ) )
=> ( ! [X595: $i,X596: $i,X597: $i] :
( ( in @ X596 @ X597 )
=> ( ( in @ X597 @ X595 )
=> ( in @ X596 @ ( setunion @ X595 ) ) ) )
=> ( ! [X598: $i,X599: $i] :
( ( in @ X599 @ ( setunion @ X598 ) )
=> ! [X600: $o] :
( ! [X601: $i] :
( ( in @ X599 @ X601 )
=> ( ( in @ X601 @ X598 )
=> X600 ) )
=> X600 ) )
=> ( ! [X602: $i,X603: $i] :
( ( in @ X603 @ X602 )
=> ( in @ X603 @ ( powerset @ ( setunion @ X602 ) ) ) )
=> ( ! [X604: $i > $o] :
( ( exu @ X604 )
=> ? [X605: $i] :
! [X606: $i] :
( ( X604 @ X606 )
<=> ( X606 = X605 ) ) )
=> ( ! [X607: $i] :
( ( nonempty @ X607 )
=> ? [X608: $i] :
( ( in @ X608 @ X607 )
& $true ) )
=> ( ! [X609: $i,X610: $i] :
( ( in @ X609 @ ( setadjoin @ X610 @ emptyset ) )
=> ( X609 = X610 ) )
=> ( ! [X611: $i,X612: $i] :
( ( X611 != X612 )
=> ~ ( in @ X612 @ ( setadjoin @ X611 @ emptyset ) ) )
=> ( ! [X613: $i,X614: $i] :
( ( X613 = X614 )
=> ( in @ X613 @ ( setadjoin @ X614 @ emptyset ) ) )
=> ( ! [X615: $i,X616: $i] :
( ( in @ X615 @ ( setadjoin @ X616 @ emptyset ) )
=> ( in @ X616 @ ( setadjoin @ X615 @ emptyset ) ) )
=> ( ! [X617: $i,X618: $i,X619: $i] :
( ( in @ X619 @ ( setadjoin @ X617 @ ( setadjoin @ X618 @ emptyset ) ) )
=> ( ( X619 = X617 )
| ( X619 = X618 ) ) )
=> ( ! [X620: $i,X621: $i] : ( in @ X620 @ ( setadjoin @ X620 @ ( setadjoin @ X621 @ emptyset ) ) )
=> ( ! [X622: $i,X623: $i] : ( in @ X623 @ ( setadjoin @ X622 @ ( setadjoin @ X623 @ emptyset ) ) )
=> ( ! [X624: $i,X625: $i > $o] :
( ? [X626: $i] :
( ( in @ X626 @ X624 )
& ( X625 @ X626 ) )
=> ( ( ( dsetconstr @ X624 @ X625 )
= emptyset )
=> ~ $true ) )
=> ( ! [X627: $i > $o,X628: $i] :
( ( in @ X628 @ emptyset )
=> ( X627 @ X628 ) )
=> ( ! [X629: $i,X630: $i > $o] :
( ~ ! [X631: $i] :
( ( in @ X631 @ X629 )
=> ( X630 @ X631 ) )
=> ? [X632: $i] :
( ( in @ X632 @ X629 )
& ~ ( X630 @ X632 ) ) )
=> ( ! [X633: $i,X634: $i > $o] :
( ! [X635: $i] :
( ( in @ X635 @ X633 )
=> ~ ( X634 @ X635 ) )
=> ~ ? [X636: $i] :
( ( in @ X636 @ X633 )
& ( X634 @ X636 ) ) )
=> ( ! [X637: $i,X638: $i > $o] :
( ~ ? [X639: $i] :
( ( in @ X639 @ X637 )
& ( X638 @ X639 ) )
=> ! [X640: $i] :
( ( in @ X640 @ X637 )
=> ~ ( X638 @ X640 ) ) )
=> ( ! [X641: $i,X642: $i > $o] :
( ? [X643: $i] :
( ( in @ X643 @ X641 )
& ~ ( X642 @ X643 ) )
=> ~ ! [X644: $i] :
( ( in @ X644 @ X641 )
=> ( X642 @ X644 ) ) )
=> ( ! [X645: $o] :
( X645
=> ( in @ emptyset @ ( prop2set @ X645 ) ) )
=> ( prop2set2propI
=> ( ! [X646: $i,X647: $i > $o] :
( ~ ? [X648: $i] :
( ( in @ X648 @ X646 )
& ( X647 @ X648 ) )
=> ! [X649: $i] :
( ( in @ X649 @ X646 )
=> ~ ( X647 @ X649 ) ) )
=> ( ! [X650: $i,X651: $i > $o] :
( ~ ! [X652: $i] :
( ( in @ X652 @ X650 )
=> ( X651 @ X652 ) )
=> ? [X653: $i] :
( ( in @ X653 @ X650 )
& ~ ( X651 @ X653 ) ) )
=> ( ! [X654: $i > $o] :
( ? [X655: $i] :
( ( X654 @ X655 )
& ! [X656: $i] :
( ( X654 @ X656 )
=> ( X655 = X656 ) ) )
=> ( exu @ X654 ) )
=> ( ! [X657: $i > $o] :
( ? [X658: $i] : ( X657 @ X658 )
=> ( ! [X659: $i,X660: $i] :
( ( X657 @ X659 )
=> ( ( X657 @ X660 )
=> ( X659 = X660 ) ) )
=> ( exu @ X657 ) ) )
=> ( ! [X661: $i > $o] :
( ? [X662: $i] :
! [X663: $i] :
( ( X661 @ X663 )
<=> ( X663 = X662 ) )
=> ( exu @ X661 ) )
=> ( ! [X664: $i,X665: $i] :
( ( X664 = X665 )
=> ! [X666: $i,X667: $i] :
( ( X666 = X667 )
=> ( ( in @ X666 @ X664 )
=> ( in @ X667 @ X665 ) ) ) )
=> ( ! [X668: $i,X669: $i] :
( ( X668 = X669 )
=> ! [X670: $i,X671: $i] :
( ( X670 = X671 )
=> ( ( in @ X670 @ X668 )
<=> ( in @ X671 @ X669 ) ) ) )
=> ( ! [X672: $i > $o] :
( ( exu @ X672 )
=> ! [X673: $i,X674: $i] :
( ( X672 @ X673 )
=> ( ( X672 @ X674 )
=> ( X673 = X674 ) ) ) )
=> ( ! [X675: $i > $o,X676: $i > $o] :
( ! [X677: $i,X678: $i] :
( ( X677 = X678 )
=> ( ( X675 @ X677 )
<=> ( X676 @ X678 ) ) )
=> ( ( exu @ X675 )
<=> ( exu @ X676 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X679: $i,X680: $i] :
( ( X679 = X680 )
=> ! [X681: $i,X682: $i] :
( ( X681 = X682 )
=> ( ( setadjoin @ X679 @ X681 )
= ( setadjoin @ X680 @ X682 ) ) ) )
=> ( ! [X683: $i,X684: $i] :
( ( X683 = X684 )
=> ( ( powerset @ X683 )
= ( powerset @ X684 ) ) )
=> ( ! [X685: $i,X686: $i] :
( ( X685 = X686 )
=> ( ( setunion @ X685 )
= ( setunion @ X686 ) ) )
=> ( ( omega = omega )
=> ( ! [X687: $i > $o] :
( ( exu @ X687 )
=> ! [X688: $i,X689: $i] :
( ( X687 @ X688 )
=> ( ( X687 @ X689 )
=> ( X688 = X689 ) ) ) )
=> ( ! [X690: $i > $o,X691: $i > $o] :
( ! [X692: $i,X693: $i] :
( ( X692 = X693 )
=> ( ( X690 @ X692 )
<=> ( X691 @ X693 ) ) )
=> ( ( exu @ X690 )
=> ( ( exu @ X691 )
=> ( ( descr @ X690 )
= ( descr @ X691 ) ) ) ) )
=> ( ! [X694: $i,X695: $i] :
( ( X694 = X695 )
=> ! [X696: $i > $o,X697: $i > $o] :
( ! [X698: $i] :
( ( in @ X698 @ X694 )
=> ! [X699: $i] :
( ( in @ X699 @ X695 )
=> ( ( X698 = X699 )
=> ( ( X696 @ X698 )
<=> ( X697 @ X699 ) ) ) ) )
=> ( ( dsetconstr @ X694 @ X696 )
= ( dsetconstr @ X695 @ X697 ) ) ) )
=> ( ! [X700: $i,X701: $i] :
( ! [X702: $i] :
( ( in @ X702 @ X700 )
=> ( in @ X702 @ X701 ) )
=> ( subset @ X700 @ X701 ) )
=> ( ! [X703: $i,X704: $i] :
( ( X703 = X704 )
=> ( subset @ X704 @ X703 ) )
=> ( ! [X705: $i,X706: $i] :
( ( X705 = X706 )
=> ( subset @ X705 @ X706 ) )
=> ( ! [X707: $i,X708: $i] :
( ! [X709: $i] :
( ( in @ X709 @ X707 )
=> ( in @ X709 @ X708 ) )
=> ( subset @ X707 @ X708 ) )
=> ( ! [X710: $i] : ( subset @ emptyset @ X710 )
=> ( ! [X711: $i,X712: $i,X713: $i] :
( ( subset @ X711 @ X712 )
=> ( ( in @ X713 @ X711 )
=> ( in @ X713 @ X712 ) ) )
=> ( ! [X714: $i,X715: $i,X716: $i] :
( ( subset @ X714 @ X715 )
=> ( ~ ( in @ X716 @ X715 )
=> ~ ( in @ X716 @ X714 ) ) )
=> ( ! [X717: $i,X718: $i,X719: $i] :
( ( in @ X719 @ X717 )
=> ( ~ ( in @ X719 @ X718 )
=> ~ ( subset @ X717 @ X718 ) ) )
=> ( ! [X720: $i,X721: $i] :
( ~ ( subset @ X720 @ X721 )
=> ( X720 != X721 ) )
=> ( ! [X722: $i,X723: $i,X724: $i] :
( ( in @ X724 @ X722 )
=> ( ~ ( in @ X724 @ X723 )
=> ( X722 != X723 ) ) )
=> ( ! [X725: $i] : ( subset @ X725 @ X725 )
=> ( ! [X726: $i,X727: $i,X728: $i] :
( ( subset @ X726 @ X727 )
=> ( ( subset @ X727 @ X728 )
=> ( subset @ X726 @ X728 ) ) )
=> ( ! [X729: $i,X730: $i] : ( subset @ X730 @ ( setadjoin @ X729 @ X730 ) )
=> ( ! [X731: $i,X732: $i,X733: $i] :
( ( subset @ X731 @ X733 )
=> ( subset @ X731 @ ( setadjoin @ X732 @ X733 ) ) )
=> ( ! [X734: $i,X735: $i] :
( ( subset @ X734 @ X735 )
=> ( in @ X734 @ ( powerset @ X735 ) ) )
=> ( ! [X736: $i,X737: $i] :
( ( subset @ X736 @ X737 )
=> ( ( subset @ X737 @ X736 )
=> ( X736 = X737 ) ) )
=> ( ! [X738: $i] :
( ( subset @ X738 @ emptyset )
=> ( X738 = emptyset ) )
=> ( ! [X739: $i,X740: $i] :
( ( subset @ X740 @ X739 )
=> ( in @ X740 @ ( powerset @ X739 ) ) )
=> ( ! [X741: $i,X742: $i] :
( ( in @ X742 @ ( powerset @ X741 ) )
=> ( subset @ X742 @ X741 ) )
=> ( ! [X743: $i] : ( in @ X743 @ ( powerset @ X743 ) )
=> ( ! [X744: $i,X745: $i] :
( ( subset @ X744 @ X745 )
=> ( subset @ ( powerset @ X744 ) @ ( powerset @ X745 ) ) )
=> ( ! [X746: $i,X747: $i > $o] : ( in @ ( dsetconstr @ X746 @ X747 ) @ ( powerset @ X746 ) )
=> ( ! [X748: $i,X749: $i > $o] : ( subset @ ( dsetconstr @ X748 @ X749 ) @ X748 )
=> ( ! [X750: $i,X751: $i,X752: $i] :
( ( in @ X752 @ X750 )
=> ( in @ X752 @ ( binunion @ X750 @ X751 ) ) )
=> ( ! [X753: $i,X754: $i] : ( in @ X754 @ ( setadjoin @ X753 @ ( setadjoin @ X754 @ emptyset ) ) )
=> ( ! [X755: $i,X756: $i,X757: $i] :
( ( in @ X757 @ X756 )
=> ( in @ X757 @ ( binunion @ X755 @ X756 ) ) )
=> ( ! [X758: $i,X759: $i,X760: $i,X761: $o] :
( ( in @ X760 @ ( binunion @ X758 @ X759 ) )
=> ( ( ( in @ X760 @ X758 )
=> X761 )
=> ( ( ( in @ X760 @ X759 )
=> X761 )
=> X761 ) ) )
=> ( ! [X762: $i,X763: $i,X764: $i] :
( ( in @ X764 @ ( binunion @ X762 @ X763 ) )
=> ( ( in @ X764 @ X762 )
| ( in @ X764 @ X763 ) ) )
=> ( ! [X765: $i,X766: $i] : ( subset @ X765 @ ( binunion @ X765 @ X766 ) )
=> ( ! [X767: $i,X768: $i] : ( subset @ X768 @ ( binunion @ X767 @ X768 ) )
=> ( ! [X769: $i,X770: $i,X771: $i] :
( ( in @ X771 @ X769 )
=> ( ( in @ X771 @ X770 )
=> ( in @ X771 @ ( binintersect @ X769 @ X770 ) ) ) )
=> ( ! [X772: $i,X773: $i,X774: $i] :
( ( subset @ X774 @ X772 )
=> ( ( subset @ X774 @ X773 )
=> ( subset @ X774 @ ( binintersect @ X772 @ X773 ) ) ) )
=> ( ! [X775: $i,X776: $i,X777: $i] :
( ( in @ X777 @ ( binintersect @ X775 @ X776 ) )
=> ( in @ X777 @ X775 ) )
=> ( ! [X778: $i,X779: $i] : ( subset @ ( binintersect @ X778 @ X779 ) @ X778 )
=> ( ! [X780: $i,X781: $i] :
( ( subset @ X780 @ X781 )
=> ( ( binintersect @ X780 @ X781 )
= X780 ) )
=> ( ! [X782: $i,X783: $i] :
( ( ( binintersect @ X782 @ X783 )
= X783 )
=> ( subset @ X783 @ X782 ) )
=> ( ! [X784: $i,X785: $i,X786: $i] :
( ( in @ X786 @ ( binintersect @ X784 @ X785 ) )
=> ( in @ X786 @ X785 ) )
=> ( ! [X787: $i,X788: $i] :
( ~ ? [X789: $i] :
( ( in @ X789 @ X787 )
& ( in @ X789 @ X788 ) )
=> ( ( binintersect @ X787 @ X788 )
= emptyset ) )
=> ( ! [X790: $i,X791: $i] : ( subset @ ( binintersect @ X790 @ X791 ) @ X791 )
=> ( ! [X792: $i,X793: $i] :
( ( subset @ X793 @ X792 )
=> ( ( binintersect @ X792 @ X793 )
= X793 ) )
=> ( ! [X794: $i,X795: $i] :
( ( ( binintersect @ X794 @ X795 )
= X794 )
=> ( subset @ X794 @ X795 ) )
=> ( ! [X796: $i,X797: $i,X798: $i] :
( ( binintersect @ X796 @ ( binunion @ X797 @ X798 ) )
= ( binunion @ ( binintersect @ X796 @ X797 ) @ ( binintersect @ X796 @ X798 ) ) )
=> ( ! [X799: $i,X800: $i,X801: $i] :
( ( in @ X801 @ X799 )
=> ( ~ ( in @ X801 @ X800 )
=> ( in @ X801 @ ( setminus @ X799 @ X800 ) ) ) )
=> ( ! [X802: $i,X803: $i,X804: $i] :
( ( in @ X804 @ ( setminus @ X802 @ X803 ) )
=> ( in @ X804 @ X802 ) )
=> ( ! [X805: $i,X806: $i,X807: $i] :
( ( in @ X807 @ ( setminus @ X805 @ X806 ) )
=> ~ ( in @ X807 @ X806 ) )
=> ( ! [X808: $i,X809: $i] :
( ( subset @ X808 @ X809 )
=> ( ( setminus @ X808 @ X809 )
= emptyset ) )
=> ( ! [X810: $i,X811: $i,X812: $i] :
( ~ ( in @ X812 @ ( setminus @ X810 @ X811 ) )
=> ( ( in @ X812 @ X810 )
=> ( in @ X812 @ X811 ) ) )
=> ( ! [X813: $i,X814: $i,X815: $i] :
( ~ ( in @ X815 @ ( setminus @ X813 @ X814 ) )
=> ( ~ ( in @ X815 @ X814 )
=> ~ ( in @ X815 @ X813 ) ) )
=> ( ! [X816: $i,X817: $i,X818: $i] :
( ~ ( in @ X818 @ X816 )
=> ~ ( in @ X818 @ ( setminus @ X816 @ X817 ) ) )
=> ( ! [X819: $i,X820: $i,X821: $i] :
( ( in @ X821 @ X820 )
=> ~ ( in @ X821 @ ( setminus @ X819 @ X820 ) ) )
=> ( ! [X822: $i,X823: $i] : ( subset @ ( setminus @ X822 @ X823 ) @ X822 )
=> ( ! [X824: $i,X825: $i] :
( ( ( setminus @ X824 @ X825 )
= emptyset )
=> ( subset @ X824 @ X825 ) )
=> ( ! [X826: $i,X827: $i,X828: $i] :
( ( in @ X828 @ ( symdiff @ X826 @ X827 ) )
=> ! [X829: $o] :
( ( ( in @ X828 @ X826 )
=> ( ~ ( in @ X828 @ X827 )
=> X829 ) )
=> ( ( ~ ( in @ X828 @ X826 )
=> ( ( in @ X828 @ X827 )
=> X829 ) )
=> X829 ) ) )
=> ( ! [X830: $i,X831: $i,X832: $i] :
( ( in @ X832 @ X830 )
=> ( ~ ( in @ X832 @ X831 )
=> ( in @ X832 @ ( symdiff @ X830 @ X831 ) ) ) )
=> ( ! [X833: $i,X834: $i,X835: $i] :
( ~ ( in @ X835 @ X833 )
=> ( ( in @ X835 @ X834 )
=> ( in @ X835 @ ( symdiff @ X833 @ X834 ) ) ) )
=> ( ! [X836: $i,X837: $i,X838: $i] :
( ( in @ X838 @ X836 )
=> ( ( in @ X838 @ X837 )
=> ~ ( in @ X838 @ ( symdiff @ X836 @ X837 ) ) ) )
=> ( ! [X839: $i,X840: $i,X841: $i] :
( ~ ( in @ X841 @ X839 )
=> ( ~ ( in @ X841 @ X840 )
=> ~ ( in @ X841 @ ( symdiff @ X839 @ X840 ) ) ) )
=> ( ! [X842: $i,X843: $i] : ( in @ X843 @ ( setadjoin @ X842 @ ( setadjoin @ X843 @ emptyset ) ) )
=> ( ! [X844: $i,X845: $i] : ( in @ X844 @ ( setunion @ ( setadjoin @ ( setadjoin @ X844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X844 @ ( setadjoin @ X845 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X846: $i,X847: $i] : ( in @ X847 @ ( setunion @ ( setadjoin @ ( setadjoin @ X846 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X846 @ ( setadjoin @ X847 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X848: $i,X849: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X848 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X848 @ ( setadjoin @ X849 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X850: $i,X851: $i] : ( iskpair @ ( kpair @ X850 @ X851 ) )
=> ( ! [X852: $i,X853: $i] :
( ( in @ X853 @ X852 )
=> ( subset @ ( setadjoin @ X853 @ emptyset ) @ X852 ) )
=> ( ! [X854: $i,X855: $i] :
( ( in @ X855 @ X854 )
=> ( in @ ( setadjoin @ X855 @ emptyset ) @ ( powerset @ X854 ) ) )
=> ( ! [X856: $i,X857: $i,X858: $i] :
( ( in @ X858 @ X856 )
=> ( in @ ( setadjoin @ X858 @ emptyset ) @ ( powerset @ ( binunion @ X856 @ X857 ) ) ) )
=> ( ! [X859: $i,X860: $i,X861: $i] :
( ( in @ X861 @ ( setadjoin @ X859 @ ( setadjoin @ X860 @ emptyset ) ) )
=> ( ( X861 = X859 )
| ( X861 = X860 ) ) )
=> ( ! [X862: $i,X863: $i,X864: $i] :
( ( in @ X864 @ X862 )
=> ! [X865: $i] :
( ( in @ X865 @ X863 )
=> ( subset @ ( setadjoin @ X864 @ ( setadjoin @ X865 @ emptyset ) ) @ ( binunion @ X862 @ X863 ) ) ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ( in @ X868 @ X866 )
=> ! [X869: $i] :
( ( in @ X869 @ X867 )
=> ( in @ ( setadjoin @ X868 @ ( setadjoin @ X869 @ emptyset ) ) @ ( powerset @ ( binunion @ X866 @ X867 ) ) ) ) )
=> ( ! [X870: $i,X871: $i,X872: $i] :
( ( in @ X872 @ X870 )
=> ! [X873: $i] :
( ( in @ X873 @ X871 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X872 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X872 @ ( setadjoin @ X873 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X870 @ X871 ) ) ) ) )
=> ( ! [X874: $i,X875: $i,X876: $i] :
( ( in @ X876 @ X874 )
=> ! [X877: $i] :
( ( in @ X877 @ X875 )
=> ( in @ ( setadjoin @ ( setadjoin @ X876 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X876 @ ( setadjoin @ X877 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X874 @ X875 ) ) ) ) ) )
=> ( ! [X878: $i,X879: $i,X880: $i] :
( ( in @ X880 @ X878 )
=> ! [X881: $i] :
( ( in @ X881 @ X879 )
=> ( in @ ( kpair @ X880 @ X881 ) @ ( powerset @ ( powerset @ ( binunion @ X878 @ X879 ) ) ) ) ) )
=> ( ! [X882: $i,X883: $i,X884: $i] :
( ( in @ X884 @ X882 )
=> ! [X885: $i] :
( ( in @ X885 @ X883 )
=> ( in @ ( kpair @ X884 @ X885 ) @ ( cartprod @ X882 @ X883 ) ) ) )
=> ( ! [X886: $i,X887: $i,X888: $i] :
( ( in @ X888 @ ( cartprod @ X886 @ X887 ) )
=> ? [X889: $i] :
( ( in @ X889 @ X886 )
& ? [X890: $i] :
( ( in @ X890 @ X887 )
& ( X888
= ( kpair @ X889 @ X890 ) ) ) ) )
=> ( ! [X891: $i,X892: $i,X893: $i] :
( ( in @ X893 @ ( cartprod @ X891 @ X892 ) )
=> ( iskpair @ X893 ) )
=> ( ! [X894: $i,X895: $i] :
( ( in @ X895 @ ( setunion @ X894 ) )
=> ? [X896: $i] :
( ( in @ X896 @ X894 )
& ( in @ X895 @ X896 ) ) )
=> ( ! [X897: $i] : ( subset @ ( setunion @ ( setadjoin @ X897 @ emptyset ) ) @ X897 )
=> ( ! [X898: $i] : ( subset @ X898 @ ( setunion @ ( setadjoin @ X898 @ emptyset ) ) )
=> ( ! [X899: $i] :
( ( setunion @ ( setadjoin @ X899 @ emptyset ) )
= X899 )
=> ( ! [X900: $i,X901: $i > $o] :
( ! [X902: $i] :
( ( in @ X902 @ X900 )
=> ! [X903: $i] :
( ( in @ X903 @ X900 )
=> ( ( X901 @ X902 )
=> ( ( X901 @ X903 )
=> ( X902 = X903 ) ) ) ) )
=> ( ? [X904: $i] :
( ( in @ X904 @ X900 )
& ( X901 @ X904 ) )
=> ( singleton @ ( dsetconstr @ X900 @ X901 ) ) ) )
=> ( ! [X905: $i,X906: $i > $o] :
( ( ex1 @ X905 @ X906 )
=> ? [X907: $i] :
( ( in @ X907 @ X905 )
& ( X906 @ X907 ) ) )
=> ( ! [X908: $i,X909: $i > $o,X910: $i] :
( ( in @ X910 @ X908 )
=> ( ( X909 @ X910 )
=> ( ! [X911: $i] :
( ( in @ X911 @ X908 )
=> ( ( X909 @ X911 )
=> ( X911 = X910 ) ) )
=> ( ex1 @ X908 @ X909 ) ) ) )
=> ( ! [X912: $i,X913: $i > $o] :
( ! [X914: $i] :
( ( in @ X914 @ X912 )
=> ! [X915: $i] :
( ( in @ X915 @ X912 )
=> ( ( X913 @ X914 )
=> ( ( X913 @ X915 )
=> ( X914 = X915 ) ) ) ) )
=> ( ? [X916: $i] :
( ( in @ X916 @ X912 )
& ( X913 @ X916 ) )
=> ( ex1 @ X912 @ X913 ) ) )
=> ( ! [X917: $i,X918: $i] :
( ( ( setadjoin @ X917 @ emptyset )
= ( setadjoin @ X918 @ emptyset ) )
=> ( X917 = X918 ) )
=> ( ! [X919: $i,X920: $i,X921: $i] :
( ( in @ ( setadjoin @ X921 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X919 @ ( setadjoin @ X920 @ emptyset ) ) @ emptyset ) ) )
=> ( X919 = X921 ) )
=> ( ! [X922: $i] :
( ( iskpair @ X922 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X922 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X922 ) ) ) )
=> ( ! [X923: $i] :
( ( singleton @ X923 )
=> ( in @ ( setunion @ X923 ) @ X923 ) )
=> ( ! [X924: $i,X925: $i] :
( ( kfst @ ( kpair @ X924 @ X925 ) )
= X924 )
=> ( ! [X926: $i,X927: $i,X928: $i] :
( ( in @ X928 @ ( cartprod @ X926 @ X927 ) )
=> ( in @ ( kfst @ X928 ) @ X926 ) )
=> ( ! [X929: $i,X930: $i,X931: $i,X932: $i] :
( ( ( setadjoin @ ( setadjoin @ X929 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X929 @ ( setadjoin @ X930 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X931 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X931 @ ( setadjoin @ X932 @ emptyset ) ) @ emptyset ) ) )
=> ( X929 = X931 ) )
=> ( ! [X933: $i,X934: $i,X935: $i,X936: $i] :
( ( ( kpair @ X933 @ X934 )
= ( kpair @ X935 @ X936 ) )
=> ( X933 = X935 ) )
=> ( ! [X937: $i,X938: $i] :
( ( X937 = X938 )
=> ( ( setadjoin @ X937 @ ( setadjoin @ X938 @ emptyset ) )
= ( setadjoin @ X937 @ emptyset ) ) )
=> ( ! [X939: $i,X940: $i] :
( ( X939 = X940 )
=> ( ( setadjoin @ ( setadjoin @ X939 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X939 @ ( setadjoin @ X940 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X939 @ emptyset ) @ emptyset ) ) )
=> ( ! [X941: $i,X942: $i,X943: $i,X944: $i] :
( ( ( setadjoin @ ( setadjoin @ X941 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X941 @ ( setadjoin @ X942 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X943 @ ( setadjoin @ X944 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X943 = X944 )
=> ( X942 = X944 ) ) )
=> ( ! [X945: $i,X946: $i,X947: $i] :
( ( ( setadjoin @ X945 @ ( setadjoin @ X946 @ emptyset ) )
= ( setadjoin @ X947 @ emptyset ) )
=> ( X945 = X946 ) )
=> ( ! [X948: $i,X949: $i,X950: $i,X951: $i] :
( ( ( setadjoin @ ( setadjoin @ X948 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X948 @ ( setadjoin @ X949 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X950 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X950 @ ( setadjoin @ X951 @ emptyset ) ) @ emptyset ) ) )
=> ( X949 = X951 ) )
=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[setukpairinjR]),c_0_171]),setukpairinjR2]),setukpairIL]),upairsetIR]),setukpairIR]),kpairiskpair]),kpairp]),c_0_172]),singletonsubset]),singletoninpowerset]),vacuousDall]),singletoninpowunion]),upairset2E]),quantDeMorgan1]),upairsubunion]),upairinpowunion]),quantDeMorgan2]),ubforcartprodlem1]),ubforcartprodlem2]),quantDeMorgan3]),ubforcartprodlem3]),cartprodpairin]),quantDeMorgan4]),cartprodmempair1]),prop2setI]),cartprodmempair]),setunionE2]),setunionsingleton1]),notdexE]),setunionsingleton2]),setunionsingleton]),c_0_173]),notdallE]),subsetI2]),c_0_174]),c_0_175]),c_0_176]),singletonsuniq]),setukpairinjL1]),c_0_177]),c_0_178]),theprop]),c_0_179]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),inCongP]),setukpairinjR11]),setukpairinjR12]),in__Cong]),setukpairinjR1]),upairequniteq]),c_0_180]),c_0_181]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_182]),c_0_183]),c_0_184]),subsetI1]),eqimpsubset2]),eqimpsubset1]),binintersectSubset4]),binintersectSubset1]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_185]),c_0_186]),binunionIL]),upairset2IR]),binunionIR]),singletonsswitch]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),upairsetE]),upairsetIL]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_187]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_188]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_189]),nonemptyE1]),c_0_190]),noeltsimpempty]),emptyI]),setext]),c_0_191]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_192]),c_0_193]),c_0_194]),c_0_195]),c_0_196]),wellorderingAx]),foundationAx]),c_0_197]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_198]) ).
thf(c_0_200,plain,
! [X952: $i,X953: $i] :
( ( kpair @ X952 @ X953 )
= ( setadjoin @ ( setadjoin @ X952 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X952 @ ( setadjoin @ X953 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_201,negated_conjecture,
! [X954: $i,X955: $i,X957: $i,X958: $i,X959: $i,X960: $i,X961: $i,X962: $i,X963: $i,X964: $i,X965: $i,X967: $i,X968: $i,X970: $i,X971: $i,X972: $i,X973: $i,X974: $i,X976: $i,X977: $i > $i > $o,X978: $i,X981: $i,X983: $i,X984: $i,X985: $i,X986: $i,X988: $i,X989: $i > $o,X990: $i,X991: $i > $o,X992: $i,X993: $i,X994: $i > $o,X995: $i,X996: $i,X997: $i > $o,X998: $i,X999: $i > $o,X1001: $i,X1002: $o,X1003: $i,X1004: $i,X1005: $o,X1006: $i,X1007: $i,X1008: $i > $o,X1010: $i,X1011: $i,X1014: $i,X1016: $i,X1018: $i,X1019: $i > $o,X1020: $i,X1021: $i,X1023: $i,X1024: $i > $o,X1025: $i,X1026: $i,X1027: $i,X1028: $i,X1029: $i,X1030: $i,X1031: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $o,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1041: $i,X1042: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $i,X1053: $i,X1054: $o,X1056: $i,X1057: $i,X1058: $i > $o,X1060: $i,X1061: $i,X1062: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $i,X1071: $i,X1072: $i,X1073: $i,X1074: $i,X1075: $i,X1076: $i,X1077: $i,X1078: $i,X1079: $i,X1080: $i > $o,X1081: $i,X1082: $i > $o,X1083: $i,X1084: $i,X1085: $i > $o,X1086: $i,X1088: $i,X1089: $i > $o,X1091: $i,X1092: $i,X1093: $i > $o,X1095: $i,X1096: $i,X1097: $i > $o,X1098: $i,X1100: $o,X1101: $i,X1102: $i > $o,X1104: $i,X1105: $i,X1106: $i > $o,X1107: $i,X1109: $i > $o,X1110: $i,X1112: $i > $o,X1113: $i,X1116: $i > $o,X1117: $i,X1119: $i,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1126: $i,X1127: $i > $o,X1128: $i,X1129: $i,X1130: $i > $o,X1131: $i > $o,X1134: $i,X1135: $i,X1136: $i,X1137: $i,X1138: $i,X1139: $i,X1140: $i,X1141: $i,X1142: $i > $o,X1143: $i,X1144: $i,X1145: $i > $o,X1146: $i > $o,X1149: $i,X1150: $i,X1151: $i > $o,X1152: $i > $o,X1155: $i,X1156: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1165: $i,X1166: $i,X1167: $i,X1168: $i,X1169: $i,X1170: $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 > $o,X1203: $i,X1204: $i > $o,X1205: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $o,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,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,X1270: $i,X1271: $i,X1272: $i,X1273: $i,X1274: $i,X1275: $i,X1276: $i,X1277: $i,X1278: $i,X1279: $i,X1280: $i,X1281: $i,X1282: $i,X1283: $i,X1284: $o,X1285: $i,X1286: $i,X1287: $i,X1288: $i,X1289: $i,X1290: $i,X1291: $i,X1292: $i,X1293: $i,X1294: $i,X1295: $i,X1296: $i,X1297: $i,X1298: $i,X1299: $i,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i,X1305: $i,X1306: $i,X1307: $i,X1308: $i,X1309: $i,X1310: $i,X1311: $i,X1312: $i,X1313: $i,X1314: $i,X1315: $i,X1316: $i,X1317: $i,X1318: $i,X1319: $i,X1320: $i,X1321: $i,X1322: $i,X1323: $i,X1324: $i,X1325: $i,X1326: $i,X1327: $i,X1328: $i,X1329: $i,X1330: $i,X1331: $i,X1332: $i,X1333: $i,X1334: $i,X1335: $i,X1336: $i,X1337: $i,X1338: $i,X1339: $i,X1340: $i,X1341: $i,X1342: $i,X1343: $i,X1346: $i,X1347: $i,X1348: $i,X1349: $i,X1350: $i,X1352: $i,X1353: $i,X1354: $i,X1355: $i,X1356: $i > $o,X1359: $i,X1360: $i,X1361: $i > $o,X1363: $i,X1364: $i > $o,X1365: $i,X1367: $i,X1368: $i > $o,X1371: $i,X1372: $i,X1373: $i,X1374: $i,X1375: $i,X1376: $i,X1377: $i,X1378: $i,X1379: $i,X1380: $i,X1381: $i,X1382: $i,X1383: $i,X1384: $i,X1385: $i,X1386: $i,X1387: $i,X1388: $i,X1389: $i,X1390: $i,X1391: $i,X1392: $i,X1393: $i,X1394: $i,X1395: $i,X1396: $i,X1397: $i,X1398: $i,X1399: $i,X1400: $i,X1401: $i,X1402: $i,X1403: $i,X1404: $i,X1405: $i,X1406: $i] :
( ( ~ ( in @ ( esk1_2 @ X954 @ X955 ) @ X954 )
| ~ ( in @ ( esk1_2 @ X954 @ X955 ) @ X955 )
| ( X954 = X955 ) )
& ( ( in @ ( esk1_2 @ X954 @ X955 ) @ X954 )
| ( in @ ( esk1_2 @ X954 @ X955 ) @ X955 )
| ( X954 = X955 ) )
& ~ ( in @ X957 @ emptyset )
& ( ~ ( in @ X960 @ ( setadjoin @ X958 @ X959 ) )
| ( X960 = X958 )
| ( in @ X960 @ X959 ) )
& ( ( X960 != X958 )
| ( in @ X960 @ ( setadjoin @ X958 @ X959 ) ) )
& ( ~ ( in @ X960 @ X959 )
| ( in @ X960 @ ( setadjoin @ X958 @ X959 ) ) )
& ( ~ ( in @ X962 @ ( powerset @ X961 ) )
| ~ ( in @ X963 @ X962 )
| ( in @ X963 @ X961 ) )
& ( ( in @ ( esk2_2 @ X964 @ X965 ) @ X965 )
| ( in @ X965 @ ( powerset @ X964 ) ) )
& ( ~ ( in @ ( esk2_2 @ X964 @ X965 ) @ X964 )
| ( in @ X965 @ ( powerset @ X964 ) ) )
& ( ( in @ X968 @ ( esk3_2 @ X967 @ X968 ) )
| ~ ( in @ X968 @ ( setunion @ X967 ) ) )
& ( ( in @ ( esk3_2 @ X967 @ X968 ) @ X967 )
| ~ ( in @ X968 @ ( setunion @ X967 ) ) )
& ( ~ ( in @ X971 @ X972 )
| ~ ( in @ X972 @ X970 )
| ( in @ X971 @ ( setunion @ X970 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X973 @ omega )
| ( in @ ( setadjoin @ X973 @ X973 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X974 ) @ omega )
| ~ ( in @ emptyset @ X974 )
| ~ ( in @ X976 @ omega )
| ( in @ X976 @ X974 ) )
& ( ( in @ ( esk4_1 @ X974 ) @ X974 )
| ~ ( in @ emptyset @ X974 )
| ~ ( in @ X976 @ omega )
| ( in @ X976 @ X974 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X974 ) @ ( esk4_1 @ X974 ) ) @ X974 )
| ~ ( in @ emptyset @ X974 )
| ~ ( in @ X976 @ omega )
| ( in @ X976 @ X974 ) )
& ( ( in @ ( esk7_3 @ X977 @ X978 @ X981 ) @ X978 )
| ~ ( in @ X981 @ ( esk6_2 @ X977 @ X978 ) )
| ( in @ ( esk5_2 @ X977 @ X978 ) @ X978 ) )
& ( ( X977 @ ( esk7_3 @ X977 @ X978 @ X981 ) @ X981 )
| ~ ( in @ X981 @ ( esk6_2 @ X977 @ X978 ) )
| ( in @ ( esk5_2 @ X977 @ X978 ) @ X978 ) )
& ( ~ ( in @ X984 @ X978 )
| ~ ( X977 @ X984 @ X983 )
| ( in @ X983 @ ( esk6_2 @ X977 @ X978 ) )
| ( in @ ( esk5_2 @ X977 @ X978 ) @ X978 ) )
& ( ( in @ ( esk7_3 @ X977 @ X978 @ X981 ) @ X978 )
| ~ ( in @ X981 @ ( esk6_2 @ X977 @ X978 ) )
| ~ ( exu @ ( X977 @ ( esk5_2 @ X977 @ X978 ) ) ) )
& ( ( X977 @ ( esk7_3 @ X977 @ X978 @ X981 ) @ X981 )
| ~ ( in @ X981 @ ( esk6_2 @ X977 @ X978 ) )
| ~ ( exu @ ( X977 @ ( esk5_2 @ X977 @ X978 ) ) ) )
& ( ~ ( in @ X984 @ X978 )
| ~ ( X977 @ X984 @ X983 )
| ( in @ X983 @ ( esk6_2 @ X977 @ X978 ) )
| ~ ( exu @ ( X977 @ ( esk5_2 @ X977 @ X978 ) ) ) )
& ( ( in @ ( esk8_1 @ X985 ) @ X985 )
| ~ ( in @ X986 @ X985 ) )
& ( ~ ( in @ X988 @ ( esk8_1 @ X985 ) )
| ~ ( in @ X988 @ X985 )
| ~ ( in @ X986 @ X985 ) )
& epred1_0
& ( ~ ( exu @ X989 )
| ( X989 @ ( descr @ X989 ) ) )
& ( ~ ( in @ X992 @ X990 )
| ~ ( X991 @ X992 )
| ( in @ X992 @ ( dsetconstr @ X990 @ X991 ) ) )
& ( ~ ( in @ X995 @ ( dsetconstr @ X993 @ X994 ) )
| ( in @ X995 @ X993 ) )
& ( ~ ( in @ X998 @ ( dsetconstr @ X996 @ X997 ) )
| ( X997 @ X998 ) )
& ( ( X999 @ ( esk9_1 @ X999 ) )
| ~ ( exu @ X999 ) )
& ( ~ ( X999 @ X1001 )
| ( ( esk9_1 @ X999 )
= X1001 )
| ~ ( exu @ X999 ) )
& ( ~ ( in @ X1003 @ ( prop2set @ X1002 ) )
| X1002 )
& ( ~ ( in @ X1004 @ emptyset )
| X1005 )
& ( ~ ( in @ X1006 @ emptyset )
| ~ $true )
& ~ ( in @ X1007 @ emptyset )
& ( ~ ( exu @ X1008 )
| ( X1008 @ ( esk10_1 @ X1008 ) ) )
& ( ( in @ ( esk12_2 @ X1010 @ X1011 ) @ X1011 )
| ( X1010 = X1011 )
| ( in @ ( esk11_2 @ X1010 @ X1011 ) @ X1010 ) )
& ( ~ ( in @ ( esk12_2 @ X1010 @ X1011 ) @ X1010 )
| ( X1010 = X1011 )
| ( in @ ( esk11_2 @ X1010 @ X1011 ) @ X1010 ) )
& ( ( in @ ( esk12_2 @ X1010 @ X1011 ) @ X1011 )
| ( X1010 = X1011 )
| ~ ( in @ ( esk11_2 @ X1010 @ X1011 ) @ X1011 ) )
& ( ~ ( in @ ( esk12_2 @ X1010 @ X1011 ) @ X1010 )
| ( X1010 = X1011 )
| ~ ( in @ ( esk11_2 @ X1010 @ X1011 ) @ X1011 ) )
& ( ( in @ ( esk13_1 @ X1014 ) @ X1014 )
| ( X1014 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1016 ) @ X1016 )
| ( X1016 = emptyset ) )
& ( ~ ( in @ X1020 @ ( dsetconstr @ X1018 @ X1019 ) )
| ( X1019 @ X1020 )
| ~ ( in @ X1020 @ X1018 ) )
& ( ~ ( X1019 @ X1020 )
| ( in @ X1020 @ ( dsetconstr @ X1018 @ X1019 ) )
| ~ ( in @ X1020 @ X1018 ) )
& ( ~ ( nonempty @ X1021 )
| ( in @ ( esk15_1 @ X1021 ) @ X1021 ) )
& ( ~ ( in @ X1025 @ X1023 )
| ~ ( X1024 @ X1025 )
| ( nonempty @ ( dsetconstr @ X1023 @ X1024 ) ) )
& ( ~ ( in @ X1027 @ X1026 )
| ( nonempty @ X1026 ) )
& ( in @ X1028 @ ( setadjoin @ X1028 @ X1029 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1032 @ X1031 )
| ( in @ X1032 @ ( setadjoin @ X1030 @ X1031 ) ) )
& ( ( in @ X1035 @ X1034 )
| X1036
| ( X1035 = X1033 )
| ~ ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ~ X1036
| X1036
| ( X1035 = X1033 )
| ~ ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ( in @ X1035 @ X1034 )
| X1036
| ~ X1036
| ~ ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ~ X1036
| X1036
| ~ X1036
| ~ ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ~ ( in @ X1039 @ ( setadjoin @ X1037 @ X1038 ) )
| ( X1039 = X1037 )
| ( in @ X1039 @ X1038 ) )
& ( ( dsetconstr @ X1040
@ ^ [Z0: $i] : $true )
= X1040 )
& ( ( in @ ( esk16_2 @ X1041 @ X1042 ) @ X1042 )
| ( in @ X1042 @ ( powerset @ X1041 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1041 @ X1042 ) @ X1041 )
| ( in @ X1042 @ ( powerset @ X1041 ) ) )
& ( in @ emptyset @ ( powerset @ X1044 ) )
& ( in @ emptyset @ ( powerset @ X1045 ) )
& ( ~ ( in @ X1047 @ ( powerset @ X1046 ) )
| ~ ( in @ X1048 @ X1047 )
| ( in @ X1048 @ X1046 ) )
& ( ~ ( in @ X1050 @ X1051 )
| ~ ( in @ X1051 @ X1049 )
| ( in @ X1050 @ ( setunion @ X1049 ) ) )
& ( ( in @ X1053 @ ( esk17_3 @ X1052 @ X1053 @ X1054 ) )
| X1054
| ~ ( in @ X1053 @ ( setunion @ X1052 ) ) )
& ( ( in @ ( esk17_3 @ X1052 @ X1053 @ X1054 ) @ X1052 )
| X1054
| ~ ( in @ X1053 @ ( setunion @ X1052 ) ) )
& ( ~ X1054
| X1054
| ~ ( in @ X1053 @ ( setunion @ X1052 ) ) )
& ( ~ ( in @ X1057 @ X1056 )
| ( in @ X1057 @ ( powerset @ ( setunion @ X1056 ) ) ) )
& ( ~ ( X1058 @ X1060 )
| ( X1060
= ( esk18_1 @ X1058 ) )
| ~ ( exu @ X1058 ) )
& ( ( X1061
!= ( esk18_1 @ X1058 ) )
| ( X1058 @ X1061 )
| ~ ( exu @ X1058 ) )
& ( ( in @ ( esk19_1 @ X1062 ) @ X1062 )
| ~ ( nonempty @ X1062 ) )
& ( $true
| ~ ( nonempty @ X1062 ) )
& ( ~ ( in @ X1064 @ ( setadjoin @ X1065 @ emptyset ) )
| ( X1064 = X1065 ) )
& ( ( X1066 = X1067 )
| ~ ( in @ X1067 @ ( setadjoin @ X1066 @ emptyset ) ) )
& ( ( X1068 != X1069 )
| ( in @ X1068 @ ( setadjoin @ X1069 @ emptyset ) ) )
& ( ~ ( in @ X1070 @ ( setadjoin @ X1071 @ emptyset ) )
| ( in @ X1071 @ ( setadjoin @ X1070 @ emptyset ) ) )
& ( ~ ( in @ X1074 @ ( setadjoin @ X1072 @ ( setadjoin @ X1073 @ emptyset ) ) )
| ( X1074 = X1072 )
| ( X1074 = X1073 ) )
& ( in @ X1075 @ ( setadjoin @ X1075 @ ( setadjoin @ X1076 @ emptyset ) ) )
& ( in @ X1078 @ ( setadjoin @ X1077 @ ( setadjoin @ X1078 @ emptyset ) ) )
& ( ~ ( in @ X1081 @ X1079 )
| ~ ( X1080 @ X1081 )
| ( ( dsetconstr @ X1079 @ X1080 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1083 @ emptyset )
| ( X1082 @ X1083 ) )
& ( ( in @ ( esk20_2 @ X1084 @ X1085 ) @ X1084 )
| ~ ( in @ X1086 @ X1084 )
| ( X1085 @ X1086 ) )
& ( ~ ( X1085 @ ( esk20_2 @ X1084 @ X1085 ) )
| ~ ( in @ X1086 @ X1084 )
| ( X1085 @ X1086 ) )
& ( ( in @ ( esk21_2 @ X1088 @ X1089 ) @ X1088 )
| ~ ( in @ X1091 @ X1088 )
| ~ ( X1089 @ X1091 ) )
& ( ( X1089 @ ( esk21_2 @ X1088 @ X1089 ) )
| ~ ( in @ X1091 @ X1088 )
| ~ ( X1089 @ X1091 ) )
& ( ( in @ ( esk22_2 @ X1092 @ X1093 ) @ X1092 )
| ~ ( in @ X1095 @ X1092 )
| ~ ( X1093 @ X1095 ) )
& ( ( X1093 @ ( esk22_2 @ X1092 @ X1093 ) )
| ~ ( in @ X1095 @ X1092 )
| ~ ( X1093 @ X1095 ) )
& ( ( in @ ( esk23_2 @ X1096 @ X1097 ) @ X1096 )
| ~ ( in @ X1098 @ X1096 )
| ( X1097 @ X1098 ) )
& ( ~ ( X1097 @ ( esk23_2 @ X1096 @ X1097 ) )
| ~ ( in @ X1098 @ X1096 )
| ( X1097 @ X1098 ) )
& ( ~ X1100
| ( in @ emptyset @ ( prop2set @ X1100 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1101 @ X1102 ) @ X1101 )
| ~ ( in @ X1104 @ X1101 )
| ~ ( X1102 @ X1104 ) )
& ( ( X1102 @ ( esk24_2 @ X1101 @ X1102 ) )
| ~ ( in @ X1104 @ X1101 )
| ~ ( X1102 @ X1104 ) )
& ( ( in @ ( esk25_2 @ X1105 @ X1106 ) @ X1105 )
| ~ ( in @ X1107 @ X1105 )
| ( X1106 @ X1107 ) )
& ( ~ ( X1106 @ ( esk25_2 @ X1105 @ X1106 ) )
| ~ ( in @ X1107 @ X1105 )
| ( X1106 @ X1107 ) )
& ( ( X1109 @ ( esk26_2 @ X1109 @ X1110 ) )
| ~ ( X1109 @ X1110 )
| ( exu @ X1109 ) )
& ( ( X1110
!= ( esk26_2 @ X1109 @ X1110 ) )
| ~ ( X1109 @ X1110 )
| ( exu @ X1109 ) )
& ( ( X1112 @ ( esk27_1 @ X1112 ) )
| ( exu @ X1112 )
| ~ ( X1112 @ X1113 ) )
& ( ( X1112 @ ( esk28_1 @ X1112 ) )
| ( exu @ X1112 )
| ~ ( X1112 @ X1113 ) )
& ( ( ( esk27_1 @ X1112 )
!= ( esk28_1 @ X1112 ) )
| ( exu @ X1112 )
| ~ ( X1112 @ X1113 ) )
& ( ~ ( X1116 @ ( esk29_2 @ X1116 @ X1117 ) )
| ( ( esk29_2 @ X1116 @ X1117 )
!= X1117 )
| ( exu @ X1116 ) )
& ( ( X1116 @ ( esk29_2 @ X1116 @ X1117 ) )
| ( ( esk29_2 @ X1116 @ X1117 )
= X1117 )
| ( exu @ X1116 ) )
& ( ( X1119 != X1120 )
| ( X1121 != X1122 )
| ~ ( in @ X1121 @ X1119 )
| ( in @ X1122 @ X1120 ) )
& ( ~ ( in @ X1125 @ X1123 )
| ( in @ X1126 @ X1124 )
| ( X1125 != X1126 )
| ( X1123 != X1124 ) )
& ( ~ ( in @ X1126 @ X1124 )
| ( in @ X1125 @ X1123 )
| ( X1125 != X1126 )
| ( X1123 != X1124 ) )
& ( ~ ( exu @ X1127 )
| ~ ( X1127 @ X1128 )
| ~ ( X1127 @ X1129 )
| ( X1128 = X1129 ) )
& ( ~ ( exu @ X1130 )
| ( exu @ X1131 )
| ( ( esk30_2 @ X1130 @ X1131 )
= ( esk31_2 @ X1130 @ X1131 ) ) )
& ( ~ ( exu @ X1131 )
| ( exu @ X1130 )
| ( ( esk30_2 @ X1130 @ X1131 )
= ( esk31_2 @ X1130 @ X1131 ) ) )
& ( ~ ( exu @ X1130 )
| ( exu @ X1131 )
| ~ ( X1130 @ ( esk30_2 @ X1130 @ X1131 ) )
| ~ ( X1131 @ ( esk31_2 @ X1130 @ X1131 ) ) )
& ( ~ ( exu @ X1131 )
| ( exu @ X1130 )
| ~ ( X1130 @ ( esk30_2 @ X1130 @ X1131 ) )
| ~ ( X1131 @ ( esk31_2 @ X1130 @ X1131 ) ) )
& ( ~ ( exu @ X1130 )
| ( exu @ X1131 )
| ( X1130 @ ( esk30_2 @ X1130 @ X1131 ) )
| ( X1131 @ ( esk31_2 @ X1130 @ X1131 ) ) )
& ( ~ ( exu @ X1131 )
| ( exu @ X1130 )
| ( X1130 @ ( esk30_2 @ X1130 @ X1131 ) )
| ( X1131 @ ( esk31_2 @ X1130 @ X1131 ) ) )
& ( emptyset = emptyset )
& ( ( X1134 != X1135 )
| ( X1136 != X1137 )
| ( ( setadjoin @ X1134 @ X1136 )
= ( setadjoin @ X1135 @ X1137 ) ) )
& ( ( X1138 != X1139 )
| ( ( powerset @ X1138 )
= ( powerset @ X1139 ) ) )
& ( ( X1140 != X1141 )
| ( ( setunion @ X1140 )
= ( setunion @ X1141 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1142 )
| ~ ( X1142 @ X1143 )
| ~ ( X1142 @ X1144 )
| ( X1143 = X1144 ) )
& ( ( ( esk32_2 @ X1145 @ X1146 )
= ( esk33_2 @ X1145 @ X1146 ) )
| ~ ( exu @ X1145 )
| ~ ( exu @ X1146 )
| ( ( descr @ X1145 )
= ( descr @ X1146 ) ) )
& ( ~ ( X1145 @ ( esk32_2 @ X1145 @ X1146 ) )
| ~ ( X1146 @ ( esk33_2 @ X1145 @ X1146 ) )
| ~ ( exu @ X1145 )
| ~ ( exu @ X1146 )
| ( ( descr @ X1145 )
= ( descr @ X1146 ) ) )
& ( ( X1145 @ ( esk32_2 @ X1145 @ X1146 ) )
| ( X1146 @ ( esk33_2 @ X1145 @ X1146 ) )
| ~ ( exu @ X1145 )
| ~ ( exu @ X1146 )
| ( ( descr @ X1145 )
= ( descr @ X1146 ) ) )
& ( ( in @ ( esk34_4 @ X1149 @ X1150 @ X1151 @ X1152 ) @ X1149 )
| ( ( dsetconstr @ X1149 @ X1151 )
= ( dsetconstr @ X1150 @ X1152 ) )
| ( X1149 != X1150 ) )
& ( ( in @ ( esk35_4 @ X1149 @ X1150 @ X1151 @ X1152 ) @ X1150 )
| ( ( dsetconstr @ X1149 @ X1151 )
= ( dsetconstr @ X1150 @ X1152 ) )
| ( X1149 != X1150 ) )
& ( ( ( esk34_4 @ X1149 @ X1150 @ X1151 @ X1152 )
= ( esk35_4 @ X1149 @ X1150 @ X1151 @ X1152 ) )
| ( ( dsetconstr @ X1149 @ X1151 )
= ( dsetconstr @ X1150 @ X1152 ) )
| ( X1149 != X1150 ) )
& ( ~ ( X1151 @ ( esk34_4 @ X1149 @ X1150 @ X1151 @ X1152 ) )
| ~ ( X1152 @ ( esk35_4 @ X1149 @ X1150 @ X1151 @ X1152 ) )
| ( ( dsetconstr @ X1149 @ X1151 )
= ( dsetconstr @ X1150 @ X1152 ) )
| ( X1149 != X1150 ) )
& ( ( X1151 @ ( esk34_4 @ X1149 @ X1150 @ X1151 @ X1152 ) )
| ( X1152 @ ( esk35_4 @ X1149 @ X1150 @ X1151 @ X1152 ) )
| ( ( dsetconstr @ X1149 @ X1151 )
= ( dsetconstr @ X1150 @ X1152 ) )
| ( X1149 != X1150 ) )
& ( ( in @ ( esk36_2 @ X1155 @ X1156 ) @ X1155 )
| ( subset @ X1155 @ X1156 ) )
& ( ~ ( in @ ( esk36_2 @ X1155 @ X1156 ) @ X1156 )
| ( subset @ X1155 @ X1156 ) )
& ( ( X1158 != X1159 )
| ( subset @ X1159 @ X1158 ) )
& ( ( X1160 != X1161 )
| ( subset @ X1160 @ X1161 ) )
& ( ( in @ ( esk37_2 @ X1162 @ X1163 ) @ X1162 )
| ( subset @ X1162 @ X1163 ) )
& ( ~ ( in @ ( esk37_2 @ X1162 @ X1163 ) @ X1163 )
| ( subset @ X1162 @ X1163 ) )
& ( subset @ emptyset @ X1165 )
& ( ~ ( subset @ X1166 @ X1167 )
| ~ ( in @ X1168 @ X1166 )
| ( in @ X1168 @ X1167 ) )
& ( ~ ( subset @ X1169 @ X1170 )
| ( in @ X1171 @ X1170 )
| ~ ( in @ X1171 @ X1169 ) )
& ( ~ ( in @ X1174 @ X1172 )
| ( in @ X1174 @ X1173 )
| ~ ( subset @ X1172 @ X1173 ) )
& ( ( subset @ X1175 @ X1176 )
| ( X1175 != X1176 ) )
& ( ~ ( in @ X1179 @ X1177 )
| ( in @ X1179 @ X1178 )
| ( X1177 != X1178 ) )
& ( subset @ X1180 @ X1180 )
& ( ~ ( subset @ X1181 @ X1182 )
| ~ ( subset @ X1182 @ X1183 )
| ( subset @ X1181 @ X1183 ) )
& ( subset @ X1185 @ ( setadjoin @ X1184 @ X1185 ) )
& ( ~ ( subset @ X1186 @ X1188 )
| ( subset @ X1186 @ ( setadjoin @ X1187 @ X1188 ) ) )
& ( ~ ( subset @ X1189 @ X1190 )
| ( in @ X1189 @ ( powerset @ X1190 ) ) )
& ( ~ ( subset @ X1191 @ X1192 )
| ~ ( subset @ X1192 @ X1191 )
| ( X1191 = X1192 ) )
& ( ~ ( subset @ X1193 @ emptyset )
| ( X1193 = emptyset ) )
& ( ~ ( subset @ X1195 @ X1194 )
| ( in @ X1195 @ ( powerset @ X1194 ) ) )
& ( ~ ( in @ X1197 @ ( powerset @ X1196 ) )
| ( subset @ X1197 @ X1196 ) )
& ( in @ X1198 @ ( powerset @ X1198 ) )
& ( ~ ( subset @ X1199 @ X1200 )
| ( subset @ ( powerset @ X1199 ) @ ( powerset @ X1200 ) ) )
& ( in @ ( dsetconstr @ X1201 @ X1202 ) @ ( powerset @ X1201 ) )
& ( subset @ ( dsetconstr @ X1203 @ X1204 ) @ X1203 )
& ( ~ ( in @ X1207 @ X1205 )
| ( in @ X1207 @ ( binunion @ X1205 @ X1206 ) ) )
& ( in @ X1209 @ ( setadjoin @ X1208 @ ( setadjoin @ X1209 @ emptyset ) ) )
& ( ~ ( in @ X1212 @ X1211 )
| ( in @ X1212 @ ( binunion @ X1210 @ X1211 ) ) )
& ( ( in @ X1215 @ X1214 )
| X1216
| ( in @ X1215 @ X1213 )
| ~ ( in @ X1215 @ ( binunion @ X1213 @ X1214 ) ) )
& ( ~ X1216
| X1216
| ( in @ X1215 @ X1213 )
| ~ ( in @ X1215 @ ( binunion @ X1213 @ X1214 ) ) )
& ( ( in @ X1215 @ X1214 )
| X1216
| ~ X1216
| ~ ( in @ X1215 @ ( binunion @ X1213 @ X1214 ) ) )
& ( ~ X1216
| X1216
| ~ X1216
| ~ ( in @ X1215 @ ( binunion @ X1213 @ X1214 ) ) )
& ( ~ ( in @ X1219 @ ( binunion @ X1217 @ X1218 ) )
| ( in @ X1219 @ X1217 )
| ( in @ X1219 @ X1218 ) )
& ( subset @ X1220 @ ( binunion @ X1220 @ X1221 ) )
& ( subset @ X1223 @ ( binunion @ X1222 @ X1223 ) )
& ( ~ ( in @ X1226 @ X1224 )
| ~ ( in @ X1226 @ X1225 )
| ( in @ X1226 @ ( binintersect @ X1224 @ X1225 ) ) )
& ( ~ ( subset @ X1229 @ X1227 )
| ~ ( subset @ X1229 @ X1228 )
| ( subset @ X1229 @ ( binintersect @ X1227 @ X1228 ) ) )
& ( ~ ( in @ X1232 @ ( binintersect @ X1230 @ X1231 ) )
| ( in @ X1232 @ X1230 ) )
& ( subset @ ( binintersect @ X1233 @ X1234 ) @ X1233 )
& ( ~ ( subset @ X1235 @ X1236 )
| ( ( binintersect @ X1235 @ X1236 )
= X1235 ) )
& ( ( ( binintersect @ X1237 @ X1238 )
!= X1238 )
| ( subset @ X1238 @ X1237 ) )
& ( ~ ( in @ X1241 @ ( binintersect @ X1239 @ X1240 ) )
| ( in @ X1241 @ X1240 ) )
& ( ( in @ ( esk38_2 @ X1242 @ X1243 ) @ X1242 )
| ( ( binintersect @ X1242 @ X1243 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1242 @ X1243 ) @ X1243 )
| ( ( binintersect @ X1242 @ X1243 )
= emptyset ) )
& ( subset @ ( binintersect @ X1245 @ X1246 ) @ X1246 )
& ( ~ ( subset @ X1248 @ X1247 )
| ( ( binintersect @ X1247 @ X1248 )
= X1248 ) )
& ( ( ( binintersect @ X1249 @ X1250 )
!= X1249 )
| ( subset @ X1249 @ X1250 ) )
& ( ( binintersect @ X1251 @ ( binunion @ X1252 @ X1253 ) )
= ( binunion @ ( binintersect @ X1251 @ X1252 ) @ ( binintersect @ X1251 @ X1253 ) ) )
& ( ~ ( in @ X1256 @ X1254 )
| ( in @ X1256 @ X1255 )
| ( in @ X1256 @ ( setminus @ X1254 @ X1255 ) ) )
& ( ~ ( in @ X1259 @ ( setminus @ X1257 @ X1258 ) )
| ( in @ X1259 @ X1257 ) )
& ( ~ ( in @ X1262 @ ( setminus @ X1260 @ X1261 ) )
| ~ ( in @ X1262 @ X1261 ) )
& ( ~ ( subset @ X1263 @ X1264 )
| ( ( setminus @ X1263 @ X1264 )
= emptyset ) )
& ( ( in @ X1267 @ ( setminus @ X1265 @ X1266 ) )
| ~ ( in @ X1267 @ X1265 )
| ( in @ X1267 @ X1266 ) )
& ( ( in @ X1270 @ ( setminus @ X1268 @ X1269 ) )
| ( in @ X1270 @ X1269 )
| ~ ( in @ X1270 @ X1268 ) )
& ( ( in @ X1273 @ X1271 )
| ~ ( in @ X1273 @ ( setminus @ X1271 @ X1272 ) ) )
& ( ~ ( in @ X1276 @ X1275 )
| ~ ( in @ X1276 @ ( setminus @ X1274 @ X1275 ) ) )
& ( subset @ ( setminus @ X1277 @ X1278 ) @ X1277 )
& ( ( ( setminus @ X1279 @ X1280 )
!= emptyset )
| ( subset @ X1279 @ X1280 ) )
& ( ~ ( in @ X1283 @ X1281 )
| X1284
| ( in @ X1283 @ X1281 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ( in @ X1283 @ X1282 )
| X1284
| ( in @ X1283 @ X1281 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ X1284
| X1284
| ( in @ X1283 @ X1281 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ ( in @ X1283 @ X1281 )
| X1284
| ~ ( in @ X1283 @ X1282 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ( in @ X1283 @ X1282 )
| X1284
| ~ ( in @ X1283 @ X1282 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ X1284
| X1284
| ~ ( in @ X1283 @ X1282 )
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ ( in @ X1283 @ X1281 )
| X1284
| ~ X1284
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ( in @ X1283 @ X1282 )
| X1284
| ~ X1284
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ X1284
| X1284
| ~ X1284
| ~ ( in @ X1283 @ ( symdiff @ X1281 @ X1282 ) ) )
& ( ~ ( in @ X1287 @ X1285 )
| ( in @ X1287 @ X1286 )
| ( in @ X1287 @ ( symdiff @ X1285 @ X1286 ) ) )
& ( ( in @ X1290 @ X1288 )
| ~ ( in @ X1290 @ X1289 )
| ( in @ X1290 @ ( symdiff @ X1288 @ X1289 ) ) )
& ( ~ ( in @ X1293 @ X1291 )
| ~ ( in @ X1293 @ X1292 )
| ~ ( in @ X1293 @ ( symdiff @ X1291 @ X1292 ) ) )
& ( ( in @ X1296 @ X1294 )
| ( in @ X1296 @ X1295 )
| ~ ( in @ X1296 @ ( symdiff @ X1294 @ X1295 ) ) )
& ( in @ X1298 @ ( setadjoin @ X1297 @ ( setadjoin @ X1298 @ emptyset ) ) )
& ( in @ X1299 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1299 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1299 @ ( setadjoin @ X1300 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1302 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1301 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1301 @ ( setadjoin @ X1302 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1303 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1303 @ ( setadjoin @ X1304 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1305 @ X1306 ) )
& ( ~ ( in @ X1308 @ X1307 )
| ( subset @ ( setadjoin @ X1308 @ emptyset ) @ X1307 ) )
& ( ~ ( in @ X1310 @ X1309 )
| ( in @ ( setadjoin @ X1310 @ emptyset ) @ ( powerset @ X1309 ) ) )
& ( ~ ( in @ X1313 @ X1311 )
| ( in @ ( setadjoin @ X1313 @ emptyset ) @ ( powerset @ ( binunion @ X1311 @ X1312 ) ) ) )
& ( ~ ( in @ X1316 @ ( setadjoin @ X1314 @ ( setadjoin @ X1315 @ emptyset ) ) )
| ( X1316 = X1314 )
| ( X1316 = X1315 ) )
& ( ~ ( in @ X1319 @ X1317 )
| ~ ( in @ X1320 @ X1318 )
| ( subset @ ( setadjoin @ X1319 @ ( setadjoin @ X1320 @ emptyset ) ) @ ( binunion @ X1317 @ X1318 ) ) )
& ( ~ ( in @ X1323 @ X1321 )
| ~ ( in @ X1324 @ X1322 )
| ( in @ ( setadjoin @ X1323 @ ( setadjoin @ X1324 @ emptyset ) ) @ ( powerset @ ( binunion @ X1321 @ X1322 ) ) ) )
& ( ~ ( in @ X1327 @ X1325 )
| ~ ( in @ X1328 @ X1326 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1327 @ ( setadjoin @ X1328 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1325 @ X1326 ) ) ) )
& ( ~ ( in @ X1331 @ X1329 )
| ~ ( in @ X1332 @ X1330 )
| ( in @ ( setadjoin @ ( setadjoin @ X1331 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1331 @ ( setadjoin @ X1332 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1329 @ X1330 ) ) ) ) )
& ( ~ ( in @ X1335 @ X1333 )
| ~ ( in @ X1336 @ X1334 )
| ( in @ ( kpair @ X1335 @ X1336 ) @ ( powerset @ ( powerset @ ( binunion @ X1333 @ X1334 ) ) ) ) )
& ( ~ ( in @ X1339 @ X1337 )
| ~ ( in @ X1340 @ X1338 )
| ( in @ ( kpair @ X1339 @ X1340 ) @ ( cartprod @ X1337 @ X1338 ) ) )
& ( ( in @ ( esk39_3 @ X1341 @ X1342 @ X1343 ) @ X1341 )
| ~ ( in @ X1343 @ ( cartprod @ X1341 @ X1342 ) ) )
& ( ( in @ ( esk40_3 @ X1341 @ X1342 @ X1343 ) @ X1342 )
| ~ ( in @ X1343 @ ( cartprod @ X1341 @ X1342 ) ) )
& ( ( X1343
= ( kpair @ ( esk39_3 @ X1341 @ X1342 @ X1343 ) @ ( esk40_3 @ X1341 @ X1342 @ X1343 ) ) )
| ~ ( in @ X1343 @ ( cartprod @ X1341 @ X1342 ) ) )
& ( ~ ( in @ X1348 @ ( cartprod @ X1346 @ X1347 ) )
| ( iskpair @ X1348 ) )
& ( ( in @ ( esk41_2 @ X1349 @ X1350 ) @ X1349 )
| ~ ( in @ X1350 @ ( setunion @ X1349 ) ) )
& ( ( in @ X1350 @ ( esk41_2 @ X1349 @ X1350 ) )
| ~ ( in @ X1350 @ ( setunion @ X1349 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1352 @ emptyset ) ) @ X1352 )
& ( subset @ X1353 @ ( setunion @ ( setadjoin @ X1353 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1354 @ emptyset ) )
= X1354 )
& ( ( in @ ( esk42_2 @ X1355 @ X1356 ) @ X1355 )
| ~ ( in @ X1359 @ X1355 )
| ~ ( X1356 @ X1359 )
| ( singleton @ ( dsetconstr @ X1355 @ X1356 ) ) )
& ( ( in @ ( esk43_2 @ X1355 @ X1356 ) @ X1355 )
| ~ ( in @ X1359 @ X1355 )
| ~ ( X1356 @ X1359 )
| ( singleton @ ( dsetconstr @ X1355 @ X1356 ) ) )
& ( ( X1356 @ ( esk42_2 @ X1355 @ X1356 ) )
| ~ ( in @ X1359 @ X1355 )
| ~ ( X1356 @ X1359 )
| ( singleton @ ( dsetconstr @ X1355 @ X1356 ) ) )
& ( ( X1356 @ ( esk43_2 @ X1355 @ X1356 ) )
| ~ ( in @ X1359 @ X1355 )
| ~ ( X1356 @ X1359 )
| ( singleton @ ( dsetconstr @ X1355 @ X1356 ) ) )
& ( ( ( esk42_2 @ X1355 @ X1356 )
!= ( esk43_2 @ X1355 @ X1356 ) )
| ~ ( in @ X1359 @ X1355 )
| ~ ( X1356 @ X1359 )
| ( singleton @ ( dsetconstr @ X1355 @ X1356 ) ) )
& ( ( in @ ( esk44_2 @ X1360 @ X1361 ) @ X1360 )
| ~ ( ex1 @ X1360 @ X1361 ) )
& ( ( X1361 @ ( esk44_2 @ X1360 @ X1361 ) )
| ~ ( ex1 @ X1360 @ X1361 ) )
& ( ( in @ ( esk45_3 @ X1363 @ X1364 @ X1365 ) @ X1363 )
| ( ex1 @ X1363 @ X1364 )
| ~ ( X1364 @ X1365 )
| ~ ( in @ X1365 @ X1363 ) )
& ( ( X1364 @ ( esk45_3 @ X1363 @ X1364 @ X1365 ) )
| ( ex1 @ X1363 @ X1364 )
| ~ ( X1364 @ X1365 )
| ~ ( in @ X1365 @ X1363 ) )
& ( ( ( esk45_3 @ X1363 @ X1364 @ X1365 )
!= X1365 )
| ( ex1 @ X1363 @ X1364 )
| ~ ( X1364 @ X1365 )
| ~ ( in @ X1365 @ X1363 ) )
& ( ( in @ ( esk46_2 @ X1367 @ X1368 ) @ X1367 )
| ~ ( in @ X1371 @ X1367 )
| ~ ( X1368 @ X1371 )
| ( ex1 @ X1367 @ X1368 ) )
& ( ( in @ ( esk47_2 @ X1367 @ X1368 ) @ X1367 )
| ~ ( in @ X1371 @ X1367 )
| ~ ( X1368 @ X1371 )
| ( ex1 @ X1367 @ X1368 ) )
& ( ( X1368 @ ( esk46_2 @ X1367 @ X1368 ) )
| ~ ( in @ X1371 @ X1367 )
| ~ ( X1368 @ X1371 )
| ( ex1 @ X1367 @ X1368 ) )
& ( ( X1368 @ ( esk47_2 @ X1367 @ X1368 ) )
| ~ ( in @ X1371 @ X1367 )
| ~ ( X1368 @ X1371 )
| ( ex1 @ X1367 @ X1368 ) )
& ( ( ( esk46_2 @ X1367 @ X1368 )
!= ( esk47_2 @ X1367 @ X1368 ) )
| ~ ( in @ X1371 @ X1367 )
| ~ ( X1368 @ X1371 )
| ( ex1 @ X1367 @ X1368 ) )
& ( ( ( setadjoin @ X1372 @ emptyset )
!= ( setadjoin @ X1373 @ emptyset ) )
| ( X1372 = X1373 ) )
& ( ~ ( in @ ( setadjoin @ X1376 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1374 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1374 @ ( setadjoin @ X1375 @ emptyset ) ) @ emptyset ) ) )
| ( X1374 = X1376 ) )
& ( ~ ( iskpair @ X1377 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1377 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1377 ) ) ) )
& ( ~ ( singleton @ X1378 )
| ( in @ ( setunion @ X1378 ) @ X1378 ) )
& ( ( kfst @ ( kpair @ X1379 @ X1380 ) )
= X1379 )
& ( ~ ( in @ X1383 @ ( cartprod @ X1381 @ X1382 ) )
| ( in @ ( kfst @ X1383 ) @ X1381 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1384 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1384 @ ( setadjoin @ X1385 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1386 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1386 @ ( setadjoin @ X1387 @ emptyset ) ) @ emptyset ) ) )
| ( X1384 = X1386 ) )
& ( ( ( kpair @ X1388 @ X1389 )
!= ( kpair @ X1390 @ X1391 ) )
| ( X1388 = X1390 ) )
& ( ( X1392 != X1393 )
| ( ( setadjoin @ X1392 @ ( setadjoin @ X1393 @ emptyset ) )
= ( setadjoin @ X1392 @ emptyset ) ) )
& ( ( X1394 != X1395 )
| ( ( setadjoin @ ( setadjoin @ X1394 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1394 @ ( setadjoin @ X1395 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1394 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1396 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1396 @ ( setadjoin @ X1397 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1398 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1398 @ ( setadjoin @ X1399 @ emptyset ) ) @ emptyset ) ) )
| ( X1398 != X1399 )
| ( X1397 = X1399 ) )
& ( ( ( setadjoin @ X1400 @ ( setadjoin @ X1401 @ emptyset ) )
!= ( setadjoin @ X1402 @ emptyset ) )
| ( X1400 = X1401 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1403 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1403 @ ( setadjoin @ X1404 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1405 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1405 @ ( setadjoin @ X1406 @ emptyset ) ) @ emptyset ) ) )
| ( X1404 = X1406 ) )
& ( ( kpair @ esk48_0 @ esk49_0 )
= ( kpair @ esk50_0 @ esk51_0 ) )
& ( esk49_0 != esk51_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_199])])])])])])]) ).
thf(c_0_202,plain,
! [X1411: $i,X1412: $i] :
( ( kpair @ X1411 @ X1412 )
= ( setadjoin @ ( setadjoin @ X1411 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1411 @ ( setadjoin @ X1412 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
thf(c_0_203,negated_conjecture,
! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_204,negated_conjecture,
( ( kpair @ esk48_0 @ esk49_0 )
= ( kpair @ esk50_0 @ esk51_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_205,negated_conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_206,plain,
! [X2: $i,X3: $i] :
( ( kpair @ X2 @ X3 )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
thf(c_0_207,negated_conjecture,
esk48_0 = esk50_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_203]) ).
thf(c_0_208,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X3: $i] :
( ( X2 = X3 )
| ( ( kpair @ X4 @ X2 )
!= ( kpair @ X5 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206]),c_0_206]) ).
thf(c_0_209,negated_conjecture,
( ( kpair @ esk50_0 @ esk49_0 )
= ( kpair @ esk50_0 @ esk51_0 ) ),
inference(rw,[status(thm)],[c_0_204,c_0_207]) ).
thf(c_0_210,negated_conjecture,
! [X3: $i,X2: $i] :
( ( X2 = esk49_0 )
| ( ( kpair @ X3 @ X2 )
!= ( kpair @ esk50_0 @ esk51_0 ) ) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
thf(c_0_211,negated_conjecture,
esk49_0 != esk51_0,
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_212,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_210]),c_0_211]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU654^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n018.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 16:42:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.23/0.49 Running higher-order theorem proving
% 0.23/0.49 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
% 0.63/0.69 # Version: 3.1.0-ho
% 0.63/0.69 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.63/0.69 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.69 # Starting ehoh_best5 with 300s (1) cores
% 0.63/0.69 # Starting almost_fo_3_lam with 300s (1) cores
% 0.63/0.69 # Starting new_bool_5 with 300s (1) cores
% 0.63/0.69 # Starting pre_casc_3 with 300s (1) cores
% 0.63/0.69 # Starting ho_unfolding_8 with 300s (1) cores
% 0.63/0.69 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.63/0.69 # Starting new_bool_3 with 300s (1) cores
% 0.63/0.69 # Starting new_ho_5 with 300s (1) cores
% 0.63/0.69 # new_bool_5 with pid 10316 completed with status 0
% 0.63/0.69 # Result found by new_bool_5
% 0.63/0.69 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.63/0.69 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.69 # Starting ehoh_best5 with 300s (1) cores
% 0.63/0.69 # Starting almost_fo_3_lam with 300s (1) cores
% 0.63/0.69 # Starting new_bool_5 with 300s (1) cores
% 0.63/0.69 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.63/0.69 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.63/0.69 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.63/0.69 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.63/0.69 # new_ho_10_cnf2 with pid 10328 completed with status 0
% 0.63/0.69 # Result found by new_ho_10_cnf2
% 0.63/0.69 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.63/0.69 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.69 # Starting ehoh_best5 with 300s (1) cores
% 0.63/0.69 # Starting almost_fo_3_lam with 300s (1) cores
% 0.63/0.69 # Starting new_bool_5 with 300s (1) cores
% 0.63/0.69 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.63/0.69 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.63/0.69 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.63/0.69 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.63/0.69 # Preprocessing time : 0.005 s
% 0.63/0.69 # Presaturation interreduction done
% 0.63/0.69
% 0.63/0.69 # Proof found!
% 0.63/0.69 # SZS status Theorem
% 0.63/0.69 # SZS output start CNFRefutation
% See solution above
% 0.63/0.69 # Parsed axioms : 377
% 0.63/0.69 # Removed by relevancy pruning/SinE : 206
% 0.63/0.69 # Initial clauses : 268
% 0.63/0.69 # Removed in clause preprocessing : 25
% 0.63/0.69 # Initial clauses in saturation : 243
% 0.63/0.69 # Processed clauses : 689
% 0.63/0.69 # ...of these trivial : 9
% 0.63/0.69 # ...subsumed : 135
% 0.63/0.69 # ...remaining for further processing : 545
% 0.63/0.69 # Other redundant clauses eliminated : 39
% 0.63/0.69 # Clauses deleted for lack of memory : 0
% 0.63/0.69 # Backward-subsumed : 3
% 0.63/0.69 # Backward-rewritten : 15
% 0.63/0.69 # Generated clauses : 5622
% 0.63/0.69 # ...of the previous two non-redundant : 5362
% 0.63/0.69 # ...aggressively subsumed : 0
% 0.63/0.69 # Contextual simplify-reflections : 0
% 0.63/0.69 # Paramodulations : 5577
% 0.63/0.69 # Factorizations : 2
% 0.63/0.69 # NegExts : 0
% 0.63/0.69 # Equation resolutions : 43
% 0.63/0.69 # Disequality decompositions : 0
% 0.63/0.69 # Total rewrite steps : 325
% 0.63/0.69 # ...of those cached : 247
% 0.63/0.69 # Propositional unsat checks : 0
% 0.63/0.69 # Propositional check models : 0
% 0.63/0.69 # Propositional check unsatisfiable : 0
% 0.63/0.69 # Propositional clauses : 0
% 0.63/0.69 # Propositional clauses after purity: 0
% 0.63/0.69 # Propositional unsat core size : 0
% 0.63/0.69 # Propositional preprocessing time : 0.000
% 0.63/0.69 # Propositional encoding time : 0.000
% 0.63/0.69 # Propositional solver time : 0.000
% 0.63/0.69 # Success case prop preproc time : 0.000
% 0.63/0.69 # Success case prop encoding time : 0.000
% 0.63/0.69 # Success case prop solver time : 0.000
% 0.63/0.69 # Current number of processed clauses : 311
% 0.63/0.69 # Positive orientable unit clauses : 55
% 0.63/0.69 # Positive unorientable unit clauses: 1
% 0.63/0.69 # Negative unit clauses : 9
% 0.63/0.69 # Non-unit-clauses : 246
% 0.63/0.69 # Current number of unprocessed clauses: 5025
% 0.63/0.69 # ...number of literals in the above : 16637
% 0.63/0.69 # Current number of archived formulas : 0
% 0.63/0.69 # Current number of archived clauses : 221
% 0.63/0.69 # Clause-clause subsumption calls (NU) : 14409
% 0.63/0.69 # Rec. Clause-clause subsumption calls : 9217
% 0.63/0.69 # Non-unit clause-clause subsumptions : 90
% 0.63/0.69 # Unit Clause-clause subsumption calls : 189
% 0.63/0.69 # Rewrite failures with RHS unbound : 0
% 0.63/0.69 # BW rewrite match attempts : 42
% 0.63/0.69 # BW rewrite match successes : 12
% 0.63/0.69 # Condensation attempts : 689
% 0.63/0.69 # Condensation successes : 10
% 0.63/0.69 # Termbank termtop insertions : 109671
% 0.63/0.69 # Search garbage collected termcells : 14933
% 0.63/0.69
% 0.63/0.69 # -------------------------------------------------
% 0.63/0.69 # User time : 0.150 s
% 0.63/0.69 # System time : 0.017 s
% 0.63/0.69 # Total time : 0.167 s
% 0.63/0.69 # Maximum resident set size: 5608 pages
% 0.63/0.69
% 0.63/0.69 # -------------------------------------------------
% 0.63/0.69 # User time : 0.159 s
% 0.63/0.69 # System time : 0.020 s
% 0.63/0.69 # Total time : 0.179 s
% 0.63/0.69 # Maximum resident set size: 2204 pages
% 0.63/0.69 % E---3.1 exiting
% 1.62/0.69 % E exiting
%------------------------------------------------------------------------------