%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU642^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 03:28:47 EDT 2024
% Result : Theorem 0.73s 0.61s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 420
% Syntax : Number of formulae : 492 ( 46 unt; 255 typ; 0 def)
% Number of atoms : 1950 ( 463 equ; 0 cnn)
% Maximal formula atoms : 589 ( 8 avg)
% Number of connectives : 8033 ( 593 ~; 648 |; 441 &;5212 @)
% ( 226 <=>; 913 =>; 0 <=; 0 <~>)
% Maximal formula depth : 699 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 406 ( 406 >; 0 *; 0 +; 0 <<)
% Number of symbols : 258 ( 255 usr; 166 con; 0-4 aty)
% Number of variables : 1626 ( 102 ^1370 !; 154 ?;1626 :)
% 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,
epred1_0: $o ).
thf(decl_210,type,
esk1_2: $i > $i > $i ).
thf(decl_211,type,
esk2_2: $i > $i > $i ).
thf(decl_212,type,
esk3_2: $i > $i > $i ).
thf(decl_213,type,
esk4_1: $i > $i ).
thf(decl_214,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_215,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_216,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_217,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_218,type,
esk9_1: $i > $i ).
thf(decl_219,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_220,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_221,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_222,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_223,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_224,type,
esk15_2: $i > $i > $i ).
thf(decl_225,type,
esk16_2: $i > $i > $i ).
thf(decl_226,type,
esk17_1: $i > $i ).
thf(decl_227,type,
esk18_1: $i > $i ).
thf(decl_228,type,
esk19_1: $i > $i ).
thf(decl_229,type,
esk20_2: $i > $i > $i ).
thf(decl_230,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_231,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_232,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_233,type,
esk24_1: $i > $i ).
thf(decl_234,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_235,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_236,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_237,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_238,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_239,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_240,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_241,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_242,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_243,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_244,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_245,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_246,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_247,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_248,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_249,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_250,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_251,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_252,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_253,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_254,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_255,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_256,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_257,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_258,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_259,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_260,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_261,type,
esk52_2: $i > $i > $i ).
thf(decl_262,type,
esk53_2: $i > $i > $i ).
thf(decl_263,type,
esk54_2: $i > $i > $i ).
thf(decl_264,type,
esk55_2: $i > $i > $i ).
thf(decl_265,type,
esk56_2: $i > $i > $i ).
thf(decl_266,type,
esk57_2: $i > $i > $i ).
thf(decl_267,type,
esk58_2: $i > $i > $i ).
thf(decl_268,type,
esk59_3: $i > $i > $i > $i ).
thf(decl_269,type,
esk60_3: $i > $i > $i > $i ).
thf(decl_270,type,
esk61_3: $i > $i > $i > $i ).
thf(decl_271,type,
esk62_3: $i > $i > $i > $i ).
thf(decl_272,type,
esk63_2: $i > $i > $i ).
thf(decl_273,type,
esk64_2: $i > ( $i > $o ) > $i ).
thf(decl_274,type,
esk65_2: $i > ( $i > $o ) > $i ).
thf(decl_275,type,
esk66_2: $i > ( $i > $o ) > $i ).
thf(decl_276,type,
esk67_2: $i > ( $i > $o ) > $i ).
thf(decl_277,type,
esk68_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_278,type,
esk69_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_279,type,
esk70_2: $i > ( $i > $o ) > $i ).
thf(decl_280,type,
esk71_2: $i > ( $i > $o ) > $i ).
thf(decl_281,type,
esk72_2: $i > ( $i > $o ) > $i ).
thf(decl_282,type,
esk73_0: $i ).
thf(decl_283,type,
esk74_0: $i ).
thf(decl_284,type,
esk75_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X4 ) )
& ( X4
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(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/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
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/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(setukpairinjL1,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
=> ! [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/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
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/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(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/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(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/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_164,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X490: $i] :
( ( in @ X490
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X490 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_165,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_166,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_167,plain,
( kpair
= ( ^ [Z0: $i,Z1: $i] : ( setadjoin @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[kpair]) ).
thf(c_0_168,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_169,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_170,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_171,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_172,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_173,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_174,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X490: $i] :
( ( in @ X490
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X490 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_164,c_0_165]) ).
thf(c_0_175,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_176,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_177,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_178,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_179,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_180,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_181,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_182,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_183,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_184,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_185,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_186,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_187,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_188,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X483: $i] :
( ( in @ X483 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X484: $i] :
( ( in @ X484 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X483 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X483 @ ( setadjoin @ X484 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_166]) ).
thf(c_0_189,axiom,
( kpairp
= ( ! [X2: $i,X3: $i] :
? [X485: $i] :
( ( in @ X485 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X486: $i] :
( ( in @ X486 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X485 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X485 @ ( setadjoin @ X486 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp,c_0_166]),c_0_167]) ).
thf(c_0_190,axiom,
( ubforcartprodlem3
= ( ! [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 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[ubforcartprodlem3,c_0_167]) ).
thf(c_0_191,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X465: $i] :
( ( X1 @ X465 )
& ! [X466: $i] :
( ( X1 @ X466 )
=> ( X465 = X466 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_168,c_0_169]) ).
thf(c_0_192,axiom,
( cartprodpairin
= ( ! [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 ) ) @ ( cartprod @ X4 @ X5 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodpairin,c_0_167]) ).
thf(c_0_193,axiom,
( cartprodmempair1
= ( ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodmempair1,c_0_167]) ).
thf(c_0_194,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X467: $i] :
( ( X1 @ X467 )
& ! [X468: $i] :
( ( X1 @ X468 )
=> ( X467 = X468 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_170,c_0_169]) ).
thf(c_0_195,axiom,
( cartprodmempair
= ( ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X487: $i] :
( ( in @ X487 @ ( setunion @ X18 ) )
& ? [X488: $i] :
( ( in @ X488 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X487 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X487 @ ( setadjoin @ X488 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodmempair,c_0_166]) ).
thf(c_0_196,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X469: $i] :
( ( X1 @ X469 )
& ! [X470: $i] :
( ( X1 @ X470 )
=> ( X469 = X470 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_171,c_0_169]) ).
thf(c_0_197,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 ) )
=> ? [X489: $i] :
( ( in @ X489
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X489 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_172,c_0_165]) ).
thf(c_0_198,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X491: $i] :
( ( in @ X491
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X491 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_173,c_0_174]) ).
thf(c_0_199,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X492: $i] :
( ( in @ X492
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X492 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_175,c_0_174]) ).
thf(c_0_200,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 ) )
=> ? [X493: $i] :
( ( in @ X493
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X493 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_176,c_0_174]) ).
thf(c_0_201,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X471: $i] :
( ( X1 @ X471 )
& ! [X472: $i] :
( ( X1 @ X472 )
=> ( X471 = X472 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_177,c_0_169]) ).
thf(c_0_202,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X473: $i] :
( ( X1 @ X473 )
& ! [X474: $i] :
( ( X1 @ X474 )
=> ( X473 = X474 ) ) )
<=> ? [X475: $i] :
( ( X17 @ X475 )
& ! [X476: $i] :
( ( X17 @ X476 )
=> ( X475 = X476 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_178,c_0_169]) ).
thf(c_0_203,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X477: $i] :
( ( X1 @ X477 )
& ! [X478: $i] :
( ( X1 @ X478 )
=> ( X477 = X478 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_179,c_0_169]) ).
thf(c_0_204,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X479: $i] :
( ( X1 @ X479 )
& ! [X480: $i] :
( ( X1 @ X480 )
=> ( X479 = X480 ) ) )
=> ( ? [X481: $i] :
( ( X17 @ X481 )
& ! [X482: $i] :
( ( X17 @ X482 )
=> ( X481 = X482 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_180,c_0_169]) ).
thf(c_0_205,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_206,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_207,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_208,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_209,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_181]) ).
thf(c_0_210,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X463: $i] :
( ( X1 @ X463 )
& ! [X464: $i] :
( ( X1 @ X464 )
=> ( X463 = X464 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_182,c_0_169]) ).
thf(c_0_211,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_212,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_181]) ).
thf(c_0_213,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_183,c_0_181]) ).
thf(c_0_214,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_181]) ).
thf(c_0_215,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_216,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X461: $i] :
( ( X1 @ X461 )
& ! [X462: $i] :
( ( X1 @ X462 )
=> ( X461 = X462 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_184,c_0_169]) ).
thf(c_0_217,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X459: $i] :
( ( X1 @ X459 )
& ! [X460: $i] :
( ( X1 @ X460 )
=> ( X459 = X460 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_185,c_0_169]) ).
thf(c_0_218,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_219,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_220,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_221,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X457: $i] :
( ( X1 @ X457 )
& ! [X458: $i] :
( ( X1 @ X458 )
=> ( X457 = X458 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_186,c_0_169]) ).
thf(c_0_222,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X455: $i] :
( ( X6 @ X2 @ X455 )
& ! [X456: $i] :
( ( X6 @ X2 @ X456 )
=> ( X455 = X456 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_187,c_0_169]) ).
thf(c_0_223,plain,
( epred1_0
<=> ! [X523: $i] :
? [X524: $i] :
( ! [X525: $i] :
( ( in @ X525 @ X524 )
=> ! [X526: $i] :
( ( in @ X526 @ X525 )
=> ( in @ X526 @ X523 ) ) )
& ! [X527: $i,X528: $i] :
( ( ( in @ X527 @ X523 )
& ( in @ X528 @ X523 ) )
=> ( ! [X529: $i] :
( ( in @ X529 @ X524 )
=> ( ( in @ X527 @ X529 )
<=> ( in @ X528 @ X529 ) ) )
=> ( X527 = X528 ) ) )
& ! [X530: $i,X531: $i] :
( ( ( in @ X530 @ X524 )
& ( in @ X531 @ X524 ) )
=> ( ! [X532: $i] :
( ( in @ X532 @ X530 )
=> ( in @ X532 @ X531 ) )
| ! [X533: $i] :
( ( in @ X533 @ X531 )
=> ( in @ X533 @ X530 ) ) ) )
& ! [X534: $i] :
( ( ! [X535: $i] :
( ( in @ X535 @ X534 )
=> ( in @ X535 @ X523 ) )
& ? [X536: $i] : ( in @ X536 @ X534 ) )
=> ? [X537: $i,X538: $i] :
( ( in @ X537 @ X524 )
& ( in @ X538 @ X534 )
& ~ ? [X539: $i] :
( ( in @ X539 @ X537 )
& ( in @ X539 @ X534 ) )
& ! [X540: $i] :
( ( in @ X540 @ X524 )
=> ( ! [X541: $i] :
( ( in @ X541 @ X540 )
=> ( in @ X541 @ X537 ) )
| ( in @ X538 @ X540 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_224,negated_conjecture,
~ ( ! [X494: $i,X495: $i] :
( ! [X496: $i] :
( ( in @ X496 @ X494 )
<=> ( in @ X496 @ X495 ) )
=> ( X494 = X495 ) )
=> ( ! [X497: $i] :
~ ( in @ X497 @ emptyset )
=> ( ! [X498: $i,X499: $i,X500: $i] :
( ( in @ X500 @ ( setadjoin @ X498 @ X499 ) )
<=> ( ( X500 = X498 )
| ( in @ X500 @ X499 ) ) )
=> ( ! [X501: $i,X502: $i] :
( ( in @ X502 @ ( powerset @ X501 ) )
<=> ! [X503: $i] :
( ( in @ X503 @ X502 )
=> ( in @ X503 @ X501 ) ) )
=> ( ! [X504: $i,X505: $i] :
( ( in @ X505 @ ( setunion @ X504 ) )
<=> ? [X506: $i] :
( ( in @ X505 @ X506 )
& ( in @ X506 @ X504 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X507: $i] :
( ( in @ X507 @ omega )
=> ( in @ ( setadjoin @ X507 @ X507 ) @ omega ) )
=> ( ! [X508: $i] :
( ( ( in @ emptyset @ X508 )
& ! [X509: $i] :
( ( ( in @ X509 @ omega )
& ( in @ X509 @ X508 ) )
=> ( in @ ( setadjoin @ X509 @ X509 ) @ X508 ) ) )
=> ! [X510: $i] :
( ( in @ X510 @ omega )
=> ( in @ X510 @ X508 ) ) )
=> ( ! [X511: $i > $i > $o,X512: $i] :
( ! [X513: $i] :
( ( in @ X513 @ X512 )
=> ? [X514: $i] :
( ( X511 @ X513 @ X514 )
& ! [X515: $i] :
( ( X511 @ X513 @ X515 )
=> ( X514 = X515 ) ) ) )
=> ? [X516: $i] :
! [X517: $i] :
( ( in @ X517 @ X516 )
<=> ? [X518: $i] :
( ( in @ X518 @ X512 )
& ( X511 @ X518 @ X517 ) ) ) )
=> ( ! [X519: $i] :
( ? [X520: $i] : ( in @ X520 @ X519 )
=> ? [X521: $i] :
( ( in @ X521 @ X519 )
& ~ ? [X522: $i] :
( ( in @ X522 @ X521 )
& ( in @ X522 @ X519 ) ) ) )
=> ( epred1_0
=> ( ! [X542: $i > $o] :
( ? [X543: $i] :
( ( X542 @ X543 )
& ! [X544: $i] :
( ( X542 @ X544 )
=> ( X543 = X544 ) ) )
=> ( X542
@ ( descr
@ ^ [Z0: $i] : ( X542 @ Z0 ) ) ) )
=> ( ! [X545: $i,X546: $i > $o,X547: $i] :
( ( in @ X547 @ X545 )
=> ( ( X546 @ X547 )
=> ( in @ X547 @ ( dsetconstr @ X545 @ X546 ) ) ) )
=> ( ! [X548: $i,X549: $i > $o,X550: $i] :
( ( in @ X550 @ ( dsetconstr @ X548 @ X549 ) )
=> ( in @ X550 @ X548 ) )
=> ( ! [X551: $i,X552: $i > $o,X553: $i] :
( ( in @ X553 @ ( dsetconstr @ X551 @ X552 ) )
=> ( X552 @ X553 ) )
=> ( ! [X554: $i > $o] :
( ? [X555: $i] :
( ( X554 @ X555 )
& ! [X556: $i] :
( ( X554 @ X556 )
=> ( X555 = X556 ) ) )
=> ? [X557: $i] :
( ( X554 @ X557 )
& ! [X558: $i] :
( ( X554 @ X558 )
=> ( X557 = X558 ) ) ) )
=> ( ! [X559: $o,X560: $i] :
( ( in @ X560 @ ( prop2set @ X559 ) )
=> X559 )
=> ( ! [X561: $i] :
( ( in @ X561 @ emptyset )
=> ! [X562: $o] : X562 )
=> ( ! [X563: $i] :
( ( in @ X563 @ emptyset )
=> ~ $true )
=> ( ! [X564: $i] :
~ ( in @ X564 @ emptyset )
=> ( ! [X565: $i > $o] :
( ? [X566: $i] :
( ( X565 @ X566 )
& ! [X567: $i] :
( ( X565 @ X567 )
=> ( X566 = X567 ) ) )
=> ? [X568: $i] : ( X565 @ X568 ) )
=> ( ! [X569: $i,X570: $i] :
( ! [X571: $i] :
( ( in @ X571 @ X569 )
=> ( in @ X571 @ X570 ) )
=> ( ! [X572: $i] :
( ( in @ X572 @ X570 )
=> ( in @ X572 @ X569 ) )
=> ( X569 = X570 ) ) )
=> ( ! [X573: $i] :
( ! [X574: $i] :
~ ( in @ X574 @ X573 )
=> ( X573 = emptyset ) )
=> ( ! [X575: $i] :
( ! [X576: $i] :
~ ( in @ X576 @ X575 )
=> ( X575 = emptyset ) )
=> ( ! [X577: $i,X578: $i > $o,X579: $i] :
( ( in @ X579 @ X577 )
=> ( ( in @ X579 @ ( dsetconstr @ X577 @ X578 ) )
<=> ( X578 @ X579 ) ) )
=> ( ! [X580: $i] :
( ( X580 != emptyset )
=> ? [X581: $i] : ( in @ X581 @ X580 ) )
=> ( ! [X582: $i,X583: $i > $o,X584: $i] :
( ( in @ X584 @ X582 )
=> ( ( X583 @ X584 )
=> ( ( dsetconstr @ X582 @ X583 )
!= emptyset ) ) )
=> ( ! [X585: $i] :
( ? [X586: $i] : ( in @ X586 @ X585 )
=> ( X585 != emptyset ) )
=> ( ! [X587: $i,X588: $i] : ( in @ X587 @ ( setadjoin @ X587 @ X588 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X589: $i,X590: $i,X591: $i] :
( ( in @ X591 @ X590 )
=> ( in @ X591 @ ( setadjoin @ X589 @ X590 ) ) )
=> ( ! [X592: $i,X593: $i,X594: $i] :
( ( in @ X594 @ ( setadjoin @ X592 @ X593 ) )
=> ! [X595: $o] :
( ( ( X594 = X592 )
=> X595 )
=> ( ( ( in @ X594 @ X593 )
=> X595 )
=> X595 ) ) )
=> ( ! [X596: $i,X597: $i,X598: $i] :
( ( in @ X598 @ ( setadjoin @ X596 @ X597 ) )
=> ( ( X598 = X596 )
| ( in @ X598 @ X597 ) ) )
=> ( ! [X599: $i] :
( ( dsetconstr @ X599
@ ^ [Z0: $i] : $true )
= X599 )
=> ( ! [X600: $i,X601: $i] :
( ! [X602: $i] :
( ( in @ X602 @ X601 )
=> ( in @ X602 @ X600 ) )
=> ( in @ X601 @ ( powerset @ X600 ) ) )
=> ( ! [X603: $i] : ( in @ emptyset @ ( powerset @ X603 ) )
=> ( ! [X604: $i] : ( in @ emptyset @ ( powerset @ X604 ) )
=> ( ! [X605: $i,X606: $i,X607: $i] :
( ( in @ X606 @ ( powerset @ X605 ) )
=> ( ( in @ X607 @ X606 )
=> ( in @ X607 @ X605 ) ) )
=> ( ! [X608: $i,X609: $i,X610: $i] :
( ( in @ X609 @ X610 )
=> ( ( in @ X610 @ X608 )
=> ( in @ X609 @ ( setunion @ X608 ) ) ) )
=> ( ! [X611: $i,X612: $i] :
( ( in @ X612 @ ( setunion @ X611 ) )
=> ! [X613: $o] :
( ! [X614: $i] :
( ( in @ X612 @ X614 )
=> ( ( in @ X614 @ X611 )
=> X613 ) )
=> X613 ) )
=> ( ! [X615: $i,X616: $i] :
( ( in @ X616 @ X615 )
=> ( in @ X616 @ ( powerset @ ( setunion @ X615 ) ) ) )
=> ( ! [X617: $i > $o] :
( ? [X618: $i] :
( ( X617 @ X618 )
& ! [X619: $i] :
( ( X617 @ X619 )
=> ( X618 = X619 ) ) )
=> ? [X620: $i] :
! [X621: $i] :
( ( X617 @ X621 )
<=> ( X621 = X620 ) ) )
=> ( ! [X622: $i] :
( ( X622 != emptyset )
=> ? [X623: $i] :
( ( in @ X623 @ X622 )
& $true ) )
=> ( ! [X624: $i,X625: $i] :
( ( in @ X624 @ ( setadjoin @ X625 @ emptyset ) )
=> ( X624 = X625 ) )
=> ( ! [X626: $i,X627: $i] :
( ( X626 != X627 )
=> ~ ( in @ X627 @ ( setadjoin @ X626 @ emptyset ) ) )
=> ( ! [X628: $i,X629: $i] :
( ( X628 = X629 )
=> ( in @ X628 @ ( setadjoin @ X629 @ emptyset ) ) )
=> ( ! [X630: $i,X631: $i] :
( ( in @ X630 @ ( setadjoin @ X631 @ emptyset ) )
=> ( in @ X631 @ ( setadjoin @ X630 @ emptyset ) ) )
=> ( ! [X632: $i,X633: $i,X634: $i] :
( ( in @ X634 @ ( setadjoin @ X632 @ ( setadjoin @ X633 @ emptyset ) ) )
=> ( ( X634 = X632 )
| ( X634 = X633 ) ) )
=> ( ! [X635: $i,X636: $i] : ( in @ X635 @ ( setadjoin @ X635 @ ( setadjoin @ X636 @ emptyset ) ) )
=> ( ! [X637: $i,X638: $i] : ( in @ X638 @ ( setadjoin @ X637 @ ( setadjoin @ X638 @ emptyset ) ) )
=> ( ! [X639: $i,X640: $i > $o] :
( ? [X641: $i] :
( ( in @ X641 @ X639 )
& ( X640 @ X641 ) )
=> ( ( ( dsetconstr @ X639 @ X640 )
= emptyset )
=> ~ $true ) )
=> ( ! [X642: $i > $o,X643: $i] :
( ( in @ X643 @ emptyset )
=> ( X642 @ X643 ) )
=> ( ! [X644: $i,X645: $i > $o] :
( ~ ! [X646: $i] :
( ( in @ X646 @ X644 )
=> ( X645 @ X646 ) )
=> ? [X647: $i] :
( ( in @ X647 @ X644 )
& ~ ( X645 @ X647 ) ) )
=> ( ! [X648: $i,X649: $i > $o] :
( ! [X650: $i] :
( ( in @ X650 @ X648 )
=> ~ ( X649 @ X650 ) )
=> ~ ? [X651: $i] :
( ( in @ X651 @ X648 )
& ( X649 @ X651 ) ) )
=> ( ! [X652: $i,X653: $i > $o] :
( ~ ? [X654: $i] :
( ( in @ X654 @ X652 )
& ( X653 @ X654 ) )
=> ! [X655: $i] :
( ( in @ X655 @ X652 )
=> ~ ( X653 @ X655 ) ) )
=> ( ! [X656: $i,X657: $i > $o] :
( ? [X658: $i] :
( ( in @ X658 @ X656 )
& ~ ( X657 @ X658 ) )
=> ~ ! [X659: $i] :
( ( in @ X659 @ X656 )
=> ( X657 @ X659 ) ) )
=> ( ! [X660: $o] :
( X660
=> ( in @ emptyset @ ( prop2set @ X660 ) ) )
=> ( prop2set2propI
=> ( ! [X661: $i,X662: $i > $o] :
( ~ ? [X663: $i] :
( ( in @ X663 @ X661 )
& ( X662 @ X663 ) )
=> ! [X664: $i] :
( ( in @ X664 @ X661 )
=> ~ ( X662 @ X664 ) ) )
=> ( ! [X665: $i,X666: $i > $o] :
( ~ ! [X667: $i] :
( ( in @ X667 @ X665 )
=> ( X666 @ X667 ) )
=> ? [X668: $i] :
( ( in @ X668 @ X665 )
& ~ ( X666 @ X668 ) ) )
=> ( ! [X669: $i > $o] :
( ? [X670: $i] :
( ( X669 @ X670 )
& ! [X671: $i] :
( ( X669 @ X671 )
=> ( X670 = X671 ) ) )
=> ? [X672: $i] :
( ( X669 @ X672 )
& ! [X673: $i] :
( ( X669 @ X673 )
=> ( X672 = X673 ) ) ) )
=> ( ! [X674: $i > $o] :
( ? [X675: $i] : ( X674 @ X675 )
=> ( ! [X676: $i,X677: $i] :
( ( X674 @ X676 )
=> ( ( X674 @ X677 )
=> ( X676 = X677 ) ) )
=> ? [X678: $i] :
( ( X674 @ X678 )
& ! [X679: $i] :
( ( X674 @ X679 )
=> ( X678 = X679 ) ) ) ) )
=> ( ! [X680: $i > $o] :
( ? [X681: $i] :
! [X682: $i] :
( ( X680 @ X682 )
<=> ( X682 = X681 ) )
=> ? [X683: $i] :
( ( X680 @ X683 )
& ! [X684: $i] :
( ( X680 @ X684 )
=> ( X683 = X684 ) ) ) )
=> ( ! [X685: $i,X686: $i] :
( ( X685 = X686 )
=> ! [X687: $i,X688: $i] :
( ( X687 = X688 )
=> ( ( in @ X687 @ X685 )
=> ( in @ X688 @ X686 ) ) ) )
=> ( ! [X689: $i,X690: $i] :
( ( X689 = X690 )
=> ! [X691: $i,X692: $i] :
( ( X691 = X692 )
=> ( ( in @ X691 @ X689 )
<=> ( in @ X692 @ X690 ) ) ) )
=> ( ! [X693: $i > $o] :
( ? [X694: $i] :
( ( X693 @ X694 )
& ! [X695: $i] :
( ( X693 @ X695 )
=> ( X694 = X695 ) ) )
=> ! [X696: $i,X697: $i] :
( ( X693 @ X696 )
=> ( ( X693 @ X697 )
=> ( X696 = X697 ) ) ) )
=> ( ! [X698: $i > $o,X699: $i > $o] :
( ! [X700: $i,X701: $i] :
( ( X700 = X701 )
=> ( ( X698 @ X700 )
<=> ( X699 @ X701 ) ) )
=> ( ? [X702: $i] :
( ( X698 @ X702 )
& ! [X703: $i] :
( ( X698 @ X703 )
=> ( X702 = X703 ) ) )
<=> ? [X704: $i] :
( ( X699 @ X704 )
& ! [X705: $i] :
( ( X699 @ X705 )
=> ( X704 = X705 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X706: $i,X707: $i] :
( ( X706 = X707 )
=> ! [X708: $i,X709: $i] :
( ( X708 = X709 )
=> ( ( setadjoin @ X706 @ X708 )
= ( setadjoin @ X707 @ X709 ) ) ) )
=> ( ! [X710: $i,X711: $i] :
( ( X710 = X711 )
=> ( ( powerset @ X710 )
= ( powerset @ X711 ) ) )
=> ( ! [X712: $i,X713: $i] :
( ( X712 = X713 )
=> ( ( setunion @ X712 )
= ( setunion @ X713 ) ) )
=> ( ( omega = omega )
=> ( ! [X714: $i > $o] :
( ? [X715: $i] :
( ( X714 @ X715 )
& ! [X716: $i] :
( ( X714 @ X716 )
=> ( X715 = X716 ) ) )
=> ! [X717: $i,X718: $i] :
( ( X714 @ X717 )
=> ( ( X714 @ X718 )
=> ( X717 = X718 ) ) ) )
=> ( ! [X719: $i > $o,X720: $i > $o] :
( ! [X721: $i,X722: $i] :
( ( X721 = X722 )
=> ( ( X719 @ X721 )
<=> ( X720 @ X722 ) ) )
=> ( ? [X723: $i] :
( ( X719 @ X723 )
& ! [X724: $i] :
( ( X719 @ X724 )
=> ( X723 = X724 ) ) )
=> ( ? [X725: $i] :
( ( X720 @ X725 )
& ! [X726: $i] :
( ( X720 @ X726 )
=> ( X725 = X726 ) ) )
=> ( ( descr @ X719 )
= ( descr @ X720 ) ) ) ) )
=> ( ! [X727: $i,X728: $i] :
( ( X727 = X728 )
=> ! [X729: $i > $o,X730: $i > $o] :
( ! [X731: $i] :
( ( in @ X731 @ X727 )
=> ! [X732: $i] :
( ( in @ X732 @ X728 )
=> ( ( X731 = X732 )
=> ( ( X729 @ X731 )
<=> ( X730 @ X732 ) ) ) ) )
=> ( ( dsetconstr @ X727 @ X729 )
= ( dsetconstr @ X728 @ X730 ) ) ) )
=> ( ! [X733: $i,X734: $i] :
( ! [X735: $i] :
( ( in @ X735 @ X733 )
=> ( in @ X735 @ X734 ) )
=> ( subset @ X733 @ X734 ) )
=> ( ! [X736: $i,X737: $i] :
( ( X736 = X737 )
=> ( subset @ X737 @ X736 ) )
=> ( ! [X738: $i,X739: $i] :
( ( X738 = X739 )
=> ( subset @ X738 @ X739 ) )
=> ( ! [X740: $i,X741: $i] :
( ! [X742: $i] :
( ( in @ X742 @ X740 )
=> ( in @ X742 @ X741 ) )
=> ( subset @ X740 @ X741 ) )
=> ( ! [X743: $i] : ( subset @ emptyset @ X743 )
=> ( ! [X744: $i,X745: $i,X746: $i] :
( ( subset @ X744 @ X745 )
=> ( ( in @ X746 @ X744 )
=> ( in @ X746 @ X745 ) ) )
=> ( ! [X747: $i,X748: $i,X749: $i] :
( ( subset @ X747 @ X748 )
=> ( ~ ( in @ X749 @ X748 )
=> ~ ( in @ X749 @ X747 ) ) )
=> ( ! [X750: $i,X751: $i,X752: $i] :
( ( in @ X752 @ X750 )
=> ( ~ ( in @ X752 @ X751 )
=> ~ ( subset @ X750 @ X751 ) ) )
=> ( ! [X753: $i,X754: $i] :
( ~ ( subset @ X753 @ X754 )
=> ( X753 != X754 ) )
=> ( ! [X755: $i,X756: $i,X757: $i] :
( ( in @ X757 @ X755 )
=> ( ~ ( in @ X757 @ X756 )
=> ( X755 != X756 ) ) )
=> ( ! [X758: $i] : ( subset @ X758 @ X758 )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ( subset @ X759 @ X760 )
=> ( ( subset @ X760 @ X761 )
=> ( subset @ X759 @ X761 ) ) )
=> ( ! [X762: $i,X763: $i] : ( subset @ X763 @ ( setadjoin @ X762 @ X763 ) )
=> ( ! [X764: $i,X765: $i,X766: $i] :
( ( subset @ X764 @ X766 )
=> ( subset @ X764 @ ( setadjoin @ X765 @ X766 ) ) )
=> ( ! [X767: $i,X768: $i] :
( ( subset @ X767 @ X768 )
=> ( in @ X767 @ ( powerset @ X768 ) ) )
=> ( ! [X769: $i,X770: $i] :
( ( subset @ X769 @ X770 )
=> ( ( subset @ X770 @ X769 )
=> ( X769 = X770 ) ) )
=> ( ! [X771: $i] :
( ( subset @ X771 @ emptyset )
=> ( X771 = emptyset ) )
=> ( ! [X772: $i,X773: $i] :
( ( subset @ X773 @ X772 )
=> ( in @ X773 @ ( powerset @ X772 ) ) )
=> ( ! [X774: $i,X775: $i] :
( ( in @ X775 @ ( powerset @ X774 ) )
=> ( subset @ X775 @ X774 ) )
=> ( ! [X776: $i] : ( in @ X776 @ ( powerset @ X776 ) )
=> ( ! [X777: $i,X778: $i] :
( ( subset @ X777 @ X778 )
=> ( subset @ ( powerset @ X777 ) @ ( powerset @ X778 ) ) )
=> ( ! [X779: $i,X780: $i > $o] : ( in @ ( dsetconstr @ X779 @ X780 ) @ ( powerset @ X779 ) )
=> ( ! [X781: $i,X782: $i > $o] : ( subset @ ( dsetconstr @ X781 @ X782 ) @ X781 )
=> ( ! [X783: $i,X784: $i,X785: $i] :
( ( in @ X785 @ X783 )
=> ( in @ X785 @ ( binunion @ X783 @ X784 ) ) )
=> ( ! [X786: $i,X787: $i] : ( in @ X787 @ ( setadjoin @ X786 @ ( setadjoin @ X787 @ emptyset ) ) )
=> ( ! [X788: $i,X789: $i,X790: $i] :
( ( in @ X790 @ X789 )
=> ( in @ X790 @ ( binunion @ X788 @ X789 ) ) )
=> ( ! [X791: $i,X792: $i,X793: $i,X794: $o] :
( ( in @ X793 @ ( binunion @ X791 @ X792 ) )
=> ( ( ( in @ X793 @ X791 )
=> X794 )
=> ( ( ( in @ X793 @ X792 )
=> X794 )
=> X794 ) ) )
=> ( ! [X795: $i,X796: $i,X797: $i] :
( ( in @ X797 @ ( binunion @ X795 @ X796 ) )
=> ( ( in @ X797 @ X795 )
| ( in @ X797 @ X796 ) ) )
=> ( ! [X798: $i,X799: $i] : ( subset @ X798 @ ( binunion @ X798 @ X799 ) )
=> ( ! [X800: $i,X801: $i] : ( subset @ X801 @ ( binunion @ X800 @ X801 ) )
=> ( ! [X802: $i,X803: $i,X804: $i] :
( ( in @ X804 @ X802 )
=> ( ( in @ X804 @ X803 )
=> ( in @ X804 @ ( binintersect @ X802 @ X803 ) ) ) )
=> ( ! [X805: $i,X806: $i,X807: $i] :
( ( subset @ X807 @ X805 )
=> ( ( subset @ X807 @ X806 )
=> ( subset @ X807 @ ( binintersect @ X805 @ X806 ) ) ) )
=> ( ! [X808: $i,X809: $i,X810: $i] :
( ( in @ X810 @ ( binintersect @ X808 @ X809 ) )
=> ( in @ X810 @ X808 ) )
=> ( ! [X811: $i,X812: $i] : ( subset @ ( binintersect @ X811 @ X812 ) @ X811 )
=> ( ! [X813: $i,X814: $i] :
( ( subset @ X813 @ X814 )
=> ( ( binintersect @ X813 @ X814 )
= X813 ) )
=> ( ! [X815: $i,X816: $i] :
( ( ( binintersect @ X815 @ X816 )
= X816 )
=> ( subset @ X816 @ X815 ) )
=> ( ! [X817: $i,X818: $i,X819: $i] :
( ( in @ X819 @ ( binintersect @ X817 @ X818 ) )
=> ( in @ X819 @ X818 ) )
=> ( ! [X820: $i,X821: $i] :
( ~ ? [X822: $i] :
( ( in @ X822 @ X820 )
& ( in @ X822 @ X821 ) )
=> ( ( binintersect @ X820 @ X821 )
= emptyset ) )
=> ( ! [X823: $i,X824: $i] : ( subset @ ( binintersect @ X823 @ X824 ) @ X824 )
=> ( ! [X825: $i,X826: $i] :
( ( subset @ X826 @ X825 )
=> ( ( binintersect @ X825 @ X826 )
= X826 ) )
=> ( ! [X827: $i,X828: $i] :
( ( ( binintersect @ X827 @ X828 )
= X827 )
=> ( subset @ X827 @ X828 ) )
=> ( ! [X829: $i,X830: $i,X831: $i] :
( ( binintersect @ X829 @ ( binunion @ X830 @ X831 ) )
= ( binunion @ ( binintersect @ X829 @ X830 ) @ ( binintersect @ X829 @ X831 ) ) )
=> ( ! [X832: $i,X833: $i,X834: $i] :
( ( in @ X834 @ X832 )
=> ( ~ ( in @ X834 @ X833 )
=> ( in @ X834 @ ( setminus @ X832 @ X833 ) ) ) )
=> ( ! [X835: $i,X836: $i,X837: $i] :
( ( in @ X837 @ ( setminus @ X835 @ X836 ) )
=> ( in @ X837 @ X835 ) )
=> ( ! [X838: $i,X839: $i,X840: $i] :
( ( in @ X840 @ ( setminus @ X838 @ X839 ) )
=> ~ ( in @ X840 @ X839 ) )
=> ( ! [X841: $i,X842: $i] :
( ( subset @ X841 @ X842 )
=> ( ( setminus @ X841 @ X842 )
= emptyset ) )
=> ( ! [X843: $i,X844: $i,X845: $i] :
( ~ ( in @ X845 @ ( setminus @ X843 @ X844 ) )
=> ( ( in @ X845 @ X843 )
=> ( in @ X845 @ X844 ) ) )
=> ( ! [X846: $i,X847: $i,X848: $i] :
( ~ ( in @ X848 @ ( setminus @ X846 @ X847 ) )
=> ( ~ ( in @ X848 @ X847 )
=> ~ ( in @ X848 @ X846 ) ) )
=> ( ! [X849: $i,X850: $i,X851: $i] :
( ~ ( in @ X851 @ X849 )
=> ~ ( in @ X851 @ ( setminus @ X849 @ X850 ) ) )
=> ( ! [X852: $i,X853: $i,X854: $i] :
( ( in @ X854 @ X853 )
=> ~ ( in @ X854 @ ( setminus @ X852 @ X853 ) ) )
=> ( ! [X855: $i,X856: $i] : ( subset @ ( setminus @ X855 @ X856 ) @ X855 )
=> ( ! [X857: $i,X858: $i] :
( ( ( setminus @ X857 @ X858 )
= emptyset )
=> ( subset @ X857 @ X858 ) )
=> ( ! [X859: $i,X860: $i,X861: $i] :
( ( in @ X861 @ ( symdiff @ X859 @ X860 ) )
=> ! [X862: $o] :
( ( ( in @ X861 @ X859 )
=> ( ~ ( in @ X861 @ X860 )
=> X862 ) )
=> ( ( ~ ( in @ X861 @ X859 )
=> ( ( in @ X861 @ X860 )
=> X862 ) )
=> X862 ) ) )
=> ( ! [X863: $i,X864: $i,X865: $i] :
( ( in @ X865 @ X863 )
=> ( ~ ( in @ X865 @ X864 )
=> ( in @ X865 @ ( symdiff @ X863 @ X864 ) ) ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ~ ( in @ X868 @ X866 )
=> ( ( in @ X868 @ X867 )
=> ( in @ X868 @ ( symdiff @ X866 @ X867 ) ) ) )
=> ( ! [X869: $i,X870: $i,X871: $i] :
( ( in @ X871 @ X869 )
=> ( ( in @ X871 @ X870 )
=> ~ ( in @ X871 @ ( symdiff @ X869 @ X870 ) ) ) )
=> ( ! [X872: $i,X873: $i,X874: $i] :
( ~ ( in @ X874 @ X872 )
=> ( ~ ( in @ X874 @ X873 )
=> ~ ( in @ X874 @ ( symdiff @ X872 @ X873 ) ) ) )
=> ( ! [X875: $i,X876: $i] : ( in @ X876 @ ( setadjoin @ X875 @ ( setadjoin @ X876 @ emptyset ) ) )
=> ( ! [X877: $i,X878: $i] : ( in @ X877 @ ( setunion @ ( setadjoin @ ( setadjoin @ X877 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X877 @ ( setadjoin @ X878 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X879: $i,X880: $i] : ( in @ X880 @ ( setunion @ ( setadjoin @ ( setadjoin @ X879 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X879 @ ( setadjoin @ X880 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X881: $i,X882: $i] :
? [X883: $i] :
( ( in @ X883 @ ( setunion @ ( setadjoin @ ( setadjoin @ X881 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X881 @ ( setadjoin @ X882 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X884: $i] :
( ( in @ X884 @ ( setunion @ ( setadjoin @ ( setadjoin @ X881 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X881 @ ( setadjoin @ X882 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X881 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X881 @ ( setadjoin @ X882 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X883 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X883 @ ( setadjoin @ X884 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X885: $i,X886: $i] :
? [X887: $i] :
( ( in @ X887 @ ( setunion @ ( setadjoin @ ( setadjoin @ X885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X885 @ ( setadjoin @ X886 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X888: $i] :
( ( in @ X888 @ ( setunion @ ( setadjoin @ ( setadjoin @ X885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X885 @ ( setadjoin @ X886 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X885 @ ( setadjoin @ X886 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X887 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X887 @ ( setadjoin @ X888 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X889: $i,X890: $i] :
( ( in @ X890 @ X889 )
=> ( subset @ ( setadjoin @ X890 @ emptyset ) @ X889 ) )
=> ( ! [X891: $i,X892: $i] :
( ( in @ X892 @ X891 )
=> ( in @ ( setadjoin @ X892 @ emptyset ) @ ( powerset @ X891 ) ) )
=> ( ! [X893: $i,X894: $i,X895: $i] :
( ( in @ X895 @ X893 )
=> ( in @ ( setadjoin @ X895 @ emptyset ) @ ( powerset @ ( binunion @ X893 @ X894 ) ) ) )
=> ( ! [X896: $i,X897: $i,X898: $i] :
( ( in @ X898 @ ( setadjoin @ X896 @ ( setadjoin @ X897 @ emptyset ) ) )
=> ( ( X898 = X896 )
| ( X898 = X897 ) ) )
=> ( ! [X899: $i,X900: $i,X901: $i] :
( ( in @ X901 @ X899 )
=> ! [X902: $i] :
( ( in @ X902 @ X900 )
=> ( subset @ ( setadjoin @ X901 @ ( setadjoin @ X902 @ emptyset ) ) @ ( binunion @ X899 @ X900 ) ) ) )
=> ( ! [X903: $i,X904: $i,X905: $i] :
( ( in @ X905 @ X903 )
=> ! [X906: $i] :
( ( in @ X906 @ X904 )
=> ( in @ ( setadjoin @ X905 @ ( setadjoin @ X906 @ emptyset ) ) @ ( powerset @ ( binunion @ X903 @ X904 ) ) ) ) )
=> ( ! [X907: $i,X908: $i,X909: $i] :
( ( in @ X909 @ X907 )
=> ! [X910: $i] :
( ( in @ X910 @ X908 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X909 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X909 @ ( setadjoin @ X910 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X907 @ X908 ) ) ) ) )
=> ( ! [X911: $i,X912: $i,X913: $i] :
( ( in @ X913 @ X911 )
=> ! [X914: $i] :
( ( in @ X914 @ X912 )
=> ( in @ ( setadjoin @ ( setadjoin @ X913 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X913 @ ( setadjoin @ X914 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X911 @ X912 ) ) ) ) ) )
=> ( ! [X915: $i,X916: $i,X917: $i] :
( ( in @ X917 @ X915 )
=> ! [X918: $i] :
( ( in @ X918 @ X916 )
=> ( in @ ( setadjoin @ ( setadjoin @ X917 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X917 @ ( setadjoin @ X918 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X915 @ X916 ) ) ) ) ) )
=> ( ! [X919: $i,X920: $i,X921: $i] :
( ( in @ X921 @ X919 )
=> ! [X922: $i] :
( ( in @ X922 @ X920 )
=> ( in @ ( setadjoin @ ( setadjoin @ X921 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X921 @ ( setadjoin @ X922 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ X919 @ X920 ) ) ) )
=> ( ! [X923: $i,X924: $i,X925: $i] :
( ( in @ X925 @ ( cartprod @ X923 @ X924 ) )
=> ? [X926: $i] :
( ( in @ X926 @ X923 )
& ? [X927: $i] :
( ( in @ X927 @ X924 )
& ( X925
= ( setadjoin @ ( setadjoin @ X926 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X926 @ ( setadjoin @ X927 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [X928: $i,X929: $i,X930: $i] :
( ( in @ X930 @ ( cartprod @ X928 @ X929 ) )
=> ? [X931: $i] :
( ( in @ X931 @ ( setunion @ X930 ) )
& ? [X932: $i] :
( ( in @ X932 @ ( setunion @ X930 ) )
& ( X930
= ( setadjoin @ ( setadjoin @ X931 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X931 @ ( setadjoin @ X932 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [X933: $i,X934: $i] :
( ( in @ X934 @ ( setunion @ X933 ) )
=> ? [X935: $i] :
( ( in @ X935 @ X933 )
& ( in @ X934 @ X935 ) ) )
=> ( ! [X936: $i] : ( subset @ ( setunion @ ( setadjoin @ X936 @ emptyset ) ) @ X936 )
=> ( ! [X937: $i] : ( subset @ X937 @ ( setunion @ ( setadjoin @ X937 @ emptyset ) ) )
=> ( ! [X938: $i] :
( ( setunion @ ( setadjoin @ X938 @ emptyset ) )
= X938 )
=> ( ! [X939: $i,X940: $i > $o] :
( ! [X941: $i] :
( ( in @ X941 @ X939 )
=> ! [X942: $i] :
( ( in @ X942 @ X939 )
=> ( ( X940 @ X941 )
=> ( ( X940 @ X942 )
=> ( X941 = X942 ) ) ) ) )
=> ( ? [X943: $i] :
( ( in @ X943 @ X939 )
& ( X940 @ X943 ) )
=> ? [X944: $i] :
( ( in @ X944 @ ( dsetconstr @ X939 @ X940 ) )
& ( ( dsetconstr @ X939 @ X940 )
= ( setadjoin @ X944 @ emptyset ) ) ) ) )
=> ( ! [X945: $i,X946: $i > $o] :
( ? [X947: $i] :
( ( in @ X947 @ ( dsetconstr @ X945 @ X946 ) )
& ( ( dsetconstr @ X945 @ X946 )
= ( setadjoin @ X947 @ emptyset ) ) )
=> ? [X948: $i] :
( ( in @ X948 @ X945 )
& ( X946 @ X948 ) ) )
=> ( ! [X949: $i,X950: $i > $o,X951: $i] :
( ( in @ X951 @ X949 )
=> ( ( X950 @ X951 )
=> ( ! [X952: $i] :
( ( in @ X952 @ X949 )
=> ( ( X950 @ X952 )
=> ( X952 = X951 ) ) )
=> ? [X953: $i] :
( ( in @ X953 @ ( dsetconstr @ X949 @ X950 ) )
& ( ( dsetconstr @ X949 @ X950 )
= ( setadjoin @ X953 @ emptyset ) ) ) ) ) )
=> ( ! [X954: $i,X955: $i > $o] :
( ! [X956: $i] :
( ( in @ X956 @ X954 )
=> ! [X957: $i] :
( ( in @ X957 @ X954 )
=> ( ( X955 @ X956 )
=> ( ( X955 @ X957 )
=> ( X956 = X957 ) ) ) ) )
=> ( ? [X958: $i] :
( ( in @ X958 @ X954 )
& ( X955 @ X958 ) )
=> ? [X959: $i] :
( ( in @ X959 @ ( dsetconstr @ X954 @ X955 ) )
& ( ( dsetconstr @ X954 @ X955 )
= ( setadjoin @ X959 @ emptyset ) ) ) ) )
=> ( ! [X960: $i,X961: $i] :
( ( ( setadjoin @ X960 @ emptyset )
= ( setadjoin @ X961 @ emptyset ) )
=> ( X960 = X961 ) )
=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[setukpairinjL1]),inCongP]),setunionsingleton]),singletonsuniq]),secondinupair]),quantDeMorgan2]),setukpairIL]),setukpairIR]),c_0_188]),quantDeMorgan3]),c_0_189]),singletonsubset]),quantDeMorgan4]),singletoninpowerset]),singletoninpowunion]),prop2setI]),upairset2E]),upairsubunion]),notdexE]),upairinpowunion]),ubforcartprodlem1]),notdallE]),ubforcartprodlem2]),c_0_190]),c_0_191]),c_0_192]),c_0_193]),c_0_194]),c_0_195]),setunionE2]),setunionsingleton1]),c_0_196]),setunionsingleton2]),subsetE2]),c_0_197]),c_0_198]),c_0_199]),in__Cong]),c_0_200]),c_0_201]),c_0_202]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_203]),c_0_204]),c_0_205]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),setminusI]),setminusEL]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_206]),c_0_207]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),vacuousDall]),binintersectER]),quantDeMorgan1]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),c_0_208]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_209]),c_0_210]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_211]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_212]),c_0_213]),c_0_214]),c_0_215]),noeltsimpempty]),emptyI]),setext]),c_0_216]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_217]),c_0_218]),c_0_219]),c_0_220]),c_0_221]),wellorderingAx]),foundationAx]),c_0_222]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_223]) ).
thf(c_0_225,negated_conjecture,
! [X962: $i,X963: $i,X965: $i,X966: $i,X967: $i,X968: $i,X969: $i,X970: $i,X971: $i,X972: $i,X973: $i,X975: $i,X976: $i,X978: $i,X979: $i,X980: $i,X981: $i,X982: $i,X984: $i,X985: $i > $i > $o,X986: $i,X988: $i,X991: $i,X993: $i,X994: $i,X995: $i,X996: $i,X998: $i,X999: $i > $o,X1000: $i,X1002: $i,X1003: $i > $o,X1004: $i,X1005: $i,X1006: $i > $o,X1007: $i,X1008: $i,X1009: $i > $o,X1010: $i,X1011: $i > $o,X1012: $i,X1015: $i,X1016: $o,X1017: $i,X1018: $i,X1019: $o,X1020: $i,X1021: $i,X1022: $i > $o,X1023: $i,X1026: $i,X1027: $i,X1030: $i,X1032: $i,X1034: $i,X1035: $i > $o,X1036: $i,X1037: $i,X1039: $i,X1040: $i > $o,X1041: $i,X1042: $i,X1043: $i,X1044: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1050: $i,X1051: $i,X1052: $o,X1053: $i,X1054: $i,X1055: $i,X1056: $i,X1057: $i,X1058: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1064: $i,X1065: $i,X1066: $i,X1067: $i,X1068: $i,X1069: $i,X1070: $o,X1072: $i,X1073: $i,X1074: $i > $o,X1075: $i,X1078: $i,X1079: $i,X1080: $i,X1082: $i,X1083: $i,X1084: $i,X1085: $i,X1086: $i,X1087: $i,X1088: $i,X1089: $i,X1090: $i,X1091: $i,X1092: $i,X1093: $i,X1094: $i,X1095: $i,X1096: $i,X1097: $i,X1098: $i > $o,X1099: $i,X1100: $i > $o,X1101: $i,X1102: $i,X1103: $i > $o,X1104: $i,X1106: $i,X1107: $i > $o,X1109: $i,X1110: $i,X1111: $i > $o,X1113: $i,X1114: $i,X1115: $i > $o,X1116: $i,X1118: $o,X1119: $i,X1120: $i > $o,X1122: $i,X1123: $i,X1124: $i > $o,X1125: $i,X1127: $i > $o,X1128: $i,X1131: $i,X1132: $i > $o,X1133: $i,X1137: $i,X1138: $i > $o,X1139: $i,X1142: $i,X1143: $i,X1144: $i,X1145: $i,X1146: $i,X1147: $i,X1148: $i,X1149: $i,X1150: $i,X1151: $i > $o,X1152: $i,X1154: $i,X1155: $i,X1156: $i > $o,X1157: $i > $o,X1160: $i,X1163: $i,X1164: $i,X1167: $i,X1168: $i,X1169: $i,X1170: $i,X1171: $i,X1172: $i,X1173: $i,X1174: $i,X1175: $i,X1176: $i > $o,X1177: $i,X1179: $i,X1180: $i,X1181: $i > $o,X1182: $i > $o,X1185: $i,X1187: $i,X1189: $i,X1190: $i,X1191: $i > $o,X1192: $i > $o,X1195: $i,X1196: $i,X1198: $i,X1199: $i,X1200: $i,X1201: $i,X1202: $i,X1203: $i,X1205: $i,X1206: $i,X1207: $i,X1208: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $i,X1217: $i,X1218: $i,X1219: $i,X1220: $i,X1221: $i,X1222: $i,X1223: $i,X1224: $i,X1225: $i,X1226: $i,X1227: $i,X1228: $i,X1229: $i,X1230: $i,X1231: $i,X1232: $i,X1233: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1241: $i,X1242: $i > $o,X1243: $i,X1244: $i > $o,X1245: $i,X1246: $i,X1247: $i,X1248: $i,X1249: $i,X1250: $i,X1251: $i,X1252: $i,X1253: $i,X1254: $i,X1255: $i,X1256: $o,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,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: $o,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,X1344: $i,X1347: $i,X1348: $i,X1351: $i,X1352: $i,X1353: $i,X1354: $i,X1355: $i,X1356: $i,X1357: $i,X1358: $i,X1359: $i,X1360: $i,X1361: $i,X1362: $i,X1363: $i,X1364: $i,X1365: $i,X1366: $i,X1367: $i,X1368: $i,X1369: $i,X1370: $i,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,X1390: $i,X1391: $i,X1392: $i,X1395: $i,X1396: $i,X1398: $i,X1399: $i,X1400: $i,X1401: $i,X1402: $i > $o,X1405: $i,X1407: $i,X1408: $i > $o,X1409: $i,X1411: $i,X1412: $i > $o,X1413: $i,X1416: $i,X1417: $i > $o,X1420: $i,X1422: $i,X1423: $i] :
( ( ~ ( in @ ( esk1_2 @ X962 @ X963 ) @ X962 )
| ~ ( in @ ( esk1_2 @ X962 @ X963 ) @ X963 )
| ( X962 = X963 ) )
& ( ( in @ ( esk1_2 @ X962 @ X963 ) @ X962 )
| ( in @ ( esk1_2 @ X962 @ X963 ) @ X963 )
| ( X962 = X963 ) )
& ~ ( in @ X965 @ emptyset )
& ( ~ ( in @ X968 @ ( setadjoin @ X966 @ X967 ) )
| ( X968 = X966 )
| ( in @ X968 @ X967 ) )
& ( ( X968 != X966 )
| ( in @ X968 @ ( setadjoin @ X966 @ X967 ) ) )
& ( ~ ( in @ X968 @ X967 )
| ( in @ X968 @ ( setadjoin @ X966 @ X967 ) ) )
& ( ~ ( in @ X970 @ ( powerset @ X969 ) )
| ~ ( in @ X971 @ X970 )
| ( in @ X971 @ X969 ) )
& ( ( in @ ( esk2_2 @ X972 @ X973 ) @ X973 )
| ( in @ X973 @ ( powerset @ X972 ) ) )
& ( ~ ( in @ ( esk2_2 @ X972 @ X973 ) @ X972 )
| ( in @ X973 @ ( powerset @ X972 ) ) )
& ( ( in @ X976 @ ( esk3_2 @ X975 @ X976 ) )
| ~ ( in @ X976 @ ( setunion @ X975 ) ) )
& ( ( in @ ( esk3_2 @ X975 @ X976 ) @ X975 )
| ~ ( in @ X976 @ ( setunion @ X975 ) ) )
& ( ~ ( in @ X979 @ X980 )
| ~ ( in @ X980 @ X978 )
| ( in @ X979 @ ( setunion @ X978 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X981 @ omega )
| ( in @ ( setadjoin @ X981 @ X981 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X982 ) @ omega )
| ~ ( in @ emptyset @ X982 )
| ~ ( in @ X984 @ omega )
| ( in @ X984 @ X982 ) )
& ( ( in @ ( esk4_1 @ X982 ) @ X982 )
| ~ ( in @ emptyset @ X982 )
| ~ ( in @ X984 @ omega )
| ( in @ X984 @ X982 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X982 ) @ ( esk4_1 @ X982 ) ) @ X982 )
| ~ ( in @ emptyset @ X982 )
| ~ ( in @ X984 @ omega )
| ( in @ X984 @ X982 ) )
& ( ( in @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X986 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( in @ ( esk5_2 @ X985 @ X986 ) @ X986 ) )
& ( ( X985 @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X991 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( in @ ( esk5_2 @ X985 @ X986 ) @ X986 ) )
& ( ~ ( in @ X994 @ X986 )
| ~ ( X985 @ X994 @ X993 )
| ( in @ X993 @ ( esk7_2 @ X985 @ X986 ) )
| ( in @ ( esk5_2 @ X985 @ X986 ) @ X986 ) )
& ( ( in @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X986 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( X985 @ ( esk5_2 @ X985 @ X986 ) @ ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ( X985 @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X991 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( X985 @ ( esk5_2 @ X985 @ X986 ) @ ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ~ ( in @ X994 @ X986 )
| ~ ( X985 @ X994 @ X993 )
| ( in @ X993 @ ( esk7_2 @ X985 @ X986 ) )
| ( X985 @ ( esk5_2 @ X985 @ X986 ) @ ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ( in @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X986 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( X988
!= ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ( X985 @ ( esk8_3 @ X985 @ X986 @ X991 ) @ X991 )
| ~ ( in @ X991 @ ( esk7_2 @ X985 @ X986 ) )
| ( X988
!= ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ~ ( in @ X994 @ X986 )
| ~ ( X985 @ X994 @ X993 )
| ( in @ X993 @ ( esk7_2 @ X985 @ X986 ) )
| ( X988
!= ( esk6_3 @ X985 @ X986 @ X988 ) )
| ~ ( X985 @ ( esk5_2 @ X985 @ X986 ) @ X988 ) )
& ( ( in @ ( esk9_1 @ X995 ) @ X995 )
| ~ ( in @ X996 @ X995 ) )
& ( ~ ( in @ X998 @ ( esk9_1 @ X995 ) )
| ~ ( in @ X998 @ X995 )
| ~ ( in @ X996 @ X995 ) )
& epred1_0
& ( ( X999 @ ( esk10_2 @ X999 @ X1000 ) )
| ~ ( X999 @ X1000 )
| ( X999 @ ( descr @ X999 ) ) )
& ( ( X1000
!= ( esk10_2 @ X999 @ X1000 ) )
| ~ ( X999 @ X1000 )
| ( X999 @ ( descr @ X999 ) ) )
& ( ~ ( in @ X1004 @ X1002 )
| ~ ( X1003 @ X1004 )
| ( in @ X1004 @ ( dsetconstr @ X1002 @ X1003 ) ) )
& ( ~ ( in @ X1007 @ ( dsetconstr @ X1005 @ X1006 ) )
| ( in @ X1007 @ X1005 ) )
& ( ~ ( in @ X1010 @ ( dsetconstr @ X1008 @ X1009 ) )
| ( X1009 @ X1010 ) )
& ( ( X1011 @ ( esk12_1 @ X1011 ) )
| ( X1011 @ ( esk11_2 @ X1011 @ X1012 ) )
| ~ ( X1011 @ X1012 ) )
& ( ~ ( X1011 @ X1015 )
| ( ( esk12_1 @ X1011 )
= X1015 )
| ( X1011 @ ( esk11_2 @ X1011 @ X1012 ) )
| ~ ( X1011 @ X1012 ) )
& ( ( X1011 @ ( esk12_1 @ X1011 ) )
| ( X1012
!= ( esk11_2 @ X1011 @ X1012 ) )
| ~ ( X1011 @ X1012 ) )
& ( ~ ( X1011 @ X1015 )
| ( ( esk12_1 @ X1011 )
= X1015 )
| ( X1012
!= ( esk11_2 @ X1011 @ X1012 ) )
| ~ ( X1011 @ X1012 ) )
& ( ~ ( in @ X1017 @ ( prop2set @ X1016 ) )
| X1016 )
& ( ~ ( in @ X1018 @ emptyset )
| X1019 )
& ( ~ ( in @ X1020 @ emptyset )
| ~ $true )
& ~ ( in @ X1021 @ emptyset )
& ( ( X1022 @ ( esk13_2 @ X1022 @ X1023 ) )
| ~ ( X1022 @ X1023 )
| ( X1022 @ ( esk14_1 @ X1022 ) ) )
& ( ( X1023
!= ( esk13_2 @ X1022 @ X1023 ) )
| ~ ( X1022 @ X1023 )
| ( X1022 @ ( esk14_1 @ X1022 ) ) )
& ( ( in @ ( esk16_2 @ X1026 @ X1027 ) @ X1027 )
| ( X1026 = X1027 )
| ( in @ ( esk15_2 @ X1026 @ X1027 ) @ X1026 ) )
& ( ~ ( in @ ( esk16_2 @ X1026 @ X1027 ) @ X1026 )
| ( X1026 = X1027 )
| ( in @ ( esk15_2 @ X1026 @ X1027 ) @ X1026 ) )
& ( ( in @ ( esk16_2 @ X1026 @ X1027 ) @ X1027 )
| ( X1026 = X1027 )
| ~ ( in @ ( esk15_2 @ X1026 @ X1027 ) @ X1027 ) )
& ( ~ ( in @ ( esk16_2 @ X1026 @ X1027 ) @ X1026 )
| ( X1026 = X1027 )
| ~ ( in @ ( esk15_2 @ X1026 @ X1027 ) @ X1027 ) )
& ( ( in @ ( esk17_1 @ X1030 ) @ X1030 )
| ( X1030 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1032 ) @ X1032 )
| ( X1032 = emptyset ) )
& ( ~ ( in @ X1036 @ ( dsetconstr @ X1034 @ X1035 ) )
| ( X1035 @ X1036 )
| ~ ( in @ X1036 @ X1034 ) )
& ( ~ ( X1035 @ X1036 )
| ( in @ X1036 @ ( dsetconstr @ X1034 @ X1035 ) )
| ~ ( in @ X1036 @ X1034 ) )
& ( ( X1037 = emptyset )
| ( in @ ( esk19_1 @ X1037 ) @ X1037 ) )
& ( ~ ( in @ X1041 @ X1039 )
| ~ ( X1040 @ X1041 )
| ( ( dsetconstr @ X1039 @ X1040 )
!= emptyset ) )
& ( ~ ( in @ X1043 @ X1042 )
| ( X1042 != emptyset ) )
& ( in @ X1044 @ ( setadjoin @ X1044 @ X1045 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1048 @ X1047 )
| ( in @ X1048 @ ( setadjoin @ X1046 @ X1047 ) ) )
& ( ( in @ X1051 @ X1050 )
| X1052
| ( X1051 = X1049 )
| ~ ( in @ X1051 @ ( setadjoin @ X1049 @ X1050 ) ) )
& ( ~ X1052
| X1052
| ( X1051 = X1049 )
| ~ ( in @ X1051 @ ( setadjoin @ X1049 @ X1050 ) ) )
& ( ( in @ X1051 @ X1050 )
| X1052
| ~ X1052
| ~ ( in @ X1051 @ ( setadjoin @ X1049 @ X1050 ) ) )
& ( ~ X1052
| X1052
| ~ X1052
| ~ ( in @ X1051 @ ( setadjoin @ X1049 @ X1050 ) ) )
& ( ~ ( in @ X1055 @ ( setadjoin @ X1053 @ X1054 ) )
| ( X1055 = X1053 )
| ( in @ X1055 @ X1054 ) )
& ( ( dsetconstr @ X1056
@ ^ [Z0: $i] : $true )
= X1056 )
& ( ( in @ ( esk20_2 @ X1057 @ X1058 ) @ X1058 )
| ( in @ X1058 @ ( powerset @ X1057 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1057 @ X1058 ) @ X1057 )
| ( in @ X1058 @ ( powerset @ X1057 ) ) )
& ( in @ emptyset @ ( powerset @ X1060 ) )
& ( in @ emptyset @ ( powerset @ X1061 ) )
& ( ~ ( in @ X1063 @ ( powerset @ X1062 ) )
| ~ ( in @ X1064 @ X1063 )
| ( in @ X1064 @ X1062 ) )
& ( ~ ( in @ X1066 @ X1067 )
| ~ ( in @ X1067 @ X1065 )
| ( in @ X1066 @ ( setunion @ X1065 ) ) )
& ( ( in @ X1069 @ ( esk21_3 @ X1068 @ X1069 @ X1070 ) )
| X1070
| ~ ( in @ X1069 @ ( setunion @ X1068 ) ) )
& ( ( in @ ( esk21_3 @ X1068 @ X1069 @ X1070 ) @ X1068 )
| X1070
| ~ ( in @ X1069 @ ( setunion @ X1068 ) ) )
& ( ~ X1070
| X1070
| ~ ( in @ X1069 @ ( setunion @ X1068 ) ) )
& ( ~ ( in @ X1073 @ X1072 )
| ( in @ X1073 @ ( powerset @ ( setunion @ X1072 ) ) ) )
& ( ~ ( X1074 @ X1078 )
| ( X1078
= ( esk23_1 @ X1074 ) )
| ( X1074 @ ( esk22_2 @ X1074 @ X1075 ) )
| ~ ( X1074 @ X1075 ) )
& ( ( X1079
!= ( esk23_1 @ X1074 ) )
| ( X1074 @ X1079 )
| ( X1074 @ ( esk22_2 @ X1074 @ X1075 ) )
| ~ ( X1074 @ X1075 ) )
& ( ~ ( X1074 @ X1078 )
| ( X1078
= ( esk23_1 @ X1074 ) )
| ( X1075
!= ( esk22_2 @ X1074 @ X1075 ) )
| ~ ( X1074 @ X1075 ) )
& ( ( X1079
!= ( esk23_1 @ X1074 ) )
| ( X1074 @ X1079 )
| ( X1075
!= ( esk22_2 @ X1074 @ X1075 ) )
| ~ ( X1074 @ X1075 ) )
& ( ( in @ ( esk24_1 @ X1080 ) @ X1080 )
| ( X1080 = emptyset ) )
& ( $true
| ( X1080 = emptyset ) )
& ( ~ ( in @ X1082 @ ( setadjoin @ X1083 @ emptyset ) )
| ( X1082 = X1083 ) )
& ( ( X1084 = X1085 )
| ~ ( in @ X1085 @ ( setadjoin @ X1084 @ emptyset ) ) )
& ( ( X1086 != X1087 )
| ( in @ X1086 @ ( setadjoin @ X1087 @ emptyset ) ) )
& ( ~ ( in @ X1088 @ ( setadjoin @ X1089 @ emptyset ) )
| ( in @ X1089 @ ( setadjoin @ X1088 @ emptyset ) ) )
& ( ~ ( in @ X1092 @ ( setadjoin @ X1090 @ ( setadjoin @ X1091 @ emptyset ) ) )
| ( X1092 = X1090 )
| ( X1092 = X1091 ) )
& ( in @ X1093 @ ( setadjoin @ X1093 @ ( setadjoin @ X1094 @ emptyset ) ) )
& ( in @ X1096 @ ( setadjoin @ X1095 @ ( setadjoin @ X1096 @ emptyset ) ) )
& ( ~ ( in @ X1099 @ X1097 )
| ~ ( X1098 @ X1099 )
| ( ( dsetconstr @ X1097 @ X1098 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1101 @ emptyset )
| ( X1100 @ X1101 ) )
& ( ( in @ ( esk25_2 @ X1102 @ X1103 ) @ X1102 )
| ~ ( in @ X1104 @ X1102 )
| ( X1103 @ X1104 ) )
& ( ~ ( X1103 @ ( esk25_2 @ X1102 @ X1103 ) )
| ~ ( in @ X1104 @ X1102 )
| ( X1103 @ X1104 ) )
& ( ( in @ ( esk26_2 @ X1106 @ X1107 ) @ X1106 )
| ~ ( in @ X1109 @ X1106 )
| ~ ( X1107 @ X1109 ) )
& ( ( X1107 @ ( esk26_2 @ X1106 @ X1107 ) )
| ~ ( in @ X1109 @ X1106 )
| ~ ( X1107 @ X1109 ) )
& ( ( in @ ( esk27_2 @ X1110 @ X1111 ) @ X1110 )
| ~ ( in @ X1113 @ X1110 )
| ~ ( X1111 @ X1113 ) )
& ( ( X1111 @ ( esk27_2 @ X1110 @ X1111 ) )
| ~ ( in @ X1113 @ X1110 )
| ~ ( X1111 @ X1113 ) )
& ( ( in @ ( esk28_2 @ X1114 @ X1115 ) @ X1114 )
| ~ ( in @ X1116 @ X1114 )
| ( X1115 @ X1116 ) )
& ( ~ ( X1115 @ ( esk28_2 @ X1114 @ X1115 ) )
| ~ ( in @ X1116 @ X1114 )
| ( X1115 @ X1116 ) )
& ( ~ X1118
| ( in @ emptyset @ ( prop2set @ X1118 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X1119 @ X1120 ) @ X1119 )
| ~ ( in @ X1122 @ X1119 )
| ~ ( X1120 @ X1122 ) )
& ( ( X1120 @ ( esk29_2 @ X1119 @ X1120 ) )
| ~ ( in @ X1122 @ X1119 )
| ~ ( X1120 @ X1122 ) )
& ( ( in @ ( esk30_2 @ X1123 @ X1124 ) @ X1123 )
| ~ ( in @ X1125 @ X1123 )
| ( X1124 @ X1125 ) )
& ( ~ ( X1124 @ ( esk30_2 @ X1123 @ X1124 ) )
| ~ ( in @ X1125 @ X1123 )
| ( X1124 @ X1125 ) )
& ( ( X1127 @ ( esk32_1 @ X1127 ) )
| ( X1127 @ ( esk31_2 @ X1127 @ X1128 ) )
| ~ ( X1127 @ X1128 ) )
& ( ~ ( X1127 @ X1131 )
| ( ( esk32_1 @ X1127 )
= X1131 )
| ( X1127 @ ( esk31_2 @ X1127 @ X1128 ) )
| ~ ( X1127 @ X1128 ) )
& ( ( X1127 @ ( esk32_1 @ X1127 ) )
| ( X1128
!= ( esk31_2 @ X1127 @ X1128 ) )
| ~ ( X1127 @ X1128 ) )
& ( ~ ( X1127 @ X1131 )
| ( ( esk32_1 @ X1127 )
= X1131 )
| ( X1128
!= ( esk31_2 @ X1127 @ X1128 ) )
| ~ ( X1127 @ X1128 ) )
& ( ( X1132 @ ( esk35_1 @ X1132 ) )
| ( X1132 @ ( esk33_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ~ ( X1132 @ X1137 )
| ( ( esk35_1 @ X1132 )
= X1137 )
| ( X1132 @ ( esk33_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ( X1132 @ ( esk35_1 @ X1132 ) )
| ( X1132 @ ( esk34_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ~ ( X1132 @ X1137 )
| ( ( esk35_1 @ X1132 )
= X1137 )
| ( X1132 @ ( esk34_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ( X1132 @ ( esk35_1 @ X1132 ) )
| ( ( esk33_1 @ X1132 )
!= ( esk34_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ~ ( X1132 @ X1137 )
| ( ( esk35_1 @ X1132 )
= X1137 )
| ( ( esk33_1 @ X1132 )
!= ( esk34_1 @ X1132 ) )
| ~ ( X1132 @ X1133 ) )
& ( ( X1138 @ ( esk37_1 @ X1138 ) )
| ~ ( X1138 @ ( esk36_2 @ X1138 @ X1139 ) )
| ( ( esk36_2 @ X1138 @ X1139 )
!= X1139 ) )
& ( ~ ( X1138 @ X1142 )
| ( ( esk37_1 @ X1138 )
= X1142 )
| ~ ( X1138 @ ( esk36_2 @ X1138 @ X1139 ) )
| ( ( esk36_2 @ X1138 @ X1139 )
!= X1139 ) )
& ( ( X1138 @ ( esk37_1 @ X1138 ) )
| ( X1138 @ ( esk36_2 @ X1138 @ X1139 ) )
| ( ( esk36_2 @ X1138 @ X1139 )
= X1139 ) )
& ( ~ ( X1138 @ X1142 )
| ( ( esk37_1 @ X1138 )
= X1142 )
| ( X1138 @ ( esk36_2 @ X1138 @ X1139 ) )
| ( ( esk36_2 @ X1138 @ X1139 )
= X1139 ) )
& ( ( X1143 != X1144 )
| ( X1145 != X1146 )
| ~ ( in @ X1145 @ X1143 )
| ( in @ X1146 @ X1144 ) )
& ( ~ ( in @ X1149 @ X1147 )
| ( in @ X1150 @ X1148 )
| ( X1149 != X1150 )
| ( X1147 != X1148 ) )
& ( ~ ( in @ X1150 @ X1148 )
| ( in @ X1149 @ X1147 )
| ( X1149 != X1150 )
| ( X1147 != X1148 ) )
& ( ( X1151 @ ( esk38_2 @ X1151 @ X1152 ) )
| ~ ( X1151 @ X1152 )
| ~ ( X1151 @ X1154 )
| ~ ( X1151 @ X1155 )
| ( X1154 = X1155 ) )
& ( ( X1152
!= ( esk38_2 @ X1151 @ X1152 ) )
| ~ ( X1151 @ X1152 )
| ~ ( X1151 @ X1154 )
| ~ ( X1151 @ X1155 )
| ( X1154 = X1155 ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( ( esk39_2 @ X1156 @ X1157 )
= ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ~ ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ~ ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1156 @ ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1157 @ ( esk42_2 @ X1156 @ X1157 ) )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1157 @ X1163 )
| ( ( esk42_2 @ X1156 @ X1157 )
= X1163 )
| ( X1160
!= ( esk41_3 @ X1156 @ X1157 @ X1160 ) )
| ~ ( X1156 @ X1160 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1157 @ ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ( X1156 @ ( esk44_2 @ X1156 @ X1157 ) )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( ~ ( X1156 @ X1167 )
| ( ( esk44_2 @ X1156 @ X1157 )
= X1167 )
| ( X1164
!= ( esk43_3 @ X1156 @ X1157 @ X1164 ) )
| ~ ( X1157 @ X1164 )
| ( X1156 @ ( esk39_2 @ X1156 @ X1157 ) )
| ( X1157 @ ( esk40_2 @ X1156 @ X1157 ) ) )
& ( emptyset = emptyset )
& ( ( X1168 != X1169 )
| ( X1170 != X1171 )
| ( ( setadjoin @ X1168 @ X1170 )
= ( setadjoin @ X1169 @ X1171 ) ) )
& ( ( X1172 != X1173 )
| ( ( powerset @ X1172 )
= ( powerset @ X1173 ) ) )
& ( ( X1174 != X1175 )
| ( ( setunion @ X1174 )
= ( setunion @ X1175 ) ) )
& ( omega = omega )
& ( ( X1176 @ ( esk45_2 @ X1176 @ X1177 ) )
| ~ ( X1176 @ X1177 )
| ~ ( X1176 @ X1179 )
| ~ ( X1176 @ X1180 )
| ( X1179 = X1180 ) )
& ( ( X1177
!= ( esk45_2 @ X1176 @ X1177 ) )
| ~ ( X1176 @ X1177 )
| ~ ( X1176 @ X1179 )
| ~ ( X1176 @ X1180 )
| ( X1179 = X1180 ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( ( esk46_2 @ X1181 @ X1182 )
= ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( ( esk46_2 @ X1181 @ X1182 )
= ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( ( esk46_2 @ X1181 @ X1182 )
= ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( ( esk46_2 @ X1181 @ X1182 )
= ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ~ ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ~ ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ~ ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ~ ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ~ ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ~ ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ~ ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ~ ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1181 @ ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1182 @ ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( X1187
!= ( esk49_3 @ X1181 @ X1182 @ X1187 ) )
| ~ ( X1182 @ X1187 )
| ( ( descr @ X1181 )
= ( descr @ X1182 ) )
| ( X1185
!= ( esk48_3 @ X1181 @ X1182 @ X1185 ) )
| ~ ( X1181 @ X1185 )
| ( X1181 @ ( esk46_2 @ X1181 @ X1182 ) )
| ( X1182 @ ( esk47_2 @ X1181 @ X1182 ) ) )
& ( ( in @ ( esk50_4 @ X1189 @ X1190 @ X1191 @ X1192 ) @ X1189 )
| ( ( dsetconstr @ X1189 @ X1191 )
= ( dsetconstr @ X1190 @ X1192 ) )
| ( X1189 != X1190 ) )
& ( ( in @ ( esk51_4 @ X1189 @ X1190 @ X1191 @ X1192 ) @ X1190 )
| ( ( dsetconstr @ X1189 @ X1191 )
= ( dsetconstr @ X1190 @ X1192 ) )
| ( X1189 != X1190 ) )
& ( ( ( esk50_4 @ X1189 @ X1190 @ X1191 @ X1192 )
= ( esk51_4 @ X1189 @ X1190 @ X1191 @ X1192 ) )
| ( ( dsetconstr @ X1189 @ X1191 )
= ( dsetconstr @ X1190 @ X1192 ) )
| ( X1189 != X1190 ) )
& ( ~ ( X1191 @ ( esk50_4 @ X1189 @ X1190 @ X1191 @ X1192 ) )
| ~ ( X1192 @ ( esk51_4 @ X1189 @ X1190 @ X1191 @ X1192 ) )
| ( ( dsetconstr @ X1189 @ X1191 )
= ( dsetconstr @ X1190 @ X1192 ) )
| ( X1189 != X1190 ) )
& ( ( X1191 @ ( esk50_4 @ X1189 @ X1190 @ X1191 @ X1192 ) )
| ( X1192 @ ( esk51_4 @ X1189 @ X1190 @ X1191 @ X1192 ) )
| ( ( dsetconstr @ X1189 @ X1191 )
= ( dsetconstr @ X1190 @ X1192 ) )
| ( X1189 != X1190 ) )
& ( ( in @ ( esk52_2 @ X1195 @ X1196 ) @ X1195 )
| ( subset @ X1195 @ X1196 ) )
& ( ~ ( in @ ( esk52_2 @ X1195 @ X1196 ) @ X1196 )
| ( subset @ X1195 @ X1196 ) )
& ( ( X1198 != X1199 )
| ( subset @ X1199 @ X1198 ) )
& ( ( X1200 != X1201 )
| ( subset @ X1200 @ X1201 ) )
& ( ( in @ ( esk53_2 @ X1202 @ X1203 ) @ X1202 )
| ( subset @ X1202 @ X1203 ) )
& ( ~ ( in @ ( esk53_2 @ X1202 @ X1203 ) @ X1203 )
| ( subset @ X1202 @ X1203 ) )
& ( subset @ emptyset @ X1205 )
& ( ~ ( subset @ X1206 @ X1207 )
| ~ ( in @ X1208 @ X1206 )
| ( in @ X1208 @ X1207 ) )
& ( ~ ( subset @ X1209 @ X1210 )
| ( in @ X1211 @ X1210 )
| ~ ( in @ X1211 @ X1209 ) )
& ( ~ ( in @ X1214 @ X1212 )
| ( in @ X1214 @ X1213 )
| ~ ( subset @ X1212 @ X1213 ) )
& ( ( subset @ X1215 @ X1216 )
| ( X1215 != X1216 ) )
& ( ~ ( in @ X1219 @ X1217 )
| ( in @ X1219 @ X1218 )
| ( X1217 != X1218 ) )
& ( subset @ X1220 @ X1220 )
& ( ~ ( subset @ X1221 @ X1222 )
| ~ ( subset @ X1222 @ X1223 )
| ( subset @ X1221 @ X1223 ) )
& ( subset @ X1225 @ ( setadjoin @ X1224 @ X1225 ) )
& ( ~ ( subset @ X1226 @ X1228 )
| ( subset @ X1226 @ ( setadjoin @ X1227 @ X1228 ) ) )
& ( ~ ( subset @ X1229 @ X1230 )
| ( in @ X1229 @ ( powerset @ X1230 ) ) )
& ( ~ ( subset @ X1231 @ X1232 )
| ~ ( subset @ X1232 @ X1231 )
| ( X1231 = X1232 ) )
& ( ~ ( subset @ X1233 @ emptyset )
| ( X1233 = emptyset ) )
& ( ~ ( subset @ X1235 @ X1234 )
| ( in @ X1235 @ ( powerset @ X1234 ) ) )
& ( ~ ( in @ X1237 @ ( powerset @ X1236 ) )
| ( subset @ X1237 @ X1236 ) )
& ( in @ X1238 @ ( powerset @ X1238 ) )
& ( ~ ( subset @ X1239 @ X1240 )
| ( subset @ ( powerset @ X1239 ) @ ( powerset @ X1240 ) ) )
& ( in @ ( dsetconstr @ X1241 @ X1242 ) @ ( powerset @ X1241 ) )
& ( subset @ ( dsetconstr @ X1243 @ X1244 ) @ X1243 )
& ( ~ ( in @ X1247 @ X1245 )
| ( in @ X1247 @ ( binunion @ X1245 @ X1246 ) ) )
& ( in @ X1249 @ ( setadjoin @ X1248 @ ( setadjoin @ X1249 @ emptyset ) ) )
& ( ~ ( in @ X1252 @ X1251 )
| ( in @ X1252 @ ( binunion @ X1250 @ X1251 ) ) )
& ( ( in @ X1255 @ X1254 )
| X1256
| ( in @ X1255 @ X1253 )
| ~ ( in @ X1255 @ ( binunion @ X1253 @ X1254 ) ) )
& ( ~ X1256
| X1256
| ( in @ X1255 @ X1253 )
| ~ ( in @ X1255 @ ( binunion @ X1253 @ X1254 ) ) )
& ( ( in @ X1255 @ X1254 )
| X1256
| ~ X1256
| ~ ( in @ X1255 @ ( binunion @ X1253 @ X1254 ) ) )
& ( ~ X1256
| X1256
| ~ X1256
| ~ ( in @ X1255 @ ( binunion @ X1253 @ X1254 ) ) )
& ( ~ ( in @ X1259 @ ( binunion @ X1257 @ X1258 ) )
| ( in @ X1259 @ X1257 )
| ( in @ X1259 @ X1258 ) )
& ( subset @ X1260 @ ( binunion @ X1260 @ X1261 ) )
& ( subset @ X1263 @ ( binunion @ X1262 @ X1263 ) )
& ( ~ ( in @ X1266 @ X1264 )
| ~ ( in @ X1266 @ X1265 )
| ( in @ X1266 @ ( binintersect @ X1264 @ X1265 ) ) )
& ( ~ ( subset @ X1269 @ X1267 )
| ~ ( subset @ X1269 @ X1268 )
| ( subset @ X1269 @ ( binintersect @ X1267 @ X1268 ) ) )
& ( ~ ( in @ X1272 @ ( binintersect @ X1270 @ X1271 ) )
| ( in @ X1272 @ X1270 ) )
& ( subset @ ( binintersect @ X1273 @ X1274 ) @ X1273 )
& ( ~ ( subset @ X1275 @ X1276 )
| ( ( binintersect @ X1275 @ X1276 )
= X1275 ) )
& ( ( ( binintersect @ X1277 @ X1278 )
!= X1278 )
| ( subset @ X1278 @ X1277 ) )
& ( ~ ( in @ X1281 @ ( binintersect @ X1279 @ X1280 ) )
| ( in @ X1281 @ X1280 ) )
& ( ( in @ ( esk54_2 @ X1282 @ X1283 ) @ X1282 )
| ( ( binintersect @ X1282 @ X1283 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1282 @ X1283 ) @ X1283 )
| ( ( binintersect @ X1282 @ X1283 )
= emptyset ) )
& ( subset @ ( binintersect @ X1285 @ X1286 ) @ X1286 )
& ( ~ ( subset @ X1288 @ X1287 )
| ( ( binintersect @ X1287 @ X1288 )
= X1288 ) )
& ( ( ( binintersect @ X1289 @ X1290 )
!= X1289 )
| ( subset @ X1289 @ X1290 ) )
& ( ( binintersect @ X1291 @ ( binunion @ X1292 @ X1293 ) )
= ( binunion @ ( binintersect @ X1291 @ X1292 ) @ ( binintersect @ X1291 @ X1293 ) ) )
& ( ~ ( in @ X1296 @ X1294 )
| ( in @ X1296 @ X1295 )
| ( in @ X1296 @ ( setminus @ X1294 @ X1295 ) ) )
& ( ~ ( in @ X1299 @ ( setminus @ X1297 @ X1298 ) )
| ( in @ X1299 @ X1297 ) )
& ( ~ ( in @ X1302 @ ( setminus @ X1300 @ X1301 ) )
| ~ ( in @ X1302 @ X1301 ) )
& ( ~ ( subset @ X1303 @ X1304 )
| ( ( setminus @ X1303 @ X1304 )
= emptyset ) )
& ( ( in @ X1307 @ ( setminus @ X1305 @ X1306 ) )
| ~ ( in @ X1307 @ X1305 )
| ( in @ X1307 @ X1306 ) )
& ( ( in @ X1310 @ ( setminus @ X1308 @ X1309 ) )
| ( in @ X1310 @ X1309 )
| ~ ( in @ X1310 @ X1308 ) )
& ( ( in @ X1313 @ X1311 )
| ~ ( in @ X1313 @ ( setminus @ X1311 @ X1312 ) ) )
& ( ~ ( in @ X1316 @ X1315 )
| ~ ( in @ X1316 @ ( setminus @ X1314 @ X1315 ) ) )
& ( subset @ ( setminus @ X1317 @ X1318 ) @ X1317 )
& ( ( ( setminus @ X1319 @ X1320 )
!= emptyset )
| ( subset @ X1319 @ X1320 ) )
& ( ~ ( in @ X1323 @ X1321 )
| X1324
| ( in @ X1323 @ X1321 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ( in @ X1323 @ X1322 )
| X1324
| ( in @ X1323 @ X1321 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ X1324
| X1324
| ( in @ X1323 @ X1321 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ ( in @ X1323 @ X1321 )
| X1324
| ~ ( in @ X1323 @ X1322 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ( in @ X1323 @ X1322 )
| X1324
| ~ ( in @ X1323 @ X1322 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ X1324
| X1324
| ~ ( in @ X1323 @ X1322 )
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ ( in @ X1323 @ X1321 )
| X1324
| ~ X1324
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ( in @ X1323 @ X1322 )
| X1324
| ~ X1324
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ X1324
| X1324
| ~ X1324
| ~ ( in @ X1323 @ ( symdiff @ X1321 @ X1322 ) ) )
& ( ~ ( in @ X1327 @ X1325 )
| ( in @ X1327 @ X1326 )
| ( in @ X1327 @ ( symdiff @ X1325 @ X1326 ) ) )
& ( ( in @ X1330 @ X1328 )
| ~ ( in @ X1330 @ X1329 )
| ( in @ X1330 @ ( symdiff @ X1328 @ X1329 ) ) )
& ( ~ ( in @ X1333 @ X1331 )
| ~ ( in @ X1333 @ X1332 )
| ~ ( in @ X1333 @ ( symdiff @ X1331 @ X1332 ) ) )
& ( ( in @ X1336 @ X1334 )
| ( in @ X1336 @ X1335 )
| ~ ( in @ X1336 @ ( symdiff @ X1334 @ X1335 ) ) )
& ( in @ X1338 @ ( setadjoin @ X1337 @ ( setadjoin @ X1338 @ emptyset ) ) )
& ( in @ X1339 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1339 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1339 @ ( setadjoin @ X1340 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1342 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1341 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1341 @ ( setadjoin @ X1342 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk55_2 @ X1343 @ X1344 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1343 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1343 @ ( setadjoin @ X1344 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk56_2 @ X1343 @ X1344 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1343 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1343 @ ( setadjoin @ X1344 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1343 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1343 @ ( setadjoin @ X1344 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1343 @ X1344 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1343 @ X1344 ) @ ( setadjoin @ ( esk56_2 @ X1343 @ X1344 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( esk57_2 @ X1347 @ X1348 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1347 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1347 @ ( setadjoin @ X1348 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk58_2 @ X1347 @ X1348 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1347 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1347 @ ( setadjoin @ X1348 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1347 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1347 @ ( setadjoin @ X1348 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1347 @ X1348 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1347 @ X1348 ) @ ( setadjoin @ ( esk58_2 @ X1347 @ X1348 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X1352 @ X1351 )
| ( subset @ ( setadjoin @ X1352 @ emptyset ) @ X1351 ) )
& ( ~ ( in @ X1354 @ X1353 )
| ( in @ ( setadjoin @ X1354 @ emptyset ) @ ( powerset @ X1353 ) ) )
& ( ~ ( in @ X1357 @ X1355 )
| ( in @ ( setadjoin @ X1357 @ emptyset ) @ ( powerset @ ( binunion @ X1355 @ X1356 ) ) ) )
& ( ~ ( in @ X1360 @ ( setadjoin @ X1358 @ ( setadjoin @ X1359 @ emptyset ) ) )
| ( X1360 = X1358 )
| ( X1360 = X1359 ) )
& ( ~ ( in @ X1363 @ X1361 )
| ~ ( in @ X1364 @ X1362 )
| ( subset @ ( setadjoin @ X1363 @ ( setadjoin @ X1364 @ emptyset ) ) @ ( binunion @ X1361 @ X1362 ) ) )
& ( ~ ( in @ X1367 @ X1365 )
| ~ ( in @ X1368 @ X1366 )
| ( in @ ( setadjoin @ X1367 @ ( setadjoin @ X1368 @ emptyset ) ) @ ( powerset @ ( binunion @ X1365 @ X1366 ) ) ) )
& ( ~ ( in @ X1371 @ X1369 )
| ~ ( in @ X1372 @ X1370 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1371 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1371 @ ( setadjoin @ X1372 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1369 @ X1370 ) ) ) )
& ( ~ ( in @ X1375 @ X1373 )
| ~ ( in @ X1376 @ X1374 )
| ( in @ ( setadjoin @ ( setadjoin @ X1375 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1375 @ ( setadjoin @ X1376 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1373 @ X1374 ) ) ) ) )
& ( ~ ( in @ X1379 @ X1377 )
| ~ ( in @ X1380 @ X1378 )
| ( in @ ( setadjoin @ ( setadjoin @ X1379 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1379 @ ( setadjoin @ X1380 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1377 @ X1378 ) ) ) ) )
& ( ~ ( in @ X1383 @ X1381 )
| ~ ( in @ X1384 @ X1382 )
| ( in @ ( setadjoin @ ( setadjoin @ X1383 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1383 @ ( setadjoin @ X1384 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ X1381 @ X1382 ) ) )
& ( ( in @ ( esk59_3 @ X1385 @ X1386 @ X1387 ) @ X1385 )
| ~ ( in @ X1387 @ ( cartprod @ X1385 @ X1386 ) ) )
& ( ( in @ ( esk60_3 @ X1385 @ X1386 @ X1387 ) @ X1386 )
| ~ ( in @ X1387 @ ( cartprod @ X1385 @ X1386 ) ) )
& ( ( X1387
= ( setadjoin @ ( setadjoin @ ( esk59_3 @ X1385 @ X1386 @ X1387 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk59_3 @ X1385 @ X1386 @ X1387 ) @ ( setadjoin @ ( esk60_3 @ X1385 @ X1386 @ X1387 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1387 @ ( cartprod @ X1385 @ X1386 ) ) )
& ( ( in @ ( esk61_3 @ X1390 @ X1391 @ X1392 ) @ ( setunion @ X1392 ) )
| ~ ( in @ X1392 @ ( cartprod @ X1390 @ X1391 ) ) )
& ( ( in @ ( esk62_3 @ X1390 @ X1391 @ X1392 ) @ ( setunion @ X1392 ) )
| ~ ( in @ X1392 @ ( cartprod @ X1390 @ X1391 ) ) )
& ( ( X1392
= ( setadjoin @ ( setadjoin @ ( esk61_3 @ X1390 @ X1391 @ X1392 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk61_3 @ X1390 @ X1391 @ X1392 ) @ ( setadjoin @ ( esk62_3 @ X1390 @ X1391 @ X1392 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1392 @ ( cartprod @ X1390 @ X1391 ) ) )
& ( ( in @ ( esk63_2 @ X1395 @ X1396 ) @ X1395 )
| ~ ( in @ X1396 @ ( setunion @ X1395 ) ) )
& ( ( in @ X1396 @ ( esk63_2 @ X1395 @ X1396 ) )
| ~ ( in @ X1396 @ ( setunion @ X1395 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1398 @ emptyset ) ) @ X1398 )
& ( subset @ X1399 @ ( setunion @ ( setadjoin @ X1399 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1400 @ emptyset ) )
= X1400 )
& ( ( in @ ( esk66_2 @ X1401 @ X1402 ) @ ( dsetconstr @ X1401 @ X1402 ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( in @ ( esk64_2 @ X1401 @ X1402 ) @ X1401 ) )
& ( ( ( dsetconstr @ X1401 @ X1402 )
= ( setadjoin @ ( esk66_2 @ X1401 @ X1402 ) @ emptyset ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( in @ ( esk64_2 @ X1401 @ X1402 ) @ X1401 ) )
& ( ( in @ ( esk66_2 @ X1401 @ X1402 ) @ ( dsetconstr @ X1401 @ X1402 ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( in @ ( esk65_2 @ X1401 @ X1402 ) @ X1401 ) )
& ( ( ( dsetconstr @ X1401 @ X1402 )
= ( setadjoin @ ( esk66_2 @ X1401 @ X1402 ) @ emptyset ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( in @ ( esk65_2 @ X1401 @ X1402 ) @ X1401 ) )
& ( ( in @ ( esk66_2 @ X1401 @ X1402 ) @ ( dsetconstr @ X1401 @ X1402 ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( X1402 @ ( esk64_2 @ X1401 @ X1402 ) ) )
& ( ( ( dsetconstr @ X1401 @ X1402 )
= ( setadjoin @ ( esk66_2 @ X1401 @ X1402 ) @ emptyset ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( X1402 @ ( esk64_2 @ X1401 @ X1402 ) ) )
& ( ( in @ ( esk66_2 @ X1401 @ X1402 ) @ ( dsetconstr @ X1401 @ X1402 ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( X1402 @ ( esk65_2 @ X1401 @ X1402 ) ) )
& ( ( ( dsetconstr @ X1401 @ X1402 )
= ( setadjoin @ ( esk66_2 @ X1401 @ X1402 ) @ emptyset ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( X1402 @ ( esk65_2 @ X1401 @ X1402 ) ) )
& ( ( in @ ( esk66_2 @ X1401 @ X1402 ) @ ( dsetconstr @ X1401 @ X1402 ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( ( esk64_2 @ X1401 @ X1402 )
!= ( esk65_2 @ X1401 @ X1402 ) ) )
& ( ( ( dsetconstr @ X1401 @ X1402 )
= ( setadjoin @ ( esk66_2 @ X1401 @ X1402 ) @ emptyset ) )
| ~ ( in @ X1405 @ X1401 )
| ~ ( X1402 @ X1405 )
| ( ( esk64_2 @ X1401 @ X1402 )
!= ( esk65_2 @ X1401 @ X1402 ) ) )
& ( ( in @ ( esk67_2 @ X1407 @ X1408 ) @ X1407 )
| ~ ( in @ X1409 @ ( dsetconstr @ X1407 @ X1408 ) )
| ( ( dsetconstr @ X1407 @ X1408 )
!= ( setadjoin @ X1409 @ emptyset ) ) )
& ( ( X1408 @ ( esk67_2 @ X1407 @ X1408 ) )
| ~ ( in @ X1409 @ ( dsetconstr @ X1407 @ X1408 ) )
| ( ( dsetconstr @ X1407 @ X1408 )
!= ( setadjoin @ X1409 @ emptyset ) ) )
& ( ( in @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ ( dsetconstr @ X1411 @ X1412 ) )
| ( in @ ( esk68_3 @ X1411 @ X1412 @ X1413 ) @ X1411 )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( ( dsetconstr @ X1411 @ X1412 )
= ( setadjoin @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ emptyset ) )
| ( in @ ( esk68_3 @ X1411 @ X1412 @ X1413 ) @ X1411 )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( in @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ ( dsetconstr @ X1411 @ X1412 ) )
| ( X1412 @ ( esk68_3 @ X1411 @ X1412 @ X1413 ) )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( ( dsetconstr @ X1411 @ X1412 )
= ( setadjoin @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ emptyset ) )
| ( X1412 @ ( esk68_3 @ X1411 @ X1412 @ X1413 ) )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( in @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ ( dsetconstr @ X1411 @ X1412 ) )
| ( ( esk68_3 @ X1411 @ X1412 @ X1413 )
!= X1413 )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( ( dsetconstr @ X1411 @ X1412 )
= ( setadjoin @ ( esk69_3 @ X1411 @ X1412 @ X1413 ) @ emptyset ) )
| ( ( esk68_3 @ X1411 @ X1412 @ X1413 )
!= X1413 )
| ~ ( X1412 @ X1413 )
| ~ ( in @ X1413 @ X1411 ) )
& ( ( in @ ( esk72_2 @ X1416 @ X1417 ) @ ( dsetconstr @ X1416 @ X1417 ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( in @ ( esk70_2 @ X1416 @ X1417 ) @ X1416 ) )
& ( ( ( dsetconstr @ X1416 @ X1417 )
= ( setadjoin @ ( esk72_2 @ X1416 @ X1417 ) @ emptyset ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( in @ ( esk70_2 @ X1416 @ X1417 ) @ X1416 ) )
& ( ( in @ ( esk72_2 @ X1416 @ X1417 ) @ ( dsetconstr @ X1416 @ X1417 ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( in @ ( esk71_2 @ X1416 @ X1417 ) @ X1416 ) )
& ( ( ( dsetconstr @ X1416 @ X1417 )
= ( setadjoin @ ( esk72_2 @ X1416 @ X1417 ) @ emptyset ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( in @ ( esk71_2 @ X1416 @ X1417 ) @ X1416 ) )
& ( ( in @ ( esk72_2 @ X1416 @ X1417 ) @ ( dsetconstr @ X1416 @ X1417 ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( X1417 @ ( esk70_2 @ X1416 @ X1417 ) ) )
& ( ( ( dsetconstr @ X1416 @ X1417 )
= ( setadjoin @ ( esk72_2 @ X1416 @ X1417 ) @ emptyset ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( X1417 @ ( esk70_2 @ X1416 @ X1417 ) ) )
& ( ( in @ ( esk72_2 @ X1416 @ X1417 ) @ ( dsetconstr @ X1416 @ X1417 ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( X1417 @ ( esk71_2 @ X1416 @ X1417 ) ) )
& ( ( ( dsetconstr @ X1416 @ X1417 )
= ( setadjoin @ ( esk72_2 @ X1416 @ X1417 ) @ emptyset ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( X1417 @ ( esk71_2 @ X1416 @ X1417 ) ) )
& ( ( in @ ( esk72_2 @ X1416 @ X1417 ) @ ( dsetconstr @ X1416 @ X1417 ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( ( esk70_2 @ X1416 @ X1417 )
!= ( esk71_2 @ X1416 @ X1417 ) ) )
& ( ( ( dsetconstr @ X1416 @ X1417 )
= ( setadjoin @ ( esk72_2 @ X1416 @ X1417 ) @ emptyset ) )
| ~ ( in @ X1420 @ X1416 )
| ~ ( X1417 @ X1420 )
| ( ( esk70_2 @ X1416 @ X1417 )
!= ( esk71_2 @ X1416 @ X1417 ) ) )
& ( ( ( setadjoin @ X1422 @ emptyset )
!= ( setadjoin @ X1423 @ emptyset ) )
| ( X1422 = X1423 ) )
& ( in @ ( setadjoin @ esk75_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk73_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk73_0 @ ( setadjoin @ esk74_0 @ emptyset ) ) @ emptyset ) ) )
& ( esk73_0 != esk75_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_224])])])])])])]) ).
thf(c_0_226,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( X2 = X4 )
| ~ ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_227,negated_conjecture,
in @ ( setadjoin @ esk75_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk73_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk73_0 @ ( setadjoin @ esk74_0 @ emptyset ) ) @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_228,negated_conjecture,
! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_229,negated_conjecture,
( ( ( setadjoin @ esk73_0 @ ( setadjoin @ esk74_0 @ emptyset ) )
= ( setadjoin @ esk75_0 @ emptyset ) )
| ( ( setadjoin @ esk75_0 @ emptyset )
= ( setadjoin @ esk73_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
thf(c_0_230,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ( X2 = X4 )
| ~ ( in @ X2 @ ( setadjoin @ X4 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_225])])]) ).
thf(c_0_231,negated_conjecture,
( ( ( setadjoin @ esk75_0 @ emptyset )
= ( setadjoin @ esk73_0 @ emptyset ) )
| ( in @ esk73_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_228,c_0_229]) ).
thf(c_0_232,negated_conjecture,
esk73_0 != esk75_0,
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_233,negated_conjecture,
! [X2: $i] :
~ ( in @ X2 @ emptyset ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_234,negated_conjecture,
! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
thf(c_0_235,negated_conjecture,
( ( setadjoin @ esk75_0 @ emptyset )
= ( setadjoin @ esk73_0 @ emptyset ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_232]),c_0_233]) ).
thf(c_0_236,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_234]),c_0_232]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU642^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 15:35:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/0.61 # Version: 3.1.0-ho
% 0.73/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.73/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.73/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.73/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.73/0.61 # Starting pre_casc_3 with 300s (1) cores
% 0.73/0.61 # Starting ho_unfolding_8 with 300s (1) cores
% 0.73/0.61 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.73/0.61 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.61 # Starting new_ho_5 with 300s (1) cores
% 0.73/0.61 # new_bool_3 with pid 17622 completed with status 0
% 0.73/0.61 # Result found by new_bool_3
% 0.73/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.73/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.73/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.73/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.73/0.61 # Starting pre_casc_3 with 300s (1) cores
% 0.73/0.61 # Starting ho_unfolding_8 with 300s (1) cores
% 0.73/0.61 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.73/0.61 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.73/0.61 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.73/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.73/0.61 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.73/0.61 # new_ho_10_cnf2 with pid 17631 completed with status 0
% 0.73/0.61 # Result found by new_ho_10_cnf2
% 0.73/0.61 # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.73/0.61 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.73/0.61 # Starting ehoh_best5 with 300s (1) cores
% 0.73/0.61 # Starting almost_fo_3_lam with 300s (1) cores
% 0.73/0.61 # Starting new_bool_5 with 300s (1) cores
% 0.73/0.61 # Starting pre_casc_3 with 300s (1) cores
% 0.73/0.61 # Starting ho_unfolding_8 with 300s (1) cores
% 0.73/0.61 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.73/0.61 # Starting new_bool_3 with 300s (1) cores
% 0.73/0.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.73/0.61 # Search class: HGHSM-FSLM31-MHFMMSBN
% 0.73/0.61 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.73/0.61 # Starting new_ho_10_cnf2 with 163s (1) cores
% 0.73/0.61 # Preprocessing time : 0.006 s
% 0.73/0.61 # Presaturation interreduction done
% 0.73/0.61
% 0.73/0.61 # Proof found!
% 0.73/0.61 # SZS status Theorem
% 0.73/0.61 # SZS output start CNFRefutation
% See solution above
% 0.73/0.61 # Parsed axioms : 352
% 0.73/0.61 # Removed by relevancy pruning/SinE : 188
% 0.73/0.61 # Initial clauses : 315
% 0.73/0.61 # Removed in clause preprocessing : 24
% 0.73/0.61 # Initial clauses in saturation : 291
% 0.73/0.61 # Processed clauses : 526
% 0.73/0.61 # ...of these trivial : 12
% 0.73/0.61 # ...subsumed : 68
% 0.73/0.61 # ...remaining for further processing : 446
% 0.73/0.61 # Other redundant clauses eliminated : 18
% 0.73/0.61 # Clauses deleted for lack of memory : 0
% 0.73/0.61 # Backward-subsumed : 0
% 0.73/0.61 # Backward-rewritten : 8
% 0.73/0.61 # Generated clauses : 2020
% 0.73/0.61 # ...of the previous two non-redundant : 1899
% 0.73/0.61 # ...aggressively subsumed : 0
% 0.73/0.61 # Contextual simplify-reflections : 0
% 0.73/0.61 # Paramodulations : 2001
% 0.73/0.61 # Factorizations : 0
% 0.73/0.61 # NegExts : 0
% 0.73/0.61 # Equation resolutions : 19
% 0.73/0.61 # Disequality decompositions : 0
% 0.73/0.61 # Total rewrite steps : 180
% 0.73/0.61 # ...of those cached : 131
% 0.73/0.61 # Propositional unsat checks : 0
% 0.73/0.61 # Propositional check models : 0
% 0.73/0.61 # Propositional check unsatisfiable : 0
% 0.73/0.61 # Propositional clauses : 0
% 0.73/0.62 # Propositional clauses after purity: 0
% 0.73/0.62 # Propositional unsat core size : 0
% 0.73/0.62 # Propositional preprocessing time : 0.000
% 0.73/0.62 # Propositional encoding time : 0.000
% 0.73/0.62 # Propositional solver time : 0.000
% 0.73/0.62 # Success case prop preproc time : 0.000
% 0.73/0.62 # Success case prop encoding time : 0.000
% 0.73/0.62 # Success case prop solver time : 0.000
% 0.73/0.62 # Current number of processed clauses : 172
% 0.73/0.62 # Positive orientable unit clauses : 41
% 0.73/0.62 # Positive unorientable unit clauses: 0
% 0.73/0.62 # Negative unit clauses : 3
% 0.73/0.62 # Non-unit-clauses : 128
% 0.73/0.62 # Current number of unprocessed clauses: 1876
% 0.73/0.62 # ...number of literals in the above : 5425
% 0.73/0.62 # Current number of archived formulas : 0
% 0.73/0.62 # Current number of archived clauses : 261
% 0.73/0.62 # Clause-clause subsumption calls (NU) : 12339
% 0.73/0.62 # Rec. Clause-clause subsumption calls : 5498
% 0.73/0.62 # Non-unit clause-clause subsumptions : 41
% 0.73/0.62 # Unit Clause-clause subsumption calls : 74
% 0.73/0.62 # Rewrite failures with RHS unbound : 0
% 0.73/0.62 # BW rewrite match attempts : 22
% 0.73/0.62 # BW rewrite match successes : 6
% 0.73/0.62 # Condensation attempts : 526
% 0.73/0.62 # Condensation successes : 4
% 0.73/0.62 # Termbank termtop insertions : 72345
% 0.73/0.62 # Search garbage collected termcells : 15882
% 0.73/0.62
% 0.73/0.62 # -------------------------------------------------
% 0.73/0.62 # User time : 0.117 s
% 0.73/0.62 # System time : 0.009 s
% 0.73/0.62 # Total time : 0.126 s
% 0.73/0.62 # Maximum resident set size: 5716 pages
% 0.73/0.62
% 0.73/0.62 # -------------------------------------------------
% 0.73/0.62 # User time : 0.125 s
% 0.73/0.62 # System time : 0.012 s
% 0.73/0.62 # Total time : 0.137 s
% 0.73/0.62 # Maximum resident set size: 2204 pages
% 0.73/0.62 % E---3.1 exiting
% 0.73/0.62 % E exiting
%------------------------------------------------------------------------------