TSTP Solution File: SEU703^1 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU703^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.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 : Mon Jun 24 15:10:14 EDT 2024
% Result : Theorem 99.05s 11.77s
% Output : CNFRefutation 99.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 230
% Syntax : Number of formulae : 340 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 2991 ( 684 equ; 0 cnn)
% Maximal formula atoms : 894 ( 8 avg)
% Number of connectives : 12079 ( 833 ~; 923 |; 570 &;8055 @)
% ( 313 <=>;1384 =>; 0 <=; 1 <~>)
% Maximal formula depth : 1014 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 257 ( 257 >; 0 *; 0 +; 0 <<)
% Number of symbols : 349 ( 345 usr; 230 con; 0-4 aty)
% Number of variables : 2557 ( 202 ^2209 !; 146 ?;2557 :)
% 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_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
epred1_0: $o ).
thf(decl_279,type,
esk1_2: $i > $i > $i ).
thf(decl_280,type,
esk2_2: $i > $i > $i ).
thf(decl_281,type,
esk3_2: $i > $i > $i ).
thf(decl_282,type,
esk4_1: $i > $i ).
thf(decl_283,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_284,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_285,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_286,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_287,type,
esk9_1: $i > $i ).
thf(decl_288,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_289,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_290,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_291,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_292,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_293,type,
esk15_2: $i > $i > $i ).
thf(decl_294,type,
esk16_2: $i > $i > $i ).
thf(decl_295,type,
esk17_1: $i > $i ).
thf(decl_296,type,
esk18_1: $i > $i ).
thf(decl_297,type,
esk19_1: $i > $i ).
thf(decl_298,type,
esk20_2: $i > $i > $i ).
thf(decl_299,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_300,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_301,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_302,type,
esk24_1: $i > $i ).
thf(decl_303,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_304,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_305,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_306,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_307,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_308,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_309,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_310,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_311,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_312,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_313,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_314,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_315,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_316,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_317,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_318,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_319,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_320,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_321,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_322,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_323,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_324,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_325,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_326,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_327,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_328,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_329,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_330,type,
esk52_2: $i > $i > $i ).
thf(decl_331,type,
esk53_2: $i > $i > $i ).
thf(decl_332,type,
esk54_2: $i > $i > $i ).
thf(decl_333,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_334,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_335,type,
esk57_2: $i > $i > $i ).
thf(decl_336,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_337,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_338,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_339,type,
esk61_2: $i > ( $i > $o ) > $i ).
thf(decl_340,type,
esk62_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_341,type,
esk63_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_342,type,
esk64_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk65_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk66_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk67_1: $i > $i ).
thf(decl_346,type,
esk68_1: $i > $i ).
thf(decl_347,type,
esk69_4: $i > $i > $i > $i > $i ).
thf(decl_348,type,
esk70_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_349,type,
esk71_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_350,type,
esk72_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_351,type,
esk73_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk74_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk75_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_354,type,
esk76_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_355,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_356,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_357,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_358,type,
esk80_4: $i > $i > $i > $i > $i ).
thf(decl_359,type,
esk81_4: $i > $i > $i > $i > $i ).
thf(decl_360,type,
esk82_4: $i > $i > $i > $i > $i ).
thf(decl_361,type,
esk83_4: $i > $i > $i > $i > $i ).
thf(decl_362,type,
esk84_4: $i > $i > $i > $i > $i ).
thf(decl_363,type,
esk85_4: $i > $i > $i > $i > $i ).
thf(decl_364,type,
esk86_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_365,type,
esk87_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_366,type,
esk88_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_367,type,
esk89_0: $i ).
thf(decl_368,type,
epred2_0: $o ).
thf(decl_369,type,
esk90_0: $i ).
thf(decl_370,type,
esk91_0: $i ).
thf(decl_376,type,
epred3_0: $i > $o ).
thf(decl_378,type,
epred5_2: $i > $i > $i > $o ).
thf(decl_442,type,
esk155_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',singleton) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',descrp) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',nonempty) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuE2) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',descr__Cong) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ksndsingleton) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',breln) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcImageSingleton) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ex1E2) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dsetconstrI) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dsetconstrEL) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dsetconstrER) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',nonemptyImpWitness) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyE1) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',sepSubset) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',theprop) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrSub) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',dpsetconstrER) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',lam2p) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',brelnall2) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',iftrueProp1) ).
thf(iftrueProp2,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',iftrueProp2) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',omegaSAx) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',omegaIndAx) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',foundationAx) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notinemptyset) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinIR) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionI) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',singletonsswitch) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',vacuousDall) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',quantDeMorgan1) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',quantDeMorgan2) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',quantDeMorgan3) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',prop2set2propI) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ubforcartprodlem2) ).
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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjL1) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p',ap2apEq2) ).
thf(c_0_225,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X746: $i] :
( ( in @ X746
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X746 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_226,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_227,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_228,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_229,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_230,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_231,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_232,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X746: $i] :
( ( in @ X746
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X746 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_225,c_0_226]) ).
thf(c_0_245,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_246,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_247,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_248,plain,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
thf(c_0_249,plain,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).
thf(c_0_250,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_251,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_252,plain,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_253,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X717: $i] :
( ( X6 @ X2 @ X717 )
& ! [X718: $i] :
( ( X6 @ X2 @ X718 )
=> ( X717 = X718 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_227,c_0_228]) ).
thf(c_0_254,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X719: $i] :
( ( X1 @ X719 )
& ! [X720: $i] :
( ( X1 @ X720 )
=> ( X719 = X720 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_229,c_0_228]) ).
thf(c_0_255,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_256,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_257,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_258,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X721: $i] :
( ( X1 @ X721 )
& ! [X722: $i] :
( ( X1 @ X722 )
=> ( X721 = X722 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_230,c_0_228]) ).
thf(c_0_259,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X723: $i] :
( ( X1 @ X723 )
& ! [X724: $i] :
( ( X1 @ X724 )
=> ( X723 = X724 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_231,c_0_228]) ).
thf(c_0_260,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_261,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_232]) ).
thf(c_0_262,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_233,c_0_232]) ).
thf(c_0_263,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_232]) ).
thf(c_0_264,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_265,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X725: $i] :
( ( X1 @ X725 )
& ! [X726: $i] :
( ( X1 @ X726 )
=> ( X725 = X726 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_234,c_0_228]) ).
thf(c_0_266,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_232]) ).
thf(c_0_267,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_268,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X727: $i] :
( ( X1 @ X727 )
& ! [X728: $i] :
( ( X1 @ X728 )
=> ( X727 = X728 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_235,c_0_228]) ).
thf(c_0_269,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X729: $i] :
( ( X1 @ X729 )
& ! [X730: $i] :
( ( X1 @ X730 )
=> ( X729 = X730 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_236,c_0_228]) ).
thf(c_0_270,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X731: $i] :
( ( X1 @ X731 )
& ! [X732: $i] :
( ( X1 @ X732 )
=> ( X731 = X732 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_237,c_0_228]) ).
thf(c_0_271,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X733: $i] :
( ( X1 @ X733 )
& ! [X734: $i] :
( ( X1 @ X734 )
=> ( X733 = X734 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_238,c_0_228]) ).
thf(c_0_272,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X735: $i] :
( ( X1 @ X735 )
& ! [X736: $i] :
( ( X1 @ X736 )
=> ( X735 = X736 ) ) )
<=> ? [X737: $i] :
( ( X17 @ X737 )
& ! [X738: $i] :
( ( X17 @ X738 )
=> ( X737 = X738 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_239,c_0_228]) ).
thf(c_0_273,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X739: $i] :
( ( X1 @ X739 )
& ! [X740: $i] :
( ( X1 @ X740 )
=> ( X739 = X740 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_240,c_0_228]) ).
thf(c_0_274,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X741: $i] :
( ( X1 @ X741 )
& ! [X742: $i] :
( ( X1 @ X742 )
=> ( X741 = X742 ) ) )
=> ( ? [X743: $i] :
( ( X17 @ X743 )
& ! [X744: $i] :
( ( X17 @ X744 )
=> ( X743 = X744 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_241,c_0_228]) ).
thf(c_0_275,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_276,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_277,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_278,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 ) )
=> ? [X745: $i] :
( ( in @ X745
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X745 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_242,c_0_226]) ).
thf(c_0_279,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X747: $i] :
( ( in @ X747
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X747 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_243,c_0_244]) ).
thf(c_0_280,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X748: $i] :
( ( in @ X748
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X748 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_245,c_0_244]) ).
thf(c_0_281,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 ) )
=> ? [X749: $i] :
( ( in @ X749
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X749 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_246,c_0_244]) ).
thf(c_0_282,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X750: $i] :
( ( in @ X750
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X750 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_247,c_0_226]) ).
thf(c_0_283,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X751: $i] :
( ( in @ X751 @ X21 )
& ( X21
= ( setadjoin @ X751 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_226]) ).
thf(c_0_284,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X752: $i] :
( ( in @ X752
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X752 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_248,c_0_226]) ).
thf(c_0_285,plain,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X22 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_286,plain,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_287,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_249,c_0_250]) ).
thf(c_0_288,plain,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).
thf(c_0_289,plain,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).
thf(c_0_290,plain,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
=> ( in @ X3 @ X5 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).
thf(c_0_291,plain,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).
thf(c_0_292,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X753: $i] :
( ( in @ X753
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) )
= ( setadjoin @ X753 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_251,c_0_226]) ).
thf(c_0_293,plain,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_294,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X30 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_295,plain,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X31 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_296,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_297,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_250]) ).
thf(c_0_298,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_250]) ).
thf(c_0_299,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ? [X754: $i] :
( ( in @ X754
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X754 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_252,c_0_244]) ).
thf(c_0_300,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_250]) ).
thf(c_0_301,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_250]) ).
thf(c_0_302,plain,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X36 @ Z0 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta1]) ).
thf(c_0_303,plain,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta1]) ).
thf(c_0_304,plain,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) )
= ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2lamEq]) ).
thf(c_0_305,plain,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X38 @ Z0 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta2]) ).
thf(c_0_306,plain,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta2]) ).
thf(c_0_307,plain,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X39
& ( Z0 = X2 ) )
| ( ~ X39
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp1]) ).
thf(c_0_308,plain,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X40
& ( Z0 = X2 ) )
| ( ~ X40
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp2]) ).
thf(c_0_309,plain,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X41
& ( Z0 = X2 ) )
| ( ~ X41
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_310,plain,
( epred1_0
<=> ! [X784: $i] :
? [X785: $i] :
( ! [X786: $i] :
( ( in @ X786 @ X785 )
=> ! [X787: $i] :
( ( in @ X787 @ X786 )
=> ( in @ X787 @ X784 ) ) )
& ! [X788: $i,X789: $i] :
( ( ( in @ X788 @ X784 )
& ( in @ X789 @ X784 ) )
=> ( ! [X790: $i] :
( ( in @ X790 @ X785 )
=> ( ( in @ X788 @ X790 )
<=> ( in @ X789 @ X790 ) ) )
=> ( X788 = X789 ) ) )
& ! [X791: $i,X792: $i] :
( ( ( in @ X791 @ X785 )
& ( in @ X792 @ X785 ) )
=> ( ! [X793: $i] :
( ( in @ X793 @ X791 )
=> ( in @ X793 @ X792 ) )
| ! [X794: $i] :
( ( in @ X794 @ X792 )
=> ( in @ X794 @ X791 ) ) ) )
& ! [X795: $i] :
( ( ! [X796: $i] :
( ( in @ X796 @ X795 )
=> ( in @ X796 @ X784 ) )
& ? [X797: $i] : ( in @ X797 @ X795 ) )
=> ? [X798: $i,X799: $i] :
( ( in @ X798 @ X785 )
& ( in @ X799 @ X795 )
& ~ ? [X800: $i] :
( ( in @ X800 @ X798 )
& ( in @ X800 @ X795 ) )
& ! [X801: $i] :
( ( in @ X801 @ X785 )
=> ( ! [X802: $i] :
( ( in @ X802 @ X801 )
=> ( in @ X802 @ X798 ) )
| ( in @ X799 @ X801 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_311,negated_conjecture,
~ ( ! [X755: $i,X756: $i] :
( ! [X757: $i] :
( ( in @ X757 @ X755 )
<=> ( in @ X757 @ X756 ) )
=> ( X755 = X756 ) )
=> ( ! [X758: $i] :
~ ( in @ X758 @ emptyset )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ( in @ X761 @ ( setadjoin @ X759 @ X760 ) )
<=> ( ( X761 = X759 )
| ( in @ X761 @ X760 ) ) )
=> ( ! [X762: $i,X763: $i] :
( ( in @ X763 @ ( powerset @ X762 ) )
<=> ! [X764: $i] :
( ( in @ X764 @ X763 )
=> ( in @ X764 @ X762 ) ) )
=> ( ! [X765: $i,X766: $i] :
( ( in @ X766 @ ( setunion @ X765 ) )
<=> ? [X767: $i] :
( ( in @ X766 @ X767 )
& ( in @ X767 @ X765 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X768: $i] :
( ( in @ X768 @ omega )
=> ( in @ ( setadjoin @ X768 @ X768 ) @ omega ) )
=> ( ! [X769: $i] :
( ( ( in @ emptyset @ X769 )
& ! [X770: $i] :
( ( ( in @ X770 @ omega )
& ( in @ X770 @ X769 ) )
=> ( in @ ( setadjoin @ X770 @ X770 ) @ X769 ) ) )
=> ! [X771: $i] :
( ( in @ X771 @ omega )
=> ( in @ X771 @ X769 ) ) )
=> ( ! [X772: $i > $i > $o,X773: $i] :
( ! [X774: $i] :
( ( in @ X774 @ X773 )
=> ? [X775: $i] :
( ( X772 @ X774 @ X775 )
& ! [X776: $i] :
( ( X772 @ X774 @ X776 )
=> ( X775 = X776 ) ) ) )
=> ? [X777: $i] :
! [X778: $i] :
( ( in @ X778 @ X777 )
<=> ? [X779: $i] :
( ( in @ X779 @ X773 )
& ( X772 @ X779 @ X778 ) ) ) )
=> ( ! [X780: $i] :
( ? [X781: $i] : ( in @ X781 @ X780 )
=> ? [X782: $i] :
( ( in @ X782 @ X780 )
& ~ ? [X783: $i] :
( ( in @ X783 @ X782 )
& ( in @ X783 @ X780 ) ) ) )
=> ( epred1_0
=> ( ! [X803: $i > $o] :
( ? [X804: $i] :
( ( X803 @ X804 )
& ! [X805: $i] :
( ( X803 @ X805 )
=> ( X804 = X805 ) ) )
=> ( X803
@ ( descr
@ ^ [Z0: $i] : ( X803 @ Z0 ) ) ) )
=> ( ! [X806: $i,X807: $i > $o,X808: $i] :
( ( in @ X808 @ X806 )
=> ( ( X807 @ X808 )
=> ( in @ X808 @ ( dsetconstr @ X806 @ X807 ) ) ) )
=> ( ! [X809: $i,X810: $i > $o,X811: $i] :
( ( in @ X811 @ ( dsetconstr @ X809 @ X810 ) )
=> ( in @ X811 @ X809 ) )
=> ( ! [X812: $i,X813: $i > $o,X814: $i] :
( ( in @ X814 @ ( dsetconstr @ X812 @ X813 ) )
=> ( X813 @ X814 ) )
=> ( ! [X815: $i > $o] :
( ? [X816: $i] :
( ( X815 @ X816 )
& ! [X817: $i] :
( ( X815 @ X817 )
=> ( X816 = X817 ) ) )
=> ? [X818: $i] :
( ( X815 @ X818 )
& ! [X819: $i] :
( ( X815 @ X819 )
=> ( X818 = X819 ) ) ) )
=> ( ! [X820: $o,X821: $i] :
( ( in @ X821 @ ( prop2set @ X820 ) )
=> X820 )
=> ( ! [X822: $i] :
( ( in @ X822 @ emptyset )
=> ! [X823: $o] : X823 )
=> ( ! [X824: $i] :
( ( in @ X824 @ emptyset )
=> ~ $true )
=> ( ! [X825: $i] :
~ ( in @ X825 @ emptyset )
=> ( ! [X826: $i > $o] :
( ? [X827: $i] :
( ( X826 @ X827 )
& ! [X828: $i] :
( ( X826 @ X828 )
=> ( X827 = X828 ) ) )
=> ? [X829: $i] : ( X826 @ X829 ) )
=> ( ! [X830: $i,X831: $i] :
( ! [X832: $i] :
( ( in @ X832 @ X830 )
=> ( in @ X832 @ X831 ) )
=> ( ! [X833: $i] :
( ( in @ X833 @ X831 )
=> ( in @ X833 @ X830 ) )
=> ( X830 = X831 ) ) )
=> ( ! [X834: $i] :
( ! [X835: $i] :
~ ( in @ X835 @ X834 )
=> ( X834 = emptyset ) )
=> ( ! [X836: $i] :
( ! [X837: $i] :
~ ( in @ X837 @ X836 )
=> ( X836 = emptyset ) )
=> ( ! [X838: $i,X839: $i > $o,X840: $i] :
( ( in @ X840 @ X838 )
=> ( ( in @ X840 @ ( dsetconstr @ X838 @ X839 ) )
<=> ( X839 @ X840 ) ) )
=> ( ! [X841: $i] :
( ( X841 != emptyset )
=> ? [X842: $i] : ( in @ X842 @ X841 ) )
=> ( ! [X843: $i,X844: $i > $o,X845: $i] :
( ( in @ X845 @ X843 )
=> ( ( X844 @ X845 )
=> ( ( dsetconstr @ X843 @ X844 )
!= emptyset ) ) )
=> ( ! [X846: $i] :
( ? [X847: $i] : ( in @ X847 @ X846 )
=> ( X846 != emptyset ) )
=> ( ! [X848: $i,X849: $i] : ( in @ X848 @ ( setadjoin @ X848 @ X849 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X850: $i,X851: $i,X852: $i] :
( ( in @ X852 @ X851 )
=> ( in @ X852 @ ( setadjoin @ X850 @ X851 ) ) )
=> ( ! [X853: $i,X854: $i,X855: $i] :
( ( in @ X855 @ ( setadjoin @ X853 @ X854 ) )
=> ! [X856: $o] :
( ( ( X855 = X853 )
=> X856 )
=> ( ( ( in @ X855 @ X854 )
=> X856 )
=> X856 ) ) )
=> ( ! [X857: $i,X858: $i,X859: $i] :
( ( in @ X859 @ ( setadjoin @ X857 @ X858 ) )
=> ( ( X859 = X857 )
| ( in @ X859 @ X858 ) ) )
=> ( ! [X860: $i] :
( ( dsetconstr @ X860
@ ^ [Z0: $i] : $true )
= X860 )
=> ( ! [X861: $i,X862: $i] :
( ! [X863: $i] :
( ( in @ X863 @ X862 )
=> ( in @ X863 @ X861 ) )
=> ( in @ X862 @ ( powerset @ X861 ) ) )
=> ( ! [X864: $i] : ( in @ emptyset @ ( powerset @ X864 ) )
=> ( ! [X865: $i] : ( in @ emptyset @ ( powerset @ X865 ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ( in @ X867 @ ( powerset @ X866 ) )
=> ( ( in @ X868 @ X867 )
=> ( in @ X868 @ X866 ) ) )
=> ( ! [X869: $i,X870: $i,X871: $i] :
( ( in @ X870 @ X871 )
=> ( ( in @ X871 @ X869 )
=> ( in @ X870 @ ( setunion @ X869 ) ) ) )
=> ( ! [X872: $i,X873: $i] :
( ( in @ X873 @ ( setunion @ X872 ) )
=> ! [X874: $o] :
( ! [X875: $i] :
( ( in @ X873 @ X875 )
=> ( ( in @ X875 @ X872 )
=> X874 ) )
=> X874 ) )
=> ( ! [X876: $i,X877: $i] :
( ( in @ X877 @ X876 )
=> ( in @ X877 @ ( powerset @ ( setunion @ X876 ) ) ) )
=> ( ! [X878: $i > $o] :
( ? [X879: $i] :
( ( X878 @ X879 )
& ! [X880: $i] :
( ( X878 @ X880 )
=> ( X879 = X880 ) ) )
=> ? [X881: $i] :
! [X882: $i] :
( ( X878 @ X882 )
<=> ( X882 = X881 ) ) )
=> ( ! [X883: $i] :
( ( X883 != emptyset )
=> ? [X884: $i] :
( ( in @ X884 @ X883 )
& $true ) )
=> ( ! [X885: $i,X886: $i] :
( ( in @ X885 @ ( setadjoin @ X886 @ emptyset ) )
=> ( X885 = X886 ) )
=> ( ! [X887: $i,X888: $i] :
( ( X887 != X888 )
=> ~ ( in @ X888 @ ( setadjoin @ X887 @ emptyset ) ) )
=> ( ! [X889: $i,X890: $i] :
( ( X889 = X890 )
=> ( in @ X889 @ ( setadjoin @ X890 @ emptyset ) ) )
=> ( ! [X891: $i,X892: $i] :
( ( in @ X891 @ ( setadjoin @ X892 @ emptyset ) )
=> ( in @ X892 @ ( setadjoin @ X891 @ emptyset ) ) )
=> ( ! [X893: $i,X894: $i,X895: $i] :
( ( in @ X895 @ ( setadjoin @ X893 @ ( setadjoin @ X894 @ emptyset ) ) )
=> ( ( X895 = X893 )
| ( X895 = X894 ) ) )
=> ( ! [X896: $i,X897: $i] : ( in @ X896 @ ( setadjoin @ X896 @ ( setadjoin @ X897 @ emptyset ) ) )
=> ( ! [X898: $i,X899: $i] : ( in @ X899 @ ( setadjoin @ X898 @ ( setadjoin @ X899 @ emptyset ) ) )
=> ( ! [X900: $i,X901: $i > $o] :
( ? [X902: $i] :
( ( in @ X902 @ X900 )
& ( X901 @ X902 ) )
=> ( ( ( dsetconstr @ X900 @ X901 )
= emptyset )
=> ~ $true ) )
=> ( ! [X903: $i > $o,X904: $i] :
( ( in @ X904 @ emptyset )
=> ( X903 @ X904 ) )
=> ( ! [X905: $i,X906: $i > $o] :
( ~ ! [X907: $i] :
( ( in @ X907 @ X905 )
=> ( X906 @ X907 ) )
=> ? [X908: $i] :
( ( in @ X908 @ X905 )
& ~ ( X906 @ X908 ) ) )
=> ( ! [X909: $i,X910: $i > $o] :
( ! [X911: $i] :
( ( in @ X911 @ X909 )
=> ~ ( X910 @ X911 ) )
=> ~ ? [X912: $i] :
( ( in @ X912 @ X909 )
& ( X910 @ X912 ) ) )
=> ( ! [X913: $i,X914: $i > $o] :
( ~ ? [X915: $i] :
( ( in @ X915 @ X913 )
& ( X914 @ X915 ) )
=> ! [X916: $i] :
( ( in @ X916 @ X913 )
=> ~ ( X914 @ X916 ) ) )
=> ( ! [X917: $i,X918: $i > $o] :
( ? [X919: $i] :
( ( in @ X919 @ X917 )
& ~ ( X918 @ X919 ) )
=> ~ ! [X920: $i] :
( ( in @ X920 @ X917 )
=> ( X918 @ X920 ) ) )
=> ( ! [X921: $o] :
( X921
=> ( in @ emptyset @ ( prop2set @ X921 ) ) )
=> ( ! [X922: $o] :
( X922
=> ( set2prop @ ( prop2set @ X922 ) ) )
=> ( ! [X923: $i,X924: $i > $o] :
( ~ ? [X925: $i] :
( ( in @ X925 @ X923 )
& ( X924 @ X925 ) )
=> ! [X926: $i] :
( ( in @ X926 @ X923 )
=> ~ ( X924 @ X926 ) ) )
=> ( ! [X927: $i,X928: $i > $o] :
( ~ ! [X929: $i] :
( ( in @ X929 @ X927 )
=> ( X928 @ X929 ) )
=> ? [X930: $i] :
( ( in @ X930 @ X927 )
& ~ ( X928 @ X930 ) ) )
=> ( ! [X931: $i > $o] :
( ? [X932: $i] :
( ( X931 @ X932 )
& ! [X933: $i] :
( ( X931 @ X933 )
=> ( X932 = X933 ) ) )
=> ? [X934: $i] :
( ( X931 @ X934 )
& ! [X935: $i] :
( ( X931 @ X935 )
=> ( X934 = X935 ) ) ) )
=> ( ! [X936: $i > $o] :
( ? [X937: $i] : ( X936 @ X937 )
=> ( ! [X938: $i,X939: $i] :
( ( X936 @ X938 )
=> ( ( X936 @ X939 )
=> ( X938 = X939 ) ) )
=> ? [X940: $i] :
( ( X936 @ X940 )
& ! [X941: $i] :
( ( X936 @ X941 )
=> ( X940 = X941 ) ) ) ) )
=> ( ! [X942: $i > $o] :
( ? [X943: $i] :
! [X944: $i] :
( ( X942 @ X944 )
<=> ( X944 = X943 ) )
=> ? [X945: $i] :
( ( X942 @ X945 )
& ! [X946: $i] :
( ( X942 @ X946 )
=> ( X945 = X946 ) ) ) )
=> ( ! [X947: $i,X948: $i] :
( ( X947 = X948 )
=> ! [X949: $i,X950: $i] :
( ( X949 = X950 )
=> ( ( in @ X949 @ X947 )
=> ( in @ X950 @ X948 ) ) ) )
=> ( ! [X951: $i,X952: $i] :
( ( X951 = X952 )
=> ! [X953: $i,X954: $i] :
( ( X953 = X954 )
=> ( ( in @ X953 @ X951 )
<=> ( in @ X954 @ X952 ) ) ) )
=> ( ! [X955: $i > $o] :
( ? [X956: $i] :
( ( X955 @ X956 )
& ! [X957: $i] :
( ( X955 @ X957 )
=> ( X956 = X957 ) ) )
=> ! [X958: $i,X959: $i] :
( ( X955 @ X958 )
=> ( ( X955 @ X959 )
=> ( X958 = X959 ) ) ) )
=> ( ! [X960: $i > $o,X961: $i > $o] :
( ! [X962: $i,X963: $i] :
( ( X962 = X963 )
=> ( ( X960 @ X962 )
<=> ( X961 @ X963 ) ) )
=> ( ? [X964: $i] :
( ( X960 @ X964 )
& ! [X965: $i] :
( ( X960 @ X965 )
=> ( X964 = X965 ) ) )
<=> ? [X966: $i] :
( ( X961 @ X966 )
& ! [X967: $i] :
( ( X961 @ X967 )
=> ( X966 = X967 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X968: $i,X969: $i] :
( ( X968 = X969 )
=> ! [X970: $i,X971: $i] :
( ( X970 = X971 )
=> ( ( setadjoin @ X968 @ X970 )
= ( setadjoin @ X969 @ X971 ) ) ) )
=> ( ! [X972: $i,X973: $i] :
( ( X972 = X973 )
=> ( ( powerset @ X972 )
= ( powerset @ X973 ) ) )
=> ( ! [X974: $i,X975: $i] :
( ( X974 = X975 )
=> ( ( setunion @ X974 )
= ( setunion @ X975 ) ) )
=> ( ( omega = omega )
=> ( ! [X976: $i > $o] :
( ? [X977: $i] :
( ( X976 @ X977 )
& ! [X978: $i] :
( ( X976 @ X978 )
=> ( X977 = X978 ) ) )
=> ! [X979: $i,X980: $i] :
( ( X976 @ X979 )
=> ( ( X976 @ X980 )
=> ( X979 = X980 ) ) ) )
=> ( ! [X981: $i > $o,X982: $i > $o] :
( ! [X983: $i,X984: $i] :
( ( X983 = X984 )
=> ( ( X981 @ X983 )
<=> ( X982 @ X984 ) ) )
=> ( ? [X985: $i] :
( ( X981 @ X985 )
& ! [X986: $i] :
( ( X981 @ X986 )
=> ( X985 = X986 ) ) )
=> ( ? [X987: $i] :
( ( X982 @ X987 )
& ! [X988: $i] :
( ( X982 @ X988 )
=> ( X987 = X988 ) ) )
=> ( ( descr @ X981 )
= ( descr @ X982 ) ) ) ) )
=> ( ! [X989: $i,X990: $i] :
( ( X989 = X990 )
=> ! [X991: $i > $o,X992: $i > $o] :
( ! [X993: $i] :
( ( in @ X993 @ X989 )
=> ! [X994: $i] :
( ( in @ X994 @ X990 )
=> ( ( X993 = X994 )
=> ( ( X991 @ X993 )
<=> ( X992 @ X994 ) ) ) ) )
=> ( ( dsetconstr @ X989 @ X991 )
= ( dsetconstr @ X990 @ X992 ) ) ) )
=> ( ! [X995: $i,X996: $i] :
( ! [X997: $i] :
( ( in @ X997 @ X995 )
=> ( in @ X997 @ X996 ) )
=> ( subset @ X995 @ X996 ) )
=> ( ! [X998: $i,X999: $i] :
( ( X998 = X999 )
=> ( subset @ X999 @ X998 ) )
=> ( ! [X1000: $i,X1001: $i] :
( ( X1000 = X1001 )
=> ( subset @ X1000 @ X1001 ) )
=> ( ! [X1002: $i,X1003: $i] :
( ! [X1004: $i] :
( ( in @ X1004 @ X1002 )
=> ( in @ X1004 @ X1003 ) )
=> ( subset @ X1002 @ X1003 ) )
=> ( ! [X1005: $i] : ( subset @ emptyset @ X1005 )
=> ( ! [X1006: $i,X1007: $i,X1008: $i] :
( ( subset @ X1006 @ X1007 )
=> ( ( in @ X1008 @ X1006 )
=> ( in @ X1008 @ X1007 ) ) )
=> ( ! [X1009: $i,X1010: $i,X1011: $i] :
( ( subset @ X1009 @ X1010 )
=> ( ~ ( in @ X1011 @ X1010 )
=> ~ ( in @ X1011 @ X1009 ) ) )
=> ( ! [X1012: $i,X1013: $i,X1014: $i] :
( ( in @ X1014 @ X1012 )
=> ( ~ ( in @ X1014 @ X1013 )
=> ~ ( subset @ X1012 @ X1013 ) ) )
=> ( ! [X1015: $i,X1016: $i] :
( ~ ( subset @ X1015 @ X1016 )
=> ( X1015 != X1016 ) )
=> ( ! [X1017: $i,X1018: $i,X1019: $i] :
( ( in @ X1019 @ X1017 )
=> ( ~ ( in @ X1019 @ X1018 )
=> ( X1017 != X1018 ) ) )
=> ( ! [X1020: $i] : ( subset @ X1020 @ X1020 )
=> ( ! [X1021: $i,X1022: $i,X1023: $i] :
( ( subset @ X1021 @ X1022 )
=> ( ( subset @ X1022 @ X1023 )
=> ( subset @ X1021 @ X1023 ) ) )
=> ( ! [X1024: $i,X1025: $i] : ( subset @ X1025 @ ( setadjoin @ X1024 @ X1025 ) )
=> ( ! [X1026: $i,X1027: $i,X1028: $i] :
( ( subset @ X1026 @ X1028 )
=> ( subset @ X1026 @ ( setadjoin @ X1027 @ X1028 ) ) )
=> ( ! [X1029: $i,X1030: $i] :
( ( subset @ X1029 @ X1030 )
=> ( in @ X1029 @ ( powerset @ X1030 ) ) )
=> ( ! [X1031: $i,X1032: $i] :
( ( subset @ X1031 @ X1032 )
=> ( ( subset @ X1032 @ X1031 )
=> ( X1031 = X1032 ) ) )
=> ( ! [X1033: $i] :
( ( subset @ X1033 @ emptyset )
=> ( X1033 = emptyset ) )
=> ( ! [X1034: $i,X1035: $i] :
( ( subset @ X1035 @ X1034 )
=> ( in @ X1035 @ ( powerset @ X1034 ) ) )
=> ( ! [X1036: $i,X1037: $i] :
( ( in @ X1037 @ ( powerset @ X1036 ) )
=> ( subset @ X1037 @ X1036 ) )
=> ( ! [X1038: $i] : ( in @ X1038 @ ( powerset @ X1038 ) )
=> ( ! [X1039: $i,X1040: $i] :
( ( subset @ X1039 @ X1040 )
=> ( subset @ ( powerset @ X1039 ) @ ( powerset @ X1040 ) ) )
=> ( ! [X1041: $i,X1042: $i > $o] : ( in @ ( dsetconstr @ X1041 @ X1042 ) @ ( powerset @ X1041 ) )
=> ( ! [X1043: $i,X1044: $i > $o] : ( subset @ ( dsetconstr @ X1043 @ X1044 ) @ X1043 )
=> ( ! [X1045: $i,X1046: $i,X1047: $i] :
( ( in @ X1047 @ X1045 )
=> ( in @ X1047 @ ( binunion @ X1045 @ X1046 ) ) )
=> ( ! [X1048: $i,X1049: $i] : ( in @ X1049 @ ( setadjoin @ X1048 @ ( setadjoin @ X1049 @ emptyset ) ) )
=> ( ! [X1050: $i,X1051: $i,X1052: $i] :
( ( in @ X1052 @ X1051 )
=> ( in @ X1052 @ ( binunion @ X1050 @ X1051 ) ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i,X1056: $o] :
( ( in @ X1055 @ ( binunion @ X1053 @ X1054 ) )
=> ( ( ( in @ X1055 @ X1053 )
=> X1056 )
=> ( ( ( in @ X1055 @ X1054 )
=> X1056 )
=> X1056 ) ) )
=> ( ! [X1057: $i,X1058: $i,X1059: $i] :
( ( in @ X1059 @ ( binunion @ X1057 @ X1058 ) )
=> ( ( in @ X1059 @ X1057 )
| ( in @ X1059 @ X1058 ) ) )
=> ( ! [X1060: $i,X1061: $i] : ( subset @ X1060 @ ( binunion @ X1060 @ X1061 ) )
=> ( ! [X1062: $i,X1063: $i] : ( subset @ X1063 @ ( binunion @ X1062 @ X1063 ) )
=> ( ! [X1064: $i,X1065: $i,X1066: $i] :
( ( in @ X1066 @ X1064 )
=> ( ( in @ X1066 @ X1065 )
=> ( in @ X1066 @ ( binintersect @ X1064 @ X1065 ) ) ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i] :
( ( subset @ X1069 @ X1067 )
=> ( ( subset @ X1069 @ X1068 )
=> ( subset @ X1069 @ ( binintersect @ X1067 @ X1068 ) ) ) )
=> ( ! [X1070: $i,X1071: $i,X1072: $i] :
( ( in @ X1072 @ ( binintersect @ X1070 @ X1071 ) )
=> ( in @ X1072 @ X1070 ) )
=> ( ! [X1073: $i,X1074: $i] : ( subset @ ( binintersect @ X1073 @ X1074 ) @ X1073 )
=> ( ! [X1075: $i,X1076: $i] :
( ( subset @ X1075 @ X1076 )
=> ( ( binintersect @ X1075 @ X1076 )
= X1075 ) )
=> ( ! [X1077: $i,X1078: $i] :
( ( ( binintersect @ X1077 @ X1078 )
= X1078 )
=> ( subset @ X1078 @ X1077 ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i] :
( ( in @ X1081 @ ( binintersect @ X1079 @ X1080 ) )
=> ( in @ X1081 @ X1080 ) )
=> ( ! [X1082: $i,X1083: $i] :
( ~ ? [X1084: $i] :
( ( in @ X1084 @ X1082 )
& ( in @ X1084 @ X1083 ) )
=> ( ( binintersect @ X1082 @ X1083 )
= emptyset ) )
=> ( ! [X1085: $i,X1086: $i] : ( subset @ ( binintersect @ X1085 @ X1086 ) @ X1086 )
=> ( ! [X1087: $i,X1088: $i] :
( ( subset @ X1088 @ X1087 )
=> ( ( binintersect @ X1087 @ X1088 )
= X1088 ) )
=> ( ! [X1089: $i,X1090: $i] :
( ( ( binintersect @ X1089 @ X1090 )
= X1089 )
=> ( subset @ X1089 @ X1090 ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( binintersect @ X1091 @ ( binunion @ X1092 @ X1093 ) )
= ( binunion @ ( binintersect @ X1091 @ X1092 ) @ ( binintersect @ X1091 @ X1093 ) ) )
=> ( ! [X1094: $i,X1095: $i,X1096: $i] :
( ( in @ X1096 @ X1094 )
=> ( ~ ( in @ X1096 @ X1095 )
=> ( in @ X1096 @ ( setminus @ X1094 @ X1095 ) ) ) )
=> ( ! [X1097: $i,X1098: $i,X1099: $i] :
( ( in @ X1099 @ ( setminus @ X1097 @ X1098 ) )
=> ( in @ X1099 @ X1097 ) )
=> ( ! [X1100: $i,X1101: $i,X1102: $i] :
( ( in @ X1102 @ ( setminus @ X1100 @ X1101 ) )
=> ~ ( in @ X1102 @ X1101 ) )
=> ( ! [X1103: $i,X1104: $i] :
( ( subset @ X1103 @ X1104 )
=> ( ( setminus @ X1103 @ X1104 )
= emptyset ) )
=> ( ! [X1105: $i,X1106: $i,X1107: $i] :
( ~ ( in @ X1107 @ ( setminus @ X1105 @ X1106 ) )
=> ( ( in @ X1107 @ X1105 )
=> ( in @ X1107 @ X1106 ) ) )
=> ( ! [X1108: $i,X1109: $i,X1110: $i] :
( ~ ( in @ X1110 @ ( setminus @ X1108 @ X1109 ) )
=> ( ~ ( in @ X1110 @ X1109 )
=> ~ ( in @ X1110 @ X1108 ) ) )
=> ( ! [X1111: $i,X1112: $i,X1113: $i] :
( ~ ( in @ X1113 @ X1111 )
=> ~ ( in @ X1113 @ ( setminus @ X1111 @ X1112 ) ) )
=> ( ! [X1114: $i,X1115: $i,X1116: $i] :
( ( in @ X1116 @ X1115 )
=> ~ ( in @ X1116 @ ( setminus @ X1114 @ X1115 ) ) )
=> ( ! [X1117: $i,X1118: $i] : ( subset @ ( setminus @ X1117 @ X1118 ) @ X1117 )
=> ( ! [X1119: $i,X1120: $i] :
( ( ( setminus @ X1119 @ X1120 )
= emptyset )
=> ( subset @ X1119 @ X1120 ) )
=> ( ! [X1121: $i,X1122: $i,X1123: $i] :
( ( in @ X1123 @ ( symdiff @ X1121 @ X1122 ) )
=> ! [X1124: $o] :
( ( ( in @ X1123 @ X1121 )
=> ( ~ ( in @ X1123 @ X1122 )
=> X1124 ) )
=> ( ( ~ ( in @ X1123 @ X1121 )
=> ( ( in @ X1123 @ X1122 )
=> X1124 ) )
=> X1124 ) ) )
=> ( ! [X1125: $i,X1126: $i,X1127: $i] :
( ( in @ X1127 @ X1125 )
=> ( ~ ( in @ X1127 @ X1126 )
=> ( in @ X1127 @ ( symdiff @ X1125 @ X1126 ) ) ) )
=> ( ! [X1128: $i,X1129: $i,X1130: $i] :
( ~ ( in @ X1130 @ X1128 )
=> ( ( in @ X1130 @ X1129 )
=> ( in @ X1130 @ ( symdiff @ X1128 @ X1129 ) ) ) )
=> ( ! [X1131: $i,X1132: $i,X1133: $i] :
( ( in @ X1133 @ X1131 )
=> ( ( in @ X1133 @ X1132 )
=> ~ ( in @ X1133 @ ( symdiff @ X1131 @ X1132 ) ) ) )
=> ( ! [X1134: $i,X1135: $i,X1136: $i] :
( ~ ( in @ X1136 @ X1134 )
=> ( ~ ( in @ X1136 @ X1135 )
=> ~ ( in @ X1136 @ ( symdiff @ X1134 @ X1135 ) ) ) )
=> ( ! [X1137: $i,X1138: $i] : ( in @ X1138 @ ( setadjoin @ X1137 @ ( setadjoin @ X1138 @ emptyset ) ) )
=> ( ! [X1139: $i,X1140: $i] : ( in @ X1139 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1139 @ ( setadjoin @ X1140 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1141: $i,X1142: $i] : ( in @ X1142 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1141 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1141 @ ( setadjoin @ X1142 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1143: $i,X1144: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1143 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1143 @ ( setadjoin @ X1144 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1145: $i,X1146: $i] : ( iskpair @ ( kpair @ X1145 @ X1146 ) )
=> ( ! [X1147: $i,X1148: $i] :
( ( in @ X1148 @ X1147 )
=> ( subset @ ( setadjoin @ X1148 @ emptyset ) @ X1147 ) )
=> ( ! [X1149: $i,X1150: $i] :
( ( in @ X1150 @ X1149 )
=> ( in @ ( setadjoin @ X1150 @ emptyset ) @ ( powerset @ X1149 ) ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i] :
( ( in @ X1153 @ X1151 )
=> ( in @ ( setadjoin @ X1153 @ emptyset ) @ ( powerset @ ( binunion @ X1151 @ X1152 ) ) ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ ( setadjoin @ X1154 @ ( setadjoin @ X1155 @ emptyset ) ) )
=> ( ( X1156 = X1154 )
| ( X1156 = X1155 ) ) )
=> ( ! [X1157: $i,X1158: $i,X1159: $i] :
( ( in @ X1159 @ X1157 )
=> ! [X1160: $i] :
( ( in @ X1160 @ X1158 )
=> ( subset @ ( setadjoin @ X1159 @ ( setadjoin @ X1160 @ emptyset ) ) @ ( binunion @ X1157 @ X1158 ) ) ) )
=> ( ! [X1161: $i,X1162: $i,X1163: $i] :
( ( in @ X1163 @ X1161 )
=> ! [X1164: $i] :
( ( in @ X1164 @ X1162 )
=> ( in @ ( setadjoin @ X1163 @ ( setadjoin @ X1164 @ emptyset ) ) @ ( powerset @ ( binunion @ X1161 @ X1162 ) ) ) ) )
=> ( ! [X1165: $i,X1166: $i,X1167: $i] :
( ( in @ X1167 @ X1165 )
=> ! [X1168: $i] :
( ( in @ X1168 @ X1166 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1167 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1167 @ ( setadjoin @ X1168 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1165 @ X1166 ) ) ) ) )
=> ( ! [X1169: $i,X1170: $i,X1171: $i] :
( ( in @ X1171 @ X1169 )
=> ! [X1172: $i] :
( ( in @ X1172 @ X1170 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1171 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1171 @ ( setadjoin @ X1172 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1169 @ X1170 ) ) ) ) ) )
=> ( ! [X1173: $i,X1174: $i,X1175: $i] :
( ( in @ X1175 @ X1173 )
=> ! [X1176: $i] :
( ( in @ X1176 @ X1174 )
=> ( in @ ( kpair @ X1175 @ X1176 ) @ ( powerset @ ( powerset @ ( binunion @ X1173 @ X1174 ) ) ) ) ) )
=> ( ! [X1177: $i,X1178: $i,X1179: $i] :
( ( in @ X1179 @ X1177 )
=> ! [X1180: $i] :
( ( in @ X1180 @ X1178 )
=> ( in @ ( kpair @ X1179 @ X1180 ) @ ( cartprod @ X1177 @ X1178 ) ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ ( cartprod @ X1181 @ X1182 ) )
=> ? [X1184: $i] :
( ( in @ X1184 @ X1181 )
& ? [X1185: $i] :
( ( in @ X1185 @ X1182 )
& ( X1183
= ( kpair @ X1184 @ X1185 ) ) ) ) )
=> ( ! [X1186: $i,X1187: $i,X1188: $i] :
( ( in @ X1188 @ ( cartprod @ X1186 @ X1187 ) )
=> ( iskpair @ X1188 ) )
=> ( ! [X1189: $i,X1190: $i] :
( ( in @ X1190 @ ( setunion @ X1189 ) )
=> ? [X1191: $i] :
( ( in @ X1191 @ X1189 )
& ( in @ X1190 @ X1191 ) ) )
=> ( ! [X1192: $i] : ( subset @ ( setunion @ ( setadjoin @ X1192 @ emptyset ) ) @ X1192 )
=> ( ! [X1193: $i] : ( subset @ X1193 @ ( setunion @ ( setadjoin @ X1193 @ emptyset ) ) )
=> ( ! [X1194: $i] :
( ( setunion @ ( setadjoin @ X1194 @ emptyset ) )
= X1194 )
=> ( ! [X1195: $i,X1196: $i > $o] :
( ! [X1197: $i] :
( ( in @ X1197 @ X1195 )
=> ! [X1198: $i] :
( ( in @ X1198 @ X1195 )
=> ( ( X1196 @ X1197 )
=> ( ( X1196 @ X1198 )
=> ( X1197 = X1198 ) ) ) ) )
=> ( ? [X1199: $i] :
( ( in @ X1199 @ X1195 )
& ( X1196 @ X1199 ) )
=> ? [X1200: $i] :
( ( in @ X1200 @ ( dsetconstr @ X1195 @ X1196 ) )
& ( ( dsetconstr @ X1195 @ X1196 )
= ( setadjoin @ X1200 @ emptyset ) ) ) ) )
=> ( ! [X1201: $i,X1202: $i > $o] :
( ? [X1203: $i] :
( ( in @ X1203 @ ( dsetconstr @ X1201 @ X1202 ) )
& ( ( dsetconstr @ X1201 @ X1202 )
= ( setadjoin @ X1203 @ emptyset ) ) )
=> ? [X1204: $i] :
( ( in @ X1204 @ X1201 )
& ( X1202 @ X1204 ) ) )
=> ( ! [X1205: $i,X1206: $i > $o,X1207: $i] :
( ( in @ X1207 @ X1205 )
=> ( ( X1206 @ X1207 )
=> ( ! [X1208: $i] :
( ( in @ X1208 @ X1205 )
=> ( ( X1206 @ X1208 )
=> ( X1208 = X1207 ) ) )
=> ? [X1209: $i] :
( ( in @ X1209 @ ( dsetconstr @ X1205 @ X1206 ) )
& ( ( dsetconstr @ X1205 @ X1206 )
= ( setadjoin @ X1209 @ emptyset ) ) ) ) ) )
=> ( ! [X1210: $i,X1211: $i > $o] :
( ! [X1212: $i] :
( ( in @ X1212 @ X1210 )
=> ! [X1213: $i] :
( ( in @ X1213 @ X1210 )
=> ( ( X1211 @ X1212 )
=> ( ( X1211 @ X1213 )
=> ( X1212 = X1213 ) ) ) ) )
=> ( ? [X1214: $i] :
( ( in @ X1214 @ X1210 )
& ( X1211 @ X1214 ) )
=> ? [X1215: $i] :
( ( in @ X1215 @ ( dsetconstr @ X1210 @ X1211 ) )
& ( ( dsetconstr @ X1210 @ X1211 )
= ( setadjoin @ X1215 @ emptyset ) ) ) ) )
=> ( ! [X1216: $i,X1217: $i] :
( ( ( setadjoin @ X1216 @ emptyset )
= ( setadjoin @ X1217 @ emptyset ) )
=> ( X1216 = X1217 ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( in @ ( setadjoin @ X1220 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1218 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1218 @ ( setadjoin @ X1219 @ emptyset ) ) @ emptyset ) ) )
=> ( X1218 = X1220 ) )
=> ( ! [X1221: $i] :
( ( iskpair @ X1221 )
=> ? [X1222: $i] :
( ( in @ X1222
@ ( dsetconstr @ ( setunion @ X1221 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1221 ) ) )
& ( ( dsetconstr @ ( setunion @ X1221 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1221 ) )
= ( setadjoin @ X1222 @ emptyset ) ) ) )
=> ( ! [X1223: $i] :
( ? [X1224: $i] :
( ( in @ X1224 @ X1223 )
& ( X1223
= ( setadjoin @ X1224 @ emptyset ) ) )
=> ( in @ ( setunion @ X1223 ) @ X1223 ) )
=> ( ! [X1225: $i,X1226: $i] :
( ( kfst @ ( kpair @ X1225 @ X1226 ) )
= X1225 )
=> ( ! [X1227: $i,X1228: $i,X1229: $i] :
( ( in @ X1229 @ ( cartprod @ X1227 @ X1228 ) )
=> ( in @ ( kfst @ X1229 ) @ X1227 ) )
=> ( ! [X1230: $i,X1231: $i,X1232: $i,X1233: $i] :
( ( ( setadjoin @ ( setadjoin @ X1230 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1230 @ ( setadjoin @ X1231 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1232 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1232 @ ( setadjoin @ X1233 @ emptyset ) ) @ emptyset ) ) )
=> ( X1230 = X1232 ) )
=> ( ! [X1234: $i,X1235: $i,X1236: $i,X1237: $i] :
( ( ( kpair @ X1234 @ X1235 )
= ( kpair @ X1236 @ X1237 ) )
=> ( X1234 = X1236 ) )
=> ( ! [X1238: $i,X1239: $i] :
( ( X1238 = X1239 )
=> ( ( setadjoin @ X1238 @ ( setadjoin @ X1239 @ emptyset ) )
= ( setadjoin @ X1238 @ emptyset ) ) )
=> ( ! [X1240: $i,X1241: $i] :
( ( X1240 = X1241 )
=> ( ( setadjoin @ ( setadjoin @ X1240 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1240 @ ( setadjoin @ X1241 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1240 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1242: $i,X1243: $i,X1244: $i,X1245: $i] :
( ( ( setadjoin @ ( setadjoin @ X1242 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1242 @ ( setadjoin @ X1243 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1244 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1244 @ ( setadjoin @ X1245 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1244 = X1245 )
=> ( X1243 = X1245 ) ) )
=> ( ! [X1246: $i,X1247: $i,X1248: $i] :
( ( ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) )
= ( setadjoin @ X1248 @ emptyset ) )
=> ( X1246 = X1247 ) )
=> ( ! [X1249: $i,X1250: $i,X1251: $i,X1252: $i] :
( ( ( setadjoin @ ( setadjoin @ X1249 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1249 @ ( setadjoin @ X1250 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1251 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1251 @ ( setadjoin @ X1252 @ emptyset ) ) @ emptyset ) ) )
=> ( X1250 = X1252 ) )
=> ( ! [X1253: $i,X1254: $i,X1255: $i,X1256: $i] :
( ( ( kpair @ X1253 @ X1254 )
= ( kpair @ X1255 @ X1256 ) )
=> ( X1254 = X1256 ) )
=> ( ! [X1257: $i] :
( ( iskpair @ X1257 )
=> ? [X1258: $i] :
( ( in @ X1258
@ ( dsetconstr @ ( setunion @ X1257 )
@ ^ [Z0: $i] :
( X1257
= ( kpair @ ( kfst @ X1257 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X1257 )
@ ^ [Z0: $i] :
( X1257
= ( kpair @ ( kfst @ X1257 ) @ Z0 ) ) )
= ( setadjoin @ X1258 @ emptyset ) ) ) )
=> ( ! [X1259: $i,X1260: $i] :
( ( ksnd @ ( kpair @ X1259 @ X1260 ) )
= X1260 )
=> ( ! [X1261: $i] :
( ( iskpair @ X1261 )
=> ( ( kpair @ ( kfst @ X1261 ) @ ( ksnd @ X1261 ) )
= X1261 ) )
=> ( ! [X1262: $i,X1263: $i,X1264: $i] :
( ( in @ X1264 @ ( cartprod @ X1262 @ X1263 ) )
=> ( in @ ( ksnd @ X1264 ) @ X1263 ) )
=> ( ! [X1265: $i,X1266: $i,X1267: $i,X1268: $i] :
( ( in @ ( kpair @ X1267 @ X1268 ) @ ( cartprod @ X1265 @ X1266 ) )
=> ( in @ X1267 @ X1265 ) )
=> ( ! [X1269: $i,X1270: $i,X1271: $i,X1272: $i] :
( ( in @ ( kpair @ X1271 @ X1272 ) @ ( cartprod @ X1269 @ X1270 ) )
=> ( in @ X1272 @ X1270 ) )
=> ( ! [X1273: $i,X1274: $i,X1275: $i] :
( ( in @ X1275 @ X1273 )
=> ! [X1276: $i] :
( ( in @ X1276 @ X1274 )
=> ( ( kpair @ X1275 @ X1276 )
= ( kpair @ X1275 @ X1276 ) ) ) )
=> ( ! [X1277: $i,X1278: $i,X1279: $i] :
( ( in @ X1279 @ X1277 )
=> ! [X1280: $i] :
( ( in @ X1280 @ X1278 )
=> ( ( kfst @ ( kpair @ X1279 @ X1280 ) )
= X1279 ) ) )
=> ( ! [X1281: $i,X1282: $i,X1283: $i] :
( ( in @ X1283 @ X1281 )
=> ! [X1284: $i] :
( ( in @ X1284 @ X1282 )
=> ( ( ksnd @ ( kpair @ X1283 @ X1284 ) )
= X1284 ) ) )
=> ( ! [X1285: $i,X1286: $i,X1287: $i] :
( ( in @ X1287 @ ( cartprod @ X1285 @ X1286 ) )
=> ( ( kpair @ ( kfst @ X1287 ) @ ( ksnd @ X1287 ) )
= X1287 ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i > $i > $o,X1291: $i] :
( ( in @ X1291 @ X1288 )
=> ! [X1292: $i] :
( ( in @ X1292 @ X1289 )
=> ( ( X1290 @ X1291 @ X1292 )
=> ( in @ ( kpair @ X1291 @ X1292 ) @ ( dpsetconstr @ X1288 @ X1289 @ X1290 ) ) ) ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1293 @ X1294 @ X1295 ) @ ( cartprod @ X1293 @ X1294 ) )
=> ( ! [X1296: $i,X1297: $i,X1298: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1296 @ X1297 @ X1298 ) @ ( cartprod @ X1296 @ X1297 ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i > $i > $o,X1302: $i] :
( ( in @ X1302 @ X1299 )
=> ! [X1303: $i] :
( ( in @ X1303 @ X1300 )
=> ( ( in @ ( kpair @ X1302 @ X1303 ) @ ( dpsetconstr @ X1299 @ X1300 @ X1301 ) )
=> ( X1301 @ X1302 @ X1303 ) ) ) )
=> ( ! [X1304: $i,X1305: $i,X1306: $i > $i > $o,X1307: $i,X1308: $i] :
( ( in @ ( kpair @ X1307 @ X1308 ) @ ( dpsetconstr @ X1304 @ X1305 @ X1306 ) )
=> ( in @ X1307 @ X1304 ) )
=> ( ! [X1309: $i,X1310: $i,X1311: $i > $i > $o,X1312: $i,X1313: $i] :
( ( in @ ( kpair @ X1312 @ X1313 ) @ ( dpsetconstr @ X1309 @ X1310 @ X1311 ) )
=> ( in @ X1313 @ X1310 ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i > $i > $o,X1317: $i,X1318: $i] :
( ( in @ ( kpair @ X1317 @ X1318 ) @ ( dpsetconstr @ X1314 @ X1315 @ X1316 ) )
=> ( X1316 @ X1317 @ X1318 ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i] :
( ( func @ X1319 @ X1320 @ X1321 )
=> ! [X1322: $i] :
( ( in @ X1322 @ X1319 )
=> ? [X1323: $i] :
( ( in @ X1323
@ ( dsetconstr @ X1320
@ ^ [Z0: $i] : ( in @ ( kpair @ X1322 @ Z0 ) @ X1321 ) ) )
& ( ( dsetconstr @ X1320
@ ^ [Z0: $i] : ( in @ ( kpair @ X1322 @ Z0 ) @ X1321 ) )
= ( setadjoin @ X1323 @ emptyset ) ) ) ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i] :
( ( func @ X1324 @ X1325 @ X1326 )
=> ! [X1327: $i] :
( ( in @ X1327 @ X1324 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1325
@ ^ [Z0: $i] : ( in @ ( kpair @ X1327 @ Z0 ) @ X1326 ) ) )
@ X1325 ) ) )
=> ( ! [X1328: $i,X1329: $i,X1330: $i] :
( ( func @ X1328 @ X1329 @ X1330 )
=> ! [X1331: $i] :
( ( in @ X1331 @ X1328 )
=> ( in @ ( ap @ X1328 @ X1329 @ X1330 @ X1331 ) @ X1329 ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( in @ X1334 @ ( funcSet @ X1332 @ X1333 ) )
=> ( func @ X1332 @ X1333 @ X1334 ) )
=> ( ! [X1335: $i,X1336: $i,X1337: $i] :
( ( in @ X1337 @ ( funcSet @ X1335 @ X1336 ) )
=> ! [X1338: $i] :
( ( in @ X1338 @ X1335 )
=> ( in @ ( ap @ X1335 @ X1336 @ X1337 @ X1338 ) @ X1336 ) ) )
=> ( ! [X1339: $i,X1340: $i,X1341: $i] :
( ( func @ X1339 @ X1340 @ X1341 )
=> ( in @ X1341 @ ( funcSet @ X1339 @ X1340 ) ) )
=> ( ! [X1342: $i,X1343: $i,X1344: $i > $i] :
( ! [X1345: $i] :
( ( in @ X1345 @ X1342 )
=> ( in @ ( X1344 @ X1345 ) @ X1343 ) )
=> ( func @ X1342 @ X1343
@ ( dpsetconstr @ X1342 @ X1343
@ ^ [Z0: $i] : ( $eq @ ( X1344 @ Z0 ) ) ) ) )
=> ( ! [X1346: $i,X1347: $i,X1348: $i > $i] :
( ! [X1349: $i] :
( ( in @ X1349 @ X1346 )
=> ( in @ ( X1348 @ X1349 ) @ X1347 ) )
=> ( func @ X1346 @ X1347 @ ( lam @ X1346 @ X1347 @ X1348 ) ) )
=> ( ! [X1350: $i,X1351: $i,X1352: $i > $i] :
( ! [X1353: $i] :
( ( in @ X1353 @ X1350 )
=> ( in @ ( X1352 @ X1353 ) @ X1351 ) )
=> ( in @ ( lam @ X1350 @ X1351 @ X1352 ) @ ( funcSet @ X1350 @ X1351 ) ) )
=> ( ! [X1354: $i,X1355: $i,X1356: $i] :
( ( subset @ X1356 @ ( cartprod @ X1354 @ X1355 ) )
=> ! [X1357: $i > $o] :
( ! [X1358: $i] :
( ( in @ X1358 @ X1354 )
=> ! [X1359: $i] :
( ( in @ X1359 @ X1355 )
=> ( ( in @ ( kpair @ X1358 @ X1359 ) @ X1356 )
=> ( X1357 @ ( kpair @ X1358 @ X1359 ) ) ) ) )
=> ! [X1360: $i] :
( ( in @ X1360 @ X1356 )
=> ( X1357 @ X1360 ) ) ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i] :
( ( subset @ X1363 @ ( cartprod @ X1361 @ X1362 ) )
=> ! [X1364: $i > $o] :
( ! [X1365: $i] :
( ( in @ X1365 @ X1361 )
=> ! [X1366: $i] :
( ( in @ X1366 @ X1362 )
=> ( ( in @ ( kpair @ X1365 @ X1366 ) @ X1363 )
=> ( X1364 @ ( kpair @ X1365 @ X1366 ) ) ) ) )
=> ! [X1367: $i] :
( ( in @ X1367 @ X1363 )
=> ( X1364 @ X1367 ) ) ) )
=> ( ! [X1368: $i,X1369: $i > $o] :
( ? [X1370: $i] :
( ( in @ X1370 @ ( dsetconstr @ X1368 @ X1369 ) )
& ( ( dsetconstr @ X1368 @ X1369 )
= ( setadjoin @ X1370 @ emptyset ) ) )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1368 )
=> ! [X1372: $i] :
( ( in @ X1372 @ X1368 )
=> ( ( X1369 @ X1371 )
=> ( ( X1369 @ X1372 )
=> ( X1371 = X1372 ) ) ) ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( func @ X1373 @ X1374 @ X1375 )
=> ! [X1376: $i] :
( ( in @ X1376 @ X1373 )
=> ( in @ ( kpair @ X1376 @ ( ap @ X1373 @ X1374 @ X1375 @ X1376 ) ) @ X1375 ) ) )
=> ( ! [X1377: $i,X1378: $i,X1379: $i] :
( ( in @ X1379 @ ( funcSet @ X1377 @ X1378 ) )
=> ! [X1380: $i] :
( ( in @ X1380 @ X1377 )
=> ( in @ ( kpair @ X1380 @ ( ap @ X1377 @ X1378 @ X1379 @ X1380 ) ) @ X1379 ) ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i] :
( ( func @ X1381 @ X1382 @ X1383 )
=> ! [X1384: $i] :
( ( in @ X1384 @ X1381 )
=> ! [X1385: $i] :
( ( in @ X1385 @ X1382 )
=> ( ( in @ ( kpair @ X1384 @ X1385 ) @ X1383 )
=> ( ( ap @ X1381 @ X1382 @ X1383 @ X1384 )
= X1385 ) ) ) ) )
=> ( ! [X1386: $i,X1387: $i,X1388: $i] :
( ( func @ X1386 @ X1387 @ X1388 )
=> ! [X1389: $i] :
( ( func @ X1386 @ X1387 @ X1389 )
=> ( ! [X1390: $i] :
( ( in @ X1390 @ X1386 )
=> ( ( ap @ X1386 @ X1387 @ X1388 @ X1390 )
= ( ap @ X1386 @ X1387 @ X1389 @ X1390 ) ) )
=> ! [X1391: $i] :
( ( in @ X1391 @ X1386 )
=> ! [X1392: $i] :
( ( in @ X1392 @ X1387 )
=> ( ( in @ ( kpair @ X1391 @ X1392 ) @ X1389 )
=> ( in @ ( kpair @ X1391 @ X1392 ) @ X1388 ) ) ) ) ) ) )
=> ( ! [X1393: $i,X1394: $i,X1395: $i] :
( ( in @ X1395 @ ( funcSet @ X1393 @ X1394 ) )
=> ! [X1396: $i] :
( ( in @ X1396 @ X1393 )
=> ! [X1397: $i] :
( ( in @ X1397 @ X1394 )
=> ( ( in @ ( kpair @ X1396 @ X1397 ) @ X1395 )
=> ( ( ap @ X1393 @ X1394 @ X1395 @ X1396 )
= X1397 ) ) ) ) )
=> ( ! [X1398: $i,X1399: $i,X1400: $i] :
( ( subset @ X1400 @ ( cartprod @ X1398 @ X1399 ) )
=> ! [X1401: $i] :
( ( subset @ X1401 @ ( cartprod @ X1398 @ X1399 ) )
=> ( ! [X1402: $i] :
( ( in @ X1402 @ X1398 )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1399 )
=> ( ( in @ ( kpair @ X1402 @ X1403 ) @ X1400 )
=> ( in @ ( kpair @ X1402 @ X1403 ) @ X1401 ) ) ) )
=> ( subset @ X1400 @ X1401 ) ) ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i] :
( ( subset @ X1406 @ ( cartprod @ X1404 @ X1405 ) )
=> ! [X1407: $i] :
( ( subset @ X1407 @ ( cartprod @ X1404 @ X1405 ) )
=> ( ! [X1408: $i] :
( ( in @ X1408 @ X1404 )
=> ! [X1409: $i] :
( ( in @ X1409 @ X1405 )
=> ( ( in @ ( kpair @ X1408 @ X1409 ) @ X1406 )
=> ( in @ ( kpair @ X1408 @ X1409 ) @ X1407 ) ) ) )
=> ( ! [X1410: $i] :
( ( in @ X1410 @ X1404 )
=> ! [X1411: $i] :
( ( in @ X1411 @ X1405 )
=> ( ( in @ ( kpair @ X1410 @ X1411 ) @ X1407 )
=> ( in @ ( kpair @ X1410 @ X1411 ) @ X1406 ) ) ) )
=> ( X1406 = X1407 ) ) ) ) )
=> ( ! [X1412: $i,X1413: $i,X1414: $i] :
( ( func @ X1412 @ X1413 @ X1414 )
=> ! [X1415: $i] :
( ( func @ X1412 @ X1413 @ X1415 )
=> ( ! [X1416: $i] :
( ( in @ X1416 @ X1412 )
=> ( ( ap @ X1412 @ X1413 @ X1414 @ X1416 )
= ( ap @ X1412 @ X1413 @ X1415 @ X1416 ) ) )
=> ( X1414 = X1415 ) ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( in @ X1419 @ ( funcSet @ X1417 @ X1418 ) )
=> ! [X1420: $i] :
( ( in @ X1420 @ ( funcSet @ X1417 @ X1418 ) )
=> ( ! [X1421: $i] :
( ( in @ X1421 @ X1417 )
=> ( ( ap @ X1417 @ X1418 @ X1419 @ X1421 )
= ( ap @ X1417 @ X1418 @ X1420 @ X1421 ) ) )
=> ( X1419 = X1420 ) ) ) )
=> ( ! [X1422: $i,X1423: $i,X1424: $i] :
( ( in @ X1424 @ ( funcSet @ X1422 @ X1423 ) )
=> ! [X1425: $i] :
( ( in @ X1425 @ X1422 )
=> ( ( ap @ X1422 @ X1423 @ X1424 @ X1425 )
= ( ap @ X1422 @ X1423 @ X1424 @ X1425 ) ) ) )
=> ( ! [X1426: $i,X1427: $i,X1428: $i] :
( ( func @ X1426 @ X1427 @ X1428 )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1426 )
=> ( ( ap @ X1426 @ X1427 @ X1428 @ X1429 )
= ( ap @ X1426 @ X1427 @ X1428 @ X1429 ) ) ) )
=> ( ! [X1430: $i,X1431: $i,X1432: $i > $i] :
( ! [X1433: $i] :
( ( in @ X1433 @ X1430 )
=> ( in @ ( X1432 @ X1433 ) @ X1431 ) )
=> ! [X1434: $i] :
( ( in @ X1434 @ X1430 )
=> ( ( ap @ X1430 @ X1431 @ ( lam @ X1430 @ X1431 @ X1432 ) @ X1434 )
= ( X1432 @ X1434 ) ) ) )
=> ( ! [X1435: $i,X1436: $i,X1437: $i] :
( ( func @ X1435 @ X1436 @ X1437 )
=> ( ( lam @ X1435 @ X1436 @ ( ap @ X1435 @ X1436 @ X1437 ) )
= X1437 ) )
=> ( ! [X1438: $i,X1439: $i,X1440: $i > $i] :
( ! [X1441: $i] :
( ( in @ X1441 @ X1438 )
=> ( in @ ( X1440 @ X1441 ) @ X1439 ) )
=> ( ( lam @ X1438 @ X1439 @ X1440 )
= ( lam @ X1438 @ X1439 @ X1440 ) ) )
=> ( ! [X1442: $i,X1443: $i,X1444: $i > $i] :
( ! [X1445: $i] :
( ( in @ X1445 @ X1442 )
=> ( in @ ( X1444 @ X1445 ) @ X1443 ) )
=> ! [X1446: $i] :
( ( in @ X1446 @ X1442 )
=> ( ( ap @ X1442 @ X1443 @ ( lam @ X1442 @ X1443 @ X1444 ) @ X1446 )
= ( X1444 @ X1446 ) ) ) )
=> ( ! [X1447: $i,X1448: $i,X1449: $i] :
( ( in @ X1449 @ ( funcSet @ X1447 @ X1448 ) )
=> ( ( lam @ X1447 @ X1448 @ ( ap @ X1447 @ X1448 @ X1449 ) )
= X1449 ) )
=> ( ! [X1450: $i,X1451: $o,X1452: $i] :
( ( in @ X1452 @ X1450 )
=> ! [X1453: $i] :
( ( in @ X1453 @ X1450 )
=> ( ~ X1451
=> ( in @ X1453
@ ( dsetconstr @ X1450
@ ^ [Z0: $i] :
( ( X1451
& ( Z0 = X1452 ) )
| ( ~ X1451
& ( Z0 = X1453 ) ) ) ) ) ) ) )
=> ( ! [X1454: $i,X1455: $o,X1456: $i] :
( ( in @ X1456 @ X1454 )
=> ! [X1457: $i] :
( ( in @ X1457 @ X1454 )
=> ( ~ X1455
=> ( ( dsetconstr @ X1454
@ ^ [Z0: $i] :
( ( X1455
& ( Z0 = X1456 ) )
| ( ~ X1455
& ( Z0 = X1457 ) ) ) )
= ( setadjoin @ X1457 @ emptyset ) ) ) ) )
=> ( ! [X1458: $i,X1459: $o,X1460: $i] :
( ( in @ X1460 @ X1458 )
=> ! [X1461: $i] :
( ( in @ X1461 @ X1458 )
=> ( X1459
=> ( in @ X1460
@ ( dsetconstr @ X1458
@ ^ [Z0: $i] :
( ( X1459
& ( Z0 = X1460 ) )
| ( ~ X1459
& ( Z0 = X1461 ) ) ) ) ) ) ) )
=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X42
& ( Z0 = X2 ) )
| ( ~ X42
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[iftrueProp2])]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_253]),foundationAx]),wellorderingAx]),c_0_254]),c_0_255]),c_0_256]),c_0_257]),c_0_258]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_259]),setext]),emptyI]),noeltsimpempty]),c_0_260]),c_0_261]),c_0_262]),c_0_263]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_264]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_265]),c_0_266]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_267]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_268]),c_0_269]),c_0_270]),inCongP]),in__Cong]),c_0_271]),c_0_272]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_273]),c_0_274]),c_0_275]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_276]),c_0_277]),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]),c_0_278]),c_0_279]),c_0_280]),c_0_281]),singletonsuniq]),setukpairinjL1]),c_0_282]),c_0_283]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_284]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_294]),c_0_295]),c_0_296]),c_0_297]),c_0_298]),c_0_299]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_300]),c_0_301]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_302]),c_0_303]),c_0_304]),c_0_305]),c_0_306]),c_0_307]),c_0_308]),c_0_309])])]),c_0_310]) ).
thf(c_0_312,negated_conjecture,
! 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$i,X1579: $i,X1580: $i,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $i,X1589: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i > $o,X1599: $i,X1600: $i > $o,X1601: $i,X1602: $i,X1603: $i > $o,X1604: $i,X1606: $i,X1607: $i > $o,X1609: $i,X1610: $i,X1611: $i > $o,X1613: $i,X1614: $i,X1615: $i > $o,X1616: $i,X1618: $o,X1619: $o,X1620: $i,X1621: $i > $o,X1623: $i,X1624: $i,X1625: $i > $o,X1626: $i,X1628: $i > $o,X1629: $i,X1632: $i,X1633: $i > $o,X1634: $i,X1638: $i,X1639: $i > $o,X1640: $i,X1643: $i,X1644: $i,X1645: $i,X1646: $i,X1647: $i,X1648: $i,X1649: $i,X1650: $i,X1651: $i,X1652: $i > $o,X1653: $i,X1655: $i,X1656: $i,X1657: $i > $o,X1658: $i > $o,X1661: $i,X1664: $i,X1665: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i > $o,X1678: $i,X1680: $i,X1681: $i,X1682: $i > $o,X1683: $i > $o,X1686: $i,X1688: $i,X1690: $i,X1691: $i,X1692: $i > $o,X1693: $i > $o,X1696: 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$i,X2007: $i > $i > $o,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i > $i > $o,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i > $i > $o,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i > $i,X2047: $i,X2048: $i,X2049: $i > $i,X2051: $i,X2052: $i,X2053: $i > $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i > $o,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i > $o,X2068: $i,X2069: $i,X2070: $i > $o,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i > $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i > $i,X2143: $i,X2144: $i,X2145: $i > $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $o,X2153: $i,X2154: $i,X2155: $i,X2156: $o,X2157: $i,X2158: $i,X2159: $i,X2160: $o,X2161: $i,X2162: $i] :
( ( ~ ( in @ ( esk1_2 @ X1462 @ X1463 ) @ X1462 )
| ~ ( in @ ( esk1_2 @ X1462 @ X1463 ) @ X1463 )
| ( X1462 = X1463 ) )
& ( ( in @ ( esk1_2 @ X1462 @ X1463 ) @ X1462 )
| ( in @ ( esk1_2 @ X1462 @ X1463 ) @ X1463 )
| ( X1462 = X1463 ) )
& ~ ( in @ X1465 @ emptyset )
& ( ~ ( in @ X1468 @ ( setadjoin @ X1466 @ X1467 ) )
| ( X1468 = X1466 )
| ( in @ X1468 @ X1467 ) )
& ( ( X1468 != X1466 )
| ( in @ X1468 @ ( setadjoin @ X1466 @ X1467 ) ) )
& ( ~ ( in @ X1468 @ X1467 )
| ( in @ X1468 @ ( setadjoin @ X1466 @ X1467 ) ) )
& ( ~ ( in @ X1470 @ ( powerset @ X1469 ) )
| ~ ( in @ X1471 @ X1470 )
| ( in @ X1471 @ X1469 ) )
& ( ( in @ ( esk2_2 @ X1472 @ X1473 ) @ X1473 )
| ( in @ X1473 @ ( powerset @ X1472 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1472 @ X1473 ) @ X1472 )
| ( in @ X1473 @ ( powerset @ X1472 ) ) )
& ( ( in @ X1476 @ ( esk3_2 @ X1475 @ X1476 ) )
| ~ ( in @ X1476 @ ( setunion @ X1475 ) ) )
& ( ( in @ ( esk3_2 @ X1475 @ X1476 ) @ X1475 )
| ~ ( in @ X1476 @ ( setunion @ X1475 ) ) )
& ( ~ ( in @ X1479 @ X1480 )
| ~ ( in @ X1480 @ X1478 )
| ( in @ X1479 @ ( setunion @ X1478 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1481 @ omega )
| ( in @ ( setadjoin @ X1481 @ X1481 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1482 ) @ omega )
| ~ ( in @ emptyset @ X1482 )
| ~ ( in @ X1484 @ omega )
| ( in @ X1484 @ X1482 ) )
& ( ( in @ ( esk4_1 @ X1482 ) @ X1482 )
| ~ ( in @ emptyset @ X1482 )
| ~ ( in @ X1484 @ omega )
| ( in @ X1484 @ X1482 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1482 ) @ ( esk4_1 @ X1482 ) ) @ X1482 )
| ~ ( in @ emptyset @ X1482 )
| ~ ( in @ X1484 @ omega )
| ( in @ X1484 @ X1482 ) )
& ( ( in @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1486 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( in @ ( esk5_2 @ X1485 @ X1486 ) @ X1486 ) )
& ( ( X1485 @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1491 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( in @ ( esk5_2 @ X1485 @ X1486 ) @ X1486 ) )
& ( ~ ( in @ X1494 @ X1486 )
| ~ ( X1485 @ X1494 @ X1493 )
| ( in @ X1493 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( in @ ( esk5_2 @ X1485 @ X1486 ) @ X1486 ) )
& ( ( in @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1486 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ( X1485 @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1491 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ~ ( in @ X1494 @ X1486 )
| ~ ( X1485 @ X1494 @ X1493 )
| ( in @ X1493 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ( in @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1486 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1488
!= ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ( X1485 @ ( esk8_3 @ X1485 @ X1486 @ X1491 ) @ X1491 )
| ~ ( in @ X1491 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1488
!= ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ~ ( in @ X1494 @ X1486 )
| ~ ( X1485 @ X1494 @ X1493 )
| ( in @ X1493 @ ( esk7_2 @ X1485 @ X1486 ) )
| ( X1488
!= ( esk6_3 @ X1485 @ X1486 @ X1488 ) )
| ~ ( X1485 @ ( esk5_2 @ X1485 @ X1486 ) @ X1488 ) )
& ( ( in @ ( esk9_1 @ X1495 ) @ X1495 )
| ~ ( in @ X1496 @ X1495 ) )
& ( ~ ( in @ X1498 @ ( esk9_1 @ X1495 ) )
| ~ ( in @ X1498 @ X1495 )
| ~ ( in @ X1496 @ X1495 ) )
& epred1_0
& ( ( X1499 @ ( esk10_2 @ X1499 @ X1500 ) )
| ~ ( X1499 @ X1500 )
| ( X1499 @ ( descr @ X1499 ) ) )
& ( ( X1500
!= ( esk10_2 @ X1499 @ X1500 ) )
| ~ ( X1499 @ X1500 )
| ( X1499 @ ( descr @ X1499 ) ) )
& ( ~ ( in @ X1504 @ X1502 )
| ~ ( X1503 @ X1504 )
| ( in @ X1504 @ ( dsetconstr @ X1502 @ X1503 ) ) )
& ( ~ ( in @ X1507 @ ( dsetconstr @ X1505 @ X1506 ) )
| ( in @ X1507 @ X1505 ) )
& ( ~ ( in @ X1510 @ ( dsetconstr @ X1508 @ X1509 ) )
| ( X1509 @ X1510 ) )
& ( ( X1511 @ ( esk12_1 @ X1511 ) )
| ( X1511 @ ( esk11_2 @ X1511 @ X1512 ) )
| ~ ( X1511 @ X1512 ) )
& ( ~ ( X1511 @ X1515 )
| ( ( esk12_1 @ X1511 )
= X1515 )
| ( X1511 @ ( esk11_2 @ X1511 @ X1512 ) )
| ~ ( X1511 @ X1512 ) )
& ( ( X1511 @ ( esk12_1 @ X1511 ) )
| ( X1512
!= ( esk11_2 @ X1511 @ X1512 ) )
| ~ ( X1511 @ X1512 ) )
& ( ~ ( X1511 @ X1515 )
| ( ( esk12_1 @ X1511 )
= X1515 )
| ( X1512
!= ( esk11_2 @ X1511 @ X1512 ) )
| ~ ( X1511 @ X1512 ) )
& ( ~ ( in @ X1517 @ ( prop2set @ X1516 ) )
| X1516 )
& ( ~ ( in @ X1518 @ emptyset )
| X1519 )
& ( ~ ( in @ X1520 @ emptyset )
| ~ $true )
& ~ ( in @ X1521 @ emptyset )
& ( ( X1522 @ ( esk13_2 @ X1522 @ X1523 ) )
| ~ ( X1522 @ X1523 )
| ( X1522 @ ( esk14_1 @ X1522 ) ) )
& ( ( X1523
!= ( esk13_2 @ X1522 @ X1523 ) )
| ~ ( X1522 @ X1523 )
| ( X1522 @ ( esk14_1 @ X1522 ) ) )
& ( ( in @ ( esk16_2 @ X1526 @ X1527 ) @ X1527 )
| ( X1526 = X1527 )
| ( in @ ( esk15_2 @ X1526 @ X1527 ) @ X1526 ) )
& ( ~ ( in @ ( esk16_2 @ X1526 @ X1527 ) @ X1526 )
| ( X1526 = X1527 )
| ( in @ ( esk15_2 @ X1526 @ X1527 ) @ X1526 ) )
& ( ( in @ ( esk16_2 @ X1526 @ X1527 ) @ X1527 )
| ( X1526 = X1527 )
| ~ ( in @ ( esk15_2 @ X1526 @ X1527 ) @ X1527 ) )
& ( ~ ( in @ ( esk16_2 @ X1526 @ X1527 ) @ X1526 )
| ( X1526 = X1527 )
| ~ ( in @ ( esk15_2 @ X1526 @ X1527 ) @ X1527 ) )
& ( ( in @ ( esk17_1 @ X1530 ) @ X1530 )
| ( X1530 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1532 ) @ X1532 )
| ( X1532 = emptyset ) )
& ( ~ ( in @ X1536 @ ( dsetconstr @ X1534 @ X1535 ) )
| ( X1535 @ X1536 )
| ~ ( in @ X1536 @ X1534 ) )
& ( ~ ( X1535 @ X1536 )
| ( in @ X1536 @ ( dsetconstr @ X1534 @ X1535 ) )
| ~ ( in @ X1536 @ X1534 ) )
& ( ( X1537 = emptyset )
| ( in @ ( esk19_1 @ X1537 ) @ X1537 ) )
& ( ~ ( in @ X1541 @ X1539 )
| ~ ( X1540 @ X1541 )
| ( ( dsetconstr @ X1539 @ X1540 )
!= emptyset ) )
& ( ~ ( in @ X1543 @ X1542 )
| ( X1542 != emptyset ) )
& ( in @ X1544 @ ( setadjoin @ X1544 @ X1545 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1548 @ X1547 )
| ( in @ X1548 @ ( setadjoin @ X1546 @ X1547 ) ) )
& ( ( in @ X1551 @ X1550 )
| X1552
| ( X1551 = X1549 )
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ X1552
| X1552
| ( X1551 = X1549 )
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ( in @ X1551 @ X1550 )
| X1552
| ~ X1552
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ X1552
| X1552
| ~ X1552
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ ( in @ X1555 @ ( setadjoin @ X1553 @ X1554 ) )
| ( X1555 = X1553 )
| ( in @ X1555 @ X1554 ) )
& ( ( dsetconstr @ X1556
@ ^ [Z0: $i] : $true )
= X1556 )
& ( ( in @ ( esk20_2 @ X1557 @ X1558 ) @ X1558 )
| ( in @ X1558 @ ( powerset @ X1557 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1557 @ X1558 ) @ X1557 )
| ( in @ X1558 @ ( powerset @ X1557 ) ) )
& ( in @ emptyset @ ( powerset @ X1560 ) )
& ( in @ emptyset @ ( powerset @ X1561 ) )
& ( ~ ( in @ X1563 @ ( powerset @ X1562 ) )
| ~ ( in @ X1564 @ X1563 )
| ( in @ X1564 @ X1562 ) )
& ( ~ ( in @ X1566 @ X1567 )
| ~ ( in @ X1567 @ X1565 )
| ( in @ X1566 @ ( setunion @ X1565 ) ) )
& ( ( in @ X1569 @ ( esk21_3 @ X1568 @ X1569 @ X1570 ) )
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ( in @ ( esk21_3 @ X1568 @ X1569 @ X1570 ) @ X1568 )
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ~ X1570
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ~ ( in @ X1573 @ X1572 )
| ( in @ X1573 @ ( powerset @ ( setunion @ X1572 ) ) ) )
& ( ~ ( X1574 @ X1578 )
| ( X1578
= ( esk23_1 @ X1574 ) )
| ( X1574 @ ( esk22_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 ) )
& ( ( X1579
!= ( esk23_1 @ X1574 ) )
| ( X1574 @ X1579 )
| ( X1574 @ ( esk22_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 ) )
& ( ~ ( X1574 @ X1578 )
| ( X1578
= ( esk23_1 @ X1574 ) )
| ( X1575
!= ( esk22_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 ) )
& ( ( X1579
!= ( esk23_1 @ X1574 ) )
| ( X1574 @ X1579 )
| ( X1575
!= ( esk22_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 ) )
& ( ( in @ ( esk24_1 @ X1580 ) @ X1580 )
| ( X1580 = emptyset ) )
& ( $true
| ( X1580 = emptyset ) )
& ( ~ ( in @ X1582 @ ( setadjoin @ X1583 @ emptyset ) )
| ( X1582 = X1583 ) )
& ( ( X1584 = X1585 )
| ~ ( in @ X1585 @ ( setadjoin @ X1584 @ emptyset ) ) )
& ( ( X1586 != X1587 )
| ( in @ X1586 @ ( setadjoin @ X1587 @ emptyset ) ) )
& ( ~ ( in @ X1588 @ ( setadjoin @ X1589 @ emptyset ) )
| ( in @ X1589 @ ( setadjoin @ X1588 @ emptyset ) ) )
& ( ~ ( in @ X1592 @ ( setadjoin @ X1590 @ ( setadjoin @ X1591 @ emptyset ) ) )
| ( X1592 = X1590 )
| ( X1592 = X1591 ) )
& ( in @ X1593 @ ( setadjoin @ X1593 @ ( setadjoin @ X1594 @ emptyset ) ) )
& ( in @ X1596 @ ( setadjoin @ X1595 @ ( setadjoin @ X1596 @ emptyset ) ) )
& ( ~ ( in @ X1599 @ X1597 )
| ~ ( X1598 @ X1599 )
| ( ( dsetconstr @ X1597 @ X1598 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1601 @ emptyset )
| ( X1600 @ X1601 ) )
& ( ( in @ ( esk25_2 @ X1602 @ X1603 ) @ X1602 )
| ~ ( in @ X1604 @ X1602 )
| ( X1603 @ X1604 ) )
& ( ~ ( X1603 @ ( esk25_2 @ X1602 @ X1603 ) )
| ~ ( in @ X1604 @ X1602 )
| ( X1603 @ X1604 ) )
& ( ( in @ ( esk26_2 @ X1606 @ X1607 ) @ X1606 )
| ~ ( in @ X1609 @ X1606 )
| ~ ( X1607 @ X1609 ) )
& ( ( X1607 @ ( esk26_2 @ X1606 @ X1607 ) )
| ~ ( in @ X1609 @ X1606 )
| ~ ( X1607 @ X1609 ) )
& ( ( in @ ( esk27_2 @ X1610 @ X1611 ) @ X1610 )
| ~ ( in @ X1613 @ X1610 )
| ~ ( X1611 @ X1613 ) )
& ( ( X1611 @ ( esk27_2 @ X1610 @ X1611 ) )
| ~ ( in @ X1613 @ X1610 )
| ~ ( X1611 @ X1613 ) )
& ( ( in @ ( esk28_2 @ X1614 @ X1615 ) @ X1614 )
| ~ ( in @ X1616 @ X1614 )
| ( X1615 @ X1616 ) )
& ( ~ ( X1615 @ ( esk28_2 @ X1614 @ X1615 ) )
| ~ ( in @ X1616 @ X1614 )
| ( X1615 @ X1616 ) )
& ( ~ X1618
| ( in @ emptyset @ ( prop2set @ X1618 ) ) )
& ( ~ X1619
| ( set2prop @ ( prop2set @ X1619 ) ) )
& ( ( in @ ( esk29_2 @ X1620 @ X1621 ) @ X1620 )
| ~ ( in @ X1623 @ X1620 )
| ~ ( X1621 @ X1623 ) )
& ( ( X1621 @ ( esk29_2 @ X1620 @ X1621 ) )
| ~ ( in @ X1623 @ X1620 )
| ~ ( X1621 @ X1623 ) )
& ( ( in @ ( esk30_2 @ X1624 @ X1625 ) @ X1624 )
| ~ ( in @ X1626 @ X1624 )
| ( X1625 @ X1626 ) )
& ( ~ ( X1625 @ ( esk30_2 @ X1624 @ X1625 ) )
| ~ ( in @ X1626 @ X1624 )
| ( X1625 @ X1626 ) )
& ( ( X1628 @ ( esk32_1 @ X1628 ) )
| ( X1628 @ ( esk31_2 @ X1628 @ X1629 ) )
| ~ ( X1628 @ X1629 ) )
& ( ~ ( X1628 @ X1632 )
| ( ( esk32_1 @ X1628 )
= X1632 )
| ( X1628 @ ( esk31_2 @ X1628 @ X1629 ) )
| ~ ( X1628 @ X1629 ) )
& ( ( X1628 @ ( esk32_1 @ X1628 ) )
| ( X1629
!= ( esk31_2 @ X1628 @ X1629 ) )
| ~ ( X1628 @ X1629 ) )
& ( ~ ( X1628 @ X1632 )
| ( ( esk32_1 @ X1628 )
= X1632 )
| ( X1629
!= ( esk31_2 @ X1628 @ X1629 ) )
| ~ ( X1628 @ X1629 ) )
& ( ( X1633 @ ( esk35_1 @ X1633 ) )
| ( X1633 @ ( esk33_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ~ ( X1633 @ X1638 )
| ( ( esk35_1 @ X1633 )
= X1638 )
| ( X1633 @ ( esk33_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ( X1633 @ ( esk35_1 @ X1633 ) )
| ( X1633 @ ( esk34_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ~ ( X1633 @ X1638 )
| ( ( esk35_1 @ X1633 )
= X1638 )
| ( X1633 @ ( esk34_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ( X1633 @ ( esk35_1 @ X1633 ) )
| ( ( esk33_1 @ X1633 )
!= ( esk34_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ~ ( X1633 @ X1638 )
| ( ( esk35_1 @ X1633 )
= X1638 )
| ( ( esk33_1 @ X1633 )
!= ( esk34_1 @ X1633 ) )
| ~ ( X1633 @ X1634 ) )
& ( ( X1639 @ ( esk37_1 @ X1639 ) )
| ~ ( X1639 @ ( esk36_2 @ X1639 @ X1640 ) )
| ( ( esk36_2 @ X1639 @ X1640 )
!= X1640 ) )
& ( ~ ( X1639 @ X1643 )
| ( ( esk37_1 @ X1639 )
= X1643 )
| ~ ( X1639 @ ( esk36_2 @ X1639 @ X1640 ) )
| ( ( esk36_2 @ X1639 @ X1640 )
!= X1640 ) )
& ( ( X1639 @ ( esk37_1 @ X1639 ) )
| ( X1639 @ ( esk36_2 @ X1639 @ X1640 ) )
| ( ( esk36_2 @ X1639 @ X1640 )
= X1640 ) )
& ( ~ ( X1639 @ X1643 )
| ( ( esk37_1 @ X1639 )
= X1643 )
| ( X1639 @ ( esk36_2 @ X1639 @ X1640 ) )
| ( ( esk36_2 @ X1639 @ X1640 )
= X1640 ) )
& ( ( X1644 != X1645 )
| ( X1646 != X1647 )
| ~ ( in @ X1646 @ X1644 )
| ( in @ X1647 @ X1645 ) )
& ( ~ ( in @ X1650 @ X1648 )
| ( in @ X1651 @ X1649 )
| ( X1650 != X1651 )
| ( X1648 != X1649 ) )
& ( ~ ( in @ X1651 @ X1649 )
| ( in @ X1650 @ X1648 )
| ( X1650 != X1651 )
| ( X1648 != X1649 ) )
& ( ( X1652 @ ( esk38_2 @ X1652 @ X1653 ) )
| ~ ( X1652 @ X1653 )
| ~ ( X1652 @ X1655 )
| ~ ( X1652 @ X1656 )
| ( X1655 = X1656 ) )
& ( ( X1653
!= ( esk38_2 @ X1652 @ X1653 ) )
| ~ ( X1652 @ X1653 )
| ~ ( X1652 @ X1655 )
| ~ ( X1652 @ X1656 )
| ( X1655 = X1656 ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( ( esk39_2 @ X1657 @ X1658 )
= ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ~ ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ~ ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1657 @ ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1658 @ ( esk42_2 @ X1657 @ X1658 ) )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1658 @ X1664 )
| ( ( esk42_2 @ X1657 @ X1658 )
= X1664 )
| ( X1661
!= ( esk41_3 @ X1657 @ X1658 @ X1661 ) )
| ~ ( X1657 @ X1661 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1658 @ ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ( X1657 @ ( esk44_2 @ X1657 @ X1658 ) )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( ~ ( X1657 @ X1668 )
| ( ( esk44_2 @ X1657 @ X1658 )
= X1668 )
| ( X1665
!= ( esk43_3 @ X1657 @ X1658 @ X1665 ) )
| ~ ( X1658 @ X1665 )
| ( X1657 @ ( esk39_2 @ X1657 @ X1658 ) )
| ( X1658 @ ( esk40_2 @ X1657 @ X1658 ) ) )
& ( emptyset = emptyset )
& ( ( X1669 != X1670 )
| ( X1671 != X1672 )
| ( ( setadjoin @ X1669 @ X1671 )
= ( setadjoin @ X1670 @ X1672 ) ) )
& ( ( X1673 != X1674 )
| ( ( powerset @ X1673 )
= ( powerset @ X1674 ) ) )
& ( ( X1675 != X1676 )
| ( ( setunion @ X1675 )
= ( setunion @ X1676 ) ) )
& ( omega = omega )
& ( ( X1677 @ ( esk45_2 @ X1677 @ X1678 ) )
| ~ ( X1677 @ X1678 )
| ~ ( X1677 @ X1680 )
| ~ ( X1677 @ X1681 )
| ( X1680 = X1681 ) )
& ( ( X1678
!= ( esk45_2 @ X1677 @ X1678 ) )
| ~ ( X1677 @ X1678 )
| ~ ( X1677 @ X1680 )
| ~ ( X1677 @ X1681 )
| ( X1680 = X1681 ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( ( esk46_2 @ X1682 @ X1683 )
= ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( ( esk46_2 @ X1682 @ X1683 )
= ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( ( esk46_2 @ X1682 @ X1683 )
= ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( ( esk46_2 @ X1682 @ X1683 )
= ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ~ ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ~ ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ~ ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ~ ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ~ ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ~ ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ~ ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ~ ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1682 @ ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1683 @ ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( X1688
!= ( esk49_3 @ X1682 @ X1683 @ X1688 ) )
| ~ ( X1683 @ X1688 )
| ( ( descr @ X1682 )
= ( descr @ X1683 ) )
| ( X1686
!= ( esk48_3 @ X1682 @ X1683 @ X1686 ) )
| ~ ( X1682 @ X1686 )
| ( X1682 @ ( esk46_2 @ X1682 @ X1683 ) )
| ( X1683 @ ( esk47_2 @ X1682 @ X1683 ) ) )
& ( ( in @ ( esk50_4 @ X1690 @ X1691 @ X1692 @ X1693 ) @ X1690 )
| ( ( dsetconstr @ X1690 @ X1692 )
= ( dsetconstr @ X1691 @ X1693 ) )
| ( X1690 != X1691 ) )
& ( ( in @ ( esk51_4 @ X1690 @ X1691 @ X1692 @ X1693 ) @ X1691 )
| ( ( dsetconstr @ X1690 @ X1692 )
= ( dsetconstr @ X1691 @ X1693 ) )
| ( X1690 != X1691 ) )
& ( ( ( esk50_4 @ X1690 @ X1691 @ X1692 @ X1693 )
= ( esk51_4 @ X1690 @ X1691 @ X1692 @ X1693 ) )
| ( ( dsetconstr @ X1690 @ X1692 )
= ( dsetconstr @ X1691 @ X1693 ) )
| ( X1690 != X1691 ) )
& ( ~ ( X1692 @ ( esk50_4 @ X1690 @ X1691 @ X1692 @ X1693 ) )
| ~ ( X1693 @ ( esk51_4 @ X1690 @ X1691 @ X1692 @ X1693 ) )
| ( ( dsetconstr @ X1690 @ X1692 )
= ( dsetconstr @ X1691 @ X1693 ) )
| ( X1690 != X1691 ) )
& ( ( X1692 @ ( esk50_4 @ X1690 @ X1691 @ X1692 @ X1693 ) )
| ( X1693 @ ( esk51_4 @ X1690 @ X1691 @ X1692 @ X1693 ) )
| ( ( dsetconstr @ X1690 @ X1692 )
= ( dsetconstr @ X1691 @ X1693 ) )
| ( X1690 != X1691 ) )
& ( ( in @ ( esk52_2 @ X1696 @ X1697 ) @ X1696 )
| ( subset @ X1696 @ X1697 ) )
& ( ~ ( in @ ( esk52_2 @ X1696 @ X1697 ) @ X1697 )
| ( subset @ X1696 @ X1697 ) )
& ( ( X1699 != X1700 )
| ( subset @ X1700 @ X1699 ) )
& ( ( X1701 != X1702 )
| ( subset @ X1701 @ X1702 ) )
& ( ( in @ ( esk53_2 @ X1703 @ X1704 ) @ X1703 )
| ( subset @ X1703 @ X1704 ) )
& ( ~ ( in @ ( esk53_2 @ X1703 @ X1704 ) @ X1704 )
| ( subset @ X1703 @ X1704 ) )
& ( subset @ emptyset @ X1706 )
& ( ~ ( subset @ X1707 @ X1708 )
| ~ ( in @ X1709 @ X1707 )
| ( in @ X1709 @ X1708 ) )
& ( ~ ( subset @ X1710 @ X1711 )
| ( in @ X1712 @ X1711 )
| ~ ( in @ X1712 @ X1710 ) )
& ( ~ ( in @ X1715 @ X1713 )
| ( in @ X1715 @ X1714 )
| ~ ( subset @ X1713 @ X1714 ) )
& ( ( subset @ X1716 @ X1717 )
| ( X1716 != X1717 ) )
& ( ~ ( in @ X1720 @ X1718 )
| ( in @ X1720 @ X1719 )
| ( X1718 != X1719 ) )
& ( subset @ X1721 @ X1721 )
& ( ~ ( subset @ X1722 @ X1723 )
| ~ ( subset @ X1723 @ X1724 )
| ( subset @ X1722 @ X1724 ) )
& ( subset @ X1726 @ ( setadjoin @ X1725 @ X1726 ) )
& ( ~ ( subset @ X1727 @ X1729 )
| ( subset @ X1727 @ ( setadjoin @ X1728 @ X1729 ) ) )
& ( ~ ( subset @ X1730 @ X1731 )
| ( in @ X1730 @ ( powerset @ X1731 ) ) )
& ( ~ ( subset @ X1732 @ X1733 )
| ~ ( subset @ X1733 @ X1732 )
| ( X1732 = X1733 ) )
& ( ~ ( subset @ X1734 @ emptyset )
| ( X1734 = emptyset ) )
& ( ~ ( subset @ X1736 @ X1735 )
| ( in @ X1736 @ ( powerset @ X1735 ) ) )
& ( ~ ( in @ X1738 @ ( powerset @ X1737 ) )
| ( subset @ X1738 @ X1737 ) )
& ( in @ X1739 @ ( powerset @ X1739 ) )
& ( ~ ( subset @ X1740 @ X1741 )
| ( subset @ ( powerset @ X1740 ) @ ( powerset @ X1741 ) ) )
& ( in @ ( dsetconstr @ X1742 @ X1743 ) @ ( powerset @ X1742 ) )
& ( subset @ ( dsetconstr @ X1744 @ X1745 ) @ X1744 )
& ( ~ ( in @ X1748 @ X1746 )
| ( in @ X1748 @ ( binunion @ X1746 @ X1747 ) ) )
& ( in @ X1750 @ ( setadjoin @ X1749 @ ( setadjoin @ X1750 @ emptyset ) ) )
& ( ~ ( in @ X1753 @ X1752 )
| ( in @ X1753 @ ( binunion @ X1751 @ X1752 ) ) )
& ( ( in @ X1756 @ X1755 )
| X1757
| ( in @ X1756 @ X1754 )
| ~ ( in @ X1756 @ ( binunion @ X1754 @ X1755 ) ) )
& ( ~ X1757
| X1757
| ( in @ X1756 @ X1754 )
| ~ ( in @ X1756 @ ( binunion @ X1754 @ X1755 ) ) )
& ( ( in @ X1756 @ X1755 )
| X1757
| ~ X1757
| ~ ( in @ X1756 @ ( binunion @ X1754 @ X1755 ) ) )
& ( ~ X1757
| X1757
| ~ X1757
| ~ ( in @ X1756 @ ( binunion @ X1754 @ X1755 ) ) )
& ( ~ ( in @ X1760 @ ( binunion @ X1758 @ X1759 ) )
| ( in @ X1760 @ X1758 )
| ( in @ X1760 @ X1759 ) )
& ( subset @ X1761 @ ( binunion @ X1761 @ X1762 ) )
& ( subset @ X1764 @ ( binunion @ X1763 @ X1764 ) )
& ( ~ ( in @ X1767 @ X1765 )
| ~ ( in @ X1767 @ X1766 )
| ( in @ X1767 @ ( binintersect @ X1765 @ X1766 ) ) )
& ( ~ ( subset @ X1770 @ X1768 )
| ~ ( subset @ X1770 @ X1769 )
| ( subset @ X1770 @ ( binintersect @ X1768 @ X1769 ) ) )
& ( ~ ( in @ X1773 @ ( binintersect @ X1771 @ X1772 ) )
| ( in @ X1773 @ X1771 ) )
& ( subset @ ( binintersect @ X1774 @ X1775 ) @ X1774 )
& ( ~ ( subset @ X1776 @ X1777 )
| ( ( binintersect @ X1776 @ X1777 )
= X1776 ) )
& ( ( ( binintersect @ X1778 @ X1779 )
!= X1779 )
| ( subset @ X1779 @ X1778 ) )
& ( ~ ( in @ X1782 @ ( binintersect @ X1780 @ X1781 ) )
| ( in @ X1782 @ X1781 ) )
& ( ( in @ ( esk54_2 @ X1783 @ X1784 ) @ X1783 )
| ( ( binintersect @ X1783 @ X1784 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1783 @ X1784 ) @ X1784 )
| ( ( binintersect @ X1783 @ X1784 )
= emptyset ) )
& ( subset @ ( binintersect @ X1786 @ X1787 ) @ X1787 )
& ( ~ ( subset @ X1789 @ X1788 )
| ( ( binintersect @ X1788 @ X1789 )
= X1789 ) )
& ( ( ( binintersect @ X1790 @ X1791 )
!= X1790 )
| ( subset @ X1790 @ X1791 ) )
& ( ( binintersect @ X1792 @ ( binunion @ X1793 @ X1794 ) )
= ( binunion @ ( binintersect @ X1792 @ X1793 ) @ ( binintersect @ X1792 @ X1794 ) ) )
& ( ~ ( in @ X1797 @ X1795 )
| ( in @ X1797 @ X1796 )
| ( in @ X1797 @ ( setminus @ X1795 @ X1796 ) ) )
& ( ~ ( in @ X1800 @ ( setminus @ X1798 @ X1799 ) )
| ( in @ X1800 @ X1798 ) )
& ( ~ ( in @ X1803 @ ( setminus @ X1801 @ X1802 ) )
| ~ ( in @ X1803 @ X1802 ) )
& ( ~ ( subset @ X1804 @ X1805 )
| ( ( setminus @ X1804 @ X1805 )
= emptyset ) )
& ( ( in @ X1808 @ ( setminus @ X1806 @ X1807 ) )
| ~ ( in @ X1808 @ X1806 )
| ( in @ X1808 @ X1807 ) )
& ( ( in @ X1811 @ ( setminus @ X1809 @ X1810 ) )
| ( in @ X1811 @ X1810 )
| ~ ( in @ X1811 @ X1809 ) )
& ( ( in @ X1814 @ X1812 )
| ~ ( in @ X1814 @ ( setminus @ X1812 @ X1813 ) ) )
& ( ~ ( in @ X1817 @ X1816 )
| ~ ( in @ X1817 @ ( setminus @ X1815 @ X1816 ) ) )
& ( subset @ ( setminus @ X1818 @ X1819 ) @ X1818 )
& ( ( ( setminus @ X1820 @ X1821 )
!= emptyset )
| ( subset @ X1820 @ X1821 ) )
& ( ~ ( in @ X1824 @ X1822 )
| X1825
| ( in @ X1824 @ X1822 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ( in @ X1824 @ X1823 )
| X1825
| ( in @ X1824 @ X1822 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ X1825
| X1825
| ( in @ X1824 @ X1822 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ ( in @ X1824 @ X1822 )
| X1825
| ~ ( in @ X1824 @ X1823 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ( in @ X1824 @ X1823 )
| X1825
| ~ ( in @ X1824 @ X1823 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ X1825
| X1825
| ~ ( in @ X1824 @ X1823 )
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ ( in @ X1824 @ X1822 )
| X1825
| ~ X1825
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ( in @ X1824 @ X1823 )
| X1825
| ~ X1825
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ X1825
| X1825
| ~ X1825
| ~ ( in @ X1824 @ ( symdiff @ X1822 @ X1823 ) ) )
& ( ~ ( in @ X1828 @ X1826 )
| ( in @ X1828 @ X1827 )
| ( in @ X1828 @ ( symdiff @ X1826 @ X1827 ) ) )
& ( ( in @ X1831 @ X1829 )
| ~ ( in @ X1831 @ X1830 )
| ( in @ X1831 @ ( symdiff @ X1829 @ X1830 ) ) )
& ( ~ ( in @ X1834 @ X1832 )
| ~ ( in @ X1834 @ X1833 )
| ~ ( in @ X1834 @ ( symdiff @ X1832 @ X1833 ) ) )
& ( ( in @ X1837 @ X1835 )
| ( in @ X1837 @ X1836 )
| ~ ( in @ X1837 @ ( symdiff @ X1835 @ X1836 ) ) )
& ( in @ X1839 @ ( setadjoin @ X1838 @ ( setadjoin @ X1839 @ emptyset ) ) )
& ( in @ X1840 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1840 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1840 @ ( setadjoin @ X1841 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1843 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1842 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1842 @ ( setadjoin @ X1843 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1844 @ ( setadjoin @ X1845 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1846 @ X1847 ) )
& ( ~ ( in @ X1849 @ X1848 )
| ( subset @ ( setadjoin @ X1849 @ emptyset ) @ X1848 ) )
& ( ~ ( in @ X1851 @ X1850 )
| ( in @ ( setadjoin @ X1851 @ emptyset ) @ ( powerset @ X1850 ) ) )
& ( ~ ( in @ X1854 @ X1852 )
| ( in @ ( setadjoin @ X1854 @ emptyset ) @ ( powerset @ ( binunion @ X1852 @ X1853 ) ) ) )
& ( ~ ( in @ X1857 @ ( setadjoin @ X1855 @ ( setadjoin @ X1856 @ emptyset ) ) )
| ( X1857 = X1855 )
| ( X1857 = X1856 ) )
& ( ~ ( in @ X1860 @ X1858 )
| ~ ( in @ X1861 @ X1859 )
| ( subset @ ( setadjoin @ X1860 @ ( setadjoin @ X1861 @ emptyset ) ) @ ( binunion @ X1858 @ X1859 ) ) )
& ( ~ ( in @ X1864 @ X1862 )
| ~ ( in @ X1865 @ X1863 )
| ( in @ ( setadjoin @ X1864 @ ( setadjoin @ X1865 @ emptyset ) ) @ ( powerset @ ( binunion @ X1862 @ X1863 ) ) ) )
& ( ~ ( in @ X1868 @ X1866 )
| ~ ( in @ X1869 @ X1867 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1868 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1868 @ ( setadjoin @ X1869 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1866 @ X1867 ) ) ) )
& ( ~ ( in @ X1872 @ X1870 )
| ~ ( in @ X1873 @ X1871 )
| ( in @ ( setadjoin @ ( setadjoin @ X1872 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1872 @ ( setadjoin @ X1873 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1870 @ X1871 ) ) ) ) )
& ( ~ ( in @ X1876 @ X1874 )
| ~ ( in @ X1877 @ X1875 )
| ( in @ ( kpair @ X1876 @ X1877 ) @ ( powerset @ ( powerset @ ( binunion @ X1874 @ X1875 ) ) ) ) )
& ( ~ ( in @ X1880 @ X1878 )
| ~ ( in @ X1881 @ X1879 )
| ( in @ ( kpair @ X1880 @ X1881 ) @ ( cartprod @ X1878 @ X1879 ) ) )
& ( ( in @ ( esk55_3 @ X1882 @ X1883 @ X1884 ) @ X1882 )
| ~ ( in @ X1884 @ ( cartprod @ X1882 @ X1883 ) ) )
& ( ( in @ ( esk56_3 @ X1882 @ X1883 @ X1884 ) @ X1883 )
| ~ ( in @ X1884 @ ( cartprod @ X1882 @ X1883 ) ) )
& ( ( X1884
= ( kpair @ ( esk55_3 @ X1882 @ X1883 @ X1884 ) @ ( esk56_3 @ X1882 @ X1883 @ X1884 ) ) )
| ~ ( in @ X1884 @ ( cartprod @ X1882 @ X1883 ) ) )
& ( ~ ( in @ X1889 @ ( cartprod @ X1887 @ X1888 ) )
| ( iskpair @ X1889 ) )
& ( ( in @ ( esk57_2 @ X1890 @ X1891 ) @ X1890 )
| ~ ( in @ X1891 @ ( setunion @ X1890 ) ) )
& ( ( in @ X1891 @ ( esk57_2 @ X1890 @ X1891 ) )
| ~ ( in @ X1891 @ ( setunion @ X1890 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1893 @ emptyset ) ) @ X1893 )
& ( subset @ X1894 @ ( setunion @ ( setadjoin @ X1894 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1895 @ emptyset ) )
= X1895 )
& ( ( in @ ( esk60_2 @ X1896 @ X1897 ) @ ( dsetconstr @ X1896 @ X1897 ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( in @ ( esk58_2 @ X1896 @ X1897 ) @ X1896 ) )
& ( ( ( dsetconstr @ X1896 @ X1897 )
= ( setadjoin @ ( esk60_2 @ X1896 @ X1897 ) @ emptyset ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( in @ ( esk58_2 @ X1896 @ X1897 ) @ X1896 ) )
& ( ( in @ ( esk60_2 @ X1896 @ X1897 ) @ ( dsetconstr @ X1896 @ X1897 ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( in @ ( esk59_2 @ X1896 @ X1897 ) @ X1896 ) )
& ( ( ( dsetconstr @ X1896 @ X1897 )
= ( setadjoin @ ( esk60_2 @ X1896 @ X1897 ) @ emptyset ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( in @ ( esk59_2 @ X1896 @ X1897 ) @ X1896 ) )
& ( ( in @ ( esk60_2 @ X1896 @ X1897 ) @ ( dsetconstr @ X1896 @ X1897 ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( X1897 @ ( esk58_2 @ X1896 @ X1897 ) ) )
& ( ( ( dsetconstr @ X1896 @ X1897 )
= ( setadjoin @ ( esk60_2 @ X1896 @ X1897 ) @ emptyset ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( X1897 @ ( esk58_2 @ X1896 @ X1897 ) ) )
& ( ( in @ ( esk60_2 @ X1896 @ X1897 ) @ ( dsetconstr @ X1896 @ X1897 ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( X1897 @ ( esk59_2 @ X1896 @ X1897 ) ) )
& ( ( ( dsetconstr @ X1896 @ X1897 )
= ( setadjoin @ ( esk60_2 @ X1896 @ X1897 ) @ emptyset ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( X1897 @ ( esk59_2 @ X1896 @ X1897 ) ) )
& ( ( in @ ( esk60_2 @ X1896 @ X1897 ) @ ( dsetconstr @ X1896 @ X1897 ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( ( esk58_2 @ X1896 @ X1897 )
!= ( esk59_2 @ X1896 @ X1897 ) ) )
& ( ( ( dsetconstr @ X1896 @ X1897 )
= ( setadjoin @ ( esk60_2 @ X1896 @ X1897 ) @ emptyset ) )
| ~ ( in @ X1900 @ X1896 )
| ~ ( X1897 @ X1900 )
| ( ( esk58_2 @ X1896 @ X1897 )
!= ( esk59_2 @ X1896 @ X1897 ) ) )
& ( ( in @ ( esk61_2 @ X1902 @ X1903 ) @ X1902 )
| ~ ( in @ X1904 @ ( dsetconstr @ X1902 @ X1903 ) )
| ( ( dsetconstr @ X1902 @ X1903 )
!= ( setadjoin @ X1904 @ emptyset ) ) )
& ( ( X1903 @ ( esk61_2 @ X1902 @ X1903 ) )
| ~ ( in @ X1904 @ ( dsetconstr @ X1902 @ X1903 ) )
| ( ( dsetconstr @ X1902 @ X1903 )
!= ( setadjoin @ X1904 @ emptyset ) ) )
& ( ( in @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ ( dsetconstr @ X1906 @ X1907 ) )
| ( in @ ( esk62_3 @ X1906 @ X1907 @ X1908 ) @ X1906 )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( ( dsetconstr @ X1906 @ X1907 )
= ( setadjoin @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ emptyset ) )
| ( in @ ( esk62_3 @ X1906 @ X1907 @ X1908 ) @ X1906 )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( in @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ ( dsetconstr @ X1906 @ X1907 ) )
| ( X1907 @ ( esk62_3 @ X1906 @ X1907 @ X1908 ) )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( ( dsetconstr @ X1906 @ X1907 )
= ( setadjoin @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ emptyset ) )
| ( X1907 @ ( esk62_3 @ X1906 @ X1907 @ X1908 ) )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( in @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ ( dsetconstr @ X1906 @ X1907 ) )
| ( ( esk62_3 @ X1906 @ X1907 @ X1908 )
!= X1908 )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( ( dsetconstr @ X1906 @ X1907 )
= ( setadjoin @ ( esk63_3 @ X1906 @ X1907 @ X1908 ) @ emptyset ) )
| ( ( esk62_3 @ X1906 @ X1907 @ X1908 )
!= X1908 )
| ~ ( X1907 @ X1908 )
| ~ ( in @ X1908 @ X1906 ) )
& ( ( in @ ( esk66_2 @ X1911 @ X1912 ) @ ( dsetconstr @ X1911 @ X1912 ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( in @ ( esk64_2 @ X1911 @ X1912 ) @ X1911 ) )
& ( ( ( dsetconstr @ X1911 @ X1912 )
= ( setadjoin @ ( esk66_2 @ X1911 @ X1912 ) @ emptyset ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( in @ ( esk64_2 @ X1911 @ X1912 ) @ X1911 ) )
& ( ( in @ ( esk66_2 @ X1911 @ X1912 ) @ ( dsetconstr @ X1911 @ X1912 ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( in @ ( esk65_2 @ X1911 @ X1912 ) @ X1911 ) )
& ( ( ( dsetconstr @ X1911 @ X1912 )
= ( setadjoin @ ( esk66_2 @ X1911 @ X1912 ) @ emptyset ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( in @ ( esk65_2 @ X1911 @ X1912 ) @ X1911 ) )
& ( ( in @ ( esk66_2 @ X1911 @ X1912 ) @ ( dsetconstr @ X1911 @ X1912 ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( X1912 @ ( esk64_2 @ X1911 @ X1912 ) ) )
& ( ( ( dsetconstr @ X1911 @ X1912 )
= ( setadjoin @ ( esk66_2 @ X1911 @ X1912 ) @ emptyset ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( X1912 @ ( esk64_2 @ X1911 @ X1912 ) ) )
& ( ( in @ ( esk66_2 @ X1911 @ X1912 ) @ ( dsetconstr @ X1911 @ X1912 ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( X1912 @ ( esk65_2 @ X1911 @ X1912 ) ) )
& ( ( ( dsetconstr @ X1911 @ X1912 )
= ( setadjoin @ ( esk66_2 @ X1911 @ X1912 ) @ emptyset ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( X1912 @ ( esk65_2 @ X1911 @ X1912 ) ) )
& ( ( in @ ( esk66_2 @ X1911 @ X1912 ) @ ( dsetconstr @ X1911 @ X1912 ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( ( esk64_2 @ X1911 @ X1912 )
!= ( esk65_2 @ X1911 @ X1912 ) ) )
& ( ( ( dsetconstr @ X1911 @ X1912 )
= ( setadjoin @ ( esk66_2 @ X1911 @ X1912 ) @ emptyset ) )
| ~ ( in @ X1915 @ X1911 )
| ~ ( X1912 @ X1915 )
| ( ( esk64_2 @ X1911 @ X1912 )
!= ( esk65_2 @ X1911 @ X1912 ) ) )
& ( ( ( setadjoin @ X1917 @ emptyset )
!= ( setadjoin @ X1918 @ emptyset ) )
| ( X1917 = X1918 ) )
& ( ~ ( in @ ( setadjoin @ X1921 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1919 @ ( setadjoin @ X1920 @ emptyset ) ) @ emptyset ) ) )
| ( X1919 = X1921 ) )
& ( ( in @ ( esk67_1 @ X1922 )
@ ( dsetconstr @ ( setunion @ X1922 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1922 ) ) )
| ~ ( iskpair @ X1922 ) )
& ( ( ( dsetconstr @ ( setunion @ X1922 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1922 ) )
= ( setadjoin @ ( esk67_1 @ X1922 ) @ emptyset ) )
| ~ ( iskpair @ X1922 ) )
& ( ~ ( in @ X1925 @ X1924 )
| ( X1924
!= ( setadjoin @ X1925 @ emptyset ) )
| ( in @ ( setunion @ X1924 ) @ X1924 ) )
& ( ( kfst @ ( kpair @ X1926 @ X1927 ) )
= X1926 )
& ( ~ ( in @ X1930 @ ( cartprod @ X1928 @ X1929 ) )
| ( in @ ( kfst @ X1930 ) @ X1928 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1931 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1931 @ ( setadjoin @ X1932 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1933 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1933 @ ( setadjoin @ X1934 @ emptyset ) ) @ emptyset ) ) )
| ( X1931 = X1933 ) )
& ( ( ( kpair @ X1935 @ X1936 )
!= ( kpair @ X1937 @ X1938 ) )
| ( X1935 = X1937 ) )
& ( ( X1939 != X1940 )
| ( ( setadjoin @ X1939 @ ( setadjoin @ X1940 @ emptyset ) )
= ( setadjoin @ X1939 @ emptyset ) ) )
& ( ( X1941 != X1942 )
| ( ( setadjoin @ ( setadjoin @ X1941 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1941 @ ( setadjoin @ X1942 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1941 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1943 @ ( setadjoin @ X1944 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1945 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1945 @ ( setadjoin @ X1946 @ emptyset ) ) @ emptyset ) ) )
| ( X1945 != X1946 )
| ( X1944 = X1946 ) )
& ( ( ( setadjoin @ X1947 @ ( setadjoin @ X1948 @ emptyset ) )
!= ( setadjoin @ X1949 @ emptyset ) )
| ( X1947 = X1948 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1950 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1950 @ ( setadjoin @ X1951 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1952 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1952 @ ( setadjoin @ X1953 @ emptyset ) ) @ emptyset ) ) )
| ( X1951 = X1953 ) )
& ( ( ( kpair @ X1954 @ X1955 )
!= ( kpair @ X1956 @ X1957 ) )
| ( X1955 = X1957 ) )
& ( ( in @ ( esk68_1 @ X1958 )
@ ( dsetconstr @ ( setunion @ X1958 )
@ ^ [Z0: $i] :
( X1958
= ( kpair @ ( kfst @ X1958 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X1958 ) )
& ( ( ( dsetconstr @ ( setunion @ X1958 )
@ ^ [Z0: $i] :
( X1958
= ( kpair @ ( kfst @ X1958 ) @ Z0 ) ) )
= ( setadjoin @ ( esk68_1 @ X1958 ) @ emptyset ) )
| ~ ( iskpair @ X1958 ) )
& ( ( ksnd @ ( kpair @ X1960 @ X1961 ) )
= X1961 )
& ( ~ ( iskpair @ X1962 )
| ( ( kpair @ ( kfst @ X1962 ) @ ( ksnd @ X1962 ) )
= X1962 ) )
& ( ~ ( in @ X1965 @ ( cartprod @ X1963 @ X1964 ) )
| ( in @ ( ksnd @ X1965 ) @ X1964 ) )
& ( ~ ( in @ ( kpair @ X1968 @ X1969 ) @ ( cartprod @ X1966 @ X1967 ) )
| ( in @ X1968 @ X1966 ) )
& ( ~ ( in @ ( kpair @ X1972 @ X1973 ) @ ( cartprod @ X1970 @ X1971 ) )
| ( in @ X1973 @ X1971 ) )
& ( ~ ( in @ X1976 @ X1974 )
| ~ ( in @ X1977 @ X1975 )
| ( ( kpair @ X1976 @ X1977 )
= ( kpair @ X1976 @ X1977 ) ) )
& ( ~ ( in @ X1980 @ X1978 )
| ~ ( in @ X1981 @ X1979 )
| ( ( kfst @ ( kpair @ X1980 @ X1981 ) )
= X1980 ) )
& ( ~ ( in @ X1984 @ X1982 )
| ~ ( in @ X1985 @ X1983 )
| ( ( ksnd @ ( kpair @ X1984 @ X1985 ) )
= X1985 ) )
& ( ~ ( in @ X1988 @ ( cartprod @ X1986 @ X1987 ) )
| ( ( kpair @ ( kfst @ X1988 ) @ ( ksnd @ X1988 ) )
= X1988 ) )
& ( ~ ( in @ X1992 @ X1989 )
| ~ ( in @ X1993 @ X1990 )
| ~ ( X1991 @ X1992 @ X1993 )
| ( in @ ( kpair @ X1992 @ X1993 ) @ ( dpsetconstr @ X1989 @ X1990 @ X1991 ) ) )
& ( subset @ ( dpsetconstr @ X1994 @ X1995 @ X1996 ) @ ( cartprod @ X1994 @ X1995 ) )
& ( subset @ ( dpsetconstr @ X1997 @ X1998 @ X1999 ) @ ( cartprod @ X1997 @ X1998 ) )
& ( ~ ( in @ X2003 @ X2000 )
| ~ ( in @ X2004 @ X2001 )
| ~ ( in @ ( kpair @ X2003 @ X2004 ) @ ( dpsetconstr @ X2000 @ X2001 @ X2002 ) )
| ( X2002 @ X2003 @ X2004 ) )
& ( ~ ( in @ ( kpair @ X2008 @ X2009 ) @ ( dpsetconstr @ X2005 @ X2006 @ X2007 ) )
| ( in @ X2008 @ X2005 ) )
& ( ~ ( in @ ( kpair @ X2013 @ X2014 ) @ ( dpsetconstr @ X2010 @ X2011 @ X2012 ) )
| ( in @ X2014 @ X2011 ) )
& ( ~ ( in @ ( kpair @ X2018 @ X2019 ) @ ( dpsetconstr @ X2015 @ X2016 @ X2017 ) )
| ( X2017 @ X2018 @ X2019 ) )
& ( ( in @ ( esk69_4 @ X2020 @ X2021 @ X2022 @ X2023 )
@ ( dsetconstr @ X2021
@ ^ [Z0: $i] : ( in @ ( kpair @ X2023 @ Z0 ) @ X2022 ) ) )
| ~ ( in @ X2023 @ X2020 )
| ~ ( func @ X2020 @ X2021 @ X2022 ) )
& ( ( ( dsetconstr @ X2021
@ ^ [Z0: $i] : ( in @ ( kpair @ X2023 @ Z0 ) @ X2022 ) )
= ( setadjoin @ ( esk69_4 @ X2020 @ X2021 @ X2022 @ X2023 ) @ emptyset ) )
| ~ ( in @ X2023 @ X2020 )
| ~ ( func @ X2020 @ X2021 @ X2022 ) )
& ( ~ ( func @ X2025 @ X2026 @ X2027 )
| ~ ( in @ X2028 @ X2025 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2026
@ ^ [Z0: $i] : ( in @ ( kpair @ X2028 @ Z0 ) @ X2027 ) ) )
@ X2026 ) )
& ( ~ ( func @ X2029 @ X2030 @ X2031 )
| ~ ( in @ X2032 @ X2029 )
| ( in @ ( ap @ X2029 @ X2030 @ X2031 @ X2032 ) @ X2030 ) )
& ( ~ ( in @ X2035 @ ( funcSet @ X2033 @ X2034 ) )
| ( func @ X2033 @ X2034 @ X2035 ) )
& ( ~ ( in @ X2038 @ ( funcSet @ X2036 @ X2037 ) )
| ~ ( in @ X2039 @ X2036 )
| ( in @ ( ap @ X2036 @ X2037 @ X2038 @ X2039 ) @ X2037 ) )
& ( ~ ( func @ X2040 @ X2041 @ X2042 )
| ( in @ X2042 @ ( funcSet @ X2040 @ X2041 ) ) )
& ( ( in @ ( esk70_3 @ X2043 @ X2044 @ X2045 ) @ X2043 )
| ( func @ X2043 @ X2044
@ ( dpsetconstr @ X2043 @ X2044
@ ^ [Z0: $i] : ( $eq @ ( X2045 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2045 @ ( esk70_3 @ X2043 @ X2044 @ X2045 ) ) @ X2044 )
| ( func @ X2043 @ X2044
@ ( dpsetconstr @ X2043 @ X2044
@ ^ [Z0: $i] : ( $eq @ ( X2045 @ Z0 ) ) ) ) )
& ( ( in @ ( esk71_3 @ X2047 @ X2048 @ X2049 ) @ X2047 )
| ( func @ X2047 @ X2048 @ ( lam @ X2047 @ X2048 @ X2049 ) ) )
& ( ~ ( in @ ( X2049 @ ( esk71_3 @ X2047 @ X2048 @ X2049 ) ) @ X2048 )
| ( func @ X2047 @ X2048 @ ( lam @ X2047 @ X2048 @ X2049 ) ) )
& ( ( in @ ( esk72_3 @ X2051 @ X2052 @ X2053 ) @ X2051 )
| ( in @ ( lam @ X2051 @ X2052 @ X2053 ) @ ( funcSet @ X2051 @ X2052 ) ) )
& ( ~ ( in @ ( X2053 @ ( esk72_3 @ X2051 @ X2052 @ X2053 ) ) @ X2052 )
| ( in @ ( lam @ X2051 @ X2052 @ X2053 ) @ ( funcSet @ X2051 @ X2052 ) ) )
& ( ( in @ ( esk73_4 @ X2055 @ X2056 @ X2057 @ X2058 ) @ X2055 )
| ~ ( in @ X2061 @ X2057 )
| ( X2058 @ X2061 )
| ~ ( subset @ X2057 @ ( cartprod @ X2055 @ X2056 ) ) )
& ( ( in @ ( esk74_4 @ X2055 @ X2056 @ X2057 @ X2058 ) @ X2056 )
| ~ ( in @ X2061 @ X2057 )
| ( X2058 @ X2061 )
| ~ ( subset @ X2057 @ ( cartprod @ X2055 @ X2056 ) ) )
& ( ( in @ ( kpair @ ( esk73_4 @ X2055 @ X2056 @ X2057 @ X2058 ) @ ( esk74_4 @ X2055 @ X2056 @ X2057 @ X2058 ) ) @ X2057 )
| ~ ( in @ X2061 @ X2057 )
| ( X2058 @ X2061 )
| ~ ( subset @ X2057 @ ( cartprod @ X2055 @ X2056 ) ) )
& ( ~ ( X2058 @ ( kpair @ ( esk73_4 @ X2055 @ X2056 @ X2057 @ X2058 ) @ ( esk74_4 @ X2055 @ X2056 @ X2057 @ X2058 ) ) )
| ~ ( in @ X2061 @ X2057 )
| ( X2058 @ X2061 )
| ~ ( subset @ X2057 @ ( cartprod @ X2055 @ X2056 ) ) )
& ( ( in @ ( esk75_4 @ X2062 @ X2063 @ X2064 @ X2065 ) @ X2062 )
| ~ ( in @ X2068 @ X2064 )
| ( X2065 @ X2068 )
| ~ ( subset @ X2064 @ ( cartprod @ X2062 @ X2063 ) ) )
& ( ( in @ ( esk76_4 @ X2062 @ X2063 @ X2064 @ X2065 ) @ X2063 )
| ~ ( in @ X2068 @ X2064 )
| ( X2065 @ X2068 )
| ~ ( subset @ X2064 @ ( cartprod @ X2062 @ X2063 ) ) )
& ( ( in @ ( kpair @ ( esk75_4 @ X2062 @ X2063 @ X2064 @ X2065 ) @ ( esk76_4 @ X2062 @ X2063 @ X2064 @ X2065 ) ) @ X2064 )
| ~ ( in @ X2068 @ X2064 )
| ( X2065 @ X2068 )
| ~ ( subset @ X2064 @ ( cartprod @ X2062 @ X2063 ) ) )
& ( ~ ( X2065 @ ( kpair @ ( esk75_4 @ X2062 @ X2063 @ X2064 @ X2065 ) @ ( esk76_4 @ X2062 @ X2063 @ X2064 @ X2065 ) ) )
| ~ ( in @ X2068 @ X2064 )
| ( X2065 @ X2068 )
| ~ ( subset @ X2064 @ ( cartprod @ X2062 @ X2063 ) ) )
& ( ~ ( in @ X2071 @ ( dsetconstr @ X2069 @ X2070 ) )
| ( ( dsetconstr @ X2069 @ X2070 )
!= ( setadjoin @ X2071 @ emptyset ) )
| ~ ( in @ X2072 @ X2069 )
| ~ ( in @ X2073 @ X2069 )
| ~ ( X2070 @ X2072 )
| ~ ( X2070 @ X2073 )
| ( X2072 = X2073 ) )
& ( ~ ( func @ X2074 @ X2075 @ X2076 )
| ~ ( in @ X2077 @ X2074 )
| ( in @ ( kpair @ X2077 @ ( ap @ X2074 @ X2075 @ X2076 @ X2077 ) ) @ X2076 ) )
& ( ~ ( in @ X2080 @ ( funcSet @ X2078 @ X2079 ) )
| ~ ( in @ X2081 @ X2078 )
| ( in @ ( kpair @ X2081 @ ( ap @ X2078 @ X2079 @ X2080 @ X2081 ) ) @ X2080 ) )
& ( ~ ( func @ X2082 @ X2083 @ X2084 )
| ~ ( in @ X2085 @ X2082 )
| ~ ( in @ X2086 @ X2083 )
| ~ ( in @ ( kpair @ X2085 @ X2086 ) @ X2084 )
| ( ( ap @ X2082 @ X2083 @ X2084 @ X2085 )
= X2086 ) )
& ( ( in @ ( esk77_4 @ X2087 @ X2088 @ X2089 @ X2090 ) @ X2087 )
| ~ ( in @ X2092 @ X2087 )
| ~ ( in @ X2093 @ X2088 )
| ~ ( in @ ( kpair @ X2092 @ X2093 ) @ X2090 )
| ( in @ ( kpair @ X2092 @ X2093 ) @ X2089 )
| ~ ( func @ X2087 @ X2088 @ X2090 )
| ~ ( func @ X2087 @ X2088 @ X2089 ) )
& ( ( ( ap @ X2087 @ X2088 @ X2089 @ ( esk77_4 @ X2087 @ X2088 @ X2089 @ X2090 ) )
!= ( ap @ X2087 @ X2088 @ X2090 @ ( esk77_4 @ X2087 @ X2088 @ X2089 @ X2090 ) ) )
| ~ ( in @ X2092 @ X2087 )
| ~ ( in @ X2093 @ X2088 )
| ~ ( in @ ( kpair @ X2092 @ X2093 ) @ X2090 )
| ( in @ ( kpair @ X2092 @ X2093 ) @ X2089 )
| ~ ( func @ X2087 @ X2088 @ X2090 )
| ~ ( func @ X2087 @ X2088 @ X2089 ) )
& ( ~ ( in @ X2096 @ ( funcSet @ X2094 @ X2095 ) )
| ~ ( in @ X2097 @ X2094 )
| ~ ( in @ X2098 @ X2095 )
| ~ ( in @ ( kpair @ X2097 @ X2098 ) @ X2096 )
| ( ( ap @ X2094 @ X2095 @ X2096 @ X2097 )
= X2098 ) )
& ( ( in @ ( esk78_4 @ X2099 @ X2100 @ X2101 @ X2102 ) @ X2099 )
| ( subset @ X2101 @ X2102 )
| ~ ( subset @ X2102 @ ( cartprod @ X2099 @ X2100 ) )
| ~ ( subset @ X2101 @ ( cartprod @ X2099 @ X2100 ) ) )
& ( ( in @ ( esk79_4 @ X2099 @ X2100 @ X2101 @ X2102 ) @ X2100 )
| ( subset @ X2101 @ X2102 )
| ~ ( subset @ X2102 @ ( cartprod @ X2099 @ X2100 ) )
| ~ ( subset @ X2101 @ ( cartprod @ X2099 @ X2100 ) ) )
& ( ( in @ ( kpair @ ( esk78_4 @ X2099 @ X2100 @ X2101 @ X2102 ) @ ( esk79_4 @ X2099 @ X2100 @ X2101 @ X2102 ) ) @ X2101 )
| ( subset @ X2101 @ X2102 )
| ~ ( subset @ X2102 @ ( cartprod @ X2099 @ X2100 ) )
| ~ ( subset @ X2101 @ ( cartprod @ X2099 @ X2100 ) ) )
& ( ~ ( in @ ( kpair @ ( esk78_4 @ X2099 @ X2100 @ X2101 @ X2102 ) @ ( esk79_4 @ X2099 @ X2100 @ X2101 @ X2102 ) ) @ X2102 )
| ( subset @ X2101 @ X2102 )
| ~ ( subset @ X2102 @ ( cartprod @ X2099 @ X2100 ) )
| ~ ( subset @ X2101 @ ( cartprod @ X2099 @ X2100 ) ) )
& ( ( in @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ( X2107 = X2108 )
| ( in @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ( X2107 = X2108 )
| ( in @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ( X2107 = X2108 )
| ( in @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ( X2107 = X2108 )
| ( in @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ( X2107 = X2108 )
| ( in @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ( X2107 = X2108 )
| ( in @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ( X2107 = X2108 )
| ( in @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ( X2107 = X2108 )
| ( in @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ( X2107 = X2108 )
| ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ( X2107 = X2108 )
| ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ( X2107 = X2108 )
| ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ( X2107 = X2108 )
| ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ( X2107 = X2108 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ( X2107 = X2108 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ( X2107 = X2108 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk83_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ( X2107 = X2108 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk81_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2108 )
| ~ ( subset @ X2108 @ ( cartprod @ X2105 @ X2106 ) )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk84_4 @ X2113 @ X2114 @ X2115 @ X2116 ) @ X2113 )
| ( X2115 = X2116 )
| ~ ( func @ X2113 @ X2114 @ X2116 )
| ~ ( func @ X2113 @ X2114 @ X2115 ) )
& ( ( ( ap @ X2113 @ X2114 @ X2115 @ ( esk84_4 @ X2113 @ X2114 @ X2115 @ X2116 ) )
!= ( ap @ X2113 @ X2114 @ X2116 @ ( esk84_4 @ X2113 @ X2114 @ X2115 @ X2116 ) ) )
| ( X2115 = X2116 )
| ~ ( func @ X2113 @ X2114 @ X2116 )
| ~ ( func @ X2113 @ X2114 @ X2115 ) )
& ( ( in @ ( esk85_4 @ X2118 @ X2119 @ X2120 @ X2121 ) @ X2118 )
| ( X2120 = X2121 )
| ~ ( in @ X2121 @ ( funcSet @ X2118 @ X2119 ) )
| ~ ( in @ X2120 @ ( funcSet @ X2118 @ X2119 ) ) )
& ( ( ( ap @ X2118 @ X2119 @ X2120 @ ( esk85_4 @ X2118 @ X2119 @ X2120 @ X2121 ) )
!= ( ap @ X2118 @ X2119 @ X2121 @ ( esk85_4 @ X2118 @ X2119 @ X2120 @ X2121 ) ) )
| ( X2120 = X2121 )
| ~ ( in @ X2121 @ ( funcSet @ X2118 @ X2119 ) )
| ~ ( in @ X2120 @ ( funcSet @ X2118 @ X2119 ) ) )
& ( ~ ( in @ X2125 @ ( funcSet @ X2123 @ X2124 ) )
| ~ ( in @ X2126 @ X2123 )
| ( ( ap @ X2123 @ X2124 @ X2125 @ X2126 )
= ( ap @ X2123 @ X2124 @ X2125 @ X2126 ) ) )
& ( ~ ( func @ X2127 @ X2128 @ X2129 )
| ~ ( in @ X2130 @ X2127 )
| ( ( ap @ X2127 @ X2128 @ X2129 @ X2130 )
= ( ap @ X2127 @ X2128 @ X2129 @ X2130 ) ) )
& ( ( in @ ( esk86_3 @ X2131 @ X2132 @ X2133 ) @ X2131 )
| ~ ( in @ X2135 @ X2131 )
| ( ( ap @ X2131 @ X2132 @ ( lam @ X2131 @ X2132 @ X2133 ) @ X2135 )
= ( X2133 @ X2135 ) ) )
& ( ~ ( in @ ( X2133 @ ( esk86_3 @ X2131 @ X2132 @ X2133 ) ) @ X2132 )
| ~ ( in @ X2135 @ X2131 )
| ( ( ap @ X2131 @ X2132 @ ( lam @ X2131 @ X2132 @ X2133 ) @ X2135 )
= ( X2133 @ X2135 ) ) )
& ( ~ ( func @ X2136 @ X2137 @ X2138 )
| ( ( lam @ X2136 @ X2137 @ ( ap @ X2136 @ X2137 @ X2138 ) )
= X2138 ) )
& ( ( in @ ( esk87_3 @ X2139 @ X2140 @ X2141 ) @ X2139 )
| ( ( lam @ X2139 @ X2140 @ X2141 )
= ( lam @ X2139 @ X2140 @ X2141 ) ) )
& ( ~ ( in @ ( X2141 @ ( esk87_3 @ X2139 @ X2140 @ X2141 ) ) @ X2140 )
| ( ( lam @ X2139 @ X2140 @ X2141 )
= ( lam @ X2139 @ X2140 @ X2141 ) ) )
& ( ( in @ ( esk88_3 @ X2143 @ X2144 @ X2145 ) @ X2143 )
| ~ ( in @ X2147 @ X2143 )
| ( ( ap @ X2143 @ X2144 @ ( lam @ X2143 @ X2144 @ X2145 ) @ X2147 )
= ( X2145 @ X2147 ) ) )
& ( ~ ( in @ ( X2145 @ ( esk88_3 @ X2143 @ X2144 @ X2145 ) ) @ X2144 )
| ~ ( in @ X2147 @ X2143 )
| ( ( ap @ X2143 @ X2144 @ ( lam @ X2143 @ X2144 @ X2145 ) @ X2147 )
= ( X2145 @ X2147 ) ) )
& ( ~ ( in @ X2150 @ ( funcSet @ X2148 @ X2149 ) )
| ( ( lam @ X2148 @ X2149 @ ( ap @ X2148 @ X2149 @ X2150 ) )
= X2150 ) )
& ( ~ ( in @ X2153 @ X2151 )
| ~ ( in @ X2154 @ X2151 )
| X2152
| ( in @ X2154
@ ( dsetconstr @ X2151
@ ^ [Z0: $i] :
( ( X2152
& ( Z0 = X2153 ) )
| ( ~ X2152
& ( Z0 = X2154 ) ) ) ) ) )
& ( ~ ( in @ X2157 @ X2155 )
| ~ ( in @ X2158 @ X2155 )
| X2156
| ( ( dsetconstr @ X2155
@ ^ [Z0: $i] :
( ( X2156
& ( Z0 = X2157 ) )
| ( ~ X2156
& ( Z0 = X2158 ) ) ) )
= ( setadjoin @ X2158 @ emptyset ) ) )
& ( ~ ( in @ X2161 @ X2159 )
| ~ ( in @ X2162 @ X2159 )
| ~ X2160
| ( in @ X2161
@ ( dsetconstr @ X2159
@ ^ [Z0: $i] :
( ( X2160
& ( Z0 = X2161 ) )
| ( ~ X2160
& ( Z0 = X2162 ) ) ) ) ) )
& ( in @ esk90_0 @ esk89_0 )
& ( in @ esk91_0 @ esk89_0 )
& epred2_0
& ( ( dsetconstr @ esk89_0
@ ^ [Z0: $i] :
( ( epred2_0
& ( Z0 = esk90_0 ) )
| ( ~ epred2_0
& ( Z0 = esk91_0 ) ) ) )
!= ( setadjoin @ esk90_0 @ emptyset ) ) ),
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_311])])])])])])]) ).
thf(c_0_313,plain,
! [X2186: $i] :
( ( epred3_0 @ X2186 )
<=> ( ( epred2_0
& ( X2186 = esk90_0 ) )
| ( ~ epred2_0
& ( X2186 = esk91_0 ) ) ) ),
introduced(definition) ).
thf(c_0_314,plain,
! [X2188: $i,X2: $i,X4: $i] :
( ( epred5_2 @ X4 @ X2 @ X2188 )
<=> ( ( ~ $true
& ( X2188 = X2 ) )
| ( ~ ~ $true
& ( X2188 = X4 ) ) ) ),
introduced(definition) ).
thf(c_0_315,negated_conjecture,
( ( dsetconstr @ esk89_0 @ epred3_0 )
!= ( setadjoin @ esk90_0 @ emptyset ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_312]),c_0_313]) ).
thf(c_0_316,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( dsetconstr @ X3 @ ( epred5_2 @ X4 @ X2 ) )
= ( setadjoin @ X4 @ emptyset ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(lift_lambdas,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_312])])]),c_0_314]) ).
thf(c_0_317,plain,
! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
!= ( setadjoin @ esk90_0 @ emptyset ) )
| ( ( epred5_2 @ X2 @ X3 )
!= epred3_0 )
| ~ ( in @ X2 @ esk89_0 )
| ~ ( in @ X3 @ esk89_0 ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_315,c_0_316])]) ).
thf(c_0_318,negated_conjecture,
in @ esk90_0 @ esk89_0,
inference(split_conjunct,[status(thm)],[c_0_312]) ).
thf(c_0_319,negated_conjecture,
! [X2: $i] :
( ( ( epred5_2 @ esk90_0 @ X2 )
!= epred3_0 )
| ~ ( in @ X2 @ esk89_0 ) ),
inference(spm,[status(thm)],[c_0_317,c_0_318]) ).
thf(c_0_320,negated_conjecture,
in @ esk91_0 @ esk89_0,
inference(split_conjunct,[status(thm)],[c_0_312]) ).
thf(c_0_321,plain,
! [X2204: $i,X2205: $i,X2206: $i] :
( ( $true
| ~ $true
| ~ ( epred5_2 @ X2206 @ X2205 @ X2204 ) )
& ( ( X2204 = X2206 )
| ~ $true
| ~ ( epred5_2 @ X2206 @ X2205 @ X2204 ) )
& ( $true
| ( X2204 = X2205 )
| ~ ( epred5_2 @ X2206 @ X2205 @ X2204 ) )
& ( ( X2204 = X2206 )
| ( X2204 = X2205 )
| ~ ( epred5_2 @ X2206 @ X2205 @ X2204 ) )
& ( $true
| ( X2204 != X2205 )
| ( epred5_2 @ X2206 @ X2205 @ X2204 ) )
& ( ~ $true
| ( X2204 != X2206 )
| ( epred5_2 @ X2206 @ X2205 @ X2204 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])]) ).
thf(c_0_322,negated_conjecture,
( ( epred5_2 @ esk90_0 @ esk91_0 )
!= epred3_0 ),
inference(spm,[status(thm)],[c_0_319,c_0_320]) ).
thf(c_0_323,plain,
! [X2200: $i] :
( ( ~ epred2_0
| epred2_0
| ~ ( epred3_0 @ X2200 ) )
& ( ( X2200 = esk91_0 )
| epred2_0
| ~ ( epred3_0 @ X2200 ) )
& ( ~ epred2_0
| ( X2200 = esk90_0 )
| ~ ( epred3_0 @ X2200 ) )
& ( ( X2200 = esk91_0 )
| ( X2200 = esk90_0 )
| ~ ( epred3_0 @ X2200 ) )
& ( ~ epred2_0
| ( X2200 != esk90_0 )
| ( epred3_0 @ X2200 ) )
& ( epred2_0
| ( X2200 != esk91_0 )
| ( epred3_0 @ X2200 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])]) ).
thf(c_0_324,plain,
! [X4: $i,X3: $i,X2: $i] :
( ( X2 = X3 )
| ~ $true
| ~ ( epred5_2 @ X3 @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
thf(c_0_325,negated_conjecture,
( ( epred5_2 @ esk90_0 @ esk91_0 @ esk155_0 )
<~> ( epred3_0 @ esk155_0 ) ),
inference(neg_ext,[status(thm)],[c_0_322]) ).
thf(c_0_326,plain,
! [X2: $i] :
( ( X2 = esk90_0 )
| ~ epred2_0
| ~ ( epred3_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
thf(c_0_327,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_312]) ).
thf(c_0_328,plain,
! [X2: $i,X4: $i,X3: $i] :
( ( epred5_2 @ X3 @ X4 @ X2 )
| ~ $true
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
thf(c_0_329,plain,
! [X4: $i,X3: $i,X2: $i] :
( ( X2 = X3 )
| ~ ( epred5_2 @ X3 @ X4 @ X2 ) ),
inference(cn,[status(thm)],[c_0_324]) ).
thf(c_0_330,negated_conjecture,
( ( epred5_2 @ esk90_0 @ esk91_0 @ esk155_0 )
| ( epred3_0 @ esk155_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_325]) ).
thf(c_0_331,plain,
! [X2: $i] :
( ( X2 = esk90_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_326,c_0_327])]) ).
thf(c_0_332,plain,
! [X2: $i,X4: $i,X3: $i] :
( ( epred5_2 @ X3 @ X4 @ X2 )
| ( X2 != X3 ) ),
inference(cn,[status(thm)],[c_0_328]) ).
thf(c_0_333,plain,
! [X2: $i] :
( ( epred3_0 @ X2 )
| ~ epred2_0
| ( X2 != esk90_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
thf(c_0_334,negated_conjecture,
( ~ ( epred5_2 @ esk90_0 @ esk91_0 @ esk155_0 )
| ~ ( epred3_0 @ esk155_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_325]) ).
thf(c_0_335,plain,
esk90_0 = esk155_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_331]) ).
thf(c_0_336,plain,
! [X3: $i,X2: $i] : ( epred5_2 @ X2 @ X3 @ X2 ),
inference(er,[status(thm)],[c_0_332]) ).
thf(c_0_337,plain,
epred3_0 @ esk90_0,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_333,c_0_327])])]) ).
thf(c_0_338,negated_conjecture,
~ ( epred3_0 @ esk155_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_334,c_0_335]),c_0_336])]) ).
thf(c_0_339,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_337,c_0_335]),c_0_338]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SEU703^1 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 21 16:49:24 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.41/0.57 Running higher-order theorem proving
% 0.41/0.57 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/tmp/tmp.zkJ7RQCIgD/E---3.1_23437.p
% 99.05/11.77 # Version: 3.2.0-ho
% 99.05/11.77 # Preprocessing class: HSLMSLSSLLLCHSA.
% 99.05/11.77 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 99.05/11.77 # Starting ho_unfolding_5 with 1200s (4) cores
% 99.05/11.77 # Starting pre_casc_3 with 300s (1) cores
% 99.05/11.77 # Starting new_ho_10_cnf2 with 300s (1) cores
% 99.05/11.77 # Starting full_lambda_10 with 300s (1) cores
% 99.05/11.77 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 99.05/11.77 # ho_unfolding_5 with pid 23515 completed with status 0
% 99.05/11.77 # Result found by ho_unfolding_5
% 99.05/11.77 # Preprocessing class: HSLMSLSSLLLCHSA.
% 99.05/11.77 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 99.05/11.77 # Starting ho_unfolding_5 with 1200s (4) cores
% 99.05/11.77 # No SInE strategy applied
% 99.05/11.77 # Search class: HGHSM-FSLM32-MHSMMSBN
% 99.05/11.77 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 99.05/11.77 # Starting full_lambda_5 with 99s (1) cores
% 99.05/11.77 # Starting ho_unfolding_5 with 121s (1) cores
% 99.05/11.77 # Starting pre_casc_4 with 99s (1) cores
% 99.05/11.77 # Starting pre_casc_3 with 99s (1) cores
% 99.05/11.77 # pre_casc_4 with pid 23526 completed with status 0
% 99.05/11.77 # Result found by pre_casc_4
% 99.05/11.77 # Preprocessing class: HSLMSLSSLLLCHSA.
% 99.05/11.77 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 99.05/11.77 # Starting ho_unfolding_5 with 1200s (4) cores
% 99.05/11.77 # No SInE strategy applied
% 99.05/11.77 # Search class: HGHSM-FSLM32-MHSMMSBN
% 99.05/11.77 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 99.05/11.77 # Starting full_lambda_5 with 99s (1) cores
% 99.05/11.77 # Starting ho_unfolding_5 with 121s (1) cores
% 99.05/11.77 # Starting pre_casc_4 with 99s (1) cores
% 99.05/11.77 # Preprocessing time : 0.008 s
% 99.05/11.77 # Presaturation interreduction done
% 99.05/11.77
% 99.05/11.77 # Proof found!
% 99.05/11.77 # SZS status Theorem
% 99.05/11.77 # SZS output start CNFRefutation
% See solution above
% 99.05/11.78 # Parsed axioms : 481
% 99.05/11.78 # Removed by relevancy pruning/SinE : 0
% 99.05/11.78 # Initial clauses : 691
% 99.05/11.78 # Removed in clause preprocessing : 295
% 99.05/11.78 # Initial clauses in saturation : 396
% 99.05/11.78 # Processed clauses : 25121
% 99.05/11.78 # ...of these trivial : 533
% 99.05/11.78 # ...subsumed : 18528
% 99.05/11.78 # ...remaining for further processing : 6059
% 99.05/11.78 # Other redundant clauses eliminated : 732
% 99.05/11.78 # Clauses deleted for lack of memory : 0
% 99.05/11.78 # Backward-subsumed : 830
% 99.05/11.78 # Backward-rewritten : 815
% 99.05/11.78 # Generated clauses : 629940
% 99.05/11.78 # ...of the previous two non-redundant : 609849
% 99.05/11.78 # ...aggressively subsumed : 0
% 99.05/11.78 # Contextual simplify-reflections : 19
% 99.05/11.78 # Paramodulations : 628884
% 99.05/11.78 # Factorizations : 46
% 99.05/11.78 # NegExts : 189
% 99.05/11.78 # Equation resolutions : 737
% 99.05/11.78 # Disequality decompositions : 0
% 99.05/11.78 # Total rewrite steps : 43729
% 99.05/11.78 # ...of those cached : 41443
% 99.05/11.78 # Propositional unsat checks : 1
% 99.05/11.78 # Propositional check models : 0
% 99.05/11.78 # Propositional check unsatisfiable : 0
% 99.05/11.78 # Propositional clauses : 0
% 99.05/11.78 # Propositional clauses after purity: 0
% 99.05/11.78 # Propositional unsat core size : 0
% 99.05/11.78 # Propositional preprocessing time : 0.000
% 99.05/11.78 # Propositional encoding time : 1.127
% 99.05/11.78 # Propositional solver time : 0.511
% 99.05/11.78 # Success case prop preproc time : 0.000
% 99.05/11.78 # Success case prop encoding time : 0.000
% 99.05/11.78 # Success case prop solver time : 0.000
% 99.05/11.78 # Current number of processed clauses : 4020
% 99.05/11.78 # Positive orientable unit clauses : 452
% 99.05/11.78 # Positive unorientable unit clauses: 0
% 99.05/11.78 # Negative unit clauses : 435
% 99.05/11.78 # Non-unit-clauses : 3133
% 99.05/11.78 # Current number of unprocessed clauses: 583178
% 99.05/11.78 # ...number of literals in the above : 2005749
% 99.05/11.78 # Current number of archived formulas : 0
% 99.05/11.78 # Current number of archived clauses : 2022
% 99.05/11.78 # Clause-clause subsumption calls (NU) : 1193738
% 99.05/11.78 # Rec. Clause-clause subsumption calls : 662389
% 99.05/11.78 # Non-unit clause-clause subsumptions : 7286
% 99.05/11.78 # Unit Clause-clause subsumption calls : 200530
% 99.05/11.78 # Rewrite failures with RHS unbound : 0
% 99.05/11.78 # BW rewrite match attempts : 192
% 99.05/11.78 # BW rewrite match successes : 40
% 99.05/11.78 # Condensation attempts : 0
% 99.05/11.78 # Condensation successes : 0
% 99.05/11.78 # Termbank termtop insertions : 19712916
% 99.05/11.78 # Search garbage collected termcells : 23369
% 99.05/11.78
% 99.05/11.78 # -------------------------------------------------
% 99.05/11.78 # User time : 10.539 s
% 99.05/11.78 # System time : 0.403 s
% 99.05/11.78 # Total time : 10.942 s
% 99.05/11.78 # Maximum resident set size: 7532 pages
% 99.05/11.78
% 99.05/11.78 # -------------------------------------------------
% 99.05/11.78 # User time : 41.933 s
% 99.05/11.78 # System time : 1.685 s
% 99.05/11.78 # Total time : 43.618 s
% 99.05/11.78 # Maximum resident set size: 2352 pages
% 99.05/11.78 % E---3.1 exiting
% 99.05/11.78 % E exiting
%------------------------------------------------------------------------------