%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU653^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 03:28:52 EDT 2024
% Result : Theorem 8.58s 1.57s
% Output : CNFRefutation 8.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 445
% Syntax : Number of formulae : 532 ( 57 unt; 269 typ; 0 def)
% Number of atoms : 2093 ( 539 equ; 0 cnn)
% Maximal formula atoms : 619 ( 7 avg)
% Number of connectives : 8795 ( 614 ~; 669 |; 461 &;5852 @)
% ( 238 <=>; 961 =>; 0 <=; 0 <~>)
% Maximal formula depth : 737 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 408 ( 408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 272 ( 269 usr; 178 con; 0-4 aty)
% Number of variables : 1751 ( 110 ^1479 !; 162 ?;1751 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
epred1_0: $o ).
thf(decl_222,type,
esk1_2: $i > $i > $i ).
thf(decl_223,type,
esk2_2: $i > $i > $i ).
thf(decl_224,type,
esk3_2: $i > $i > $i ).
thf(decl_225,type,
esk4_1: $i > $i ).
thf(decl_226,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_227,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_228,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_229,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_230,type,
esk9_1: $i > $i ).
thf(decl_231,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_232,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_233,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_234,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_235,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_236,type,
esk15_2: $i > $i > $i ).
thf(decl_237,type,
esk16_2: $i > $i > $i ).
thf(decl_238,type,
esk17_1: $i > $i ).
thf(decl_239,type,
esk18_1: $i > $i ).
thf(decl_240,type,
esk19_1: $i > $i ).
thf(decl_241,type,
esk20_2: $i > $i > $i ).
thf(decl_242,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_243,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_244,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_245,type,
esk24_1: $i > $i ).
thf(decl_246,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_247,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_248,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_249,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_250,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_251,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_252,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_253,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_254,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_255,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_256,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_257,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_258,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_259,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_260,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_261,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_262,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_263,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_264,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_265,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_266,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_267,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_268,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_269,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_270,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_271,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_272,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_273,type,
esk52_2: $i > $i > $i ).
thf(decl_274,type,
esk53_2: $i > $i > $i ).
thf(decl_275,type,
esk54_2: $i > $i > $i ).
thf(decl_276,type,
esk55_2: $i > $i > $i ).
thf(decl_277,type,
esk56_2: $i > $i > $i ).
thf(decl_278,type,
esk57_2: $i > $i > $i ).
thf(decl_279,type,
esk58_2: $i > $i > $i ).
thf(decl_280,type,
esk59_3: $i > $i > $i > $i ).
thf(decl_281,type,
esk60_3: $i > $i > $i > $i ).
thf(decl_282,type,
esk61_3: $i > $i > $i > $i ).
thf(decl_283,type,
esk62_3: $i > $i > $i > $i ).
thf(decl_284,type,
esk63_2: $i > $i > $i ).
thf(decl_285,type,
esk64_2: $i > ( $i > $o ) > $i ).
thf(decl_286,type,
esk65_2: $i > ( $i > $o ) > $i ).
thf(decl_287,type,
esk66_2: $i > ( $i > $o ) > $i ).
thf(decl_288,type,
esk67_2: $i > ( $i > $o ) > $i ).
thf(decl_289,type,
esk68_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_290,type,
esk69_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_291,type,
esk70_2: $i > ( $i > $o ) > $i ).
thf(decl_292,type,
esk71_2: $i > ( $i > $o ) > $i ).
thf(decl_293,type,
esk72_2: $i > ( $i > $o ) > $i ).
thf(decl_294,type,
esk73_1: $i > $i ).
thf(decl_295,type,
esk74_0: $i ).
thf(decl_296,type,
esk75_0: $i ).
thf(decl_297,type,
esk76_0: $i ).
thf(decl_298,type,
esk77_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(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(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(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(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(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(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(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
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(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(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
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(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(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(setukpairinjR2,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
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(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
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(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(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(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(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(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(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
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(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
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(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
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(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(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(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(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(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(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(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
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(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(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(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(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(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
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(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
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(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(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(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(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(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(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
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_175,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X520: $i] :
( ( in @ X520
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X520 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_176,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_177,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_178,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_179,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_180,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_181,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_182,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_183,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_184,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_185,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X520: $i] :
( ( in @ X520
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X520 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_175,c_0_176]) ).
thf(c_0_186,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_187,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_188,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_189,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_190,plain,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_191,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_192,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_193,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_194,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_195,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_196,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_197,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_198,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_199,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_200,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_177]) ).
thf(c_0_201,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X495: $i] :
( ( X1 @ X495 )
& ! [X496: $i] :
( ( X1 @ X496 )
=> ( X495 = X496 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_178,c_0_179]) ).
thf(c_0_202,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_177]) ).
thf(c_0_203,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_177]) ).
thf(c_0_204,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X497: $i] :
( ( X1 @ X497 )
& ! [X498: $i] :
( ( X1 @ X498 )
=> ( X497 = X498 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_180,c_0_179]) ).
thf(c_0_205,axiom,
( cartprodmempair
= ( ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X517: $i] :
( ( in @ X517 @ ( setunion @ X18 ) )
& ? [X518: $i] :
( ( in @ X518 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X517 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X517 @ ( setadjoin @ X518 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodmempair,c_0_181]) ).
thf(c_0_206,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X499: $i] :
( ( X1 @ X499 )
& ! [X500: $i] :
( ( X1 @ X500 )
=> ( X499 = X500 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_182,c_0_179]) ).
thf(c_0_207,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 ) )
=> ? [X519: $i] :
( ( in @ X519
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X519 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_183,c_0_176]) ).
thf(c_0_208,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X521: $i] :
( ( in @ X521
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X521 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_184,c_0_185]) ).
thf(c_0_209,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X522: $i] :
( ( in @ X522
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X522 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_186,c_0_185]) ).
thf(c_0_210,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X501: $i] :
( ( X1 @ X501 )
& ! [X502: $i] :
( ( X1 @ X502 )
=> ( X501 = X502 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_187,c_0_179]) ).
thf(c_0_211,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 ) )
=> ? [X523: $i] :
( ( in @ X523
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X523 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_188,c_0_185]) ).
thf(c_0_212,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X503: $i] :
( ( X1 @ X503 )
& ! [X504: $i] :
( ( X1 @ X504 )
=> ( X503 = X504 ) ) )
<=> ? [X505: $i] :
( ( X17 @ X505 )
& ! [X506: $i] :
( ( X17 @ X506 )
=> ( X505 = X506 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_189,c_0_179]) ).
thf(c_0_213,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ? [X524: $i] :
( ( in @ X524 @ ( setunion @ X18 ) )
& ? [X525: $i] :
( ( in @ X525 @ ( setunion @ X18 ) )
& ( X18
= ( setadjoin @ ( setadjoin @ X524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X524 @ ( setadjoin @ X525 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X526: $i] :
( ( in @ X526
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X526 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_190,c_0_176]),c_0_181]) ).
thf(c_0_214,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X527: $i] :
( ( in @ X527 @ X21 )
& ( X21
= ( setadjoin @ X527 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_176]) ).
thf(c_0_215,axiom,
( kfstpairEq
= ( ! [X2: $i,X3: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ) ),
inference(apply_def,[status(thm)],[kfstpairEq,c_0_177]) ).
thf(c_0_216,axiom,
( setukpairinjL
= ( ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ) ),
inference(apply_def,[status(thm)],[setukpairinjL,c_0_177]) ).
thf(c_0_217,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X507: $i] :
( ( X1 @ X507 )
& ! [X508: $i] :
( ( X1 @ X508 )
=> ( X507 = X508 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_191,c_0_179]) ).
thf(c_0_218,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X509: $i] :
( ( X1 @ X509 )
& ! [X510: $i] :
( ( X1 @ X510 )
=> ( X509 = X510 ) ) )
=> ( ? [X511: $i] :
( ( X17 @ X511 )
& ! [X512: $i] :
( ( X17 @ X512 )
=> ( X511 = X512 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_192,c_0_179]) ).
thf(c_0_219,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_220,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_221,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_222,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X513: $i] :
( ( in @ X513 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X514: $i] :
( ( in @ X514 @ ( 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 @ X513 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X513 @ ( setadjoin @ X514 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_181]) ).
thf(c_0_223,axiom,
( kpairp
= ( ! [X2: $i,X3: $i] :
? [X515: $i] :
( ( in @ X515 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X516: $i] :
( ( in @ X516 @ ( 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 @ X515 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X515 @ ( setadjoin @ X516 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp,c_0_177]),c_0_181]) ).
thf(c_0_224,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_225,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_193]) ).
thf(c_0_226,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X493: $i] :
( ( X1 @ X493 )
& ! [X494: $i] :
( ( X1 @ X494 )
=> ( X493 = X494 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_194,c_0_179]) ).
thf(c_0_227,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_228,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_193]) ).
thf(c_0_229,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_195,c_0_193]) ).
thf(c_0_230,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_193]) ).
thf(c_0_231,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_232,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X491: $i] :
( ( X1 @ X491 )
& ! [X492: $i] :
( ( X1 @ X492 )
=> ( X491 = X492 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_196,c_0_179]) ).
thf(c_0_233,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X489: $i] :
( ( X1 @ X489 )
& ! [X490: $i] :
( ( X1 @ X490 )
=> ( X489 = X490 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_197,c_0_179]) ).
thf(c_0_234,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_235,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_236,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_237,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X487: $i] :
( ( X1 @ X487 )
& ! [X488: $i] :
( ( X1 @ X488 )
=> ( X487 = X488 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_198,c_0_179]) ).
thf(c_0_238,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X485: $i] :
( ( X6 @ X2 @ X485 )
& ! [X486: $i] :
( ( X6 @ X2 @ X486 )
=> ( X485 = X486 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_199,c_0_179]) ).
thf(c_0_239,plain,
( epred1_0
<=> ! [X557: $i] :
? [X558: $i] :
( ! [X559: $i] :
( ( in @ X559 @ X558 )
=> ! [X560: $i] :
( ( in @ X560 @ X559 )
=> ( in @ X560 @ X557 ) ) )
& ! [X561: $i,X562: $i] :
( ( ( in @ X561 @ X557 )
& ( in @ X562 @ X557 ) )
=> ( ! [X563: $i] :
( ( in @ X563 @ X558 )
=> ( ( in @ X561 @ X563 )
<=> ( in @ X562 @ X563 ) ) )
=> ( X561 = X562 ) ) )
& ! [X564: $i,X565: $i] :
( ( ( in @ X564 @ X558 )
& ( in @ X565 @ X558 ) )
=> ( ! [X566: $i] :
( ( in @ X566 @ X564 )
=> ( in @ X566 @ X565 ) )
| ! [X567: $i] :
( ( in @ X567 @ X565 )
=> ( in @ X567 @ X564 ) ) ) )
& ! [X568: $i] :
( ( ! [X569: $i] :
( ( in @ X569 @ X568 )
=> ( in @ X569 @ X557 ) )
& ? [X570: $i] : ( in @ X570 @ X568 ) )
=> ? [X571: $i,X572: $i] :
( ( in @ X571 @ X558 )
& ( in @ X572 @ X568 )
& ~ ? [X573: $i] :
( ( in @ X573 @ X571 )
& ( in @ X573 @ X568 ) )
& ! [X574: $i] :
( ( in @ X574 @ X558 )
=> ( ! [X575: $i] :
( ( in @ X575 @ X574 )
=> ( in @ X575 @ X571 ) )
| ( in @ X572 @ X574 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_240,negated_conjecture,
~ ( ! [X528: $i,X529: $i] :
( ! [X530: $i] :
( ( in @ X530 @ X528 )
<=> ( in @ X530 @ X529 ) )
=> ( X528 = X529 ) )
=> ( ! [X531: $i] :
~ ( in @ X531 @ emptyset )
=> ( ! [X532: $i,X533: $i,X534: $i] :
( ( in @ X534 @ ( setadjoin @ X532 @ X533 ) )
<=> ( ( X534 = X532 )
| ( in @ X534 @ X533 ) ) )
=> ( ! [X535: $i,X536: $i] :
( ( in @ X536 @ ( powerset @ X535 ) )
<=> ! [X537: $i] :
( ( in @ X537 @ X536 )
=> ( in @ X537 @ X535 ) ) )
=> ( ! [X538: $i,X539: $i] :
( ( in @ X539 @ ( setunion @ X538 ) )
<=> ? [X540: $i] :
( ( in @ X539 @ X540 )
& ( in @ X540 @ X538 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X541: $i] :
( ( in @ X541 @ omega )
=> ( in @ ( setadjoin @ X541 @ X541 ) @ omega ) )
=> ( ! [X542: $i] :
( ( ( in @ emptyset @ X542 )
& ! [X543: $i] :
( ( ( in @ X543 @ omega )
& ( in @ X543 @ X542 ) )
=> ( in @ ( setadjoin @ X543 @ X543 ) @ X542 ) ) )
=> ! [X544: $i] :
( ( in @ X544 @ omega )
=> ( in @ X544 @ X542 ) ) )
=> ( ! [X545: $i > $i > $o,X546: $i] :
( ! [X547: $i] :
( ( in @ X547 @ X546 )
=> ? [X548: $i] :
( ( X545 @ X547 @ X548 )
& ! [X549: $i] :
( ( X545 @ X547 @ X549 )
=> ( X548 = X549 ) ) ) )
=> ? [X550: $i] :
! [X551: $i] :
( ( in @ X551 @ X550 )
<=> ? [X552: $i] :
( ( in @ X552 @ X546 )
& ( X545 @ X552 @ X551 ) ) ) )
=> ( ! [X553: $i] :
( ? [X554: $i] : ( in @ X554 @ X553 )
=> ? [X555: $i] :
( ( in @ X555 @ X553 )
& ~ ? [X556: $i] :
( ( in @ X556 @ X555 )
& ( in @ X556 @ X553 ) ) ) )
=> ( epred1_0
=> ( ! [X576: $i > $o] :
( ? [X577: $i] :
( ( X576 @ X577 )
& ! [X578: $i] :
( ( X576 @ X578 )
=> ( X577 = X578 ) ) )
=> ( X576
@ ( descr
@ ^ [Z0: $i] : ( X576 @ Z0 ) ) ) )
=> ( ! [X579: $i,X580: $i > $o,X581: $i] :
( ( in @ X581 @ X579 )
=> ( ( X580 @ X581 )
=> ( in @ X581 @ ( dsetconstr @ X579 @ X580 ) ) ) )
=> ( ! [X582: $i,X583: $i > $o,X584: $i] :
( ( in @ X584 @ ( dsetconstr @ X582 @ X583 ) )
=> ( in @ X584 @ X582 ) )
=> ( ! [X585: $i,X586: $i > $o,X587: $i] :
( ( in @ X587 @ ( dsetconstr @ X585 @ X586 ) )
=> ( X586 @ X587 ) )
=> ( ! [X588: $i > $o] :
( ? [X589: $i] :
( ( X588 @ X589 )
& ! [X590: $i] :
( ( X588 @ X590 )
=> ( X589 = X590 ) ) )
=> ? [X591: $i] :
( ( X588 @ X591 )
& ! [X592: $i] :
( ( X588 @ X592 )
=> ( X591 = X592 ) ) ) )
=> ( ! [X593: $o,X594: $i] :
( ( in @ X594 @ ( prop2set @ X593 ) )
=> X593 )
=> ( ! [X595: $i] :
( ( in @ X595 @ emptyset )
=> ! [X596: $o] : X596 )
=> ( ! [X597: $i] :
( ( in @ X597 @ emptyset )
=> ~ $true )
=> ( ! [X598: $i] :
~ ( in @ X598 @ emptyset )
=> ( ! [X599: $i > $o] :
( ? [X600: $i] :
( ( X599 @ X600 )
& ! [X601: $i] :
( ( X599 @ X601 )
=> ( X600 = X601 ) ) )
=> ? [X602: $i] : ( X599 @ X602 ) )
=> ( ! [X603: $i,X604: $i] :
( ! [X605: $i] :
( ( in @ X605 @ X603 )
=> ( in @ X605 @ X604 ) )
=> ( ! [X606: $i] :
( ( in @ X606 @ X604 )
=> ( in @ X606 @ X603 ) )
=> ( X603 = X604 ) ) )
=> ( ! [X607: $i] :
( ! [X608: $i] :
~ ( in @ X608 @ X607 )
=> ( X607 = emptyset ) )
=> ( ! [X609: $i] :
( ! [X610: $i] :
~ ( in @ X610 @ X609 )
=> ( X609 = emptyset ) )
=> ( ! [X611: $i,X612: $i > $o,X613: $i] :
( ( in @ X613 @ X611 )
=> ( ( in @ X613 @ ( dsetconstr @ X611 @ X612 ) )
<=> ( X612 @ X613 ) ) )
=> ( ! [X614: $i] :
( ( X614 != emptyset )
=> ? [X615: $i] : ( in @ X615 @ X614 ) )
=> ( ! [X616: $i,X617: $i > $o,X618: $i] :
( ( in @ X618 @ X616 )
=> ( ( X617 @ X618 )
=> ( ( dsetconstr @ X616 @ X617 )
!= emptyset ) ) )
=> ( ! [X619: $i] :
( ? [X620: $i] : ( in @ X620 @ X619 )
=> ( X619 != emptyset ) )
=> ( ! [X621: $i,X622: $i] : ( in @ X621 @ ( setadjoin @ X621 @ X622 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X623: $i,X624: $i,X625: $i] :
( ( in @ X625 @ X624 )
=> ( in @ X625 @ ( setadjoin @ X623 @ X624 ) ) )
=> ( ! [X626: $i,X627: $i,X628: $i] :
( ( in @ X628 @ ( setadjoin @ X626 @ X627 ) )
=> ! [X629: $o] :
( ( ( X628 = X626 )
=> X629 )
=> ( ( ( in @ X628 @ X627 )
=> X629 )
=> X629 ) ) )
=> ( ! [X630: $i,X631: $i,X632: $i] :
( ( in @ X632 @ ( setadjoin @ X630 @ X631 ) )
=> ( ( X632 = X630 )
| ( in @ X632 @ X631 ) ) )
=> ( ! [X633: $i] :
( ( dsetconstr @ X633
@ ^ [Z0: $i] : $true )
= X633 )
=> ( ! [X634: $i,X635: $i] :
( ! [X636: $i] :
( ( in @ X636 @ X635 )
=> ( in @ X636 @ X634 ) )
=> ( in @ X635 @ ( powerset @ X634 ) ) )
=> ( ! [X637: $i] : ( in @ emptyset @ ( powerset @ X637 ) )
=> ( ! [X638: $i] : ( in @ emptyset @ ( powerset @ X638 ) )
=> ( ! [X639: $i,X640: $i,X641: $i] :
( ( in @ X640 @ ( powerset @ X639 ) )
=> ( ( in @ X641 @ X640 )
=> ( in @ X641 @ X639 ) ) )
=> ( ! [X642: $i,X643: $i,X644: $i] :
( ( in @ X643 @ X644 )
=> ( ( in @ X644 @ X642 )
=> ( in @ X643 @ ( setunion @ X642 ) ) ) )
=> ( ! [X645: $i,X646: $i] :
( ( in @ X646 @ ( setunion @ X645 ) )
=> ! [X647: $o] :
( ! [X648: $i] :
( ( in @ X646 @ X648 )
=> ( ( in @ X648 @ X645 )
=> X647 ) )
=> X647 ) )
=> ( ! [X649: $i,X650: $i] :
( ( in @ X650 @ X649 )
=> ( in @ X650 @ ( powerset @ ( setunion @ X649 ) ) ) )
=> ( ! [X651: $i > $o] :
( ? [X652: $i] :
( ( X651 @ X652 )
& ! [X653: $i] :
( ( X651 @ X653 )
=> ( X652 = X653 ) ) )
=> ? [X654: $i] :
! [X655: $i] :
( ( X651 @ X655 )
<=> ( X655 = X654 ) ) )
=> ( ! [X656: $i] :
( ( X656 != emptyset )
=> ? [X657: $i] :
( ( in @ X657 @ X656 )
& $true ) )
=> ( ! [X658: $i,X659: $i] :
( ( in @ X658 @ ( setadjoin @ X659 @ emptyset ) )
=> ( X658 = X659 ) )
=> ( ! [X660: $i,X661: $i] :
( ( X660 != X661 )
=> ~ ( in @ X661 @ ( setadjoin @ X660 @ emptyset ) ) )
=> ( ! [X662: $i,X663: $i] :
( ( X662 = X663 )
=> ( in @ X662 @ ( setadjoin @ X663 @ emptyset ) ) )
=> ( ! [X664: $i,X665: $i] :
( ( in @ X664 @ ( setadjoin @ X665 @ emptyset ) )
=> ( in @ X665 @ ( setadjoin @ X664 @ emptyset ) ) )
=> ( ! [X666: $i,X667: $i,X668: $i] :
( ( in @ X668 @ ( setadjoin @ X666 @ ( setadjoin @ X667 @ emptyset ) ) )
=> ( ( X668 = X666 )
| ( X668 = X667 ) ) )
=> ( ! [X669: $i,X670: $i] : ( in @ X669 @ ( setadjoin @ X669 @ ( setadjoin @ X670 @ emptyset ) ) )
=> ( ! [X671: $i,X672: $i] : ( in @ X672 @ ( setadjoin @ X671 @ ( setadjoin @ X672 @ emptyset ) ) )
=> ( ! [X673: $i,X674: $i > $o] :
( ? [X675: $i] :
( ( in @ X675 @ X673 )
& ( X674 @ X675 ) )
=> ( ( ( dsetconstr @ X673 @ X674 )
= emptyset )
=> ~ $true ) )
=> ( ! [X676: $i > $o,X677: $i] :
( ( in @ X677 @ emptyset )
=> ( X676 @ X677 ) )
=> ( ! [X678: $i,X679: $i > $o] :
( ~ ! [X680: $i] :
( ( in @ X680 @ X678 )
=> ( X679 @ X680 ) )
=> ? [X681: $i] :
( ( in @ X681 @ X678 )
& ~ ( X679 @ X681 ) ) )
=> ( ! [X682: $i,X683: $i > $o] :
( ! [X684: $i] :
( ( in @ X684 @ X682 )
=> ~ ( X683 @ X684 ) )
=> ~ ? [X685: $i] :
( ( in @ X685 @ X682 )
& ( X683 @ X685 ) ) )
=> ( ! [X686: $i,X687: $i > $o] :
( ~ ? [X688: $i] :
( ( in @ X688 @ X686 )
& ( X687 @ X688 ) )
=> ! [X689: $i] :
( ( in @ X689 @ X686 )
=> ~ ( X687 @ X689 ) ) )
=> ( ! [X690: $i,X691: $i > $o] :
( ? [X692: $i] :
( ( in @ X692 @ X690 )
& ~ ( X691 @ X692 ) )
=> ~ ! [X693: $i] :
( ( in @ X693 @ X690 )
=> ( X691 @ X693 ) ) )
=> ( ! [X694: $o] :
( X694
=> ( in @ emptyset @ ( prop2set @ X694 ) ) )
=> ( prop2set2propI
=> ( ! [X695: $i,X696: $i > $o] :
( ~ ? [X697: $i] :
( ( in @ X697 @ X695 )
& ( X696 @ X697 ) )
=> ! [X698: $i] :
( ( in @ X698 @ X695 )
=> ~ ( X696 @ X698 ) ) )
=> ( ! [X699: $i,X700: $i > $o] :
( ~ ! [X701: $i] :
( ( in @ X701 @ X699 )
=> ( X700 @ X701 ) )
=> ? [X702: $i] :
( ( in @ X702 @ X699 )
& ~ ( X700 @ X702 ) ) )
=> ( ! [X703: $i > $o] :
( ? [X704: $i] :
( ( X703 @ X704 )
& ! [X705: $i] :
( ( X703 @ X705 )
=> ( X704 = X705 ) ) )
=> ? [X706: $i] :
( ( X703 @ X706 )
& ! [X707: $i] :
( ( X703 @ X707 )
=> ( X706 = X707 ) ) ) )
=> ( ! [X708: $i > $o] :
( ? [X709: $i] : ( X708 @ X709 )
=> ( ! [X710: $i,X711: $i] :
( ( X708 @ X710 )
=> ( ( X708 @ X711 )
=> ( X710 = X711 ) ) )
=> ? [X712: $i] :
( ( X708 @ X712 )
& ! [X713: $i] :
( ( X708 @ X713 )
=> ( X712 = X713 ) ) ) ) )
=> ( ! [X714: $i > $o] :
( ? [X715: $i] :
! [X716: $i] :
( ( X714 @ X716 )
<=> ( X716 = X715 ) )
=> ? [X717: $i] :
( ( X714 @ X717 )
& ! [X718: $i] :
( ( X714 @ X718 )
=> ( X717 = X718 ) ) ) )
=> ( ! [X719: $i,X720: $i] :
( ( X719 = X720 )
=> ! [X721: $i,X722: $i] :
( ( X721 = X722 )
=> ( ( in @ X721 @ X719 )
=> ( in @ X722 @ X720 ) ) ) )
=> ( ! [X723: $i,X724: $i] :
( ( X723 = X724 )
=> ! [X725: $i,X726: $i] :
( ( X725 = X726 )
=> ( ( in @ X725 @ X723 )
<=> ( in @ X726 @ X724 ) ) ) )
=> ( ! [X727: $i > $o] :
( ? [X728: $i] :
( ( X727 @ X728 )
& ! [X729: $i] :
( ( X727 @ X729 )
=> ( X728 = X729 ) ) )
=> ! [X730: $i,X731: $i] :
( ( X727 @ X730 )
=> ( ( X727 @ X731 )
=> ( X730 = X731 ) ) ) )
=> ( ! [X732: $i > $o,X733: $i > $o] :
( ! [X734: $i,X735: $i] :
( ( X734 = X735 )
=> ( ( X732 @ X734 )
<=> ( X733 @ X735 ) ) )
=> ( ? [X736: $i] :
( ( X732 @ X736 )
& ! [X737: $i] :
( ( X732 @ X737 )
=> ( X736 = X737 ) ) )
<=> ? [X738: $i] :
( ( X733 @ X738 )
& ! [X739: $i] :
( ( X733 @ X739 )
=> ( X738 = X739 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X740: $i,X741: $i] :
( ( X740 = X741 )
=> ! [X742: $i,X743: $i] :
( ( X742 = X743 )
=> ( ( setadjoin @ X740 @ X742 )
= ( setadjoin @ X741 @ X743 ) ) ) )
=> ( ! [X744: $i,X745: $i] :
( ( X744 = X745 )
=> ( ( powerset @ X744 )
= ( powerset @ X745 ) ) )
=> ( ! [X746: $i,X747: $i] :
( ( X746 = X747 )
=> ( ( setunion @ X746 )
= ( setunion @ X747 ) ) )
=> ( ( omega = omega )
=> ( ! [X748: $i > $o] :
( ? [X749: $i] :
( ( X748 @ X749 )
& ! [X750: $i] :
( ( X748 @ X750 )
=> ( X749 = X750 ) ) )
=> ! [X751: $i,X752: $i] :
( ( X748 @ X751 )
=> ( ( X748 @ X752 )
=> ( X751 = X752 ) ) ) )
=> ( ! [X753: $i > $o,X754: $i > $o] :
( ! [X755: $i,X756: $i] :
( ( X755 = X756 )
=> ( ( X753 @ X755 )
<=> ( X754 @ X756 ) ) )
=> ( ? [X757: $i] :
( ( X753 @ X757 )
& ! [X758: $i] :
( ( X753 @ X758 )
=> ( X757 = X758 ) ) )
=> ( ? [X759: $i] :
( ( X754 @ X759 )
& ! [X760: $i] :
( ( X754 @ X760 )
=> ( X759 = X760 ) ) )
=> ( ( descr @ X753 )
= ( descr @ X754 ) ) ) ) )
=> ( ! [X761: $i,X762: $i] :
( ( X761 = X762 )
=> ! [X763: $i > $o,X764: $i > $o] :
( ! [X765: $i] :
( ( in @ X765 @ X761 )
=> ! [X766: $i] :
( ( in @ X766 @ X762 )
=> ( ( X765 = X766 )
=> ( ( X763 @ X765 )
<=> ( X764 @ X766 ) ) ) ) )
=> ( ( dsetconstr @ X761 @ X763 )
= ( dsetconstr @ X762 @ X764 ) ) ) )
=> ( ! [X767: $i,X768: $i] :
( ! [X769: $i] :
( ( in @ X769 @ X767 )
=> ( in @ X769 @ X768 ) )
=> ( subset @ X767 @ X768 ) )
=> ( ! [X770: $i,X771: $i] :
( ( X770 = X771 )
=> ( subset @ X771 @ X770 ) )
=> ( ! [X772: $i,X773: $i] :
( ( X772 = X773 )
=> ( subset @ X772 @ X773 ) )
=> ( ! [X774: $i,X775: $i] :
( ! [X776: $i] :
( ( in @ X776 @ X774 )
=> ( in @ X776 @ X775 ) )
=> ( subset @ X774 @ X775 ) )
=> ( ! [X777: $i] : ( subset @ emptyset @ X777 )
=> ( ! [X778: $i,X779: $i,X780: $i] :
( ( subset @ X778 @ X779 )
=> ( ( in @ X780 @ X778 )
=> ( in @ X780 @ X779 ) ) )
=> ( ! [X781: $i,X782: $i,X783: $i] :
( ( subset @ X781 @ X782 )
=> ( ~ ( in @ X783 @ X782 )
=> ~ ( in @ X783 @ X781 ) ) )
=> ( ! [X784: $i,X785: $i,X786: $i] :
( ( in @ X786 @ X784 )
=> ( ~ ( in @ X786 @ X785 )
=> ~ ( subset @ X784 @ X785 ) ) )
=> ( ! [X787: $i,X788: $i] :
( ~ ( subset @ X787 @ X788 )
=> ( X787 != X788 ) )
=> ( ! [X789: $i,X790: $i,X791: $i] :
( ( in @ X791 @ X789 )
=> ( ~ ( in @ X791 @ X790 )
=> ( X789 != X790 ) ) )
=> ( ! [X792: $i] : ( subset @ X792 @ X792 )
=> ( ! [X793: $i,X794: $i,X795: $i] :
( ( subset @ X793 @ X794 )
=> ( ( subset @ X794 @ X795 )
=> ( subset @ X793 @ X795 ) ) )
=> ( ! [X796: $i,X797: $i] : ( subset @ X797 @ ( setadjoin @ X796 @ X797 ) )
=> ( ! [X798: $i,X799: $i,X800: $i] :
( ( subset @ X798 @ X800 )
=> ( subset @ X798 @ ( setadjoin @ X799 @ X800 ) ) )
=> ( ! [X801: $i,X802: $i] :
( ( subset @ X801 @ X802 )
=> ( in @ X801 @ ( powerset @ X802 ) ) )
=> ( ! [X803: $i,X804: $i] :
( ( subset @ X803 @ X804 )
=> ( ( subset @ X804 @ X803 )
=> ( X803 = X804 ) ) )
=> ( ! [X805: $i] :
( ( subset @ X805 @ emptyset )
=> ( X805 = emptyset ) )
=> ( ! [X806: $i,X807: $i] :
( ( subset @ X807 @ X806 )
=> ( in @ X807 @ ( powerset @ X806 ) ) )
=> ( ! [X808: $i,X809: $i] :
( ( in @ X809 @ ( powerset @ X808 ) )
=> ( subset @ X809 @ X808 ) )
=> ( ! [X810: $i] : ( in @ X810 @ ( powerset @ X810 ) )
=> ( ! [X811: $i,X812: $i] :
( ( subset @ X811 @ X812 )
=> ( subset @ ( powerset @ X811 ) @ ( powerset @ X812 ) ) )
=> ( ! [X813: $i,X814: $i > $o] : ( in @ ( dsetconstr @ X813 @ X814 ) @ ( powerset @ X813 ) )
=> ( ! [X815: $i,X816: $i > $o] : ( subset @ ( dsetconstr @ X815 @ X816 ) @ X815 )
=> ( ! [X817: $i,X818: $i,X819: $i] :
( ( in @ X819 @ X817 )
=> ( in @ X819 @ ( binunion @ X817 @ X818 ) ) )
=> ( ! [X820: $i,X821: $i] : ( in @ X821 @ ( setadjoin @ X820 @ ( setadjoin @ X821 @ emptyset ) ) )
=> ( ! [X822: $i,X823: $i,X824: $i] :
( ( in @ X824 @ X823 )
=> ( in @ X824 @ ( binunion @ X822 @ X823 ) ) )
=> ( ! [X825: $i,X826: $i,X827: $i,X828: $o] :
( ( in @ X827 @ ( binunion @ X825 @ X826 ) )
=> ( ( ( in @ X827 @ X825 )
=> X828 )
=> ( ( ( in @ X827 @ X826 )
=> X828 )
=> X828 ) ) )
=> ( ! [X829: $i,X830: $i,X831: $i] :
( ( in @ X831 @ ( binunion @ X829 @ X830 ) )
=> ( ( in @ X831 @ X829 )
| ( in @ X831 @ X830 ) ) )
=> ( ! [X832: $i,X833: $i] : ( subset @ X832 @ ( binunion @ X832 @ X833 ) )
=> ( ! [X834: $i,X835: $i] : ( subset @ X835 @ ( binunion @ X834 @ X835 ) )
=> ( ! [X836: $i,X837: $i,X838: $i] :
( ( in @ X838 @ X836 )
=> ( ( in @ X838 @ X837 )
=> ( in @ X838 @ ( binintersect @ X836 @ X837 ) ) ) )
=> ( ! [X839: $i,X840: $i,X841: $i] :
( ( subset @ X841 @ X839 )
=> ( ( subset @ X841 @ X840 )
=> ( subset @ X841 @ ( binintersect @ X839 @ X840 ) ) ) )
=> ( ! [X842: $i,X843: $i,X844: $i] :
( ( in @ X844 @ ( binintersect @ X842 @ X843 ) )
=> ( in @ X844 @ X842 ) )
=> ( ! [X845: $i,X846: $i] : ( subset @ ( binintersect @ X845 @ X846 ) @ X845 )
=> ( ! [X847: $i,X848: $i] :
( ( subset @ X847 @ X848 )
=> ( ( binintersect @ X847 @ X848 )
= X847 ) )
=> ( ! [X849: $i,X850: $i] :
( ( ( binintersect @ X849 @ X850 )
= X850 )
=> ( subset @ X850 @ X849 ) )
=> ( ! [X851: $i,X852: $i,X853: $i] :
( ( in @ X853 @ ( binintersect @ X851 @ X852 ) )
=> ( in @ X853 @ X852 ) )
=> ( ! [X854: $i,X855: $i] :
( ~ ? [X856: $i] :
( ( in @ X856 @ X854 )
& ( in @ X856 @ X855 ) )
=> ( ( binintersect @ X854 @ X855 )
= emptyset ) )
=> ( ! [X857: $i,X858: $i] : ( subset @ ( binintersect @ X857 @ X858 ) @ X858 )
=> ( ! [X859: $i,X860: $i] :
( ( subset @ X860 @ X859 )
=> ( ( binintersect @ X859 @ X860 )
= X860 ) )
=> ( ! [X861: $i,X862: $i] :
( ( ( binintersect @ X861 @ X862 )
= X861 )
=> ( subset @ X861 @ X862 ) )
=> ( ! [X863: $i,X864: $i,X865: $i] :
( ( binintersect @ X863 @ ( binunion @ X864 @ X865 ) )
= ( binunion @ ( binintersect @ X863 @ X864 ) @ ( binintersect @ X863 @ X865 ) ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ( in @ X868 @ X866 )
=> ( ~ ( in @ X868 @ X867 )
=> ( in @ X868 @ ( setminus @ X866 @ X867 ) ) ) )
=> ( ! [X869: $i,X870: $i,X871: $i] :
( ( in @ X871 @ ( setminus @ X869 @ X870 ) )
=> ( in @ X871 @ X869 ) )
=> ( ! [X872: $i,X873: $i,X874: $i] :
( ( in @ X874 @ ( setminus @ X872 @ X873 ) )
=> ~ ( in @ X874 @ X873 ) )
=> ( ! [X875: $i,X876: $i] :
( ( subset @ X875 @ X876 )
=> ( ( setminus @ X875 @ X876 )
= emptyset ) )
=> ( ! [X877: $i,X878: $i,X879: $i] :
( ~ ( in @ X879 @ ( setminus @ X877 @ X878 ) )
=> ( ( in @ X879 @ X877 )
=> ( in @ X879 @ X878 ) ) )
=> ( ! [X880: $i,X881: $i,X882: $i] :
( ~ ( in @ X882 @ ( setminus @ X880 @ X881 ) )
=> ( ~ ( in @ X882 @ X881 )
=> ~ ( in @ X882 @ X880 ) ) )
=> ( ! [X883: $i,X884: $i,X885: $i] :
( ~ ( in @ X885 @ X883 )
=> ~ ( in @ X885 @ ( setminus @ X883 @ X884 ) ) )
=> ( ! [X886: $i,X887: $i,X888: $i] :
( ( in @ X888 @ X887 )
=> ~ ( in @ X888 @ ( setminus @ X886 @ X887 ) ) )
=> ( ! [X889: $i,X890: $i] : ( subset @ ( setminus @ X889 @ X890 ) @ X889 )
=> ( ! [X891: $i,X892: $i] :
( ( ( setminus @ X891 @ X892 )
= emptyset )
=> ( subset @ X891 @ X892 ) )
=> ( ! [X893: $i,X894: $i,X895: $i] :
( ( in @ X895 @ ( symdiff @ X893 @ X894 ) )
=> ! [X896: $o] :
( ( ( in @ X895 @ X893 )
=> ( ~ ( in @ X895 @ X894 )
=> X896 ) )
=> ( ( ~ ( in @ X895 @ X893 )
=> ( ( in @ X895 @ X894 )
=> X896 ) )
=> X896 ) ) )
=> ( ! [X897: $i,X898: $i,X899: $i] :
( ( in @ X899 @ X897 )
=> ( ~ ( in @ X899 @ X898 )
=> ( in @ X899 @ ( symdiff @ X897 @ X898 ) ) ) )
=> ( ! [X900: $i,X901: $i,X902: $i] :
( ~ ( in @ X902 @ X900 )
=> ( ( in @ X902 @ X901 )
=> ( in @ X902 @ ( symdiff @ X900 @ X901 ) ) ) )
=> ( ! [X903: $i,X904: $i,X905: $i] :
( ( in @ X905 @ X903 )
=> ( ( in @ X905 @ X904 )
=> ~ ( in @ X905 @ ( symdiff @ X903 @ X904 ) ) ) )
=> ( ! [X906: $i,X907: $i,X908: $i] :
( ~ ( in @ X908 @ X906 )
=> ( ~ ( in @ X908 @ X907 )
=> ~ ( in @ X908 @ ( symdiff @ X906 @ X907 ) ) ) )
=> ( ! [X909: $i,X910: $i] : ( in @ X910 @ ( setadjoin @ X909 @ ( setadjoin @ X910 @ emptyset ) ) )
=> ( ! [X911: $i,X912: $i] : ( in @ X911 @ ( setunion @ ( setadjoin @ ( setadjoin @ X911 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X911 @ ( setadjoin @ X912 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X913: $i,X914: $i] : ( in @ X914 @ ( setunion @ ( setadjoin @ ( setadjoin @ X913 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X913 @ ( setadjoin @ X914 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X915: $i,X916: $i] :
? [X917: $i] :
( ( in @ X917 @ ( setunion @ ( setadjoin @ ( setadjoin @ X915 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X915 @ ( setadjoin @ X916 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X918: $i] :
( ( in @ X918 @ ( setunion @ ( setadjoin @ ( setadjoin @ X915 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X915 @ ( setadjoin @ X916 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X915 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X915 @ ( setadjoin @ X916 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X917 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X917 @ ( setadjoin @ X918 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X919: $i,X920: $i] :
? [X921: $i] :
( ( in @ X921 @ ( setunion @ ( setadjoin @ ( setadjoin @ X919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X919 @ ( setadjoin @ X920 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X922: $i] :
( ( in @ X922 @ ( setunion @ ( setadjoin @ ( setadjoin @ X919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X919 @ ( setadjoin @ X920 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X919 @ ( setadjoin @ X920 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X921 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X921 @ ( setadjoin @ X922 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X923: $i,X924: $i] :
( ( in @ X924 @ X923 )
=> ( subset @ ( setadjoin @ X924 @ emptyset ) @ X923 ) )
=> ( ! [X925: $i,X926: $i] :
( ( in @ X926 @ X925 )
=> ( in @ ( setadjoin @ X926 @ emptyset ) @ ( powerset @ X925 ) ) )
=> ( ! [X927: $i,X928: $i,X929: $i] :
( ( in @ X929 @ X927 )
=> ( in @ ( setadjoin @ X929 @ emptyset ) @ ( powerset @ ( binunion @ X927 @ X928 ) ) ) )
=> ( ! [X930: $i,X931: $i,X932: $i] :
( ( in @ X932 @ ( setadjoin @ X930 @ ( setadjoin @ X931 @ emptyset ) ) )
=> ( ( X932 = X930 )
| ( X932 = X931 ) ) )
=> ( ! [X933: $i,X934: $i,X935: $i] :
( ( in @ X935 @ X933 )
=> ! [X936: $i] :
( ( in @ X936 @ X934 )
=> ( subset @ ( setadjoin @ X935 @ ( setadjoin @ X936 @ emptyset ) ) @ ( binunion @ X933 @ X934 ) ) ) )
=> ( ! [X937: $i,X938: $i,X939: $i] :
( ( in @ X939 @ X937 )
=> ! [X940: $i] :
( ( in @ X940 @ X938 )
=> ( in @ ( setadjoin @ X939 @ ( setadjoin @ X940 @ emptyset ) ) @ ( powerset @ ( binunion @ X937 @ X938 ) ) ) ) )
=> ( ! [X941: $i,X942: $i,X943: $i] :
( ( in @ X943 @ X941 )
=> ! [X944: $i] :
( ( in @ X944 @ X942 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X943 @ ( setadjoin @ X944 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X941 @ X942 ) ) ) ) )
=> ( ! [X945: $i,X946: $i,X947: $i] :
( ( in @ X947 @ X945 )
=> ! [X948: $i] :
( ( in @ X948 @ X946 )
=> ( in @ ( setadjoin @ ( setadjoin @ X947 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X947 @ ( setadjoin @ X948 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X945 @ X946 ) ) ) ) ) )
=> ( ! [X949: $i,X950: $i,X951: $i] :
( ( in @ X951 @ X949 )
=> ! [X952: $i] :
( ( in @ X952 @ X950 )
=> ( in @ ( setadjoin @ ( setadjoin @ X951 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X951 @ ( setadjoin @ X952 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X949 @ X950 ) ) ) ) ) )
=> ( ! [X953: $i,X954: $i,X955: $i] :
( ( in @ X955 @ X953 )
=> ! [X956: $i] :
( ( in @ X956 @ X954 )
=> ( in @ ( setadjoin @ ( setadjoin @ X955 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X955 @ ( setadjoin @ X956 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ X953 @ X954 ) ) ) )
=> ( ! [X957: $i,X958: $i,X959: $i] :
( ( in @ X959 @ ( cartprod @ X957 @ X958 ) )
=> ? [X960: $i] :
( ( in @ X960 @ X957 )
& ? [X961: $i] :
( ( in @ X961 @ X958 )
& ( X959
= ( setadjoin @ ( setadjoin @ X960 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X960 @ ( setadjoin @ X961 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [X962: $i,X963: $i,X964: $i] :
( ( in @ X964 @ ( cartprod @ X962 @ X963 ) )
=> ? [X965: $i] :
( ( in @ X965 @ ( setunion @ X964 ) )
& ? [X966: $i] :
( ( in @ X966 @ ( setunion @ X964 ) )
& ( X964
= ( setadjoin @ ( setadjoin @ X965 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X965 @ ( setadjoin @ X966 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [X967: $i,X968: $i] :
( ( in @ X968 @ ( setunion @ X967 ) )
=> ? [X969: $i] :
( ( in @ X969 @ X967 )
& ( in @ X968 @ X969 ) ) )
=> ( ! [X970: $i] : ( subset @ ( setunion @ ( setadjoin @ X970 @ emptyset ) ) @ X970 )
=> ( ! [X971: $i] : ( subset @ X971 @ ( setunion @ ( setadjoin @ X971 @ emptyset ) ) )
=> ( ! [X972: $i] :
( ( setunion @ ( setadjoin @ X972 @ emptyset ) )
= X972 )
=> ( ! [X973: $i,X974: $i > $o] :
( ! [X975: $i] :
( ( in @ X975 @ X973 )
=> ! [X976: $i] :
( ( in @ X976 @ X973 )
=> ( ( X974 @ X975 )
=> ( ( X974 @ X976 )
=> ( X975 = X976 ) ) ) ) )
=> ( ? [X977: $i] :
( ( in @ X977 @ X973 )
& ( X974 @ X977 ) )
=> ? [X978: $i] :
( ( in @ X978 @ ( dsetconstr @ X973 @ X974 ) )
& ( ( dsetconstr @ X973 @ X974 )
= ( setadjoin @ X978 @ emptyset ) ) ) ) )
=> ( ! [X979: $i,X980: $i > $o] :
( ? [X981: $i] :
( ( in @ X981 @ ( dsetconstr @ X979 @ X980 ) )
& ( ( dsetconstr @ X979 @ X980 )
= ( setadjoin @ X981 @ emptyset ) ) )
=> ? [X982: $i] :
( ( in @ X982 @ X979 )
& ( X980 @ X982 ) ) )
=> ( ! [X983: $i,X984: $i > $o,X985: $i] :
( ( in @ X985 @ X983 )
=> ( ( X984 @ X985 )
=> ( ! [X986: $i] :
( ( in @ X986 @ X983 )
=> ( ( X984 @ X986 )
=> ( X986 = X985 ) ) )
=> ? [X987: $i] :
( ( in @ X987 @ ( dsetconstr @ X983 @ X984 ) )
& ( ( dsetconstr @ X983 @ X984 )
= ( setadjoin @ X987 @ emptyset ) ) ) ) ) )
=> ( ! [X988: $i,X989: $i > $o] :
( ! [X990: $i] :
( ( in @ X990 @ X988 )
=> ! [X991: $i] :
( ( in @ X991 @ X988 )
=> ( ( X989 @ X990 )
=> ( ( X989 @ X991 )
=> ( X990 = X991 ) ) ) ) )
=> ( ? [X992: $i] :
( ( in @ X992 @ X988 )
& ( X989 @ X992 ) )
=> ? [X993: $i] :
( ( in @ X993 @ ( dsetconstr @ X988 @ X989 ) )
& ( ( dsetconstr @ X988 @ X989 )
= ( setadjoin @ X993 @ emptyset ) ) ) ) )
=> ( ! [X994: $i,X995: $i] :
( ( ( setadjoin @ X994 @ emptyset )
= ( setadjoin @ X995 @ emptyset ) )
=> ( X994 = X995 ) )
=> ( ! [X996: $i,X997: $i,X998: $i] :
( ( in @ ( setadjoin @ X998 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X996 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X996 @ ( setadjoin @ X997 @ emptyset ) ) @ emptyset ) ) )
=> ( X996 = X998 ) )
=> ( ! [X999: $i] :
( ? [X1000: $i] :
( ( in @ X1000 @ ( setunion @ X999 ) )
& ? [X1001: $i] :
( ( in @ X1001 @ ( setunion @ X999 ) )
& ( X999
= ( setadjoin @ ( setadjoin @ X1000 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1000 @ ( setadjoin @ X1001 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X1002: $i] :
( ( in @ X1002
@ ( dsetconstr @ ( setunion @ X999 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X999 ) ) )
& ( ( dsetconstr @ ( setunion @ X999 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X999 ) )
= ( setadjoin @ X1002 @ emptyset ) ) ) )
=> ( ! [X1003: $i] :
( ? [X1004: $i] :
( ( in @ X1004 @ X1003 )
& ( X1003
= ( setadjoin @ X1004 @ emptyset ) ) )
=> ( in @ ( setunion @ X1003 ) @ X1003 ) )
=> ( ! [X1005: $i,X1006: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1005 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1005 @ ( setadjoin @ X1006 @ emptyset ) ) @ emptyset ) ) )
= X1005 )
=> ( ! [X1007: $i,X1008: $i,X1009: $i] :
( ( in @ X1009 @ ( cartprod @ X1007 @ X1008 ) )
=> ( in @ ( kfst @ X1009 ) @ X1007 ) )
=> ( ! [X1010: $i,X1011: $i,X1012: $i,X1013: $i] :
( ( ( setadjoin @ ( setadjoin @ X1010 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1010 @ ( setadjoin @ X1011 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1012 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1012 @ ( setadjoin @ X1013 @ emptyset ) ) @ emptyset ) ) )
=> ( X1010 = X1012 ) )
=> ( ! [X1014: $i,X1015: $i,X1016: $i,X1017: $i] :
( ( ( setadjoin @ ( setadjoin @ X1014 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1014 @ ( setadjoin @ X1015 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1016 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1016 @ ( setadjoin @ X1017 @ emptyset ) ) @ emptyset ) ) )
=> ( X1014 = X1016 ) )
=> ( ! [X1018: $i,X1019: $i] :
( ( X1018 = X1019 )
=> ( ( setadjoin @ X1018 @ ( setadjoin @ X1019 @ emptyset ) )
= ( setadjoin @ X1018 @ emptyset ) ) )
=> ( ! [X1020: $i,X1021: $i] :
( ( X1020 = X1021 )
=> ( ( setadjoin @ ( setadjoin @ X1020 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1020 @ ( setadjoin @ X1021 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1020 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1022: $i,X1023: $i,X1024: $i,X1025: $i] :
( ( ( setadjoin @ ( setadjoin @ X1022 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1022 @ ( setadjoin @ X1023 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1024 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1024 @ ( setadjoin @ X1025 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1024 = X1025 )
=> ( X1023 = X1025 ) ) )
=> ( ! [X1026: $i,X1027: $i,X1028: $i] :
( ( ( setadjoin @ X1026 @ ( setadjoin @ X1027 @ emptyset ) )
= ( setadjoin @ X1028 @ emptyset ) )
=> ( X1026 = X1027 ) )
=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setukpairinjR2]),setadjoin__Cong]),cartprodfstin]),upairequniteq]),upairinpowunion]),notdallE]),ubforcartprodlem1]),ubforcartprodlem2]),c_0_200]),c_0_201]),c_0_202]),c_0_203]),c_0_204]),c_0_205]),setunionE2]),c_0_206]),setunionsingleton1]),setunionsingleton2]),inCongP]),setunionsingleton]),c_0_207]),in__Cong]),c_0_208]),c_0_209]),c_0_210]),c_0_211]),singletonsuniq]),c_0_212]),setukpairinjL1]),c_0_213]),c_0_214]),emptyset__Cong]),c_0_215]),subsetTrans]),setukpairinjL2]),c_0_216]),setukpairinjR11]),powerset__Cong]),setukpairinjR12]),setukpairinjR1]),setunion__Cong]),omega__Cong]),c_0_217]),c_0_218]),c_0_219]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),setminusELneg]),setminusILneg]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_220]),c_0_221]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),prop2setI]),bs114d]),notdexE]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),c_0_222]),c_0_223]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_224]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_225]),c_0_226]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_227]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_228]),c_0_229]),c_0_230]),c_0_231]),noeltsimpempty]),emptyI]),setext]),c_0_232]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_233]),c_0_234]),c_0_235]),c_0_236]),c_0_237]),wellorderingAx]),foundationAx]),c_0_238]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_239]) ).
thf(c_0_241,negated_conjecture,
! [X1029: $i,X1030: $i,X1032: $i,X1033: $i,X1034: $i,X1035: $i,X1036: $i,X1037: $i,X1038: $i,X1039: $i,X1040: $i,X1042: $i,X1043: $i,X1045: $i,X1046: $i,X1047: $i,X1048: $i,X1049: $i,X1051: $i,X1052: $i > $i > $o,X1053: $i,X1055: $i,X1058: $i,X1060: $i,X1061: $i,X1062: $i,X1063: $i,X1065: $i,X1066: $i > $o,X1067: $i,X1069: $i,X1070: $i > $o,X1071: $i,X1072: $i,X1073: $i > $o,X1074: $i,X1075: $i,X1076: $i > $o,X1077: $i,X1078: $i > $o,X1079: $i,X1082: $i,X1083: $o,X1084: $i,X1085: $i,X1086: $o,X1087: $i,X1088: $i,X1089: $i > $o,X1090: $i,X1093: $i,X1094: $i,X1097: $i,X1099: $i,X1101: $i,X1102: $i > $o,X1103: $i,X1104: $i,X1106: $i,X1107: $i > $o,X1108: $i,X1109: $i,X1110: $i,X1111: $i,X1112: $i,X1113: $i,X1114: $i,X1115: $i,X1116: $i,X1117: $i,X1118: $i,X1119: $o,X1120: $i,X1121: $i,X1122: $i,X1123: $i,X1124: $i,X1125: $i,X1127: $i,X1128: $i,X1129: $i,X1130: $i,X1131: $i,X1132: $i,X1133: $i,X1134: $i,X1135: $i,X1136: $i,X1137: $o,X1139: $i,X1140: $i,X1141: $i > $o,X1142: $i,X1145: $i,X1146: $i,X1147: $i,X1149: $i,X1150: $i,X1151: $i,X1152: $i,X1153: $i,X1154: $i,X1155: $i,X1156: $i,X1157: $i,X1158: $i,X1159: $i,X1160: $i,X1161: $i,X1162: $i,X1163: $i,X1164: $i,X1165: $i > $o,X1166: $i,X1167: $i > $o,X1168: $i,X1169: $i,X1170: $i > $o,X1171: $i,X1173: $i,X1174: $i > $o,X1176: $i,X1177: $i,X1178: $i > $o,X1180: $i,X1181: $i,X1182: $i > $o,X1183: $i,X1185: $o,X1186: $i,X1187: $i > $o,X1189: $i,X1190: $i,X1191: $i > $o,X1192: $i,X1194: $i > $o,X1195: $i,X1198: $i,X1199: $i > $o,X1200: $i,X1204: $i,X1205: $i > $o,X1206: $i,X1209: $i,X1210: $i,X1211: $i,X1212: $i,X1213: $i,X1214: $i,X1215: $i,X1216: $i,X1217: $i,X1218: $i > $o,X1219: $i,X1221: $i,X1222: $i,X1223: $i > $o,X1224: $i > $o,X1227: $i,X1230: $i,X1231: $i,X1234: $i,X1235: $i,X1236: $i,X1237: $i,X1238: $i,X1239: $i,X1240: $i,X1241: $i,X1242: $i,X1243: $i > $o,X1244: $i,X1246: $i,X1247: $i,X1248: $i > $o,X1249: $i > $o,X1252: $i,X1254: $i,X1256: $i,X1257: $i,X1258: $i > $o,X1259: $i > $o,X1262: $i,X1263: $i,X1265: $i,X1266: $i,X1267: $i,X1268: $i,X1269: $i,X1270: $i,X1272: $i,X1273: $i,X1274: $i,X1275: $i,X1276: $i,X1277: $i,X1278: $i,X1279: $i,X1280: $i,X1281: $i,X1282: $i,X1283: $i,X1284: $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 > $o,X1310: $i,X1311: $i > $o,X1312: $i,X1313: $i,X1314: $i,X1315: $i,X1316: $i,X1317: $i,X1318: $i,X1319: $i,X1320: $i,X1321: $i,X1322: $i,X1323: $o,X1324: $i,X1325: $i,X1326: $i,X1327: $i,X1328: $i,X1329: $i,X1330: $i,X1331: $i,X1332: $i,X1333: $i,X1334: $i,X1335: $i,X1336: $i,X1337: $i,X1338: $i,X1339: $i,X1340: $i,X1341: $i,X1342: $i,X1343: $i,X1344: $i,X1345: $i,X1346: $i,X1347: $i,X1348: $i,X1349: $i,X1350: $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,X1388: $i,X1389: $i,X1390: $i,X1391: $o,X1392: $i,X1393: $i,X1394: $i,X1395: $i,X1396: $i,X1397: $i,X1398: $i,X1399: $i,X1400: $i,X1401: $i,X1402: $i,X1403: $i,X1404: $i,X1405: $i,X1406: $i,X1407: $i,X1408: $i,X1409: $i,X1410: $i,X1411: $i,X1414: $i,X1415: $i,X1418: $i,X1419: $i,X1420: $i,X1421: $i,X1422: $i,X1423: $i,X1424: $i,X1425: $i,X1426: $i,X1427: $i,X1428: $i,X1429: $i,X1430: $i,X1431: $i,X1432: $i,X1433: $i,X1434: $i,X1435: $i,X1436: $i,X1437: $i,X1438: $i,X1439: $i,X1440: $i,X1441: $i,X1442: $i,X1443: $i,X1444: $i,X1445: $i,X1446: $i,X1447: $i,X1448: $i,X1449: $i,X1450: $i,X1451: $i,X1452: $i,X1453: $i,X1454: $i,X1457: $i,X1458: $i,X1459: $i,X1462: $i,X1463: $i,X1465: $i,X1466: $i,X1467: $i,X1468: $i,X1469: $i > $o,X1472: $i,X1474: $i,X1475: $i > $o,X1476: $i,X1478: $i,X1479: $i > $o,X1480: $i,X1483: $i,X1484: $i > $o,X1487: $i,X1489: $i,X1490: $i,X1491: $i,X1492: $i,X1493: $i,X1494: $i,X1495: $i,X1496: $i,X1498: $i,X1499: $i,X1500: $i,X1501: $i,X1502: $i,X1503: $i,X1504: $i,X1505: $i,X1506: $i,X1507: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1513: $i,X1514: $i,X1515: $i,X1516: $i,X1517: $i,X1518: $i,X1519: $i,X1520: $i,X1521: $i,X1522: $i,X1523: $i] :
( ( ~ ( in @ ( esk1_2 @ X1029 @ X1030 ) @ X1029 )
| ~ ( in @ ( esk1_2 @ X1029 @ X1030 ) @ X1030 )
| ( X1029 = X1030 ) )
& ( ( in @ ( esk1_2 @ X1029 @ X1030 ) @ X1029 )
| ( in @ ( esk1_2 @ X1029 @ X1030 ) @ X1030 )
| ( X1029 = X1030 ) )
& ~ ( in @ X1032 @ emptyset )
& ( ~ ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) )
| ( X1035 = X1033 )
| ( in @ X1035 @ X1034 ) )
& ( ( X1035 != X1033 )
| ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ~ ( in @ X1035 @ X1034 )
| ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) ) )
& ( ~ ( in @ X1037 @ ( powerset @ X1036 ) )
| ~ ( in @ X1038 @ X1037 )
| ( in @ X1038 @ X1036 ) )
& ( ( in @ ( esk2_2 @ X1039 @ X1040 ) @ X1040 )
| ( in @ X1040 @ ( powerset @ X1039 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1039 @ X1040 ) @ X1039 )
| ( in @ X1040 @ ( powerset @ X1039 ) ) )
& ( ( in @ X1043 @ ( esk3_2 @ X1042 @ X1043 ) )
| ~ ( in @ X1043 @ ( setunion @ X1042 ) ) )
& ( ( in @ ( esk3_2 @ X1042 @ X1043 ) @ X1042 )
| ~ ( in @ X1043 @ ( setunion @ X1042 ) ) )
& ( ~ ( in @ X1046 @ X1047 )
| ~ ( in @ X1047 @ X1045 )
| ( in @ X1046 @ ( setunion @ X1045 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1048 @ omega )
| ( in @ ( setadjoin @ X1048 @ X1048 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1049 ) @ omega )
| ~ ( in @ emptyset @ X1049 )
| ~ ( in @ X1051 @ omega )
| ( in @ X1051 @ X1049 ) )
& ( ( in @ ( esk4_1 @ X1049 ) @ X1049 )
| ~ ( in @ emptyset @ X1049 )
| ~ ( in @ X1051 @ omega )
| ( in @ X1051 @ X1049 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1049 ) @ ( esk4_1 @ X1049 ) ) @ X1049 )
| ~ ( in @ emptyset @ X1049 )
| ~ ( in @ X1051 @ omega )
| ( in @ X1051 @ X1049 ) )
& ( ( in @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1053 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( in @ ( esk5_2 @ X1052 @ X1053 ) @ X1053 ) )
& ( ( X1052 @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1058 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( in @ ( esk5_2 @ X1052 @ X1053 ) @ X1053 ) )
& ( ~ ( in @ X1061 @ X1053 )
| ~ ( X1052 @ X1061 @ X1060 )
| ( in @ X1060 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( in @ ( esk5_2 @ X1052 @ X1053 ) @ X1053 ) )
& ( ( in @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1053 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ( X1052 @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1058 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ~ ( in @ X1061 @ X1053 )
| ~ ( X1052 @ X1061 @ X1060 )
| ( in @ X1060 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ( in @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1053 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1055
!= ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ( X1052 @ ( esk8_3 @ X1052 @ X1053 @ X1058 ) @ X1058 )
| ~ ( in @ X1058 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1055
!= ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ~ ( in @ X1061 @ X1053 )
| ~ ( X1052 @ X1061 @ X1060 )
| ( in @ X1060 @ ( esk7_2 @ X1052 @ X1053 ) )
| ( X1055
!= ( esk6_3 @ X1052 @ X1053 @ X1055 ) )
| ~ ( X1052 @ ( esk5_2 @ X1052 @ X1053 ) @ X1055 ) )
& ( ( in @ ( esk9_1 @ X1062 ) @ X1062 )
| ~ ( in @ X1063 @ X1062 ) )
& ( ~ ( in @ X1065 @ ( esk9_1 @ X1062 ) )
| ~ ( in @ X1065 @ X1062 )
| ~ ( in @ X1063 @ X1062 ) )
& epred1_0
& ( ( X1066 @ ( esk10_2 @ X1066 @ X1067 ) )
| ~ ( X1066 @ X1067 )
| ( X1066 @ ( descr @ X1066 ) ) )
& ( ( X1067
!= ( esk10_2 @ X1066 @ X1067 ) )
| ~ ( X1066 @ X1067 )
| ( X1066 @ ( descr @ X1066 ) ) )
& ( ~ ( in @ X1071 @ X1069 )
| ~ ( X1070 @ X1071 )
| ( in @ X1071 @ ( dsetconstr @ X1069 @ X1070 ) ) )
& ( ~ ( in @ X1074 @ ( dsetconstr @ X1072 @ X1073 ) )
| ( in @ X1074 @ X1072 ) )
& ( ~ ( in @ X1077 @ ( dsetconstr @ X1075 @ X1076 ) )
| ( X1076 @ X1077 ) )
& ( ( X1078 @ ( esk12_1 @ X1078 ) )
| ( X1078 @ ( esk11_2 @ X1078 @ X1079 ) )
| ~ ( X1078 @ X1079 ) )
& ( ~ ( X1078 @ X1082 )
| ( ( esk12_1 @ X1078 )
= X1082 )
| ( X1078 @ ( esk11_2 @ X1078 @ X1079 ) )
| ~ ( X1078 @ X1079 ) )
& ( ( X1078 @ ( esk12_1 @ X1078 ) )
| ( X1079
!= ( esk11_2 @ X1078 @ X1079 ) )
| ~ ( X1078 @ X1079 ) )
& ( ~ ( X1078 @ X1082 )
| ( ( esk12_1 @ X1078 )
= X1082 )
| ( X1079
!= ( esk11_2 @ X1078 @ X1079 ) )
| ~ ( X1078 @ X1079 ) )
& ( ~ ( in @ X1084 @ ( prop2set @ X1083 ) )
| X1083 )
& ( ~ ( in @ X1085 @ emptyset )
| X1086 )
& ( ~ ( in @ X1087 @ emptyset )
| ~ $true )
& ~ ( in @ X1088 @ emptyset )
& ( ( X1089 @ ( esk13_2 @ X1089 @ X1090 ) )
| ~ ( X1089 @ X1090 )
| ( X1089 @ ( esk14_1 @ X1089 ) ) )
& ( ( X1090
!= ( esk13_2 @ X1089 @ X1090 ) )
| ~ ( X1089 @ X1090 )
| ( X1089 @ ( esk14_1 @ X1089 ) ) )
& ( ( in @ ( esk16_2 @ X1093 @ X1094 ) @ X1094 )
| ( X1093 = X1094 )
| ( in @ ( esk15_2 @ X1093 @ X1094 ) @ X1093 ) )
& ( ~ ( in @ ( esk16_2 @ X1093 @ X1094 ) @ X1093 )
| ( X1093 = X1094 )
| ( in @ ( esk15_2 @ X1093 @ X1094 ) @ X1093 ) )
& ( ( in @ ( esk16_2 @ X1093 @ X1094 ) @ X1094 )
| ( X1093 = X1094 )
| ~ ( in @ ( esk15_2 @ X1093 @ X1094 ) @ X1094 ) )
& ( ~ ( in @ ( esk16_2 @ X1093 @ X1094 ) @ X1093 )
| ( X1093 = X1094 )
| ~ ( in @ ( esk15_2 @ X1093 @ X1094 ) @ X1094 ) )
& ( ( in @ ( esk17_1 @ X1097 ) @ X1097 )
| ( X1097 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1099 ) @ X1099 )
| ( X1099 = emptyset ) )
& ( ~ ( in @ X1103 @ ( dsetconstr @ X1101 @ X1102 ) )
| ( X1102 @ X1103 )
| ~ ( in @ X1103 @ X1101 ) )
& ( ~ ( X1102 @ X1103 )
| ( in @ X1103 @ ( dsetconstr @ X1101 @ X1102 ) )
| ~ ( in @ X1103 @ X1101 ) )
& ( ( X1104 = emptyset )
| ( in @ ( esk19_1 @ X1104 ) @ X1104 ) )
& ( ~ ( in @ X1108 @ X1106 )
| ~ ( X1107 @ X1108 )
| ( ( dsetconstr @ X1106 @ X1107 )
!= emptyset ) )
& ( ~ ( in @ X1110 @ X1109 )
| ( X1109 != emptyset ) )
& ( in @ X1111 @ ( setadjoin @ X1111 @ X1112 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1115 @ X1114 )
| ( in @ X1115 @ ( setadjoin @ X1113 @ X1114 ) ) )
& ( ( in @ X1118 @ X1117 )
| X1119
| ( X1118 = X1116 )
| ~ ( in @ X1118 @ ( setadjoin @ X1116 @ X1117 ) ) )
& ( ~ X1119
| X1119
| ( X1118 = X1116 )
| ~ ( in @ X1118 @ ( setadjoin @ X1116 @ X1117 ) ) )
& ( ( in @ X1118 @ X1117 )
| X1119
| ~ X1119
| ~ ( in @ X1118 @ ( setadjoin @ X1116 @ X1117 ) ) )
& ( ~ X1119
| X1119
| ~ X1119
| ~ ( in @ X1118 @ ( setadjoin @ X1116 @ X1117 ) ) )
& ( ~ ( in @ X1122 @ ( setadjoin @ X1120 @ X1121 ) )
| ( X1122 = X1120 )
| ( in @ X1122 @ X1121 ) )
& ( ( dsetconstr @ X1123
@ ^ [Z0: $i] : $true )
= X1123 )
& ( ( in @ ( esk20_2 @ X1124 @ X1125 ) @ X1125 )
| ( in @ X1125 @ ( powerset @ X1124 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1124 @ X1125 ) @ X1124 )
| ( in @ X1125 @ ( powerset @ X1124 ) ) )
& ( in @ emptyset @ ( powerset @ X1127 ) )
& ( in @ emptyset @ ( powerset @ X1128 ) )
& ( ~ ( in @ X1130 @ ( powerset @ X1129 ) )
| ~ ( in @ X1131 @ X1130 )
| ( in @ X1131 @ X1129 ) )
& ( ~ ( in @ X1133 @ X1134 )
| ~ ( in @ X1134 @ X1132 )
| ( in @ X1133 @ ( setunion @ X1132 ) ) )
& ( ( in @ X1136 @ ( esk21_3 @ X1135 @ X1136 @ X1137 ) )
| X1137
| ~ ( in @ X1136 @ ( setunion @ X1135 ) ) )
& ( ( in @ ( esk21_3 @ X1135 @ X1136 @ X1137 ) @ X1135 )
| X1137
| ~ ( in @ X1136 @ ( setunion @ X1135 ) ) )
& ( ~ X1137
| X1137
| ~ ( in @ X1136 @ ( setunion @ X1135 ) ) )
& ( ~ ( in @ X1140 @ X1139 )
| ( in @ X1140 @ ( powerset @ ( setunion @ X1139 ) ) ) )
& ( ~ ( X1141 @ X1145 )
| ( X1145
= ( esk23_1 @ X1141 ) )
| ( X1141 @ ( esk22_2 @ X1141 @ X1142 ) )
| ~ ( X1141 @ X1142 ) )
& ( ( X1146
!= ( esk23_1 @ X1141 ) )
| ( X1141 @ X1146 )
| ( X1141 @ ( esk22_2 @ X1141 @ X1142 ) )
| ~ ( X1141 @ X1142 ) )
& ( ~ ( X1141 @ X1145 )
| ( X1145
= ( esk23_1 @ X1141 ) )
| ( X1142
!= ( esk22_2 @ X1141 @ X1142 ) )
| ~ ( X1141 @ X1142 ) )
& ( ( X1146
!= ( esk23_1 @ X1141 ) )
| ( X1141 @ X1146 )
| ( X1142
!= ( esk22_2 @ X1141 @ X1142 ) )
| ~ ( X1141 @ X1142 ) )
& ( ( in @ ( esk24_1 @ X1147 ) @ X1147 )
| ( X1147 = emptyset ) )
& ( $true
| ( X1147 = emptyset ) )
& ( ~ ( in @ X1149 @ ( setadjoin @ X1150 @ emptyset ) )
| ( X1149 = X1150 ) )
& ( ( X1151 = X1152 )
| ~ ( in @ X1152 @ ( setadjoin @ X1151 @ emptyset ) ) )
& ( ( X1153 != X1154 )
| ( in @ X1153 @ ( setadjoin @ X1154 @ emptyset ) ) )
& ( ~ ( in @ X1155 @ ( setadjoin @ X1156 @ emptyset ) )
| ( in @ X1156 @ ( setadjoin @ X1155 @ emptyset ) ) )
& ( ~ ( in @ X1159 @ ( setadjoin @ X1157 @ ( setadjoin @ X1158 @ emptyset ) ) )
| ( X1159 = X1157 )
| ( X1159 = X1158 ) )
& ( in @ X1160 @ ( setadjoin @ X1160 @ ( setadjoin @ X1161 @ emptyset ) ) )
& ( in @ X1163 @ ( setadjoin @ X1162 @ ( setadjoin @ X1163 @ emptyset ) ) )
& ( ~ ( in @ X1166 @ X1164 )
| ~ ( X1165 @ X1166 )
| ( ( dsetconstr @ X1164 @ X1165 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1168 @ emptyset )
| ( X1167 @ X1168 ) )
& ( ( in @ ( esk25_2 @ X1169 @ X1170 ) @ X1169 )
| ~ ( in @ X1171 @ X1169 )
| ( X1170 @ X1171 ) )
& ( ~ ( X1170 @ ( esk25_2 @ X1169 @ X1170 ) )
| ~ ( in @ X1171 @ X1169 )
| ( X1170 @ X1171 ) )
& ( ( in @ ( esk26_2 @ X1173 @ X1174 ) @ X1173 )
| ~ ( in @ X1176 @ X1173 )
| ~ ( X1174 @ X1176 ) )
& ( ( X1174 @ ( esk26_2 @ X1173 @ X1174 ) )
| ~ ( in @ X1176 @ X1173 )
| ~ ( X1174 @ X1176 ) )
& ( ( in @ ( esk27_2 @ X1177 @ X1178 ) @ X1177 )
| ~ ( in @ X1180 @ X1177 )
| ~ ( X1178 @ X1180 ) )
& ( ( X1178 @ ( esk27_2 @ X1177 @ X1178 ) )
| ~ ( in @ X1180 @ X1177 )
| ~ ( X1178 @ X1180 ) )
& ( ( in @ ( esk28_2 @ X1181 @ X1182 ) @ X1181 )
| ~ ( in @ X1183 @ X1181 )
| ( X1182 @ X1183 ) )
& ( ~ ( X1182 @ ( esk28_2 @ X1181 @ X1182 ) )
| ~ ( in @ X1183 @ X1181 )
| ( X1182 @ X1183 ) )
& ( ~ X1185
| ( in @ emptyset @ ( prop2set @ X1185 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X1186 @ X1187 ) @ X1186 )
| ~ ( in @ X1189 @ X1186 )
| ~ ( X1187 @ X1189 ) )
& ( ( X1187 @ ( esk29_2 @ X1186 @ X1187 ) )
| ~ ( in @ X1189 @ X1186 )
| ~ ( X1187 @ X1189 ) )
& ( ( in @ ( esk30_2 @ X1190 @ X1191 ) @ X1190 )
| ~ ( in @ X1192 @ X1190 )
| ( X1191 @ X1192 ) )
& ( ~ ( X1191 @ ( esk30_2 @ X1190 @ X1191 ) )
| ~ ( in @ X1192 @ X1190 )
| ( X1191 @ X1192 ) )
& ( ( X1194 @ ( esk32_1 @ X1194 ) )
| ( X1194 @ ( esk31_2 @ X1194 @ X1195 ) )
| ~ ( X1194 @ X1195 ) )
& ( ~ ( X1194 @ X1198 )
| ( ( esk32_1 @ X1194 )
= X1198 )
| ( X1194 @ ( esk31_2 @ X1194 @ X1195 ) )
| ~ ( X1194 @ X1195 ) )
& ( ( X1194 @ ( esk32_1 @ X1194 ) )
| ( X1195
!= ( esk31_2 @ X1194 @ X1195 ) )
| ~ ( X1194 @ X1195 ) )
& ( ~ ( X1194 @ X1198 )
| ( ( esk32_1 @ X1194 )
= X1198 )
| ( X1195
!= ( esk31_2 @ X1194 @ X1195 ) )
| ~ ( X1194 @ X1195 ) )
& ( ( X1199 @ ( esk35_1 @ X1199 ) )
| ( X1199 @ ( esk33_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ~ ( X1199 @ X1204 )
| ( ( esk35_1 @ X1199 )
= X1204 )
| ( X1199 @ ( esk33_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ( X1199 @ ( esk35_1 @ X1199 ) )
| ( X1199 @ ( esk34_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ~ ( X1199 @ X1204 )
| ( ( esk35_1 @ X1199 )
= X1204 )
| ( X1199 @ ( esk34_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ( X1199 @ ( esk35_1 @ X1199 ) )
| ( ( esk33_1 @ X1199 )
!= ( esk34_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ~ ( X1199 @ X1204 )
| ( ( esk35_1 @ X1199 )
= X1204 )
| ( ( esk33_1 @ X1199 )
!= ( esk34_1 @ X1199 ) )
| ~ ( X1199 @ X1200 ) )
& ( ( X1205 @ ( esk37_1 @ X1205 ) )
| ~ ( X1205 @ ( esk36_2 @ X1205 @ X1206 ) )
| ( ( esk36_2 @ X1205 @ X1206 )
!= X1206 ) )
& ( ~ ( X1205 @ X1209 )
| ( ( esk37_1 @ X1205 )
= X1209 )
| ~ ( X1205 @ ( esk36_2 @ X1205 @ X1206 ) )
| ( ( esk36_2 @ X1205 @ X1206 )
!= X1206 ) )
& ( ( X1205 @ ( esk37_1 @ X1205 ) )
| ( X1205 @ ( esk36_2 @ X1205 @ X1206 ) )
| ( ( esk36_2 @ X1205 @ X1206 )
= X1206 ) )
& ( ~ ( X1205 @ X1209 )
| ( ( esk37_1 @ X1205 )
= X1209 )
| ( X1205 @ ( esk36_2 @ X1205 @ X1206 ) )
| ( ( esk36_2 @ X1205 @ X1206 )
= X1206 ) )
& ( ( X1210 != X1211 )
| ( X1212 != X1213 )
| ~ ( in @ X1212 @ X1210 )
| ( in @ X1213 @ X1211 ) )
& ( ~ ( in @ X1216 @ X1214 )
| ( in @ X1217 @ X1215 )
| ( X1216 != X1217 )
| ( X1214 != X1215 ) )
& ( ~ ( in @ X1217 @ X1215 )
| ( in @ X1216 @ X1214 )
| ( X1216 != X1217 )
| ( X1214 != X1215 ) )
& ( ( X1218 @ ( esk38_2 @ X1218 @ X1219 ) )
| ~ ( X1218 @ X1219 )
| ~ ( X1218 @ X1221 )
| ~ ( X1218 @ X1222 )
| ( X1221 = X1222 ) )
& ( ( X1219
!= ( esk38_2 @ X1218 @ X1219 ) )
| ~ ( X1218 @ X1219 )
| ~ ( X1218 @ X1221 )
| ~ ( X1218 @ X1222 )
| ( X1221 = X1222 ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( ( esk39_2 @ X1223 @ X1224 )
= ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ~ ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ~ ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1223 @ ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1224 @ ( esk42_2 @ X1223 @ X1224 ) )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1224 @ X1230 )
| ( ( esk42_2 @ X1223 @ X1224 )
= X1230 )
| ( X1227
!= ( esk41_3 @ X1223 @ X1224 @ X1227 ) )
| ~ ( X1223 @ X1227 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1224 @ ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ( X1223 @ ( esk44_2 @ X1223 @ X1224 ) )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( ~ ( X1223 @ X1234 )
| ( ( esk44_2 @ X1223 @ X1224 )
= X1234 )
| ( X1231
!= ( esk43_3 @ X1223 @ X1224 @ X1231 ) )
| ~ ( X1224 @ X1231 )
| ( X1223 @ ( esk39_2 @ X1223 @ X1224 ) )
| ( X1224 @ ( esk40_2 @ X1223 @ X1224 ) ) )
& ( emptyset = emptyset )
& ( ( X1235 != X1236 )
| ( X1237 != X1238 )
| ( ( setadjoin @ X1235 @ X1237 )
= ( setadjoin @ X1236 @ X1238 ) ) )
& ( ( X1239 != X1240 )
| ( ( powerset @ X1239 )
= ( powerset @ X1240 ) ) )
& ( ( X1241 != X1242 )
| ( ( setunion @ X1241 )
= ( setunion @ X1242 ) ) )
& ( omega = omega )
& ( ( X1243 @ ( esk45_2 @ X1243 @ X1244 ) )
| ~ ( X1243 @ X1244 )
| ~ ( X1243 @ X1246 )
| ~ ( X1243 @ X1247 )
| ( X1246 = X1247 ) )
& ( ( X1244
!= ( esk45_2 @ X1243 @ X1244 ) )
| ~ ( X1243 @ X1244 )
| ~ ( X1243 @ X1246 )
| ~ ( X1243 @ X1247 )
| ( X1246 = X1247 ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( ( esk46_2 @ X1248 @ X1249 )
= ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( ( esk46_2 @ X1248 @ X1249 )
= ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( ( esk46_2 @ X1248 @ X1249 )
= ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( ( esk46_2 @ X1248 @ X1249 )
= ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ~ ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ~ ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ~ ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ~ ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ~ ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ~ ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ~ ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ~ ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1248 @ ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1249 @ ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( X1254
!= ( esk49_3 @ X1248 @ X1249 @ X1254 ) )
| ~ ( X1249 @ X1254 )
| ( ( descr @ X1248 )
= ( descr @ X1249 ) )
| ( X1252
!= ( esk48_3 @ X1248 @ X1249 @ X1252 ) )
| ~ ( X1248 @ X1252 )
| ( X1248 @ ( esk46_2 @ X1248 @ X1249 ) )
| ( X1249 @ ( esk47_2 @ X1248 @ X1249 ) ) )
& ( ( in @ ( esk50_4 @ X1256 @ X1257 @ X1258 @ X1259 ) @ X1256 )
| ( ( dsetconstr @ X1256 @ X1258 )
= ( dsetconstr @ X1257 @ X1259 ) )
| ( X1256 != X1257 ) )
& ( ( in @ ( esk51_4 @ X1256 @ X1257 @ X1258 @ X1259 ) @ X1257 )
| ( ( dsetconstr @ X1256 @ X1258 )
= ( dsetconstr @ X1257 @ X1259 ) )
| ( X1256 != X1257 ) )
& ( ( ( esk50_4 @ X1256 @ X1257 @ X1258 @ X1259 )
= ( esk51_4 @ X1256 @ X1257 @ X1258 @ X1259 ) )
| ( ( dsetconstr @ X1256 @ X1258 )
= ( dsetconstr @ X1257 @ X1259 ) )
| ( X1256 != X1257 ) )
& ( ~ ( X1258 @ ( esk50_4 @ X1256 @ X1257 @ X1258 @ X1259 ) )
| ~ ( X1259 @ ( esk51_4 @ X1256 @ X1257 @ X1258 @ X1259 ) )
| ( ( dsetconstr @ X1256 @ X1258 )
= ( dsetconstr @ X1257 @ X1259 ) )
| ( X1256 != X1257 ) )
& ( ( X1258 @ ( esk50_4 @ X1256 @ X1257 @ X1258 @ X1259 ) )
| ( X1259 @ ( esk51_4 @ X1256 @ X1257 @ X1258 @ X1259 ) )
| ( ( dsetconstr @ X1256 @ X1258 )
= ( dsetconstr @ X1257 @ X1259 ) )
| ( X1256 != X1257 ) )
& ( ( in @ ( esk52_2 @ X1262 @ X1263 ) @ X1262 )
| ( subset @ X1262 @ X1263 ) )
& ( ~ ( in @ ( esk52_2 @ X1262 @ X1263 ) @ X1263 )
| ( subset @ X1262 @ X1263 ) )
& ( ( X1265 != X1266 )
| ( subset @ X1266 @ X1265 ) )
& ( ( X1267 != X1268 )
| ( subset @ X1267 @ X1268 ) )
& ( ( in @ ( esk53_2 @ X1269 @ X1270 ) @ X1269 )
| ( subset @ X1269 @ X1270 ) )
& ( ~ ( in @ ( esk53_2 @ X1269 @ X1270 ) @ X1270 )
| ( subset @ X1269 @ X1270 ) )
& ( subset @ emptyset @ X1272 )
& ( ~ ( subset @ X1273 @ X1274 )
| ~ ( in @ X1275 @ X1273 )
| ( in @ X1275 @ X1274 ) )
& ( ~ ( subset @ X1276 @ X1277 )
| ( in @ X1278 @ X1277 )
| ~ ( in @ X1278 @ X1276 ) )
& ( ~ ( in @ X1281 @ X1279 )
| ( in @ X1281 @ X1280 )
| ~ ( subset @ X1279 @ X1280 ) )
& ( ( subset @ X1282 @ X1283 )
| ( X1282 != X1283 ) )
& ( ~ ( in @ X1286 @ X1284 )
| ( in @ X1286 @ X1285 )
| ( X1284 != X1285 ) )
& ( subset @ X1287 @ X1287 )
& ( ~ ( subset @ X1288 @ X1289 )
| ~ ( subset @ X1289 @ X1290 )
| ( subset @ X1288 @ X1290 ) )
& ( subset @ X1292 @ ( setadjoin @ X1291 @ X1292 ) )
& ( ~ ( subset @ X1293 @ X1295 )
| ( subset @ X1293 @ ( setadjoin @ X1294 @ X1295 ) ) )
& ( ~ ( subset @ X1296 @ X1297 )
| ( in @ X1296 @ ( powerset @ X1297 ) ) )
& ( ~ ( subset @ X1298 @ X1299 )
| ~ ( subset @ X1299 @ X1298 )
| ( X1298 = X1299 ) )
& ( ~ ( subset @ X1300 @ emptyset )
| ( X1300 = emptyset ) )
& ( ~ ( subset @ X1302 @ X1301 )
| ( in @ X1302 @ ( powerset @ X1301 ) ) )
& ( ~ ( in @ X1304 @ ( powerset @ X1303 ) )
| ( subset @ X1304 @ X1303 ) )
& ( in @ X1305 @ ( powerset @ X1305 ) )
& ( ~ ( subset @ X1306 @ X1307 )
| ( subset @ ( powerset @ X1306 ) @ ( powerset @ X1307 ) ) )
& ( in @ ( dsetconstr @ X1308 @ X1309 ) @ ( powerset @ X1308 ) )
& ( subset @ ( dsetconstr @ X1310 @ X1311 ) @ X1310 )
& ( ~ ( in @ X1314 @ X1312 )
| ( in @ X1314 @ ( binunion @ X1312 @ X1313 ) ) )
& ( in @ X1316 @ ( setadjoin @ X1315 @ ( setadjoin @ X1316 @ emptyset ) ) )
& ( ~ ( in @ X1319 @ X1318 )
| ( in @ X1319 @ ( binunion @ X1317 @ X1318 ) ) )
& ( ( in @ X1322 @ X1321 )
| X1323
| ( in @ X1322 @ X1320 )
| ~ ( in @ X1322 @ ( binunion @ X1320 @ X1321 ) ) )
& ( ~ X1323
| X1323
| ( in @ X1322 @ X1320 )
| ~ ( in @ X1322 @ ( binunion @ X1320 @ X1321 ) ) )
& ( ( in @ X1322 @ X1321 )
| X1323
| ~ X1323
| ~ ( in @ X1322 @ ( binunion @ X1320 @ X1321 ) ) )
& ( ~ X1323
| X1323
| ~ X1323
| ~ ( in @ X1322 @ ( binunion @ X1320 @ X1321 ) ) )
& ( ~ ( in @ X1326 @ ( binunion @ X1324 @ X1325 ) )
| ( in @ X1326 @ X1324 )
| ( in @ X1326 @ X1325 ) )
& ( subset @ X1327 @ ( binunion @ X1327 @ X1328 ) )
& ( subset @ X1330 @ ( binunion @ X1329 @ X1330 ) )
& ( ~ ( in @ X1333 @ X1331 )
| ~ ( in @ X1333 @ X1332 )
| ( in @ X1333 @ ( binintersect @ X1331 @ X1332 ) ) )
& ( ~ ( subset @ X1336 @ X1334 )
| ~ ( subset @ X1336 @ X1335 )
| ( subset @ X1336 @ ( binintersect @ X1334 @ X1335 ) ) )
& ( ~ ( in @ X1339 @ ( binintersect @ X1337 @ X1338 ) )
| ( in @ X1339 @ X1337 ) )
& ( subset @ ( binintersect @ X1340 @ X1341 ) @ X1340 )
& ( ~ ( subset @ X1342 @ X1343 )
| ( ( binintersect @ X1342 @ X1343 )
= X1342 ) )
& ( ( ( binintersect @ X1344 @ X1345 )
!= X1345 )
| ( subset @ X1345 @ X1344 ) )
& ( ~ ( in @ X1348 @ ( binintersect @ X1346 @ X1347 ) )
| ( in @ X1348 @ X1347 ) )
& ( ( in @ ( esk54_2 @ X1349 @ X1350 ) @ X1349 )
| ( ( binintersect @ X1349 @ X1350 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1349 @ X1350 ) @ X1350 )
| ( ( binintersect @ X1349 @ X1350 )
= emptyset ) )
& ( subset @ ( binintersect @ X1352 @ X1353 ) @ X1353 )
& ( ~ ( subset @ X1355 @ X1354 )
| ( ( binintersect @ X1354 @ X1355 )
= X1355 ) )
& ( ( ( binintersect @ X1356 @ X1357 )
!= X1356 )
| ( subset @ X1356 @ X1357 ) )
& ( ( binintersect @ X1358 @ ( binunion @ X1359 @ X1360 ) )
= ( binunion @ ( binintersect @ X1358 @ X1359 ) @ ( binintersect @ X1358 @ X1360 ) ) )
& ( ~ ( in @ X1363 @ X1361 )
| ( in @ X1363 @ X1362 )
| ( in @ X1363 @ ( setminus @ X1361 @ X1362 ) ) )
& ( ~ ( in @ X1366 @ ( setminus @ X1364 @ X1365 ) )
| ( in @ X1366 @ X1364 ) )
& ( ~ ( in @ X1369 @ ( setminus @ X1367 @ X1368 ) )
| ~ ( in @ X1369 @ X1368 ) )
& ( ~ ( subset @ X1370 @ X1371 )
| ( ( setminus @ X1370 @ X1371 )
= emptyset ) )
& ( ( in @ X1374 @ ( setminus @ X1372 @ X1373 ) )
| ~ ( in @ X1374 @ X1372 )
| ( in @ X1374 @ X1373 ) )
& ( ( in @ X1377 @ ( setminus @ X1375 @ X1376 ) )
| ( in @ X1377 @ X1376 )
| ~ ( in @ X1377 @ X1375 ) )
& ( ( in @ X1380 @ X1378 )
| ~ ( in @ X1380 @ ( setminus @ X1378 @ X1379 ) ) )
& ( ~ ( in @ X1383 @ X1382 )
| ~ ( in @ X1383 @ ( setminus @ X1381 @ X1382 ) ) )
& ( subset @ ( setminus @ X1384 @ X1385 ) @ X1384 )
& ( ( ( setminus @ X1386 @ X1387 )
!= emptyset )
| ( subset @ X1386 @ X1387 ) )
& ( ~ ( in @ X1390 @ X1388 )
| X1391
| ( in @ X1390 @ X1388 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ( in @ X1390 @ X1389 )
| X1391
| ( in @ X1390 @ X1388 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ X1391
| X1391
| ( in @ X1390 @ X1388 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ ( in @ X1390 @ X1388 )
| X1391
| ~ ( in @ X1390 @ X1389 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ( in @ X1390 @ X1389 )
| X1391
| ~ ( in @ X1390 @ X1389 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ X1391
| X1391
| ~ ( in @ X1390 @ X1389 )
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ ( in @ X1390 @ X1388 )
| X1391
| ~ X1391
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ( in @ X1390 @ X1389 )
| X1391
| ~ X1391
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ X1391
| X1391
| ~ X1391
| ~ ( in @ X1390 @ ( symdiff @ X1388 @ X1389 ) ) )
& ( ~ ( in @ X1394 @ X1392 )
| ( in @ X1394 @ X1393 )
| ( in @ X1394 @ ( symdiff @ X1392 @ X1393 ) ) )
& ( ( in @ X1397 @ X1395 )
| ~ ( in @ X1397 @ X1396 )
| ( in @ X1397 @ ( symdiff @ X1395 @ X1396 ) ) )
& ( ~ ( in @ X1400 @ X1398 )
| ~ ( in @ X1400 @ X1399 )
| ~ ( in @ X1400 @ ( symdiff @ X1398 @ X1399 ) ) )
& ( ( in @ X1403 @ X1401 )
| ( in @ X1403 @ X1402 )
| ~ ( in @ X1403 @ ( symdiff @ X1401 @ X1402 ) ) )
& ( in @ X1405 @ ( setadjoin @ X1404 @ ( setadjoin @ X1405 @ emptyset ) ) )
& ( in @ X1406 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1406 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1406 @ ( setadjoin @ X1407 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1409 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1408 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1408 @ ( setadjoin @ X1409 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk55_2 @ X1410 @ X1411 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1410 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1410 @ ( setadjoin @ X1411 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk56_2 @ X1410 @ X1411 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1410 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1410 @ ( setadjoin @ X1411 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1410 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1410 @ ( setadjoin @ X1411 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1410 @ X1411 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk55_2 @ X1410 @ X1411 ) @ ( setadjoin @ ( esk56_2 @ X1410 @ X1411 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( esk57_2 @ X1414 @ X1415 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1414 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1414 @ ( setadjoin @ X1415 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk58_2 @ X1414 @ X1415 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1414 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1414 @ ( setadjoin @ X1415 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1414 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1414 @ ( setadjoin @ X1415 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1414 @ X1415 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk57_2 @ X1414 @ X1415 ) @ ( setadjoin @ ( esk58_2 @ X1414 @ X1415 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X1419 @ X1418 )
| ( subset @ ( setadjoin @ X1419 @ emptyset ) @ X1418 ) )
& ( ~ ( in @ X1421 @ X1420 )
| ( in @ ( setadjoin @ X1421 @ emptyset ) @ ( powerset @ X1420 ) ) )
& ( ~ ( in @ X1424 @ X1422 )
| ( in @ ( setadjoin @ X1424 @ emptyset ) @ ( powerset @ ( binunion @ X1422 @ X1423 ) ) ) )
& ( ~ ( in @ X1427 @ ( setadjoin @ X1425 @ ( setadjoin @ X1426 @ emptyset ) ) )
| ( X1427 = X1425 )
| ( X1427 = X1426 ) )
& ( ~ ( in @ X1430 @ X1428 )
| ~ ( in @ X1431 @ X1429 )
| ( subset @ ( setadjoin @ X1430 @ ( setadjoin @ X1431 @ emptyset ) ) @ ( binunion @ X1428 @ X1429 ) ) )
& ( ~ ( in @ X1434 @ X1432 )
| ~ ( in @ X1435 @ X1433 )
| ( in @ ( setadjoin @ X1434 @ ( setadjoin @ X1435 @ emptyset ) ) @ ( powerset @ ( binunion @ X1432 @ X1433 ) ) ) )
& ( ~ ( in @ X1438 @ X1436 )
| ~ ( in @ X1439 @ X1437 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1438 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1438 @ ( setadjoin @ X1439 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1436 @ X1437 ) ) ) )
& ( ~ ( in @ X1442 @ X1440 )
| ~ ( in @ X1443 @ X1441 )
| ( in @ ( setadjoin @ ( setadjoin @ X1442 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1442 @ ( setadjoin @ X1443 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1440 @ X1441 ) ) ) ) )
& ( ~ ( in @ X1446 @ X1444 )
| ~ ( in @ X1447 @ X1445 )
| ( in @ ( setadjoin @ ( setadjoin @ X1446 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1446 @ ( setadjoin @ X1447 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1444 @ X1445 ) ) ) ) )
& ( ~ ( in @ X1450 @ X1448 )
| ~ ( in @ X1451 @ X1449 )
| ( in @ ( setadjoin @ ( setadjoin @ X1450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1450 @ ( setadjoin @ X1451 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ X1448 @ X1449 ) ) )
& ( ( in @ ( esk59_3 @ X1452 @ X1453 @ X1454 ) @ X1452 )
| ~ ( in @ X1454 @ ( cartprod @ X1452 @ X1453 ) ) )
& ( ( in @ ( esk60_3 @ X1452 @ X1453 @ X1454 ) @ X1453 )
| ~ ( in @ X1454 @ ( cartprod @ X1452 @ X1453 ) ) )
& ( ( X1454
= ( setadjoin @ ( setadjoin @ ( esk59_3 @ X1452 @ X1453 @ X1454 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk59_3 @ X1452 @ X1453 @ X1454 ) @ ( setadjoin @ ( esk60_3 @ X1452 @ X1453 @ X1454 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1454 @ ( cartprod @ X1452 @ X1453 ) ) )
& ( ( in @ ( esk61_3 @ X1457 @ X1458 @ X1459 ) @ ( setunion @ X1459 ) )
| ~ ( in @ X1459 @ ( cartprod @ X1457 @ X1458 ) ) )
& ( ( in @ ( esk62_3 @ X1457 @ X1458 @ X1459 ) @ ( setunion @ X1459 ) )
| ~ ( in @ X1459 @ ( cartprod @ X1457 @ X1458 ) ) )
& ( ( X1459
= ( setadjoin @ ( setadjoin @ ( esk61_3 @ X1457 @ X1458 @ X1459 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk61_3 @ X1457 @ X1458 @ X1459 ) @ ( setadjoin @ ( esk62_3 @ X1457 @ X1458 @ X1459 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1459 @ ( cartprod @ X1457 @ X1458 ) ) )
& ( ( in @ ( esk63_2 @ X1462 @ X1463 ) @ X1462 )
| ~ ( in @ X1463 @ ( setunion @ X1462 ) ) )
& ( ( in @ X1463 @ ( esk63_2 @ X1462 @ X1463 ) )
| ~ ( in @ X1463 @ ( setunion @ X1462 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1465 @ emptyset ) ) @ X1465 )
& ( subset @ X1466 @ ( setunion @ ( setadjoin @ X1466 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1467 @ emptyset ) )
= X1467 )
& ( ( in @ ( esk66_2 @ X1468 @ X1469 ) @ ( dsetconstr @ X1468 @ X1469 ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( in @ ( esk64_2 @ X1468 @ X1469 ) @ X1468 ) )
& ( ( ( dsetconstr @ X1468 @ X1469 )
= ( setadjoin @ ( esk66_2 @ X1468 @ X1469 ) @ emptyset ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( in @ ( esk64_2 @ X1468 @ X1469 ) @ X1468 ) )
& ( ( in @ ( esk66_2 @ X1468 @ X1469 ) @ ( dsetconstr @ X1468 @ X1469 ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( in @ ( esk65_2 @ X1468 @ X1469 ) @ X1468 ) )
& ( ( ( dsetconstr @ X1468 @ X1469 )
= ( setadjoin @ ( esk66_2 @ X1468 @ X1469 ) @ emptyset ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( in @ ( esk65_2 @ X1468 @ X1469 ) @ X1468 ) )
& ( ( in @ ( esk66_2 @ X1468 @ X1469 ) @ ( dsetconstr @ X1468 @ X1469 ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( X1469 @ ( esk64_2 @ X1468 @ X1469 ) ) )
& ( ( ( dsetconstr @ X1468 @ X1469 )
= ( setadjoin @ ( esk66_2 @ X1468 @ X1469 ) @ emptyset ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( X1469 @ ( esk64_2 @ X1468 @ X1469 ) ) )
& ( ( in @ ( esk66_2 @ X1468 @ X1469 ) @ ( dsetconstr @ X1468 @ X1469 ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( X1469 @ ( esk65_2 @ X1468 @ X1469 ) ) )
& ( ( ( dsetconstr @ X1468 @ X1469 )
= ( setadjoin @ ( esk66_2 @ X1468 @ X1469 ) @ emptyset ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( X1469 @ ( esk65_2 @ X1468 @ X1469 ) ) )
& ( ( in @ ( esk66_2 @ X1468 @ X1469 ) @ ( dsetconstr @ X1468 @ X1469 ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( ( esk64_2 @ X1468 @ X1469 )
!= ( esk65_2 @ X1468 @ X1469 ) ) )
& ( ( ( dsetconstr @ X1468 @ X1469 )
= ( setadjoin @ ( esk66_2 @ X1468 @ X1469 ) @ emptyset ) )
| ~ ( in @ X1472 @ X1468 )
| ~ ( X1469 @ X1472 )
| ( ( esk64_2 @ X1468 @ X1469 )
!= ( esk65_2 @ X1468 @ X1469 ) ) )
& ( ( in @ ( esk67_2 @ X1474 @ X1475 ) @ X1474 )
| ~ ( in @ X1476 @ ( dsetconstr @ X1474 @ X1475 ) )
| ( ( dsetconstr @ X1474 @ X1475 )
!= ( setadjoin @ X1476 @ emptyset ) ) )
& ( ( X1475 @ ( esk67_2 @ X1474 @ X1475 ) )
| ~ ( in @ X1476 @ ( dsetconstr @ X1474 @ X1475 ) )
| ( ( dsetconstr @ X1474 @ X1475 )
!= ( setadjoin @ X1476 @ emptyset ) ) )
& ( ( in @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ ( dsetconstr @ X1478 @ X1479 ) )
| ( in @ ( esk68_3 @ X1478 @ X1479 @ X1480 ) @ X1478 )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( ( dsetconstr @ X1478 @ X1479 )
= ( setadjoin @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ emptyset ) )
| ( in @ ( esk68_3 @ X1478 @ X1479 @ X1480 ) @ X1478 )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( in @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ ( dsetconstr @ X1478 @ X1479 ) )
| ( X1479 @ ( esk68_3 @ X1478 @ X1479 @ X1480 ) )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( ( dsetconstr @ X1478 @ X1479 )
= ( setadjoin @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ emptyset ) )
| ( X1479 @ ( esk68_3 @ X1478 @ X1479 @ X1480 ) )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( in @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ ( dsetconstr @ X1478 @ X1479 ) )
| ( ( esk68_3 @ X1478 @ X1479 @ X1480 )
!= X1480 )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( ( dsetconstr @ X1478 @ X1479 )
= ( setadjoin @ ( esk69_3 @ X1478 @ X1479 @ X1480 ) @ emptyset ) )
| ( ( esk68_3 @ X1478 @ X1479 @ X1480 )
!= X1480 )
| ~ ( X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 ) )
& ( ( in @ ( esk72_2 @ X1483 @ X1484 ) @ ( dsetconstr @ X1483 @ X1484 ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( in @ ( esk70_2 @ X1483 @ X1484 ) @ X1483 ) )
& ( ( ( dsetconstr @ X1483 @ X1484 )
= ( setadjoin @ ( esk72_2 @ X1483 @ X1484 ) @ emptyset ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( in @ ( esk70_2 @ X1483 @ X1484 ) @ X1483 ) )
& ( ( in @ ( esk72_2 @ X1483 @ X1484 ) @ ( dsetconstr @ X1483 @ X1484 ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( in @ ( esk71_2 @ X1483 @ X1484 ) @ X1483 ) )
& ( ( ( dsetconstr @ X1483 @ X1484 )
= ( setadjoin @ ( esk72_2 @ X1483 @ X1484 ) @ emptyset ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( in @ ( esk71_2 @ X1483 @ X1484 ) @ X1483 ) )
& ( ( in @ ( esk72_2 @ X1483 @ X1484 ) @ ( dsetconstr @ X1483 @ X1484 ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( X1484 @ ( esk70_2 @ X1483 @ X1484 ) ) )
& ( ( ( dsetconstr @ X1483 @ X1484 )
= ( setadjoin @ ( esk72_2 @ X1483 @ X1484 ) @ emptyset ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( X1484 @ ( esk70_2 @ X1483 @ X1484 ) ) )
& ( ( in @ ( esk72_2 @ X1483 @ X1484 ) @ ( dsetconstr @ X1483 @ X1484 ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( X1484 @ ( esk71_2 @ X1483 @ X1484 ) ) )
& ( ( ( dsetconstr @ X1483 @ X1484 )
= ( setadjoin @ ( esk72_2 @ X1483 @ X1484 ) @ emptyset ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( X1484 @ ( esk71_2 @ X1483 @ X1484 ) ) )
& ( ( in @ ( esk72_2 @ X1483 @ X1484 ) @ ( dsetconstr @ X1483 @ X1484 ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( ( esk70_2 @ X1483 @ X1484 )
!= ( esk71_2 @ X1483 @ X1484 ) ) )
& ( ( ( dsetconstr @ X1483 @ X1484 )
= ( setadjoin @ ( esk72_2 @ X1483 @ X1484 ) @ emptyset ) )
| ~ ( in @ X1487 @ X1483 )
| ~ ( X1484 @ X1487 )
| ( ( esk70_2 @ X1483 @ X1484 )
!= ( esk71_2 @ X1483 @ X1484 ) ) )
& ( ( ( setadjoin @ X1489 @ emptyset )
!= ( setadjoin @ X1490 @ emptyset ) )
| ( X1489 = X1490 ) )
& ( ~ ( in @ ( setadjoin @ X1493 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1491 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1491 @ ( setadjoin @ X1492 @ emptyset ) ) @ emptyset ) ) )
| ( X1491 = X1493 ) )
& ( ( in @ ( esk73_1 @ X1494 )
@ ( dsetconstr @ ( setunion @ X1494 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1494 ) ) )
| ~ ( in @ X1495 @ ( setunion @ X1494 ) )
| ~ ( in @ X1496 @ ( setunion @ X1494 ) )
| ( X1494
!= ( setadjoin @ ( setadjoin @ X1495 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1495 @ ( setadjoin @ X1496 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X1494 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1494 ) )
= ( setadjoin @ ( esk73_1 @ X1494 ) @ emptyset ) )
| ~ ( in @ X1495 @ ( setunion @ X1494 ) )
| ~ ( in @ X1496 @ ( setunion @ X1494 ) )
| ( X1494
!= ( setadjoin @ ( setadjoin @ X1495 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1495 @ ( setadjoin @ X1496 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X1499 @ X1498 )
| ( X1498
!= ( setadjoin @ X1499 @ emptyset ) )
| ( in @ ( setunion @ X1498 ) @ X1498 ) )
& ( ( kfst @ ( setadjoin @ ( setadjoin @ X1500 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1500 @ ( setadjoin @ X1501 @ emptyset ) ) @ emptyset ) ) )
= X1500 )
& ( ~ ( in @ X1504 @ ( cartprod @ X1502 @ X1503 ) )
| ( in @ ( kfst @ X1504 ) @ X1502 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1505 @ ( setadjoin @ X1506 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1507 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1507 @ ( setadjoin @ X1508 @ emptyset ) ) @ emptyset ) ) )
| ( X1505 = X1507 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1509 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1509 @ ( setadjoin @ X1510 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1511 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1511 @ ( setadjoin @ X1512 @ emptyset ) ) @ emptyset ) ) )
| ( X1509 = X1511 ) )
& ( ( X1513 != X1514 )
| ( ( setadjoin @ X1513 @ ( setadjoin @ X1514 @ emptyset ) )
= ( setadjoin @ X1513 @ emptyset ) ) )
& ( ( X1515 != X1516 )
| ( ( setadjoin @ ( setadjoin @ X1515 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1515 @ ( setadjoin @ X1516 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1515 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1517 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1517 @ ( setadjoin @ X1518 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1519 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1519 @ ( setadjoin @ X1520 @ emptyset ) ) @ emptyset ) ) )
| ( X1519 != X1520 )
| ( X1518 = X1520 ) )
& ( ( ( setadjoin @ X1521 @ ( setadjoin @ X1522 @ emptyset ) )
!= ( setadjoin @ X1523 @ emptyset ) )
| ( X1521 = X1522 ) )
& ( ( setadjoin @ ( setadjoin @ esk74_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk74_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk76_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) @ emptyset ) ) )
& ( esk75_0 != esk77_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_240])])])])])])]) ).
thf(c_0_242,negated_conjecture,
! [X3: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_243,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk74_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk74_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk76_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_244,negated_conjecture,
! [X3: $i,X2: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_245,negated_conjecture,
in @ ( setadjoin @ esk74_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) @ emptyset ) ),
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
thf(c_0_246,negated_conjecture,
esk74_0 = esk76_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_243]),c_0_244]) ).
thf(c_0_247,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_241]) ).
thf(c_0_248,negated_conjecture,
in @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) @ emptyset ) ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
thf(c_0_249,negated_conjecture,
( ( ( setadjoin @ esk76_0 @ ( setadjoin @ esk75_0 @ emptyset ) )
= ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) )
| ( ( setadjoin @ esk76_0 @ ( setadjoin @ esk75_0 @ emptyset ) )
= ( setadjoin @ esk76_0 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
thf(c_0_250,negated_conjecture,
( ( ( setadjoin @ esk76_0 @ ( setadjoin @ esk75_0 @ emptyset ) )
= ( setadjoin @ esk76_0 @ emptyset ) )
| ( in @ esk75_0 @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_242,c_0_249]) ).
thf(c_0_251,negated_conjecture,
esk75_0 != esk77_0,
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_252,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( X2 = X3 )
| ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
!= ( setadjoin @ X4 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_253,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_254,negated_conjecture,
! [X2: $i] :
( ( X2
= ( setadjoin @ esk76_0 @ ( setadjoin @ esk75_0 @ emptyset ) ) )
| ( X2
= ( setadjoin @ esk76_0 @ emptyset ) )
| ~ ( in @ X2 @ ( setadjoin @ ( setadjoin @ esk76_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_243]),c_0_246]),c_0_246]) ).
thf(c_0_255,negated_conjecture,
esk75_0 = esk76_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_250]),c_0_251]),c_0_252]) ).
thf(c_0_256,negated_conjecture,
! [X2: $i] :
( ( setadjoin @ X2 @ ( setadjoin @ X2 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ),
inference(er,[status(thm)],[c_0_253]) ).
thf(c_0_257,negated_conjecture,
( ( setadjoin @ esk76_0 @ ( setadjoin @ esk77_0 @ emptyset ) )
= ( setadjoin @ esk76_0 @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_242]),c_0_255]),c_0_256])]) ).
thf(c_0_258,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_241])])]) ).
thf(c_0_259,negated_conjecture,
in @ esk77_0 @ ( setadjoin @ esk76_0 @ emptyset ),
inference(spm,[status(thm)],[c_0_242,c_0_257]) ).
thf(c_0_260,negated_conjecture,
esk77_0 != esk76_0,
inference(rw,[status(thm)],[c_0_251,c_0_255]) ).
thf(c_0_261,negated_conjecture,
! [X2: $i] :
~ ( in @ X2 @ emptyset ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
thf(c_0_262,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_260]),c_0_261]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU653^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.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 17:32:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 8.58/1.57 # Version: 3.1.0-ho
% 8.58/1.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 8.58/1.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 8.58/1.57 # Starting ehoh_best5 with 300s (1) cores
% 8.58/1.57 # Starting almost_fo_3_lam with 300s (1) cores
% 8.58/1.57 # Starting new_bool_5 with 300s (1) cores
% 8.58/1.57 # Starting pre_casc_3 with 300s (1) cores
% 8.58/1.57 # Starting ho_unfolding_8 with 300s (1) cores
% 8.58/1.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 8.58/1.57 # Starting new_bool_3 with 300s (1) cores
% 8.58/1.57 # Starting new_ho_5 with 300s (1) cores
% 8.58/1.57 # new_bool_3 with pid 23960 completed with status 0
% 8.58/1.57 # Result found by new_bool_3
% 8.58/1.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 8.58/1.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 8.58/1.57 # Starting ehoh_best5 with 300s (1) cores
% 8.58/1.57 # Starting almost_fo_3_lam with 300s (1) cores
% 8.58/1.57 # Starting new_bool_5 with 300s (1) cores
% 8.58/1.57 # Starting pre_casc_3 with 300s (1) cores
% 8.58/1.57 # Starting ho_unfolding_8 with 300s (1) cores
% 8.58/1.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 8.58/1.57 # Starting new_bool_3 with 300s (1) cores
% 8.58/1.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.58/1.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 8.58/1.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 8.58/1.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 8.58/1.57 # new_ho_10_cnf2 with pid 23965 completed with status 0
% 8.58/1.57 # Result found by new_ho_10_cnf2
% 8.58/1.57 # Preprocessing class: HSLMSLSSLLLCHFA.
% 8.58/1.57 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 8.58/1.57 # Starting ehoh_best5 with 300s (1) cores
% 8.58/1.57 # Starting almost_fo_3_lam with 300s (1) cores
% 8.58/1.57 # Starting new_bool_5 with 300s (1) cores
% 8.58/1.57 # Starting pre_casc_3 with 300s (1) cores
% 8.58/1.57 # Starting ho_unfolding_8 with 300s (1) cores
% 8.58/1.57 # Starting new_ho_10_cnf2 with 300s (1) cores
% 8.58/1.57 # Starting new_bool_3 with 300s (1) cores
% 8.58/1.57 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.58/1.57 # Search class: HGHSM-FSLM31-MHFMMSBN
% 8.58/1.57 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 8.58/1.57 # Starting new_ho_10_cnf2 with 163s (1) cores
% 8.58/1.57 # Preprocessing time : 0.007 s
% 8.58/1.57 # Presaturation interreduction done
% 8.58/1.57
% 8.58/1.57 # Proof found!
% 8.58/1.57 # SZS status Theorem
% 8.58/1.57 # SZS output start CNFRefutation
% See solution above
% 8.58/1.57 # Parsed axioms : 375
% 8.58/1.57 # Removed by relevancy pruning/SinE : 200
% 8.58/1.57 # Initial clauses : 327
% 8.58/1.57 # Removed in clause preprocessing : 24
% 8.58/1.57 # Initial clauses in saturation : 303
% 8.58/1.57 # Processed clauses : 2002
% 8.58/1.57 # ...of these trivial : 38
% 8.58/1.57 # ...subsumed : 620
% 8.58/1.57 # ...remaining for further processing : 1344
% 8.58/1.57 # Other redundant clauses eliminated : 41
% 8.58/1.57 # Clauses deleted for lack of memory : 0
% 8.58/1.57 # Backward-subsumed : 11
% 8.58/1.57 # Backward-rewritten : 40
% 8.58/1.57 # Generated clauses : 65080
% 8.58/1.57 # ...of the previous two non-redundant : 63942
% 8.58/1.57 # ...aggressively subsumed : 0
% 8.58/1.57 # Contextual simplify-reflections : 1
% 8.58/1.57 # Paramodulations : 65033
% 8.58/1.57 # Factorizations : 4
% 8.58/1.57 # NegExts : 0
% 8.58/1.57 # Equation resolutions : 43
% 8.58/1.57 # Disequality decompositions : 0
% 8.58/1.57 # Total rewrite steps : 5583
% 8.58/1.57 # ...of those cached : 5332
% 8.58/1.57 # Propositional unsat checks : 0
% 8.58/1.57 # Propositional check models : 0
% 8.58/1.57 # Propositional check unsatisfiable : 0
% 8.58/1.57 # Propositional clauses : 0
% 8.58/1.57 # Propositional clauses after purity: 0
% 8.58/1.57 # Propositional unsat core size : 0
% 8.58/1.57 # Propositional preprocessing time : 0.000
% 8.58/1.57 # Propositional encoding time : 0.000
% 8.58/1.57 # Propositional solver time : 0.000
% 8.58/1.57 # Success case prop preproc time : 0.000
% 8.58/1.57 # Success case prop encoding time : 0.000
% 8.58/1.57 # Success case prop solver time : 0.000
% 8.58/1.57 # Current number of processed clauses : 1013
% 8.58/1.57 # Positive orientable unit clauses : 75
% 8.58/1.57 # Positive unorientable unit clauses: 0
% 8.58/1.57 # Negative unit clauses : 42
% 8.58/1.57 # Non-unit-clauses : 896
% 8.58/1.57 # Current number of unprocessed clauses: 62312
% 8.58/1.57 # ...number of literals in the above : 230844
% 8.58/1.57 # Current number of archived formulas : 0
% 8.58/1.57 # Current number of archived clauses : 312
% 8.58/1.57 # Clause-clause subsumption calls (NU) : 73347
% 8.58/1.57 # Rec. Clause-clause subsumption calls : 48478
% 8.58/1.57 # Non-unit clause-clause subsumptions : 412
% 8.58/1.57 # Unit Clause-clause subsumption calls : 4529
% 8.58/1.57 # Rewrite failures with RHS unbound : 0
% 8.58/1.57 # BW rewrite match attempts : 41
% 8.58/1.57 # BW rewrite match successes : 13
% 8.58/1.57 # Condensation attempts : 2002
% 8.58/1.57 # Condensation successes : 16
% 8.58/1.57 # Termbank termtop insertions : 1323422
% 8.58/1.57 # Search garbage collected termcells : 16714
% 8.58/1.57
% 8.58/1.57 # -------------------------------------------------
% 8.58/1.57 # User time : 0.988 s
% 8.58/1.57 # System time : 0.046 s
% 8.58/1.57 # Total time : 1.034 s
% 8.58/1.57 # Maximum resident set size: 5988 pages
% 8.58/1.57
% 8.58/1.57 # -------------------------------------------------
% 8.58/1.57 # User time : 0.996 s
% 8.58/1.57 # System time : 0.050 s
% 8.58/1.57 # Total time : 1.046 s
% 8.58/1.57 # Maximum resident set size: 2200 pages
% 8.58/1.57 % E---3.1 exiting
% 8.58/1.57 % E exiting
%------------------------------------------------------------------------------