%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU708^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.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 15:10:18 EDT 2024
% Result : Theorem 2.16s 1.04s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 231
% Syntax : Number of formulae : 327 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 2907 ( 643 equ; 0 cnn)
% Maximal formula atoms : 873 ( 8 avg)
% Number of connectives : 11637 ( 795 ~; 866 |; 547 &;7699 @)
% ( 318 <=>;1412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1017 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 255 ( 255 >; 0 *; 0 +; 0 <<)
% Number of symbols : 346 ( 342 usr; 234 con; 0-4 aty)
% Number of variables : 2565 ( 194 ^2248 !; 123 ?;2565 :)
% 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,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
epred1_0: $o ).
thf(decl_285,type,
esk1_2: $i > $i > $i ).
thf(decl_286,type,
esk2_2: $i > $i > $i ).
thf(decl_287,type,
esk3_2: $i > $i > $i ).
thf(decl_288,type,
esk4_1: $i > $i ).
thf(decl_289,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_290,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_291,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_292,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_293,type,
esk9_1: $i > $i ).
thf(decl_294,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_295,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_296,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_297,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_298,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_299,type,
esk15_2: $i > $i > $i ).
thf(decl_300,type,
esk16_2: $i > $i > $i ).
thf(decl_301,type,
esk17_1: $i > $i ).
thf(decl_302,type,
esk18_1: $i > $i ).
thf(decl_303,type,
esk19_1: $i > $i ).
thf(decl_304,type,
esk20_2: $i > $i > $i ).
thf(decl_305,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_306,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_307,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_308,type,
esk24_1: $i > $i ).
thf(decl_309,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_310,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_311,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_312,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_313,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_314,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_316,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_317,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_318,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_319,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_320,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_321,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_322,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_323,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_324,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_325,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_326,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_327,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_328,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_329,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_330,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_331,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_332,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_333,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_334,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_335,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_336,type,
esk52_2: $i > $i > $i ).
thf(decl_337,type,
esk53_2: $i > $i > $i ).
thf(decl_338,type,
esk54_2: $i > $i > $i ).
thf(decl_339,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_340,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_341,type,
esk57_2: $i > $i > $i ).
thf(decl_342,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_346,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_347,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_349,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_350,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_351,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_354,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_355,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_356,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_357,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_358,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_359,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_360,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_361,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_362,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_363,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_364,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_365,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_366,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_367,type,
esk83_0: $i ).
thf(decl_368,type,
epred2_0: $o ).
thf(decl_369,type,
esk84_0: $i ).
thf(decl_370,type,
esk85_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',descr__Cong) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ex1I2) ).
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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',breln) ).
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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ksndsingleton) ).
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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',dpsetconstrER) ).
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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',funcImageSingleton) ).
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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ifSingleton) ).
thf(iffalse,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
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X47
=> ( ( if @ X4 @ X47 @ X2 @ X3 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',iffalse) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.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/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ap2apEq2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X45 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',iftrue) ).
thf(if,axiom,
( if
= ( ^ [X4: $i,X44: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X44
& ( X14 = X2 ) )
| ( ~ X44
& ( X14 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p',if) ).
thf(c_0_230,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_231,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_232,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_233,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_234,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_235,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_247,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_248,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_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,
( 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_252,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X740: $i] :
( ( X6 @ X2 @ X740 )
& ! [X741: $i] :
( ( X6 @ X2 @ X741 )
=> ( X740 = X741 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_230,c_0_231]) ).
thf(c_0_253,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X742: $i] :
( ( X1 @ X742 )
& ! [X743: $i] :
( ( X1 @ X743 )
=> ( X742 = X743 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_232,c_0_231]) ).
thf(c_0_254,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_255,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_256,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_257,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X744: $i] :
( ( X1 @ X744 )
& ! [X745: $i] :
( ( X1 @ X745 )
=> ( X744 = X745 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_233,c_0_231]) ).
thf(c_0_258,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X746: $i] :
( ( X1 @ X746 )
& ! [X747: $i] :
( ( X1 @ X747 )
=> ( X746 = X747 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_234,c_0_231]) ).
thf(c_0_259,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_260,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_235]) ).
thf(c_0_261,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_236,c_0_235]) ).
thf(c_0_262,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_235]) ).
thf(c_0_263,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_264,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X748: $i] :
( ( X1 @ X748 )
& ! [X749: $i] :
( ( X1 @ X749 )
=> ( X748 = X749 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_237,c_0_231]) ).
thf(c_0_265,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_235]) ).
thf(c_0_266,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_267,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X750: $i] :
( ( X1 @ X750 )
& ! [X751: $i] :
( ( X1 @ X751 )
=> ( X750 = X751 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_238,c_0_231]) ).
thf(c_0_268,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X752: $i] :
( ( X1 @ X752 )
& ! [X753: $i] :
( ( X1 @ X753 )
=> ( X752 = X753 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_239,c_0_231]) ).
thf(c_0_269,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X754: $i] :
( ( X1 @ X754 )
& ! [X755: $i] :
( ( X1 @ X755 )
=> ( X754 = X755 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_240,c_0_231]) ).
thf(c_0_270,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X756: $i] :
( ( X1 @ X756 )
& ! [X757: $i] :
( ( X1 @ X757 )
=> ( X756 = X757 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_241,c_0_231]) ).
thf(c_0_271,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X758: $i] :
( ( X1 @ X758 )
& ! [X759: $i] :
( ( X1 @ X759 )
=> ( X758 = X759 ) ) )
<=> ? [X760: $i] :
( ( X17 @ X760 )
& ! [X761: $i] :
( ( X17 @ X761 )
=> ( X760 = X761 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_242,c_0_231]) ).
thf(c_0_272,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X762: $i] :
( ( X1 @ X762 )
& ! [X763: $i] :
( ( X1 @ X763 )
=> ( X762 = X763 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_243,c_0_231]) ).
thf(c_0_273,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X764: $i] :
( ( X1 @ X764 )
& ! [X765: $i] :
( ( X1 @ X765 )
=> ( X764 = X765 ) ) )
=> ( ? [X766: $i] :
( ( X17 @ X766 )
& ! [X767: $i] :
( ( X17 @ X767 )
=> ( X766 = X767 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_244,c_0_231]) ).
thf(c_0_274,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_275,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_276,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_277,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_278,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_245,c_0_246]) ).
thf(c_0_279,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_247,c_0_246]) ).
thf(c_0_280,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 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_248,c_0_246]) ).
thf(c_0_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_251,c_0_246]) ).
thf(c_0_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,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_307,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_308,plain,
( iftrueProp2
<=> ! [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(fof_simplification,[status(thm)],[iftrueProp2]) ).
thf(c_0_309,plain,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifSingleton]) ).
thf(c_0_310,plain,
( epred1_0
<=> ! [X797: $i] :
? [X798: $i] :
( ! [X799: $i] :
( ( in @ X799 @ X798 )
=> ! [X800: $i] :
( ( in @ X800 @ X799 )
=> ( in @ X800 @ X797 ) ) )
& ! [X801: $i,X802: $i] :
( ( ( in @ X801 @ X797 )
& ( in @ X802 @ X797 ) )
=> ( ! [X803: $i] :
( ( in @ X803 @ X798 )
=> ( ( in @ X801 @ X803 )
<=> ( in @ X802 @ X803 ) ) )
=> ( X801 = X802 ) ) )
& ! [X804: $i,X805: $i] :
( ( ( in @ X804 @ X798 )
& ( in @ X805 @ X798 ) )
=> ( ! [X806: $i] :
( ( in @ X806 @ X804 )
=> ( in @ X806 @ X805 ) )
| ! [X807: $i] :
( ( in @ X807 @ X805 )
=> ( in @ X807 @ X804 ) ) ) )
& ! [X808: $i] :
( ( ! [X809: $i] :
( ( in @ X809 @ X808 )
=> ( in @ X809 @ X797 ) )
& ? [X810: $i] : ( in @ X810 @ X808 ) )
=> ? [X811: $i,X812: $i] :
( ( in @ X811 @ X798 )
& ( in @ X812 @ X808 )
& ~ ? [X813: $i] :
( ( in @ X813 @ X811 )
& ( in @ X813 @ X808 ) )
& ! [X814: $i] :
( ( in @ X814 @ X798 )
=> ( ! [X815: $i] :
( ( in @ X815 @ X814 )
=> ( in @ X815 @ X811 ) )
| ( in @ X812 @ X814 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_311,negated_conjecture,
~ ( ! [X768: $i,X769: $i] :
( ! [X770: $i] :
( ( in @ X770 @ X768 )
<=> ( in @ X770 @ X769 ) )
=> ( X768 = X769 ) )
=> ( ! [X771: $i] :
~ ( in @ X771 @ emptyset )
=> ( ! [X772: $i,X773: $i,X774: $i] :
( ( in @ X774 @ ( setadjoin @ X772 @ X773 ) )
<=> ( ( X774 = X772 )
| ( in @ X774 @ X773 ) ) )
=> ( ! [X775: $i,X776: $i] :
( ( in @ X776 @ ( powerset @ X775 ) )
<=> ! [X777: $i] :
( ( in @ X777 @ X776 )
=> ( in @ X777 @ X775 ) ) )
=> ( ! [X778: $i,X779: $i] :
( ( in @ X779 @ ( setunion @ X778 ) )
<=> ? [X780: $i] :
( ( in @ X779 @ X780 )
& ( in @ X780 @ X778 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X781: $i] :
( ( in @ X781 @ omega )
=> ( in @ ( setadjoin @ X781 @ X781 ) @ omega ) )
=> ( ! [X782: $i] :
( ( ( in @ emptyset @ X782 )
& ! [X783: $i] :
( ( ( in @ X783 @ omega )
& ( in @ X783 @ X782 ) )
=> ( in @ ( setadjoin @ X783 @ X783 ) @ X782 ) ) )
=> ! [X784: $i] :
( ( in @ X784 @ omega )
=> ( in @ X784 @ X782 ) ) )
=> ( ! [X785: $i > $i > $o,X786: $i] :
( ! [X787: $i] :
( ( in @ X787 @ X786 )
=> ? [X788: $i] :
( ( X785 @ X787 @ X788 )
& ! [X789: $i] :
( ( X785 @ X787 @ X789 )
=> ( X788 = X789 ) ) ) )
=> ? [X790: $i] :
! [X791: $i] :
( ( in @ X791 @ X790 )
<=> ? [X792: $i] :
( ( in @ X792 @ X786 )
& ( X785 @ X792 @ X791 ) ) ) )
=> ( ! [X793: $i] :
( ? [X794: $i] : ( in @ X794 @ X793 )
=> ? [X795: $i] :
( ( in @ X795 @ X793 )
& ~ ? [X796: $i] :
( ( in @ X796 @ X795 )
& ( in @ X796 @ X793 ) ) ) )
=> ( epred1_0
=> ( ! [X816: $i > $o] :
( ? [X817: $i] :
( ( X816 @ X817 )
& ! [X818: $i] :
( ( X816 @ X818 )
=> ( X817 = X818 ) ) )
=> ( X816
@ ( descr
@ ^ [Z0: $i] : ( X816 @ Z0 ) ) ) )
=> ( ! [X819: $i,X820: $i > $o,X821: $i] :
( ( in @ X821 @ X819 )
=> ( ( X820 @ X821 )
=> ( in @ X821 @ ( dsetconstr @ X819 @ X820 ) ) ) )
=> ( ! [X822: $i,X823: $i > $o,X824: $i] :
( ( in @ X824 @ ( dsetconstr @ X822 @ X823 ) )
=> ( in @ X824 @ X822 ) )
=> ( ! [X825: $i,X826: $i > $o,X827: $i] :
( ( in @ X827 @ ( dsetconstr @ X825 @ X826 ) )
=> ( X826 @ X827 ) )
=> ( ! [X828: $i > $o] :
( ? [X829: $i] :
( ( X828 @ X829 )
& ! [X830: $i] :
( ( X828 @ X830 )
=> ( X829 = X830 ) ) )
=> ? [X831: $i] :
( ( X828 @ X831 )
& ! [X832: $i] :
( ( X828 @ X832 )
=> ( X831 = X832 ) ) ) )
=> ( ! [X833: $o,X834: $i] :
( ( in @ X834 @ ( prop2set @ X833 ) )
=> X833 )
=> ( ! [X835: $i] :
( ( in @ X835 @ emptyset )
=> ! [X836: $o] : X836 )
=> ( ! [X837: $i] :
( ( in @ X837 @ emptyset )
=> ~ $true )
=> ( ! [X838: $i] :
~ ( in @ X838 @ emptyset )
=> ( ! [X839: $i > $o] :
( ? [X840: $i] :
( ( X839 @ X840 )
& ! [X841: $i] :
( ( X839 @ X841 )
=> ( X840 = X841 ) ) )
=> ? [X842: $i] : ( X839 @ X842 ) )
=> ( ! [X843: $i,X844: $i] :
( ! [X845: $i] :
( ( in @ X845 @ X843 )
=> ( in @ X845 @ X844 ) )
=> ( ! [X846: $i] :
( ( in @ X846 @ X844 )
=> ( in @ X846 @ X843 ) )
=> ( X843 = X844 ) ) )
=> ( ! [X847: $i] :
( ! [X848: $i] :
~ ( in @ X848 @ X847 )
=> ( X847 = emptyset ) )
=> ( ! [X849: $i] :
( ! [X850: $i] :
~ ( in @ X850 @ X849 )
=> ( X849 = emptyset ) )
=> ( ! [X851: $i,X852: $i > $o,X853: $i] :
( ( in @ X853 @ X851 )
=> ( ( in @ X853 @ ( dsetconstr @ X851 @ X852 ) )
<=> ( X852 @ X853 ) ) )
=> ( ! [X854: $i] :
( ( X854 != emptyset )
=> ? [X855: $i] : ( in @ X855 @ X854 ) )
=> ( ! [X856: $i,X857: $i > $o,X858: $i] :
( ( in @ X858 @ X856 )
=> ( ( X857 @ X858 )
=> ( ( dsetconstr @ X856 @ X857 )
!= emptyset ) ) )
=> ( ! [X859: $i] :
( ? [X860: $i] : ( in @ X860 @ X859 )
=> ( X859 != emptyset ) )
=> ( ! [X861: $i,X862: $i] : ( in @ X861 @ ( setadjoin @ X861 @ X862 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X863: $i,X864: $i,X865: $i] :
( ( in @ X865 @ X864 )
=> ( in @ X865 @ ( setadjoin @ X863 @ X864 ) ) )
=> ( ! [X866: $i,X867: $i,X868: $i] :
( ( in @ X868 @ ( setadjoin @ X866 @ X867 ) )
=> ! [X869: $o] :
( ( ( X868 = X866 )
=> X869 )
=> ( ( ( in @ X868 @ X867 )
=> X869 )
=> X869 ) ) )
=> ( ! [X870: $i,X871: $i,X872: $i] :
( ( in @ X872 @ ( setadjoin @ X870 @ X871 ) )
=> ( ( X872 = X870 )
| ( in @ X872 @ X871 ) ) )
=> ( ! [X873: $i] :
( ( dsetconstr @ X873
@ ^ [Z0: $i] : $true )
= X873 )
=> ( ! [X874: $i,X875: $i] :
( ! [X876: $i] :
( ( in @ X876 @ X875 )
=> ( in @ X876 @ X874 ) )
=> ( in @ X875 @ ( powerset @ X874 ) ) )
=> ( ! [X877: $i] : ( in @ emptyset @ ( powerset @ X877 ) )
=> ( ! [X878: $i] : ( in @ emptyset @ ( powerset @ X878 ) )
=> ( ! [X879: $i,X880: $i,X881: $i] :
( ( in @ X880 @ ( powerset @ X879 ) )
=> ( ( in @ X881 @ X880 )
=> ( in @ X881 @ X879 ) ) )
=> ( ! [X882: $i,X883: $i,X884: $i] :
( ( in @ X883 @ X884 )
=> ( ( in @ X884 @ X882 )
=> ( in @ X883 @ ( setunion @ X882 ) ) ) )
=> ( ! [X885: $i,X886: $i] :
( ( in @ X886 @ ( setunion @ X885 ) )
=> ! [X887: $o] :
( ! [X888: $i] :
( ( in @ X886 @ X888 )
=> ( ( in @ X888 @ X885 )
=> X887 ) )
=> X887 ) )
=> ( ! [X889: $i,X890: $i] :
( ( in @ X890 @ X889 )
=> ( in @ X890 @ ( powerset @ ( setunion @ X889 ) ) ) )
=> ( ! [X891: $i > $o] :
( ? [X892: $i] :
( ( X891 @ X892 )
& ! [X893: $i] :
( ( X891 @ X893 )
=> ( X892 = X893 ) ) )
=> ? [X894: $i] :
! [X895: $i] :
( ( X891 @ X895 )
<=> ( X895 = X894 ) ) )
=> ( ! [X896: $i] :
( ( X896 != emptyset )
=> ? [X897: $i] :
( ( in @ X897 @ X896 )
& $true ) )
=> ( ! [X898: $i,X899: $i] :
( ( in @ X898 @ ( setadjoin @ X899 @ emptyset ) )
=> ( X898 = X899 ) )
=> ( ! [X900: $i,X901: $i] :
( ( X900 != X901 )
=> ~ ( in @ X901 @ ( setadjoin @ X900 @ emptyset ) ) )
=> ( ! [X902: $i,X903: $i] :
( ( X902 = X903 )
=> ( in @ X902 @ ( setadjoin @ X903 @ emptyset ) ) )
=> ( ! [X904: $i,X905: $i] :
( ( in @ X904 @ ( setadjoin @ X905 @ emptyset ) )
=> ( in @ X905 @ ( setadjoin @ X904 @ emptyset ) ) )
=> ( ! [X906: $i,X907: $i,X908: $i] :
( ( in @ X908 @ ( setadjoin @ X906 @ ( setadjoin @ X907 @ emptyset ) ) )
=> ( ( X908 = X906 )
| ( X908 = X907 ) ) )
=> ( ! [X909: $i,X910: $i] : ( in @ X909 @ ( setadjoin @ X909 @ ( setadjoin @ X910 @ emptyset ) ) )
=> ( ! [X911: $i,X912: $i] : ( in @ X912 @ ( setadjoin @ X911 @ ( setadjoin @ X912 @ emptyset ) ) )
=> ( ! [X913: $i,X914: $i > $o] :
( ? [X915: $i] :
( ( in @ X915 @ X913 )
& ( X914 @ X915 ) )
=> ( ( ( dsetconstr @ X913 @ X914 )
= emptyset )
=> ~ $true ) )
=> ( ! [X916: $i > $o,X917: $i] :
( ( in @ X917 @ emptyset )
=> ( X916 @ X917 ) )
=> ( ! [X918: $i,X919: $i > $o] :
( ~ ! [X920: $i] :
( ( in @ X920 @ X918 )
=> ( X919 @ X920 ) )
=> ? [X921: $i] :
( ( in @ X921 @ X918 )
& ~ ( X919 @ X921 ) ) )
=> ( ! [X922: $i,X923: $i > $o] :
( ! [X924: $i] :
( ( in @ X924 @ X922 )
=> ~ ( X923 @ X924 ) )
=> ~ ? [X925: $i] :
( ( in @ X925 @ X922 )
& ( X923 @ X925 ) ) )
=> ( ! [X926: $i,X927: $i > $o] :
( ~ ? [X928: $i] :
( ( in @ X928 @ X926 )
& ( X927 @ X928 ) )
=> ! [X929: $i] :
( ( in @ X929 @ X926 )
=> ~ ( X927 @ X929 ) ) )
=> ( ! [X930: $i,X931: $i > $o] :
( ? [X932: $i] :
( ( in @ X932 @ X930 )
& ~ ( X931 @ X932 ) )
=> ~ ! [X933: $i] :
( ( in @ X933 @ X930 )
=> ( X931 @ X933 ) ) )
=> ( ! [X934: $o] :
( X934
=> ( in @ emptyset @ ( prop2set @ X934 ) ) )
=> ( ! [X935: $o] :
( X935
=> ( set2prop @ ( prop2set @ X935 ) ) )
=> ( ! [X936: $i,X937: $i > $o] :
( ~ ? [X938: $i] :
( ( in @ X938 @ X936 )
& ( X937 @ X938 ) )
=> ! [X939: $i] :
( ( in @ X939 @ X936 )
=> ~ ( X937 @ X939 ) ) )
=> ( ! [X940: $i,X941: $i > $o] :
( ~ ! [X942: $i] :
( ( in @ X942 @ X940 )
=> ( X941 @ X942 ) )
=> ? [X943: $i] :
( ( in @ X943 @ X940 )
& ~ ( X941 @ X943 ) ) )
=> ( ! [X944: $i > $o] :
( ? [X945: $i] :
( ( X944 @ X945 )
& ! [X946: $i] :
( ( X944 @ X946 )
=> ( X945 = X946 ) ) )
=> ? [X947: $i] :
( ( X944 @ X947 )
& ! [X948: $i] :
( ( X944 @ X948 )
=> ( X947 = X948 ) ) ) )
=> ( ! [X949: $i > $o] :
( ? [X950: $i] : ( X949 @ X950 )
=> ( ! [X951: $i,X952: $i] :
( ( X949 @ X951 )
=> ( ( X949 @ X952 )
=> ( X951 = X952 ) ) )
=> ? [X953: $i] :
( ( X949 @ X953 )
& ! [X954: $i] :
( ( X949 @ X954 )
=> ( X953 = X954 ) ) ) ) )
=> ( ! [X955: $i > $o] :
( ? [X956: $i] :
! [X957: $i] :
( ( X955 @ X957 )
<=> ( X957 = X956 ) )
=> ? [X958: $i] :
( ( X955 @ X958 )
& ! [X959: $i] :
( ( X955 @ X959 )
=> ( X958 = X959 ) ) ) )
=> ( ! [X960: $i,X961: $i] :
( ( X960 = X961 )
=> ! [X962: $i,X963: $i] :
( ( X962 = X963 )
=> ( ( in @ X962 @ X960 )
=> ( in @ X963 @ X961 ) ) ) )
=> ( ! [X964: $i,X965: $i] :
( ( X964 = X965 )
=> ! [X966: $i,X967: $i] :
( ( X966 = X967 )
=> ( ( in @ X966 @ X964 )
<=> ( in @ X967 @ X965 ) ) ) )
=> ( ! [X968: $i > $o] :
( ? [X969: $i] :
( ( X968 @ X969 )
& ! [X970: $i] :
( ( X968 @ X970 )
=> ( X969 = X970 ) ) )
=> ! [X971: $i,X972: $i] :
( ( X968 @ X971 )
=> ( ( X968 @ X972 )
=> ( X971 = X972 ) ) ) )
=> ( ! [X973: $i > $o,X974: $i > $o] :
( ! [X975: $i,X976: $i] :
( ( X975 = X976 )
=> ( ( X973 @ X975 )
<=> ( X974 @ X976 ) ) )
=> ( ? [X977: $i] :
( ( X973 @ X977 )
& ! [X978: $i] :
( ( X973 @ X978 )
=> ( X977 = X978 ) ) )
<=> ? [X979: $i] :
( ( X974 @ X979 )
& ! [X980: $i] :
( ( X974 @ X980 )
=> ( X979 = X980 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X981: $i,X982: $i] :
( ( X981 = X982 )
=> ! [X983: $i,X984: $i] :
( ( X983 = X984 )
=> ( ( setadjoin @ X981 @ X983 )
= ( setadjoin @ X982 @ X984 ) ) ) )
=> ( ! [X985: $i,X986: $i] :
( ( X985 = X986 )
=> ( ( powerset @ X985 )
= ( powerset @ X986 ) ) )
=> ( ! [X987: $i,X988: $i] :
( ( X987 = X988 )
=> ( ( setunion @ X987 )
= ( setunion @ X988 ) ) )
=> ( ( omega = omega )
=> ( ! [X989: $i > $o] :
( ? [X990: $i] :
( ( X989 @ X990 )
& ! [X991: $i] :
( ( X989 @ X991 )
=> ( X990 = X991 ) ) )
=> ! [X992: $i,X993: $i] :
( ( X989 @ X992 )
=> ( ( X989 @ X993 )
=> ( X992 = X993 ) ) ) )
=> ( ! [X994: $i > $o,X995: $i > $o] :
( ! [X996: $i,X997: $i] :
( ( X996 = X997 )
=> ( ( X994 @ X996 )
<=> ( X995 @ X997 ) ) )
=> ( ? [X998: $i] :
( ( X994 @ X998 )
& ! [X999: $i] :
( ( X994 @ X999 )
=> ( X998 = X999 ) ) )
=> ( ? [X1000: $i] :
( ( X995 @ X1000 )
& ! [X1001: $i] :
( ( X995 @ X1001 )
=> ( X1000 = X1001 ) ) )
=> ( ( descr @ X994 )
= ( descr @ X995 ) ) ) ) )
=> ( ! [X1002: $i,X1003: $i] :
( ( X1002 = X1003 )
=> ! [X1004: $i > $o,X1005: $i > $o] :
( ! [X1006: $i] :
( ( in @ X1006 @ X1002 )
=> ! [X1007: $i] :
( ( in @ X1007 @ X1003 )
=> ( ( X1006 = X1007 )
=> ( ( X1004 @ X1006 )
<=> ( X1005 @ X1007 ) ) ) ) )
=> ( ( dsetconstr @ X1002 @ X1004 )
= ( dsetconstr @ X1003 @ X1005 ) ) ) )
=> ( ! [X1008: $i,X1009: $i] :
( ! [X1010: $i] :
( ( in @ X1010 @ X1008 )
=> ( in @ X1010 @ X1009 ) )
=> ( subset @ X1008 @ X1009 ) )
=> ( ! [X1011: $i,X1012: $i] :
( ( X1011 = X1012 )
=> ( subset @ X1012 @ X1011 ) )
=> ( ! [X1013: $i,X1014: $i] :
( ( X1013 = X1014 )
=> ( subset @ X1013 @ X1014 ) )
=> ( ! [X1015: $i,X1016: $i] :
( ! [X1017: $i] :
( ( in @ X1017 @ X1015 )
=> ( in @ X1017 @ X1016 ) )
=> ( subset @ X1015 @ X1016 ) )
=> ( ! [X1018: $i] : ( subset @ emptyset @ X1018 )
=> ( ! [X1019: $i,X1020: $i,X1021: $i] :
( ( subset @ X1019 @ X1020 )
=> ( ( in @ X1021 @ X1019 )
=> ( in @ X1021 @ X1020 ) ) )
=> ( ! [X1022: $i,X1023: $i,X1024: $i] :
( ( subset @ X1022 @ X1023 )
=> ( ~ ( in @ X1024 @ X1023 )
=> ~ ( in @ X1024 @ X1022 ) ) )
=> ( ! [X1025: $i,X1026: $i,X1027: $i] :
( ( in @ X1027 @ X1025 )
=> ( ~ ( in @ X1027 @ X1026 )
=> ~ ( subset @ X1025 @ X1026 ) ) )
=> ( ! [X1028: $i,X1029: $i] :
( ~ ( subset @ X1028 @ X1029 )
=> ( X1028 != X1029 ) )
=> ( ! [X1030: $i,X1031: $i,X1032: $i] :
( ( in @ X1032 @ X1030 )
=> ( ~ ( in @ X1032 @ X1031 )
=> ( X1030 != X1031 ) ) )
=> ( ! [X1033: $i] : ( subset @ X1033 @ X1033 )
=> ( ! [X1034: $i,X1035: $i,X1036: $i] :
( ( subset @ X1034 @ X1035 )
=> ( ( subset @ X1035 @ X1036 )
=> ( subset @ X1034 @ X1036 ) ) )
=> ( ! [X1037: $i,X1038: $i] : ( subset @ X1038 @ ( setadjoin @ X1037 @ X1038 ) )
=> ( ! [X1039: $i,X1040: $i,X1041: $i] :
( ( subset @ X1039 @ X1041 )
=> ( subset @ X1039 @ ( setadjoin @ X1040 @ X1041 ) ) )
=> ( ! [X1042: $i,X1043: $i] :
( ( subset @ X1042 @ X1043 )
=> ( in @ X1042 @ ( powerset @ X1043 ) ) )
=> ( ! [X1044: $i,X1045: $i] :
( ( subset @ X1044 @ X1045 )
=> ( ( subset @ X1045 @ X1044 )
=> ( X1044 = X1045 ) ) )
=> ( ! [X1046: $i] :
( ( subset @ X1046 @ emptyset )
=> ( X1046 = emptyset ) )
=> ( ! [X1047: $i,X1048: $i] :
( ( subset @ X1048 @ X1047 )
=> ( in @ X1048 @ ( powerset @ X1047 ) ) )
=> ( ! [X1049: $i,X1050: $i] :
( ( in @ X1050 @ ( powerset @ X1049 ) )
=> ( subset @ X1050 @ X1049 ) )
=> ( ! [X1051: $i] : ( in @ X1051 @ ( powerset @ X1051 ) )
=> ( ! [X1052: $i,X1053: $i] :
( ( subset @ X1052 @ X1053 )
=> ( subset @ ( powerset @ X1052 ) @ ( powerset @ X1053 ) ) )
=> ( ! [X1054: $i,X1055: $i > $o] : ( in @ ( dsetconstr @ X1054 @ X1055 ) @ ( powerset @ X1054 ) )
=> ( ! [X1056: $i,X1057: $i > $o] : ( subset @ ( dsetconstr @ X1056 @ X1057 ) @ X1056 )
=> ( ! [X1058: $i,X1059: $i,X1060: $i] :
( ( in @ X1060 @ X1058 )
=> ( in @ X1060 @ ( binunion @ X1058 @ X1059 ) ) )
=> ( ! [X1061: $i,X1062: $i] : ( in @ X1062 @ ( setadjoin @ X1061 @ ( setadjoin @ X1062 @ emptyset ) ) )
=> ( ! [X1063: $i,X1064: $i,X1065: $i] :
( ( in @ X1065 @ X1064 )
=> ( in @ X1065 @ ( binunion @ X1063 @ X1064 ) ) )
=> ( ! [X1066: $i,X1067: $i,X1068: $i,X1069: $o] :
( ( in @ X1068 @ ( binunion @ X1066 @ X1067 ) )
=> ( ( ( in @ X1068 @ X1066 )
=> X1069 )
=> ( ( ( in @ X1068 @ X1067 )
=> X1069 )
=> X1069 ) ) )
=> ( ! [X1070: $i,X1071: $i,X1072: $i] :
( ( in @ X1072 @ ( binunion @ X1070 @ X1071 ) )
=> ( ( in @ X1072 @ X1070 )
| ( in @ X1072 @ X1071 ) ) )
=> ( ! [X1073: $i,X1074: $i] : ( subset @ X1073 @ ( binunion @ X1073 @ X1074 ) )
=> ( ! [X1075: $i,X1076: $i] : ( subset @ X1076 @ ( binunion @ X1075 @ X1076 ) )
=> ( ! [X1077: $i,X1078: $i,X1079: $i] :
( ( in @ X1079 @ X1077 )
=> ( ( in @ X1079 @ X1078 )
=> ( in @ X1079 @ ( binintersect @ X1077 @ X1078 ) ) ) )
=> ( ! [X1080: $i,X1081: $i,X1082: $i] :
( ( subset @ X1082 @ X1080 )
=> ( ( subset @ X1082 @ X1081 )
=> ( subset @ X1082 @ ( binintersect @ X1080 @ X1081 ) ) ) )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ( in @ X1085 @ ( binintersect @ X1083 @ X1084 ) )
=> ( in @ X1085 @ X1083 ) )
=> ( ! [X1086: $i,X1087: $i] : ( subset @ ( binintersect @ X1086 @ X1087 ) @ X1086 )
=> ( ! [X1088: $i,X1089: $i] :
( ( subset @ X1088 @ X1089 )
=> ( ( binintersect @ X1088 @ X1089 )
= X1088 ) )
=> ( ! [X1090: $i,X1091: $i] :
( ( ( binintersect @ X1090 @ X1091 )
= X1091 )
=> ( subset @ X1091 @ X1090 ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i] :
( ( in @ X1094 @ ( binintersect @ X1092 @ X1093 ) )
=> ( in @ X1094 @ X1093 ) )
=> ( ! [X1095: $i,X1096: $i] :
( ~ ? [X1097: $i] :
( ( in @ X1097 @ X1095 )
& ( in @ X1097 @ X1096 ) )
=> ( ( binintersect @ X1095 @ X1096 )
= emptyset ) )
=> ( ! [X1098: $i,X1099: $i] : ( subset @ ( binintersect @ X1098 @ X1099 ) @ X1099 )
=> ( ! [X1100: $i,X1101: $i] :
( ( subset @ X1101 @ X1100 )
=> ( ( binintersect @ X1100 @ X1101 )
= X1101 ) )
=> ( ! [X1102: $i,X1103: $i] :
( ( ( binintersect @ X1102 @ X1103 )
= X1102 )
=> ( subset @ X1102 @ X1103 ) )
=> ( ! [X1104: $i,X1105: $i,X1106: $i] :
( ( binintersect @ X1104 @ ( binunion @ X1105 @ X1106 ) )
= ( binunion @ ( binintersect @ X1104 @ X1105 ) @ ( binintersect @ X1104 @ X1106 ) ) )
=> ( ! [X1107: $i,X1108: $i,X1109: $i] :
( ( in @ X1109 @ X1107 )
=> ( ~ ( in @ X1109 @ X1108 )
=> ( in @ X1109 @ ( setminus @ X1107 @ X1108 ) ) ) )
=> ( ! [X1110: $i,X1111: $i,X1112: $i] :
( ( in @ X1112 @ ( setminus @ X1110 @ X1111 ) )
=> ( in @ X1112 @ X1110 ) )
=> ( ! [X1113: $i,X1114: $i,X1115: $i] :
( ( in @ X1115 @ ( setminus @ X1113 @ X1114 ) )
=> ~ ( in @ X1115 @ X1114 ) )
=> ( ! [X1116: $i,X1117: $i] :
( ( subset @ X1116 @ X1117 )
=> ( ( setminus @ X1116 @ X1117 )
= emptyset ) )
=> ( ! [X1118: $i,X1119: $i,X1120: $i] :
( ~ ( in @ X1120 @ ( setminus @ X1118 @ X1119 ) )
=> ( ( in @ X1120 @ X1118 )
=> ( in @ X1120 @ X1119 ) ) )
=> ( ! [X1121: $i,X1122: $i,X1123: $i] :
( ~ ( in @ X1123 @ ( setminus @ X1121 @ X1122 ) )
=> ( ~ ( in @ X1123 @ X1122 )
=> ~ ( in @ X1123 @ X1121 ) ) )
=> ( ! [X1124: $i,X1125: $i,X1126: $i] :
( ~ ( in @ X1126 @ X1124 )
=> ~ ( in @ X1126 @ ( setminus @ X1124 @ X1125 ) ) )
=> ( ! [X1127: $i,X1128: $i,X1129: $i] :
( ( in @ X1129 @ X1128 )
=> ~ ( in @ X1129 @ ( setminus @ X1127 @ X1128 ) ) )
=> ( ! [X1130: $i,X1131: $i] : ( subset @ ( setminus @ X1130 @ X1131 ) @ X1130 )
=> ( ! [X1132: $i,X1133: $i] :
( ( ( setminus @ X1132 @ X1133 )
= emptyset )
=> ( subset @ X1132 @ X1133 ) )
=> ( ! [X1134: $i,X1135: $i,X1136: $i] :
( ( in @ X1136 @ ( symdiff @ X1134 @ X1135 ) )
=> ! [X1137: $o] :
( ( ( in @ X1136 @ X1134 )
=> ( ~ ( in @ X1136 @ X1135 )
=> X1137 ) )
=> ( ( ~ ( in @ X1136 @ X1134 )
=> ( ( in @ X1136 @ X1135 )
=> X1137 ) )
=> X1137 ) ) )
=> ( ! [X1138: $i,X1139: $i,X1140: $i] :
( ( in @ X1140 @ X1138 )
=> ( ~ ( in @ X1140 @ X1139 )
=> ( in @ X1140 @ ( symdiff @ X1138 @ X1139 ) ) ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i] :
( ~ ( in @ X1143 @ X1141 )
=> ( ( in @ X1143 @ X1142 )
=> ( in @ X1143 @ ( symdiff @ X1141 @ X1142 ) ) ) )
=> ( ! [X1144: $i,X1145: $i,X1146: $i] :
( ( in @ X1146 @ X1144 )
=> ( ( in @ X1146 @ X1145 )
=> ~ ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) ) )
=> ( ! [X1147: $i,X1148: $i,X1149: $i] :
( ~ ( in @ X1149 @ X1147 )
=> ( ~ ( in @ X1149 @ X1148 )
=> ~ ( in @ X1149 @ ( symdiff @ X1147 @ X1148 ) ) ) )
=> ( ! [X1150: $i,X1151: $i] : ( in @ X1151 @ ( setadjoin @ X1150 @ ( setadjoin @ X1151 @ emptyset ) ) )
=> ( ! [X1152: $i,X1153: $i] : ( in @ X1152 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1152 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1152 @ ( setadjoin @ X1153 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1154: $i,X1155: $i] : ( in @ X1155 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1154 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1154 @ ( setadjoin @ X1155 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1156: $i,X1157: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1156 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1156 @ ( setadjoin @ X1157 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1158: $i,X1159: $i] : ( iskpair @ ( kpair @ X1158 @ X1159 ) )
=> ( ! [X1160: $i,X1161: $i] :
( ( in @ X1161 @ X1160 )
=> ( subset @ ( setadjoin @ X1161 @ emptyset ) @ X1160 ) )
=> ( ! [X1162: $i,X1163: $i] :
( ( in @ X1163 @ X1162 )
=> ( in @ ( setadjoin @ X1163 @ emptyset ) @ ( powerset @ X1162 ) ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( in @ X1166 @ X1164 )
=> ( in @ ( setadjoin @ X1166 @ emptyset ) @ ( powerset @ ( binunion @ X1164 @ X1165 ) ) ) )
=> ( ! [X1167: $i,X1168: $i,X1169: $i] :
( ( in @ X1169 @ ( setadjoin @ X1167 @ ( setadjoin @ X1168 @ emptyset ) ) )
=> ( ( X1169 = X1167 )
| ( X1169 = X1168 ) ) )
=> ( ! [X1170: $i,X1171: $i,X1172: $i] :
( ( in @ X1172 @ X1170 )
=> ! [X1173: $i] :
( ( in @ X1173 @ X1171 )
=> ( subset @ ( setadjoin @ X1172 @ ( setadjoin @ X1173 @ emptyset ) ) @ ( binunion @ X1170 @ X1171 ) ) ) )
=> ( ! [X1174: $i,X1175: $i,X1176: $i] :
( ( in @ X1176 @ X1174 )
=> ! [X1177: $i] :
( ( in @ X1177 @ X1175 )
=> ( in @ ( setadjoin @ X1176 @ ( setadjoin @ X1177 @ emptyset ) ) @ ( powerset @ ( binunion @ X1174 @ X1175 ) ) ) ) )
=> ( ! [X1178: $i,X1179: $i,X1180: $i] :
( ( in @ X1180 @ X1178 )
=> ! [X1181: $i] :
( ( in @ X1181 @ X1179 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1180 @ ( setadjoin @ X1181 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1178 @ X1179 ) ) ) ) )
=> ( ! [X1182: $i,X1183: $i,X1184: $i] :
( ( in @ X1184 @ X1182 )
=> ! [X1185: $i] :
( ( in @ X1185 @ X1183 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1184 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1184 @ ( setadjoin @ X1185 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1182 @ X1183 ) ) ) ) ) )
=> ( ! [X1186: $i,X1187: $i,X1188: $i] :
( ( in @ X1188 @ X1186 )
=> ! [X1189: $i] :
( ( in @ X1189 @ X1187 )
=> ( in @ ( kpair @ X1188 @ X1189 ) @ ( powerset @ ( powerset @ ( binunion @ X1186 @ X1187 ) ) ) ) ) )
=> ( ! [X1190: $i,X1191: $i,X1192: $i] :
( ( in @ X1192 @ X1190 )
=> ! [X1193: $i] :
( ( in @ X1193 @ X1191 )
=> ( in @ ( kpair @ X1192 @ X1193 ) @ ( cartprod @ X1190 @ X1191 ) ) ) )
=> ( ! [X1194: $i,X1195: $i,X1196: $i] :
( ( in @ X1196 @ ( cartprod @ X1194 @ X1195 ) )
=> ? [X1197: $i] :
( ( in @ X1197 @ X1194 )
& ? [X1198: $i] :
( ( in @ X1198 @ X1195 )
& ( X1196
= ( kpair @ X1197 @ X1198 ) ) ) ) )
=> ( ! [X1199: $i,X1200: $i,X1201: $i] :
( ( in @ X1201 @ ( cartprod @ X1199 @ X1200 ) )
=> ( iskpair @ X1201 ) )
=> ( ! [X1202: $i,X1203: $i] :
( ( in @ X1203 @ ( setunion @ X1202 ) )
=> ? [X1204: $i] :
( ( in @ X1204 @ X1202 )
& ( in @ X1203 @ X1204 ) ) )
=> ( ! [X1205: $i] : ( subset @ ( setunion @ ( setadjoin @ X1205 @ emptyset ) ) @ X1205 )
=> ( ! [X1206: $i] : ( subset @ X1206 @ ( setunion @ ( setadjoin @ X1206 @ emptyset ) ) )
=> ( ! [X1207: $i] :
( ( setunion @ ( setadjoin @ X1207 @ emptyset ) )
= X1207 )
=> ( ! [X1208: $i,X1209: $i > $o] :
( ! [X1210: $i] :
( ( in @ X1210 @ X1208 )
=> ! [X1211: $i] :
( ( in @ X1211 @ X1208 )
=> ( ( X1209 @ X1210 )
=> ( ( X1209 @ X1211 )
=> ( X1210 = X1211 ) ) ) ) )
=> ( ? [X1212: $i] :
( ( in @ X1212 @ X1208 )
& ( X1209 @ X1212 ) )
=> ( singleton @ ( dsetconstr @ X1208 @ X1209 ) ) ) )
=> ( ! [X1213: $i,X1214: $i > $o] :
( ( singleton @ ( dsetconstr @ X1213 @ X1214 ) )
=> ? [X1215: $i] :
( ( in @ X1215 @ X1213 )
& ( X1214 @ X1215 ) ) )
=> ( ! [X1216: $i,X1217: $i > $o,X1218: $i] :
( ( in @ X1218 @ X1216 )
=> ( ( X1217 @ X1218 )
=> ( ! [X1219: $i] :
( ( in @ X1219 @ X1216 )
=> ( ( X1217 @ X1219 )
=> ( X1219 = X1218 ) ) )
=> ( singleton @ ( dsetconstr @ X1216 @ X1217 ) ) ) ) )
=> ( ! [X1220: $i,X1221: $i > $o] :
( ! [X1222: $i] :
( ( in @ X1222 @ X1220 )
=> ! [X1223: $i] :
( ( in @ X1223 @ X1220 )
=> ( ( X1221 @ X1222 )
=> ( ( X1221 @ X1223 )
=> ( X1222 = X1223 ) ) ) ) )
=> ( ? [X1224: $i] :
( ( in @ X1224 @ X1220 )
& ( X1221 @ X1224 ) )
=> ( singleton @ ( dsetconstr @ X1220 @ X1221 ) ) ) )
=> ( ! [X1225: $i,X1226: $i] :
( ( ( setadjoin @ X1225 @ emptyset )
= ( setadjoin @ X1226 @ emptyset ) )
=> ( X1225 = X1226 ) )
=> ( ! [X1227: $i,X1228: $i,X1229: $i] :
( ( in @ ( setadjoin @ X1229 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1227 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1227 @ ( setadjoin @ X1228 @ emptyset ) ) @ emptyset ) ) )
=> ( X1227 = X1229 ) )
=> ( ! [X1230: $i] :
( ( iskpair @ X1230 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1230 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1230 ) ) ) )
=> ( ! [X1231: $i] :
( ( singleton @ X1231 )
=> ( in @ ( setunion @ X1231 ) @ X1231 ) )
=> ( ! [X1232: $i,X1233: $i] :
( ( kfst @ ( kpair @ X1232 @ X1233 ) )
= X1232 )
=> ( ! [X1234: $i,X1235: $i,X1236: $i] :
( ( in @ X1236 @ ( cartprod @ X1234 @ X1235 ) )
=> ( in @ ( kfst @ X1236 ) @ X1234 ) )
=> ( ! [X1237: $i,X1238: $i,X1239: $i,X1240: $i] :
( ( ( setadjoin @ ( setadjoin @ X1237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1237 @ ( setadjoin @ X1238 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1239 @ ( setadjoin @ X1240 @ emptyset ) ) @ emptyset ) ) )
=> ( X1237 = X1239 ) )
=> ( ! [X1241: $i,X1242: $i,X1243: $i,X1244: $i] :
( ( ( kpair @ X1241 @ X1242 )
= ( kpair @ X1243 @ X1244 ) )
=> ( X1241 = X1243 ) )
=> ( ! [X1245: $i,X1246: $i] :
( ( X1245 = X1246 )
=> ( ( setadjoin @ X1245 @ ( setadjoin @ X1246 @ emptyset ) )
= ( setadjoin @ X1245 @ emptyset ) ) )
=> ( ! [X1247: $i,X1248: $i] :
( ( X1247 = X1248 )
=> ( ( setadjoin @ ( setadjoin @ X1247 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1247 @ ( setadjoin @ X1248 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1247 @ emptyset ) @ emptyset ) ) )
=> ( ! [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 ) ) )
=> ( ( X1251 = X1252 )
=> ( X1250 = X1252 ) ) )
=> ( ! [X1253: $i,X1254: $i,X1255: $i] :
( ( ( setadjoin @ X1253 @ ( setadjoin @ X1254 @ emptyset ) )
= ( setadjoin @ X1255 @ emptyset ) )
=> ( X1253 = X1254 ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i,X1259: $i] :
( ( ( setadjoin @ ( setadjoin @ X1256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1256 @ ( setadjoin @ X1257 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1258 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1258 @ ( setadjoin @ X1259 @ emptyset ) ) @ emptyset ) ) )
=> ( X1257 = X1259 ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i,X1263: $i] :
( ( ( kpair @ X1260 @ X1261 )
= ( kpair @ X1262 @ X1263 ) )
=> ( X1261 = X1263 ) )
=> ( ! [X1264: $i] :
( ( iskpair @ X1264 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1264 )
@ ^ [Z0: $i] :
( X1264
= ( kpair @ ( kfst @ X1264 ) @ Z0 ) ) ) ) )
=> ( ! [X1265: $i,X1266: $i] :
( ( ksnd @ ( kpair @ X1265 @ X1266 ) )
= X1266 )
=> ( ! [X1267: $i] :
( ( iskpair @ X1267 )
=> ( ( kpair @ ( kfst @ X1267 ) @ ( ksnd @ X1267 ) )
= X1267 ) )
=> ( ! [X1268: $i,X1269: $i,X1270: $i] :
( ( in @ X1270 @ ( cartprod @ X1268 @ X1269 ) )
=> ( in @ ( ksnd @ X1270 ) @ X1269 ) )
=> ( ! [X1271: $i,X1272: $i,X1273: $i,X1274: $i] :
( ( in @ ( kpair @ X1273 @ X1274 ) @ ( cartprod @ X1271 @ X1272 ) )
=> ( in @ X1273 @ X1271 ) )
=> ( ! [X1275: $i,X1276: $i,X1277: $i,X1278: $i] :
( ( in @ ( kpair @ X1277 @ X1278 ) @ ( cartprod @ X1275 @ X1276 ) )
=> ( in @ X1278 @ X1276 ) )
=> ( ! [X1279: $i,X1280: $i,X1281: $i] :
( ( in @ X1281 @ X1279 )
=> ! [X1282: $i] :
( ( in @ X1282 @ X1280 )
=> ( ( kpair @ X1281 @ X1282 )
= ( kpair @ X1281 @ X1282 ) ) ) )
=> ( ! [X1283: $i,X1284: $i,X1285: $i] :
( ( in @ X1285 @ X1283 )
=> ! [X1286: $i] :
( ( in @ X1286 @ X1284 )
=> ( ( kfst @ ( kpair @ X1285 @ X1286 ) )
= X1285 ) ) )
=> ( ! [X1287: $i,X1288: $i,X1289: $i] :
( ( in @ X1289 @ X1287 )
=> ! [X1290: $i] :
( ( in @ X1290 @ X1288 )
=> ( ( ksnd @ ( kpair @ X1289 @ X1290 ) )
= X1290 ) ) )
=> ( ! [X1291: $i,X1292: $i,X1293: $i] :
( ( in @ X1293 @ ( cartprod @ X1291 @ X1292 ) )
=> ( ( kpair @ ( kfst @ X1293 ) @ ( ksnd @ X1293 ) )
= X1293 ) )
=> ( ! [X1294: $i,X1295: $i,X1296: $i > $i > $o,X1297: $i] :
( ( in @ X1297 @ X1294 )
=> ! [X1298: $i] :
( ( in @ X1298 @ X1295 )
=> ( ( X1296 @ X1297 @ X1298 )
=> ( in @ ( kpair @ X1297 @ X1298 ) @ ( dpsetconstr @ X1294 @ X1295 @ X1296 ) ) ) ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1299 @ X1300 @ X1301 ) @ ( cartprod @ X1299 @ X1300 ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1302 @ X1303 @ X1304 ) @ ( cartprod @ X1302 @ X1303 ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i > $i > $o,X1308: $i] :
( ( in @ X1308 @ X1305 )
=> ! [X1309: $i] :
( ( in @ X1309 @ X1306 )
=> ( ( in @ ( kpair @ X1308 @ X1309 ) @ ( dpsetconstr @ X1305 @ X1306 @ X1307 ) )
=> ( X1307 @ X1308 @ X1309 ) ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i > $i > $o,X1313: $i,X1314: $i] :
( ( in @ ( kpair @ X1313 @ X1314 ) @ ( dpsetconstr @ X1310 @ X1311 @ X1312 ) )
=> ( in @ X1313 @ X1310 ) )
=> ( ! [X1315: $i,X1316: $i,X1317: $i > $i > $o,X1318: $i,X1319: $i] :
( ( in @ ( kpair @ X1318 @ X1319 ) @ ( dpsetconstr @ X1315 @ X1316 @ X1317 ) )
=> ( in @ X1319 @ X1316 ) )
=> ( ! [X1320: $i,X1321: $i,X1322: $i > $i > $o,X1323: $i,X1324: $i] :
( ( in @ ( kpair @ X1323 @ X1324 ) @ ( dpsetconstr @ X1320 @ X1321 @ X1322 ) )
=> ( X1322 @ X1323 @ X1324 ) )
=> ( ! [X1325: $i,X1326: $i,X1327: $i] :
( ( func @ X1325 @ X1326 @ X1327 )
=> ! [X1328: $i] :
( ( in @ X1328 @ X1325 )
=> ( singleton
@ ( dsetconstr @ X1326
@ ^ [Z0: $i] : ( in @ ( kpair @ X1328 @ Z0 ) @ X1327 ) ) ) ) )
=> ( ! [X1329: $i,X1330: $i,X1331: $i] :
( ( func @ X1329 @ X1330 @ X1331 )
=> ! [X1332: $i] :
( ( in @ X1332 @ X1329 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1330
@ ^ [Z0: $i] : ( in @ ( kpair @ X1332 @ Z0 ) @ X1331 ) ) )
@ X1330 ) ) )
=> ( ! [X1333: $i,X1334: $i,X1335: $i] :
( ( func @ X1333 @ X1334 @ X1335 )
=> ! [X1336: $i] :
( ( in @ X1336 @ X1333 )
=> ( in @ ( ap @ X1333 @ X1334 @ X1335 @ X1336 ) @ X1334 ) ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i] :
( ( in @ X1339 @ ( funcSet @ X1337 @ X1338 ) )
=> ( func @ X1337 @ X1338 @ X1339 ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i] :
( ( in @ X1342 @ ( funcSet @ X1340 @ X1341 ) )
=> ! [X1343: $i] :
( ( in @ X1343 @ X1340 )
=> ( in @ ( ap @ X1340 @ X1341 @ X1342 @ X1343 ) @ X1341 ) ) )
=> ( ! [X1344: $i,X1345: $i,X1346: $i] :
( ( func @ X1344 @ X1345 @ X1346 )
=> ( in @ X1346 @ ( funcSet @ X1344 @ X1345 ) ) )
=> ( ! [X1347: $i,X1348: $i,X1349: $i > $i] :
( ! [X1350: $i] :
( ( in @ X1350 @ X1347 )
=> ( in @ ( X1349 @ X1350 ) @ X1348 ) )
=> ( func @ X1347 @ X1348
@ ( dpsetconstr @ X1347 @ X1348
@ ^ [Z0: $i] : ( $eq @ ( X1349 @ Z0 ) ) ) ) )
=> ( ! [X1351: $i,X1352: $i,X1353: $i > $i] :
( ! [X1354: $i] :
( ( in @ X1354 @ X1351 )
=> ( in @ ( X1353 @ X1354 ) @ X1352 ) )
=> ( func @ X1351 @ X1352 @ ( lam @ X1351 @ X1352 @ X1353 ) ) )
=> ( ! [X1355: $i,X1356: $i,X1357: $i > $i] :
( ! [X1358: $i] :
( ( in @ X1358 @ X1355 )
=> ( in @ ( X1357 @ X1358 ) @ X1356 ) )
=> ( in @ ( lam @ X1355 @ X1356 @ X1357 ) @ ( funcSet @ X1355 @ X1356 ) ) )
=> ( ! [X1359: $i,X1360: $i,X1361: $i] :
( ( subset @ X1361 @ ( cartprod @ X1359 @ X1360 ) )
=> ! [X1362: $i > $o] :
( ! [X1363: $i] :
( ( in @ X1363 @ X1359 )
=> ! [X1364: $i] :
( ( in @ X1364 @ X1360 )
=> ( ( in @ ( kpair @ X1363 @ X1364 ) @ X1361 )
=> ( X1362 @ ( kpair @ X1363 @ X1364 ) ) ) ) )
=> ! [X1365: $i] :
( ( in @ X1365 @ X1361 )
=> ( X1362 @ X1365 ) ) ) )
=> ( ! [X1366: $i,X1367: $i,X1368: $i] :
( ( subset @ X1368 @ ( cartprod @ X1366 @ X1367 ) )
=> ! [X1369: $i > $o] :
( ! [X1370: $i] :
( ( in @ X1370 @ X1366 )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1367 )
=> ( ( in @ ( kpair @ X1370 @ X1371 ) @ X1368 )
=> ( X1369 @ ( kpair @ X1370 @ X1371 ) ) ) ) )
=> ! [X1372: $i] :
( ( in @ X1372 @ X1368 )
=> ( X1369 @ X1372 ) ) ) )
=> ( ! [X1373: $i,X1374: $i > $o] :
( ( singleton @ ( dsetconstr @ X1373 @ X1374 ) )
=> ! [X1375: $i] :
( ( in @ X1375 @ X1373 )
=> ! [X1376: $i] :
( ( in @ X1376 @ X1373 )
=> ( ( X1374 @ X1375 )
=> ( ( X1374 @ X1376 )
=> ( X1375 = X1376 ) ) ) ) ) )
=> ( ! [X1377: $i,X1378: $i,X1379: $i] :
( ( func @ X1377 @ X1378 @ X1379 )
=> ! [X1380: $i] :
( ( in @ X1380 @ X1377 )
=> ( in @ ( kpair @ X1380 @ ( ap @ X1377 @ X1378 @ X1379 @ X1380 ) ) @ X1379 ) ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i] :
( ( in @ X1383 @ ( funcSet @ X1381 @ X1382 ) )
=> ! [X1384: $i] :
( ( in @ X1384 @ X1381 )
=> ( in @ ( kpair @ X1384 @ ( ap @ X1381 @ X1382 @ X1383 @ X1384 ) ) @ X1383 ) ) )
=> ( ! [X1385: $i,X1386: $i,X1387: $i] :
( ( func @ X1385 @ X1386 @ X1387 )
=> ! [X1388: $i] :
( ( in @ X1388 @ X1385 )
=> ! [X1389: $i] :
( ( in @ X1389 @ X1386 )
=> ( ( in @ ( kpair @ X1388 @ X1389 ) @ X1387 )
=> ( ( ap @ X1385 @ X1386 @ X1387 @ X1388 )
= X1389 ) ) ) ) )
=> ( ! [X1390: $i,X1391: $i,X1392: $i] :
( ( func @ X1390 @ X1391 @ X1392 )
=> ! [X1393: $i] :
( ( func @ X1390 @ X1391 @ X1393 )
=> ( ! [X1394: $i] :
( ( in @ X1394 @ X1390 )
=> ( ( ap @ X1390 @ X1391 @ X1392 @ X1394 )
= ( ap @ X1390 @ X1391 @ X1393 @ X1394 ) ) )
=> ! [X1395: $i] :
( ( in @ X1395 @ X1390 )
=> ! [X1396: $i] :
( ( in @ X1396 @ X1391 )
=> ( ( in @ ( kpair @ X1395 @ X1396 ) @ X1393 )
=> ( in @ ( kpair @ X1395 @ X1396 ) @ X1392 ) ) ) ) ) ) )
=> ( ! [X1397: $i,X1398: $i,X1399: $i] :
( ( in @ X1399 @ ( funcSet @ X1397 @ X1398 ) )
=> ! [X1400: $i] :
( ( in @ X1400 @ X1397 )
=> ! [X1401: $i] :
( ( in @ X1401 @ X1398 )
=> ( ( in @ ( kpair @ X1400 @ X1401 ) @ X1399 )
=> ( ( ap @ X1397 @ X1398 @ X1399 @ X1400 )
= X1401 ) ) ) ) )
=> ( ! [X1402: $i,X1403: $i,X1404: $i] :
( ( subset @ X1404 @ ( cartprod @ X1402 @ X1403 ) )
=> ! [X1405: $i] :
( ( subset @ X1405 @ ( cartprod @ X1402 @ X1403 ) )
=> ( ! [X1406: $i] :
( ( in @ X1406 @ X1402 )
=> ! [X1407: $i] :
( ( in @ X1407 @ X1403 )
=> ( ( in @ ( kpair @ X1406 @ X1407 ) @ X1404 )
=> ( in @ ( kpair @ X1406 @ X1407 ) @ X1405 ) ) ) )
=> ( subset @ X1404 @ X1405 ) ) ) )
=> ( ! [X1408: $i,X1409: $i,X1410: $i] :
( ( subset @ X1410 @ ( cartprod @ X1408 @ X1409 ) )
=> ! [X1411: $i] :
( ( subset @ X1411 @ ( cartprod @ X1408 @ X1409 ) )
=> ( ! [X1412: $i] :
( ( in @ X1412 @ X1408 )
=> ! [X1413: $i] :
( ( in @ X1413 @ X1409 )
=> ( ( in @ ( kpair @ X1412 @ X1413 ) @ X1410 )
=> ( in @ ( kpair @ X1412 @ X1413 ) @ X1411 ) ) ) )
=> ( ! [X1414: $i] :
( ( in @ X1414 @ X1408 )
=> ! [X1415: $i] :
( ( in @ X1415 @ X1409 )
=> ( ( in @ ( kpair @ X1414 @ X1415 ) @ X1411 )
=> ( in @ ( kpair @ X1414 @ X1415 ) @ X1410 ) ) ) )
=> ( X1410 = X1411 ) ) ) ) )
=> ( ! [X1416: $i,X1417: $i,X1418: $i] :
( ( func @ X1416 @ X1417 @ X1418 )
=> ! [X1419: $i] :
( ( func @ X1416 @ X1417 @ X1419 )
=> ( ! [X1420: $i] :
( ( in @ X1420 @ X1416 )
=> ( ( ap @ X1416 @ X1417 @ X1418 @ X1420 )
= ( ap @ X1416 @ X1417 @ X1419 @ X1420 ) ) )
=> ( X1418 = X1419 ) ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i] :
( ( in @ X1423 @ ( funcSet @ X1421 @ X1422 ) )
=> ! [X1424: $i] :
( ( in @ X1424 @ ( funcSet @ X1421 @ X1422 ) )
=> ( ! [X1425: $i] :
( ( in @ X1425 @ X1421 )
=> ( ( ap @ X1421 @ X1422 @ X1423 @ X1425 )
= ( ap @ X1421 @ X1422 @ X1424 @ X1425 ) ) )
=> ( X1423 = X1424 ) ) ) )
=> ( ! [X1426: $i,X1427: $i,X1428: $i] :
( ( in @ X1428 @ ( funcSet @ X1426 @ X1427 ) )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1426 )
=> ( ( ap @ X1426 @ X1427 @ X1428 @ X1429 )
= ( ap @ X1426 @ X1427 @ X1428 @ X1429 ) ) ) )
=> ( ! [X1430: $i,X1431: $i,X1432: $i] :
( ( func @ X1430 @ X1431 @ X1432 )
=> ! [X1433: $i] :
( ( in @ X1433 @ X1430 )
=> ( ( ap @ X1430 @ X1431 @ X1432 @ X1433 )
= ( ap @ X1430 @ X1431 @ X1432 @ X1433 ) ) ) )
=> ( ! [X1434: $i,X1435: $i,X1436: $i > $i] :
( ! [X1437: $i] :
( ( in @ X1437 @ X1434 )
=> ( in @ ( X1436 @ X1437 ) @ X1435 ) )
=> ! [X1438: $i] :
( ( in @ X1438 @ X1434 )
=> ( ( ap @ X1434 @ X1435 @ ( lam @ X1434 @ X1435 @ X1436 ) @ X1438 )
= ( X1436 @ X1438 ) ) ) )
=> ( ! [X1439: $i,X1440: $i,X1441: $i] :
( ( func @ X1439 @ X1440 @ X1441 )
=> ( ( lam @ X1439 @ X1440 @ ( ap @ X1439 @ X1440 @ X1441 ) )
= X1441 ) )
=> ( ! [X1442: $i,X1443: $i,X1444: $i > $i] :
( ! [X1445: $i] :
( ( in @ X1445 @ X1442 )
=> ( in @ ( X1444 @ X1445 ) @ X1443 ) )
=> ( ( lam @ X1442 @ X1443 @ X1444 )
= ( lam @ X1442 @ X1443 @ X1444 ) ) )
=> ( ! [X1446: $i,X1447: $i,X1448: $i > $i] :
( ! [X1449: $i] :
( ( in @ X1449 @ X1446 )
=> ( in @ ( X1448 @ X1449 ) @ X1447 ) )
=> ! [X1450: $i] :
( ( in @ X1450 @ X1446 )
=> ( ( ap @ X1446 @ X1447 @ ( lam @ X1446 @ X1447 @ X1448 ) @ X1450 )
= ( X1448 @ X1450 ) ) ) )
=> ( ! [X1451: $i,X1452: $i,X1453: $i] :
( ( in @ X1453 @ ( funcSet @ X1451 @ X1452 ) )
=> ( ( lam @ X1451 @ X1452 @ ( ap @ X1451 @ X1452 @ X1453 ) )
= X1453 ) )
=> ( ! [X1454: $i,X1455: $o,X1456: $i] :
( ( in @ X1456 @ X1454 )
=> ! [X1457: $i] :
( ( in @ X1457 @ X1454 )
=> ( ~ X1455
=> ( in @ X1457
@ ( dsetconstr @ X1454
@ ^ [Z0: $i] :
( ( X1455
& ( Z0 = X1456 ) )
| ( ~ X1455
& ( Z0 = X1457 ) ) ) ) ) ) ) )
=> ( ! [X1458: $i,X1459: $o,X1460: $i] :
( ( in @ X1460 @ X1458 )
=> ! [X1461: $i] :
( ( in @ X1461 @ X1458 )
=> ( ~ X1459
=> ( ( dsetconstr @ X1458
@ ^ [Z0: $i] :
( ( X1459
& ( Z0 = X1460 ) )
| ( ~ X1459
& ( Z0 = X1461 ) ) ) )
= ( setadjoin @ X1461 @ emptyset ) ) ) ) )
=> ( ! [X1462: $i,X1463: $o,X1464: $i] :
( ( in @ X1464 @ X1462 )
=> ! [X1465: $i] :
( ( in @ X1465 @ X1462 )
=> ( X1463
=> ( in @ X1464
@ ( dsetconstr @ X1462
@ ^ [Z0: $i] :
( ( X1463
& ( Z0 = X1464 ) )
| ( ~ X1463
& ( Z0 = X1465 ) ) ) ) ) ) ) )
=> ( ! [X1466: $i,X1467: $o,X1468: $i] :
( ( in @ X1468 @ X1466 )
=> ! [X1469: $i] :
( ( in @ X1469 @ X1466 )
=> ( X1467
=> ( ( dsetconstr @ X1466
@ ^ [Z0: $i] :
( ( X1467
& ( Z0 = X1468 ) )
| ( ~ X1467
& ( Z0 = X1469 ) ) ) )
= ( setadjoin @ X1468 @ emptyset ) ) ) ) )
=> ( ! [X1470: $i,X1471: $o,X1472: $i] :
( ( in @ X1472 @ X1470 )
=> ! [X1473: $i] :
( ( in @ X1473 @ X1470 )
=> ( singleton
@ ( dsetconstr @ X1470
@ ^ [Z0: $i] :
( ( X1471
& ( Z0 = X1472 ) )
| ( ~ X1471
& ( Z0 = X1473 ) ) ) ) ) ) )
=> ( ! [X1474: $i,X1475: $o,X1476: $i] :
( ( in @ X1476 @ X1474 )
=> ! [X1477: $i] :
( ( in @ X1477 @ X1474 )
=> ( in @ ( if @ X1474 @ X1475 @ X1476 @ X1477 ) @ X1474 ) ) )
=> ( ! [X1478: $i] :
( ( singleton @ X1478 )
=> ! [X1479: $i] :
( ( in @ X1479 @ X1478 )
=> ( ( setunion @ X1478 )
= X1479 ) ) )
=> ( ! [X1480: $i,X1481: $o,X1482: $i] :
( ( in @ X1482 @ X1480 )
=> ! [X1483: $i] :
( ( in @ X1483 @ X1480 )
=> ( X1481
=> ( ( if @ X1480 @ X1481 @ X1482 @ X1483 )
= X1482 ) ) ) )
=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X47
=> ( ( if @ X4 @ X47 @ X2 @ X3 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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forcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_277]),c_0_278]),c_0_279]),c_0_280]),singletonsuniq]),setukpairinjL1]),c_0_281]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_282]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_283]),c_0_284]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),c_0_291]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_292]),c_0_293]),c_0_294]),c_0_295]),c_0_296]),c_0_297]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_298]),c_0_299]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_300]),c_0_301]),c_0_302]),c_0_303]),c_0_304]),c_0_305]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),ifp]),theeq]),iftrue])])]),c_0_310]) ).
thf(c_0_312,plain,
! [X1484: $i,X1485: $o,X1486: $i,X1487: $i] :
( ( if @ X1484 @ X1485 @ X1486 @ X1487 )
= ( setunion
@ ( dsetconstr @ X1484
@ ^ [Z0: $i] :
( ( X1485
& ( Z0 = X1486 ) )
| ( ~ X1485
& ( Z0 = X1487 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])]) ).
thf(c_0_313,negated_conjecture,
! [X1492: $i,X1493: $i,X1495: $i,X1496: $i,X1497: $i,X1498: $i,X1499: $i,X1500: $i,X1501: $i,X1502: $i,X1503: $i,X1505: $i,X1506: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1512: $i,X1514: $i,X1515: $i > $i > $o,X1516: $i,X1518: $i,X1521: $i,X1523: $i,X1524: $i,X1525: $i,X1526: $i,X1528: $i,X1529: $i > $o,X1530: $i,X1532: $i,X1533: $i > $o,X1534: $i,X1535: $i,X1536: $i > $o,X1537: $i,X1538: $i,X1539: $i > $o,X1540: $i,X1541: $i > $o,X1542: $i,X1545: $i,X1546: $o,X1547: $i,X1548: $i,X1549: $o,X1550: $i,X1551: $i,X1552: $i > $o,X1553: $i,X1556: $i,X1557: $i,X1560: $i,X1562: $i,X1564: $i,X1565: $i > $o,X1566: $i,X1567: $i,X1569: $i,X1570: $i > $o,X1571: $i,X1572: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $i,X1580: $i,X1581: $i,X1582: $o,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $i,X1600: $o,X1602: $i,X1603: $i,X1604: $i > $o,X1605: $i,X1608: $i,X1609: $i,X1610: $i,X1612: $i,X1613: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1626: $i,X1627: $i,X1628: $i > $o,X1629: $i,X1630: $i > $o,X1631: $i,X1632: $i,X1633: $i > $o,X1634: $i,X1636: $i,X1637: $i > $o,X1639: $i,X1640: $i,X1641: $i > $o,X1643: $i,X1644: $i,X1645: $i > $o,X1646: $i,X1648: $o,X1649: $o,X1650: $i,X1651: $i > $o,X1653: $i,X1654: $i,X1655: $i > $o,X1656: $i,X1658: $i > $o,X1659: $i,X1662: $i,X1663: $i > $o,X1664: $i,X1668: $i,X1669: $i > $o,X1670: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i > $o,X1683: $i,X1685: $i,X1686: $i,X1687: $i > $o,X1688: $i > $o,X1691: $i,X1694: $i,X1695: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i > $o,X1708: $i,X1710: $i,X1711: $i,X1712: $i > $o,X1713: $i > $o,X1716: $i,X1718: $i,X1720: $i,X1721: $i,X1722: $i > $o,X1723: $i > $o,X1726: $i,X1727: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i,X1772: $i,X1773: $i > $o,X1774: $i,X1775: $i > $o,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i,X1787: $o,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $i,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1814: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $o,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i > $o,X1930: $i,X1931: $i,X1932: $i > $o,X1934: $i,X1935: $i > $o,X1936: $i,X1938: $i,X1939: $i > $o,X1942: $i,X1943: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i,X1950: $i,X1951: $i,X1952: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i,X1988: $i,X1989: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i > $i > $o,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i > $i > $o,X2020: $i,X2021: $i,X2022: $i > $i > $o,X2023: $i,X2024: $i,X2025: $i > $i > $o,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i > $i > $o,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i > $i > $o,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i > $i > $o,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i > $i,X2069: $i,X2070: $i,X2071: $i > $i,X2073: $i,X2074: $i,X2075: $i > $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i > $o,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i > $o,X2090: $i,X2091: $i,X2092: $i > $o,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i > $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i > $i,X2164: $i,X2165: $i,X2166: $i > $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $o,X2174: $i,X2175: $i,X2176: $i,X2177: $o,X2178: $i,X2179: $i,X2180: $i,X2181: $o,X2182: $i,X2183: $i,X2184: $i,X2185: $o,X2186: $i,X2187: $i,X2188: $i,X2189: $o,X2190: $i,X2191: $i,X2192: $i,X2193: $o,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i,X2199: $o,X2200: $i,X2201: $i] :
( ( ~ ( in @ ( esk1_2 @ X1492 @ X1493 ) @ X1492 )
| ~ ( in @ ( esk1_2 @ X1492 @ X1493 ) @ X1493 )
| ( X1492 = X1493 ) )
& ( ( in @ ( esk1_2 @ X1492 @ X1493 ) @ X1492 )
| ( in @ ( esk1_2 @ X1492 @ X1493 ) @ X1493 )
| ( X1492 = X1493 ) )
& ~ ( in @ X1495 @ emptyset )
& ( ~ ( in @ X1498 @ ( setadjoin @ X1496 @ X1497 ) )
| ( X1498 = X1496 )
| ( in @ X1498 @ X1497 ) )
& ( ( X1498 != X1496 )
| ( in @ X1498 @ ( setadjoin @ X1496 @ X1497 ) ) )
& ( ~ ( in @ X1498 @ X1497 )
| ( in @ X1498 @ ( setadjoin @ X1496 @ X1497 ) ) )
& ( ~ ( in @ X1500 @ ( powerset @ X1499 ) )
| ~ ( in @ X1501 @ X1500 )
| ( in @ X1501 @ X1499 ) )
& ( ( in @ ( esk2_2 @ X1502 @ X1503 ) @ X1503 )
| ( in @ X1503 @ ( powerset @ X1502 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1502 @ X1503 ) @ X1502 )
| ( in @ X1503 @ ( powerset @ X1502 ) ) )
& ( ( in @ X1506 @ ( esk3_2 @ X1505 @ X1506 ) )
| ~ ( in @ X1506 @ ( setunion @ X1505 ) ) )
& ( ( in @ ( esk3_2 @ X1505 @ X1506 ) @ X1505 )
| ~ ( in @ X1506 @ ( setunion @ X1505 ) ) )
& ( ~ ( in @ X1509 @ X1510 )
| ~ ( in @ X1510 @ X1508 )
| ( in @ X1509 @ ( setunion @ X1508 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1511 @ omega )
| ( in @ ( setadjoin @ X1511 @ X1511 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1512 ) @ omega )
| ~ ( in @ emptyset @ X1512 )
| ~ ( in @ X1514 @ omega )
| ( in @ X1514 @ X1512 ) )
& ( ( in @ ( esk4_1 @ X1512 ) @ X1512 )
| ~ ( in @ emptyset @ X1512 )
| ~ ( in @ X1514 @ omega )
| ( in @ X1514 @ X1512 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1512 ) @ ( esk4_1 @ X1512 ) ) @ X1512 )
| ~ ( in @ emptyset @ X1512 )
| ~ ( in @ X1514 @ omega )
| ( in @ X1514 @ X1512 ) )
& ( ( in @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1516 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( in @ ( esk5_2 @ X1515 @ X1516 ) @ X1516 ) )
& ( ( X1515 @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1521 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( in @ ( esk5_2 @ X1515 @ X1516 ) @ X1516 ) )
& ( ~ ( in @ X1524 @ X1516 )
| ~ ( X1515 @ X1524 @ X1523 )
| ( in @ X1523 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( in @ ( esk5_2 @ X1515 @ X1516 ) @ X1516 ) )
& ( ( in @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1516 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ( X1515 @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1521 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ~ ( in @ X1524 @ X1516 )
| ~ ( X1515 @ X1524 @ X1523 )
| ( in @ X1523 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ( in @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1516 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1518
!= ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ( X1515 @ ( esk8_3 @ X1515 @ X1516 @ X1521 ) @ X1521 )
| ~ ( in @ X1521 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1518
!= ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ~ ( in @ X1524 @ X1516 )
| ~ ( X1515 @ X1524 @ X1523 )
| ( in @ X1523 @ ( esk7_2 @ X1515 @ X1516 ) )
| ( X1518
!= ( esk6_3 @ X1515 @ X1516 @ X1518 ) )
| ~ ( X1515 @ ( esk5_2 @ X1515 @ X1516 ) @ X1518 ) )
& ( ( in @ ( esk9_1 @ X1525 ) @ X1525 )
| ~ ( in @ X1526 @ X1525 ) )
& ( ~ ( in @ X1528 @ ( esk9_1 @ X1525 ) )
| ~ ( in @ X1528 @ X1525 )
| ~ ( in @ X1526 @ X1525 ) )
& epred1_0
& ( ( X1529 @ ( esk10_2 @ X1529 @ X1530 ) )
| ~ ( X1529 @ X1530 )
| ( X1529 @ ( descr @ X1529 ) ) )
& ( ( X1530
!= ( esk10_2 @ X1529 @ X1530 ) )
| ~ ( X1529 @ X1530 )
| ( X1529 @ ( descr @ X1529 ) ) )
& ( ~ ( in @ X1534 @ X1532 )
| ~ ( X1533 @ X1534 )
| ( in @ X1534 @ ( dsetconstr @ X1532 @ X1533 ) ) )
& ( ~ ( in @ X1537 @ ( dsetconstr @ X1535 @ X1536 ) )
| ( in @ X1537 @ X1535 ) )
& ( ~ ( in @ X1540 @ ( dsetconstr @ X1538 @ X1539 ) )
| ( X1539 @ X1540 ) )
& ( ( X1541 @ ( esk12_1 @ X1541 ) )
| ( X1541 @ ( esk11_2 @ X1541 @ X1542 ) )
| ~ ( X1541 @ X1542 ) )
& ( ~ ( X1541 @ X1545 )
| ( ( esk12_1 @ X1541 )
= X1545 )
| ( X1541 @ ( esk11_2 @ X1541 @ X1542 ) )
| ~ ( X1541 @ X1542 ) )
& ( ( X1541 @ ( esk12_1 @ X1541 ) )
| ( X1542
!= ( esk11_2 @ X1541 @ X1542 ) )
| ~ ( X1541 @ X1542 ) )
& ( ~ ( X1541 @ X1545 )
| ( ( esk12_1 @ X1541 )
= X1545 )
| ( X1542
!= ( esk11_2 @ X1541 @ X1542 ) )
| ~ ( X1541 @ X1542 ) )
& ( ~ ( in @ X1547 @ ( prop2set @ X1546 ) )
| X1546 )
& ( ~ ( in @ X1548 @ emptyset )
| X1549 )
& ( ~ ( in @ X1550 @ emptyset )
| ~ $true )
& ~ ( in @ X1551 @ emptyset )
& ( ( X1552 @ ( esk13_2 @ X1552 @ X1553 ) )
| ~ ( X1552 @ X1553 )
| ( X1552 @ ( esk14_1 @ X1552 ) ) )
& ( ( X1553
!= ( esk13_2 @ X1552 @ X1553 ) )
| ~ ( X1552 @ X1553 )
| ( X1552 @ ( esk14_1 @ X1552 ) ) )
& ( ( in @ ( esk16_2 @ X1556 @ X1557 ) @ X1557 )
| ( X1556 = X1557 )
| ( in @ ( esk15_2 @ X1556 @ X1557 ) @ X1556 ) )
& ( ~ ( in @ ( esk16_2 @ X1556 @ X1557 ) @ X1556 )
| ( X1556 = X1557 )
| ( in @ ( esk15_2 @ X1556 @ X1557 ) @ X1556 ) )
& ( ( in @ ( esk16_2 @ X1556 @ X1557 ) @ X1557 )
| ( X1556 = X1557 )
| ~ ( in @ ( esk15_2 @ X1556 @ X1557 ) @ X1557 ) )
& ( ~ ( in @ ( esk16_2 @ X1556 @ X1557 ) @ X1556 )
| ( X1556 = X1557 )
| ~ ( in @ ( esk15_2 @ X1556 @ X1557 ) @ X1557 ) )
& ( ( in @ ( esk17_1 @ X1560 ) @ X1560 )
| ( X1560 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1562 ) @ X1562 )
| ( X1562 = emptyset ) )
& ( ~ ( in @ X1566 @ ( dsetconstr @ X1564 @ X1565 ) )
| ( X1565 @ X1566 )
| ~ ( in @ X1566 @ X1564 ) )
& ( ~ ( X1565 @ X1566 )
| ( in @ X1566 @ ( dsetconstr @ X1564 @ X1565 ) )
| ~ ( in @ X1566 @ X1564 ) )
& ( ( X1567 = emptyset )
| ( in @ ( esk19_1 @ X1567 ) @ X1567 ) )
& ( ~ ( in @ X1571 @ X1569 )
| ~ ( X1570 @ X1571 )
| ( ( dsetconstr @ X1569 @ X1570 )
!= emptyset ) )
& ( ~ ( in @ X1573 @ X1572 )
| ( X1572 != emptyset ) )
& ( in @ X1574 @ ( setadjoin @ X1574 @ X1575 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1578 @ X1577 )
| ( in @ X1578 @ ( setadjoin @ X1576 @ X1577 ) ) )
& ( ( in @ X1581 @ X1580 )
| X1582
| ( X1581 = X1579 )
| ~ ( in @ X1581 @ ( setadjoin @ X1579 @ X1580 ) ) )
& ( ~ X1582
| X1582
| ( X1581 = X1579 )
| ~ ( in @ X1581 @ ( setadjoin @ X1579 @ X1580 ) ) )
& ( ( in @ X1581 @ X1580 )
| X1582
| ~ X1582
| ~ ( in @ X1581 @ ( setadjoin @ X1579 @ X1580 ) ) )
& ( ~ X1582
| X1582
| ~ X1582
| ~ ( in @ X1581 @ ( setadjoin @ X1579 @ X1580 ) ) )
& ( ~ ( in @ X1585 @ ( setadjoin @ X1583 @ X1584 ) )
| ( X1585 = X1583 )
| ( in @ X1585 @ X1584 ) )
& ( ( dsetconstr @ X1586
@ ^ [Z0: $i] : $true )
= X1586 )
& ( ( in @ ( esk20_2 @ X1587 @ X1588 ) @ X1588 )
| ( in @ X1588 @ ( powerset @ X1587 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1587 @ X1588 ) @ X1587 )
| ( in @ X1588 @ ( powerset @ X1587 ) ) )
& ( in @ emptyset @ ( powerset @ X1590 ) )
& ( in @ emptyset @ ( powerset @ X1591 ) )
& ( ~ ( in @ X1593 @ ( powerset @ X1592 ) )
| ~ ( in @ X1594 @ X1593 )
| ( in @ X1594 @ X1592 ) )
& ( ~ ( in @ X1596 @ X1597 )
| ~ ( in @ X1597 @ X1595 )
| ( in @ X1596 @ ( setunion @ X1595 ) ) )
& ( ( in @ X1599 @ ( esk21_3 @ X1598 @ X1599 @ X1600 ) )
| X1600
| ~ ( in @ X1599 @ ( setunion @ X1598 ) ) )
& ( ( in @ ( esk21_3 @ X1598 @ X1599 @ X1600 ) @ X1598 )
| X1600
| ~ ( in @ X1599 @ ( setunion @ X1598 ) ) )
& ( ~ X1600
| X1600
| ~ ( in @ X1599 @ ( setunion @ X1598 ) ) )
& ( ~ ( in @ X1603 @ X1602 )
| ( in @ X1603 @ ( powerset @ ( setunion @ X1602 ) ) ) )
& ( ~ ( X1604 @ X1608 )
| ( X1608
= ( esk23_1 @ X1604 ) )
| ( X1604 @ ( esk22_2 @ X1604 @ X1605 ) )
| ~ ( X1604 @ X1605 ) )
& ( ( X1609
!= ( esk23_1 @ X1604 ) )
| ( X1604 @ X1609 )
| ( X1604 @ ( esk22_2 @ X1604 @ X1605 ) )
| ~ ( X1604 @ X1605 ) )
& ( ~ ( X1604 @ X1608 )
| ( X1608
= ( esk23_1 @ X1604 ) )
| ( X1605
!= ( esk22_2 @ X1604 @ X1605 ) )
| ~ ( X1604 @ X1605 ) )
& ( ( X1609
!= ( esk23_1 @ X1604 ) )
| ( X1604 @ X1609 )
| ( X1605
!= ( esk22_2 @ X1604 @ X1605 ) )
| ~ ( X1604 @ X1605 ) )
& ( ( in @ ( esk24_1 @ X1610 ) @ X1610 )
| ( X1610 = emptyset ) )
& ( $true
| ( X1610 = emptyset ) )
& ( ~ ( in @ X1612 @ ( setadjoin @ X1613 @ emptyset ) )
| ( X1612 = X1613 ) )
& ( ( X1614 = X1615 )
| ~ ( in @ X1615 @ ( setadjoin @ X1614 @ emptyset ) ) )
& ( ( X1616 != X1617 )
| ( in @ X1616 @ ( setadjoin @ X1617 @ emptyset ) ) )
& ( ~ ( in @ X1618 @ ( setadjoin @ X1619 @ emptyset ) )
| ( in @ X1619 @ ( setadjoin @ X1618 @ emptyset ) ) )
& ( ~ ( in @ X1622 @ ( setadjoin @ X1620 @ ( setadjoin @ X1621 @ emptyset ) ) )
| ( X1622 = X1620 )
| ( X1622 = X1621 ) )
& ( in @ X1623 @ ( setadjoin @ X1623 @ ( setadjoin @ X1624 @ emptyset ) ) )
& ( in @ X1626 @ ( setadjoin @ X1625 @ ( setadjoin @ X1626 @ emptyset ) ) )
& ( ~ ( in @ X1629 @ X1627 )
| ~ ( X1628 @ X1629 )
| ( ( dsetconstr @ X1627 @ X1628 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1631 @ emptyset )
| ( X1630 @ X1631 ) )
& ( ( in @ ( esk25_2 @ X1632 @ X1633 ) @ X1632 )
| ~ ( in @ X1634 @ X1632 )
| ( X1633 @ X1634 ) )
& ( ~ ( X1633 @ ( esk25_2 @ X1632 @ X1633 ) )
| ~ ( in @ X1634 @ X1632 )
| ( X1633 @ X1634 ) )
& ( ( in @ ( esk26_2 @ X1636 @ X1637 ) @ X1636 )
| ~ ( in @ X1639 @ X1636 )
| ~ ( X1637 @ X1639 ) )
& ( ( X1637 @ ( esk26_2 @ X1636 @ X1637 ) )
| ~ ( in @ X1639 @ X1636 )
| ~ ( X1637 @ X1639 ) )
& ( ( in @ ( esk27_2 @ X1640 @ X1641 ) @ X1640 )
| ~ ( in @ X1643 @ X1640 )
| ~ ( X1641 @ X1643 ) )
& ( ( X1641 @ ( esk27_2 @ X1640 @ X1641 ) )
| ~ ( in @ X1643 @ X1640 )
| ~ ( X1641 @ X1643 ) )
& ( ( in @ ( esk28_2 @ X1644 @ X1645 ) @ X1644 )
| ~ ( in @ X1646 @ X1644 )
| ( X1645 @ X1646 ) )
& ( ~ ( X1645 @ ( esk28_2 @ X1644 @ X1645 ) )
| ~ ( in @ X1646 @ X1644 )
| ( X1645 @ X1646 ) )
& ( ~ X1648
| ( in @ emptyset @ ( prop2set @ X1648 ) ) )
& ( ~ X1649
| ( set2prop @ ( prop2set @ X1649 ) ) )
& ( ( in @ ( esk29_2 @ X1650 @ X1651 ) @ X1650 )
| ~ ( in @ X1653 @ X1650 )
| ~ ( X1651 @ X1653 ) )
& ( ( X1651 @ ( esk29_2 @ X1650 @ X1651 ) )
| ~ ( in @ X1653 @ X1650 )
| ~ ( X1651 @ X1653 ) )
& ( ( in @ ( esk30_2 @ X1654 @ X1655 ) @ X1654 )
| ~ ( in @ X1656 @ X1654 )
| ( X1655 @ X1656 ) )
& ( ~ ( X1655 @ ( esk30_2 @ X1654 @ X1655 ) )
| ~ ( in @ X1656 @ X1654 )
| ( X1655 @ X1656 ) )
& ( ( X1658 @ ( esk32_1 @ X1658 ) )
| ( X1658 @ ( esk31_2 @ X1658 @ X1659 ) )
| ~ ( X1658 @ X1659 ) )
& ( ~ ( X1658 @ X1662 )
| ( ( esk32_1 @ X1658 )
= X1662 )
| ( X1658 @ ( esk31_2 @ X1658 @ X1659 ) )
| ~ ( X1658 @ X1659 ) )
& ( ( X1658 @ ( esk32_1 @ X1658 ) )
| ( X1659
!= ( esk31_2 @ X1658 @ X1659 ) )
| ~ ( X1658 @ X1659 ) )
& ( ~ ( X1658 @ X1662 )
| ( ( esk32_1 @ X1658 )
= X1662 )
| ( X1659
!= ( esk31_2 @ X1658 @ X1659 ) )
| ~ ( X1658 @ X1659 ) )
& ( ( X1663 @ ( esk35_1 @ X1663 ) )
| ( X1663 @ ( esk33_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ~ ( X1663 @ X1668 )
| ( ( esk35_1 @ X1663 )
= X1668 )
| ( X1663 @ ( esk33_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ( X1663 @ ( esk35_1 @ X1663 ) )
| ( X1663 @ ( esk34_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ~ ( X1663 @ X1668 )
| ( ( esk35_1 @ X1663 )
= X1668 )
| ( X1663 @ ( esk34_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ( X1663 @ ( esk35_1 @ X1663 ) )
| ( ( esk33_1 @ X1663 )
!= ( esk34_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ~ ( X1663 @ X1668 )
| ( ( esk35_1 @ X1663 )
= X1668 )
| ( ( esk33_1 @ X1663 )
!= ( esk34_1 @ X1663 ) )
| ~ ( X1663 @ X1664 ) )
& ( ( X1669 @ ( esk37_1 @ X1669 ) )
| ~ ( X1669 @ ( esk36_2 @ X1669 @ X1670 ) )
| ( ( esk36_2 @ X1669 @ X1670 )
!= X1670 ) )
& ( ~ ( X1669 @ X1673 )
| ( ( esk37_1 @ X1669 )
= X1673 )
| ~ ( X1669 @ ( esk36_2 @ X1669 @ X1670 ) )
| ( ( esk36_2 @ X1669 @ X1670 )
!= X1670 ) )
& ( ( X1669 @ ( esk37_1 @ X1669 ) )
| ( X1669 @ ( esk36_2 @ X1669 @ X1670 ) )
| ( ( esk36_2 @ X1669 @ X1670 )
= X1670 ) )
& ( ~ ( X1669 @ X1673 )
| ( ( esk37_1 @ X1669 )
= X1673 )
| ( X1669 @ ( esk36_2 @ X1669 @ X1670 ) )
| ( ( esk36_2 @ X1669 @ X1670 )
= X1670 ) )
& ( ( X1674 != X1675 )
| ( X1676 != X1677 )
| ~ ( in @ X1676 @ X1674 )
| ( in @ X1677 @ X1675 ) )
& ( ~ ( in @ X1680 @ X1678 )
| ( in @ X1681 @ X1679 )
| ( X1680 != X1681 )
| ( X1678 != X1679 ) )
& ( ~ ( in @ X1681 @ X1679 )
| ( in @ X1680 @ X1678 )
| ( X1680 != X1681 )
| ( X1678 != X1679 ) )
& ( ( X1682 @ ( esk38_2 @ X1682 @ X1683 ) )
| ~ ( X1682 @ X1683 )
| ~ ( X1682 @ X1685 )
| ~ ( X1682 @ X1686 )
| ( X1685 = X1686 ) )
& ( ( X1683
!= ( esk38_2 @ X1682 @ X1683 ) )
| ~ ( X1682 @ X1683 )
| ~ ( X1682 @ X1685 )
| ~ ( X1682 @ X1686 )
| ( X1685 = X1686 ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( ( esk39_2 @ X1687 @ X1688 )
= ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ~ ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ~ ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1687 @ ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1688 @ ( esk42_2 @ X1687 @ X1688 ) )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1688 @ X1694 )
| ( ( esk42_2 @ X1687 @ X1688 )
= X1694 )
| ( X1691
!= ( esk41_3 @ X1687 @ X1688 @ X1691 ) )
| ~ ( X1687 @ X1691 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1688 @ ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ( X1687 @ ( esk44_2 @ X1687 @ X1688 ) )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( ~ ( X1687 @ X1698 )
| ( ( esk44_2 @ X1687 @ X1688 )
= X1698 )
| ( X1695
!= ( esk43_3 @ X1687 @ X1688 @ X1695 ) )
| ~ ( X1688 @ X1695 )
| ( X1687 @ ( esk39_2 @ X1687 @ X1688 ) )
| ( X1688 @ ( esk40_2 @ X1687 @ X1688 ) ) )
& ( emptyset = emptyset )
& ( ( X1699 != X1700 )
| ( X1701 != X1702 )
| ( ( setadjoin @ X1699 @ X1701 )
= ( setadjoin @ X1700 @ X1702 ) ) )
& ( ( X1703 != X1704 )
| ( ( powerset @ X1703 )
= ( powerset @ X1704 ) ) )
& ( ( X1705 != X1706 )
| ( ( setunion @ X1705 )
= ( setunion @ X1706 ) ) )
& ( omega = omega )
& ( ( X1707 @ ( esk45_2 @ X1707 @ X1708 ) )
| ~ ( X1707 @ X1708 )
| ~ ( X1707 @ X1710 )
| ~ ( X1707 @ X1711 )
| ( X1710 = X1711 ) )
& ( ( X1708
!= ( esk45_2 @ X1707 @ X1708 ) )
| ~ ( X1707 @ X1708 )
| ~ ( X1707 @ X1710 )
| ~ ( X1707 @ X1711 )
| ( X1710 = X1711 ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( ( esk46_2 @ X1712 @ X1713 )
= ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( ( esk46_2 @ X1712 @ X1713 )
= ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( ( esk46_2 @ X1712 @ X1713 )
= ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( ( esk46_2 @ X1712 @ X1713 )
= ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ~ ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ~ ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ~ ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ~ ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ~ ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ~ ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ~ ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ~ ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1712 @ ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1713 @ ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( X1718
!= ( esk49_3 @ X1712 @ X1713 @ X1718 ) )
| ~ ( X1713 @ X1718 )
| ( ( descr @ X1712 )
= ( descr @ X1713 ) )
| ( X1716
!= ( esk48_3 @ X1712 @ X1713 @ X1716 ) )
| ~ ( X1712 @ X1716 )
| ( X1712 @ ( esk46_2 @ X1712 @ X1713 ) )
| ( X1713 @ ( esk47_2 @ X1712 @ X1713 ) ) )
& ( ( in @ ( esk50_4 @ X1720 @ X1721 @ X1722 @ X1723 ) @ X1720 )
| ( ( dsetconstr @ X1720 @ X1722 )
= ( dsetconstr @ X1721 @ X1723 ) )
| ( X1720 != X1721 ) )
& ( ( in @ ( esk51_4 @ X1720 @ X1721 @ X1722 @ X1723 ) @ X1721 )
| ( ( dsetconstr @ X1720 @ X1722 )
= ( dsetconstr @ X1721 @ X1723 ) )
| ( X1720 != X1721 ) )
& ( ( ( esk50_4 @ X1720 @ X1721 @ X1722 @ X1723 )
= ( esk51_4 @ X1720 @ X1721 @ X1722 @ X1723 ) )
| ( ( dsetconstr @ X1720 @ X1722 )
= ( dsetconstr @ X1721 @ X1723 ) )
| ( X1720 != X1721 ) )
& ( ~ ( X1722 @ ( esk50_4 @ X1720 @ X1721 @ X1722 @ X1723 ) )
| ~ ( X1723 @ ( esk51_4 @ X1720 @ X1721 @ X1722 @ X1723 ) )
| ( ( dsetconstr @ X1720 @ X1722 )
= ( dsetconstr @ X1721 @ X1723 ) )
| ( X1720 != X1721 ) )
& ( ( X1722 @ ( esk50_4 @ X1720 @ X1721 @ X1722 @ X1723 ) )
| ( X1723 @ ( esk51_4 @ X1720 @ X1721 @ X1722 @ X1723 ) )
| ( ( dsetconstr @ X1720 @ X1722 )
= ( dsetconstr @ X1721 @ X1723 ) )
| ( X1720 != X1721 ) )
& ( ( in @ ( esk52_2 @ X1726 @ X1727 ) @ X1726 )
| ( subset @ X1726 @ X1727 ) )
& ( ~ ( in @ ( esk52_2 @ X1726 @ X1727 ) @ X1727 )
| ( subset @ X1726 @ X1727 ) )
& ( ( X1729 != X1730 )
| ( subset @ X1730 @ X1729 ) )
& ( ( X1731 != X1732 )
| ( subset @ X1731 @ X1732 ) )
& ( ( in @ ( esk53_2 @ X1733 @ X1734 ) @ X1733 )
| ( subset @ X1733 @ X1734 ) )
& ( ~ ( in @ ( esk53_2 @ X1733 @ X1734 ) @ X1734 )
| ( subset @ X1733 @ X1734 ) )
& ( subset @ emptyset @ X1736 )
& ( ~ ( subset @ X1737 @ X1738 )
| ~ ( in @ X1739 @ X1737 )
| ( in @ X1739 @ X1738 ) )
& ( ~ ( subset @ X1740 @ X1741 )
| ( in @ X1742 @ X1741 )
| ~ ( in @ X1742 @ X1740 ) )
& ( ~ ( in @ X1745 @ X1743 )
| ( in @ X1745 @ X1744 )
| ~ ( subset @ X1743 @ X1744 ) )
& ( ( subset @ X1746 @ X1747 )
| ( X1746 != X1747 ) )
& ( ~ ( in @ X1750 @ X1748 )
| ( in @ X1750 @ X1749 )
| ( X1748 != X1749 ) )
& ( subset @ X1751 @ X1751 )
& ( ~ ( subset @ X1752 @ X1753 )
| ~ ( subset @ X1753 @ X1754 )
| ( subset @ X1752 @ X1754 ) )
& ( subset @ X1756 @ ( setadjoin @ X1755 @ X1756 ) )
& ( ~ ( subset @ X1757 @ X1759 )
| ( subset @ X1757 @ ( setadjoin @ X1758 @ X1759 ) ) )
& ( ~ ( subset @ X1760 @ X1761 )
| ( in @ X1760 @ ( powerset @ X1761 ) ) )
& ( ~ ( subset @ X1762 @ X1763 )
| ~ ( subset @ X1763 @ X1762 )
| ( X1762 = X1763 ) )
& ( ~ ( subset @ X1764 @ emptyset )
| ( X1764 = emptyset ) )
& ( ~ ( subset @ X1766 @ X1765 )
| ( in @ X1766 @ ( powerset @ X1765 ) ) )
& ( ~ ( in @ X1768 @ ( powerset @ X1767 ) )
| ( subset @ X1768 @ X1767 ) )
& ( in @ X1769 @ ( powerset @ X1769 ) )
& ( ~ ( subset @ X1770 @ X1771 )
| ( subset @ ( powerset @ X1770 ) @ ( powerset @ X1771 ) ) )
& ( in @ ( dsetconstr @ X1772 @ X1773 ) @ ( powerset @ X1772 ) )
& ( subset @ ( dsetconstr @ X1774 @ X1775 ) @ X1774 )
& ( ~ ( in @ X1778 @ X1776 )
| ( in @ X1778 @ ( binunion @ X1776 @ X1777 ) ) )
& ( in @ X1780 @ ( setadjoin @ X1779 @ ( setadjoin @ X1780 @ emptyset ) ) )
& ( ~ ( in @ X1783 @ X1782 )
| ( in @ X1783 @ ( binunion @ X1781 @ X1782 ) ) )
& ( ( in @ X1786 @ X1785 )
| X1787
| ( in @ X1786 @ X1784 )
| ~ ( in @ X1786 @ ( binunion @ X1784 @ X1785 ) ) )
& ( ~ X1787
| X1787
| ( in @ X1786 @ X1784 )
| ~ ( in @ X1786 @ ( binunion @ X1784 @ X1785 ) ) )
& ( ( in @ X1786 @ X1785 )
| X1787
| ~ X1787
| ~ ( in @ X1786 @ ( binunion @ X1784 @ X1785 ) ) )
& ( ~ X1787
| X1787
| ~ X1787
| ~ ( in @ X1786 @ ( binunion @ X1784 @ X1785 ) ) )
& ( ~ ( in @ X1790 @ ( binunion @ X1788 @ X1789 ) )
| ( in @ X1790 @ X1788 )
| ( in @ X1790 @ X1789 ) )
& ( subset @ X1791 @ ( binunion @ X1791 @ X1792 ) )
& ( subset @ X1794 @ ( binunion @ X1793 @ X1794 ) )
& ( ~ ( in @ X1797 @ X1795 )
| ~ ( in @ X1797 @ X1796 )
| ( in @ X1797 @ ( binintersect @ X1795 @ X1796 ) ) )
& ( ~ ( subset @ X1800 @ X1798 )
| ~ ( subset @ X1800 @ X1799 )
| ( subset @ X1800 @ ( binintersect @ X1798 @ X1799 ) ) )
& ( ~ ( in @ X1803 @ ( binintersect @ X1801 @ X1802 ) )
| ( in @ X1803 @ X1801 ) )
& ( subset @ ( binintersect @ X1804 @ X1805 ) @ X1804 )
& ( ~ ( subset @ X1806 @ X1807 )
| ( ( binintersect @ X1806 @ X1807 )
= X1806 ) )
& ( ( ( binintersect @ X1808 @ X1809 )
!= X1809 )
| ( subset @ X1809 @ X1808 ) )
& ( ~ ( in @ X1812 @ ( binintersect @ X1810 @ X1811 ) )
| ( in @ X1812 @ X1811 ) )
& ( ( in @ ( esk54_2 @ X1813 @ X1814 ) @ X1813 )
| ( ( binintersect @ X1813 @ X1814 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1813 @ X1814 ) @ X1814 )
| ( ( binintersect @ X1813 @ X1814 )
= emptyset ) )
& ( subset @ ( binintersect @ X1816 @ X1817 ) @ X1817 )
& ( ~ ( subset @ X1819 @ X1818 )
| ( ( binintersect @ X1818 @ X1819 )
= X1819 ) )
& ( ( ( binintersect @ X1820 @ X1821 )
!= X1820 )
| ( subset @ X1820 @ X1821 ) )
& ( ( binintersect @ X1822 @ ( binunion @ X1823 @ X1824 ) )
= ( binunion @ ( binintersect @ X1822 @ X1823 ) @ ( binintersect @ X1822 @ X1824 ) ) )
& ( ~ ( in @ X1827 @ X1825 )
| ( in @ X1827 @ X1826 )
| ( in @ X1827 @ ( setminus @ X1825 @ X1826 ) ) )
& ( ~ ( in @ X1830 @ ( setminus @ X1828 @ X1829 ) )
| ( in @ X1830 @ X1828 ) )
& ( ~ ( in @ X1833 @ ( setminus @ X1831 @ X1832 ) )
| ~ ( in @ X1833 @ X1832 ) )
& ( ~ ( subset @ X1834 @ X1835 )
| ( ( setminus @ X1834 @ X1835 )
= emptyset ) )
& ( ( in @ X1838 @ ( setminus @ X1836 @ X1837 ) )
| ~ ( in @ X1838 @ X1836 )
| ( in @ X1838 @ X1837 ) )
& ( ( in @ X1841 @ ( setminus @ X1839 @ X1840 ) )
| ( in @ X1841 @ X1840 )
| ~ ( in @ X1841 @ X1839 ) )
& ( ( in @ X1844 @ X1842 )
| ~ ( in @ X1844 @ ( setminus @ X1842 @ X1843 ) ) )
& ( ~ ( in @ X1847 @ X1846 )
| ~ ( in @ X1847 @ ( setminus @ X1845 @ X1846 ) ) )
& ( subset @ ( setminus @ X1848 @ X1849 ) @ X1848 )
& ( ( ( setminus @ X1850 @ X1851 )
!= emptyset )
| ( subset @ X1850 @ X1851 ) )
& ( ~ ( in @ X1854 @ X1852 )
| X1855
| ( in @ X1854 @ X1852 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ( in @ X1854 @ X1853 )
| X1855
| ( in @ X1854 @ X1852 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ X1855
| X1855
| ( in @ X1854 @ X1852 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ ( in @ X1854 @ X1852 )
| X1855
| ~ ( in @ X1854 @ X1853 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ( in @ X1854 @ X1853 )
| X1855
| ~ ( in @ X1854 @ X1853 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ X1855
| X1855
| ~ ( in @ X1854 @ X1853 )
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ ( in @ X1854 @ X1852 )
| X1855
| ~ X1855
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ( in @ X1854 @ X1853 )
| X1855
| ~ X1855
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ X1855
| X1855
| ~ X1855
| ~ ( in @ X1854 @ ( symdiff @ X1852 @ X1853 ) ) )
& ( ~ ( in @ X1858 @ X1856 )
| ( in @ X1858 @ X1857 )
| ( in @ X1858 @ ( symdiff @ X1856 @ X1857 ) ) )
& ( ( in @ X1861 @ X1859 )
| ~ ( in @ X1861 @ X1860 )
| ( in @ X1861 @ ( symdiff @ X1859 @ X1860 ) ) )
& ( ~ ( in @ X1864 @ X1862 )
| ~ ( in @ X1864 @ X1863 )
| ~ ( in @ X1864 @ ( symdiff @ X1862 @ X1863 ) ) )
& ( ( in @ X1867 @ X1865 )
| ( in @ X1867 @ X1866 )
| ~ ( in @ X1867 @ ( symdiff @ X1865 @ X1866 ) ) )
& ( in @ X1869 @ ( setadjoin @ X1868 @ ( setadjoin @ X1869 @ emptyset ) ) )
& ( in @ X1870 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1870 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1870 @ ( setadjoin @ X1871 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1873 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1872 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1872 @ ( setadjoin @ X1873 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1874 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1874 @ ( setadjoin @ X1875 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1876 @ X1877 ) )
& ( ~ ( in @ X1879 @ X1878 )
| ( subset @ ( setadjoin @ X1879 @ emptyset ) @ X1878 ) )
& ( ~ ( in @ X1881 @ X1880 )
| ( in @ ( setadjoin @ X1881 @ emptyset ) @ ( powerset @ X1880 ) ) )
& ( ~ ( in @ X1884 @ X1882 )
| ( in @ ( setadjoin @ X1884 @ emptyset ) @ ( powerset @ ( binunion @ X1882 @ X1883 ) ) ) )
& ( ~ ( in @ X1887 @ ( setadjoin @ X1885 @ ( setadjoin @ X1886 @ emptyset ) ) )
| ( X1887 = X1885 )
| ( X1887 = X1886 ) )
& ( ~ ( in @ X1890 @ X1888 )
| ~ ( in @ X1891 @ X1889 )
| ( subset @ ( setadjoin @ X1890 @ ( setadjoin @ X1891 @ emptyset ) ) @ ( binunion @ X1888 @ X1889 ) ) )
& ( ~ ( in @ X1894 @ X1892 )
| ~ ( in @ X1895 @ X1893 )
| ( in @ ( setadjoin @ X1894 @ ( setadjoin @ X1895 @ emptyset ) ) @ ( powerset @ ( binunion @ X1892 @ X1893 ) ) ) )
& ( ~ ( in @ X1898 @ X1896 )
| ~ ( in @ X1899 @ X1897 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1898 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1898 @ ( setadjoin @ X1899 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1896 @ X1897 ) ) ) )
& ( ~ ( in @ X1902 @ X1900 )
| ~ ( in @ X1903 @ X1901 )
| ( in @ ( setadjoin @ ( setadjoin @ X1902 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1902 @ ( setadjoin @ X1903 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1900 @ X1901 ) ) ) ) )
& ( ~ ( in @ X1906 @ X1904 )
| ~ ( in @ X1907 @ X1905 )
| ( in @ ( kpair @ X1906 @ X1907 ) @ ( powerset @ ( powerset @ ( binunion @ X1904 @ X1905 ) ) ) ) )
& ( ~ ( in @ X1910 @ X1908 )
| ~ ( in @ X1911 @ X1909 )
| ( in @ ( kpair @ X1910 @ X1911 ) @ ( cartprod @ X1908 @ X1909 ) ) )
& ( ( in @ ( esk55_3 @ X1912 @ X1913 @ X1914 ) @ X1912 )
| ~ ( in @ X1914 @ ( cartprod @ X1912 @ X1913 ) ) )
& ( ( in @ ( esk56_3 @ X1912 @ X1913 @ X1914 ) @ X1913 )
| ~ ( in @ X1914 @ ( cartprod @ X1912 @ X1913 ) ) )
& ( ( X1914
= ( kpair @ ( esk55_3 @ X1912 @ X1913 @ X1914 ) @ ( esk56_3 @ X1912 @ X1913 @ X1914 ) ) )
| ~ ( in @ X1914 @ ( cartprod @ X1912 @ X1913 ) ) )
& ( ~ ( in @ X1919 @ ( cartprod @ X1917 @ X1918 ) )
| ( iskpair @ X1919 ) )
& ( ( in @ ( esk57_2 @ X1920 @ X1921 ) @ X1920 )
| ~ ( in @ X1921 @ ( setunion @ X1920 ) ) )
& ( ( in @ X1921 @ ( esk57_2 @ X1920 @ X1921 ) )
| ~ ( in @ X1921 @ ( setunion @ X1920 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1923 @ emptyset ) ) @ X1923 )
& ( subset @ X1924 @ ( setunion @ ( setadjoin @ X1924 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1925 @ emptyset ) )
= X1925 )
& ( ( in @ ( esk58_2 @ X1926 @ X1927 ) @ X1926 )
| ~ ( in @ X1930 @ X1926 )
| ~ ( X1927 @ X1930 )
| ( singleton @ ( dsetconstr @ X1926 @ X1927 ) ) )
& ( ( in @ ( esk59_2 @ X1926 @ X1927 ) @ X1926 )
| ~ ( in @ X1930 @ X1926 )
| ~ ( X1927 @ X1930 )
| ( singleton @ ( dsetconstr @ X1926 @ X1927 ) ) )
& ( ( X1927 @ ( esk58_2 @ X1926 @ X1927 ) )
| ~ ( in @ X1930 @ X1926 )
| ~ ( X1927 @ X1930 )
| ( singleton @ ( dsetconstr @ X1926 @ X1927 ) ) )
& ( ( X1927 @ ( esk59_2 @ X1926 @ X1927 ) )
| ~ ( in @ X1930 @ X1926 )
| ~ ( X1927 @ X1930 )
| ( singleton @ ( dsetconstr @ X1926 @ X1927 ) ) )
& ( ( ( esk58_2 @ X1926 @ X1927 )
!= ( esk59_2 @ X1926 @ X1927 ) )
| ~ ( in @ X1930 @ X1926 )
| ~ ( X1927 @ X1930 )
| ( singleton @ ( dsetconstr @ X1926 @ X1927 ) ) )
& ( ( in @ ( esk60_2 @ X1931 @ X1932 ) @ X1931 )
| ~ ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
& ( ( X1932 @ ( esk60_2 @ X1931 @ X1932 ) )
| ~ ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
& ( ( in @ ( esk61_3 @ X1934 @ X1935 @ X1936 ) @ X1934 )
| ( singleton @ ( dsetconstr @ X1934 @ X1935 ) )
| ~ ( X1935 @ X1936 )
| ~ ( in @ X1936 @ X1934 ) )
& ( ( X1935 @ ( esk61_3 @ X1934 @ X1935 @ X1936 ) )
| ( singleton @ ( dsetconstr @ X1934 @ X1935 ) )
| ~ ( X1935 @ X1936 )
| ~ ( in @ X1936 @ X1934 ) )
& ( ( ( esk61_3 @ X1934 @ X1935 @ X1936 )
!= X1936 )
| ( singleton @ ( dsetconstr @ X1934 @ X1935 ) )
| ~ ( X1935 @ X1936 )
| ~ ( in @ X1936 @ X1934 ) )
& ( ( in @ ( esk62_2 @ X1938 @ X1939 ) @ X1938 )
| ~ ( in @ X1942 @ X1938 )
| ~ ( X1939 @ X1942 )
| ( singleton @ ( dsetconstr @ X1938 @ X1939 ) ) )
& ( ( in @ ( esk63_2 @ X1938 @ X1939 ) @ X1938 )
| ~ ( in @ X1942 @ X1938 )
| ~ ( X1939 @ X1942 )
| ( singleton @ ( dsetconstr @ X1938 @ X1939 ) ) )
& ( ( X1939 @ ( esk62_2 @ X1938 @ X1939 ) )
| ~ ( in @ X1942 @ X1938 )
| ~ ( X1939 @ X1942 )
| ( singleton @ ( dsetconstr @ X1938 @ X1939 ) ) )
& ( ( X1939 @ ( esk63_2 @ X1938 @ X1939 ) )
| ~ ( in @ X1942 @ X1938 )
| ~ ( X1939 @ X1942 )
| ( singleton @ ( dsetconstr @ X1938 @ X1939 ) ) )
& ( ( ( esk62_2 @ X1938 @ X1939 )
!= ( esk63_2 @ X1938 @ X1939 ) )
| ~ ( in @ X1942 @ X1938 )
| ~ ( X1939 @ X1942 )
| ( singleton @ ( dsetconstr @ X1938 @ X1939 ) ) )
& ( ( ( setadjoin @ X1943 @ emptyset )
!= ( setadjoin @ X1944 @ emptyset ) )
| ( X1943 = X1944 ) )
& ( ~ ( in @ ( setadjoin @ X1947 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1945 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1945 @ ( setadjoin @ X1946 @ emptyset ) ) @ emptyset ) ) )
| ( X1945 = X1947 ) )
& ( ~ ( iskpair @ X1948 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1948 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1948 ) ) ) )
& ( ~ ( singleton @ X1949 )
| ( in @ ( setunion @ X1949 ) @ X1949 ) )
& ( ( kfst @ ( kpair @ X1950 @ X1951 ) )
= X1950 )
& ( ~ ( in @ X1954 @ ( cartprod @ X1952 @ X1953 ) )
| ( in @ ( kfst @ X1954 ) @ X1952 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1955 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1955 @ ( setadjoin @ X1956 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1957 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1957 @ ( setadjoin @ X1958 @ emptyset ) ) @ emptyset ) ) )
| ( X1955 = X1957 ) )
& ( ( ( kpair @ X1959 @ X1960 )
!= ( kpair @ X1961 @ X1962 ) )
| ( X1959 = X1961 ) )
& ( ( X1963 != X1964 )
| ( ( setadjoin @ X1963 @ ( setadjoin @ X1964 @ emptyset ) )
= ( setadjoin @ X1963 @ emptyset ) ) )
& ( ( X1965 != X1966 )
| ( ( setadjoin @ ( setadjoin @ X1965 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1965 @ ( setadjoin @ X1966 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1965 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1967 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1967 @ ( setadjoin @ X1968 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1969 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1969 @ ( setadjoin @ X1970 @ emptyset ) ) @ emptyset ) ) )
| ( X1969 != X1970 )
| ( X1968 = X1970 ) )
& ( ( ( setadjoin @ X1971 @ ( setadjoin @ X1972 @ emptyset ) )
!= ( setadjoin @ X1973 @ emptyset ) )
| ( X1971 = X1972 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1974 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1974 @ ( setadjoin @ X1975 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1976 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1976 @ ( setadjoin @ X1977 @ emptyset ) ) @ emptyset ) ) )
| ( X1975 = X1977 ) )
& ( ( ( kpair @ X1978 @ X1979 )
!= ( kpair @ X1980 @ X1981 ) )
| ( X1979 = X1981 ) )
& ( ~ ( iskpair @ X1982 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1982 )
@ ^ [Z0: $i] :
( X1982
= ( kpair @ ( kfst @ X1982 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1983 @ X1984 ) )
= X1984 )
& ( ~ ( iskpair @ X1985 )
| ( ( kpair @ ( kfst @ X1985 ) @ ( ksnd @ X1985 ) )
= X1985 ) )
& ( ~ ( in @ X1988 @ ( cartprod @ X1986 @ X1987 ) )
| ( in @ ( ksnd @ X1988 ) @ X1987 ) )
& ( ~ ( in @ ( kpair @ X1991 @ X1992 ) @ ( cartprod @ X1989 @ X1990 ) )
| ( in @ X1991 @ X1989 ) )
& ( ~ ( in @ ( kpair @ X1995 @ X1996 ) @ ( cartprod @ X1993 @ X1994 ) )
| ( in @ X1996 @ X1994 ) )
& ( ~ ( in @ X1999 @ X1997 )
| ~ ( in @ X2000 @ X1998 )
| ( ( kpair @ X1999 @ X2000 )
= ( kpair @ X1999 @ X2000 ) ) )
& ( ~ ( in @ X2003 @ X2001 )
| ~ ( in @ X2004 @ X2002 )
| ( ( kfst @ ( kpair @ X2003 @ X2004 ) )
= X2003 ) )
& ( ~ ( in @ X2007 @ X2005 )
| ~ ( in @ X2008 @ X2006 )
| ( ( ksnd @ ( kpair @ X2007 @ X2008 ) )
= X2008 ) )
& ( ~ ( in @ X2011 @ ( cartprod @ X2009 @ X2010 ) )
| ( ( kpair @ ( kfst @ X2011 ) @ ( ksnd @ X2011 ) )
= X2011 ) )
& ( ~ ( in @ X2015 @ X2012 )
| ~ ( in @ X2016 @ X2013 )
| ~ ( X2014 @ X2015 @ X2016 )
| ( in @ ( kpair @ X2015 @ X2016 ) @ ( dpsetconstr @ X2012 @ X2013 @ X2014 ) ) )
& ( subset @ ( dpsetconstr @ X2017 @ X2018 @ X2019 ) @ ( cartprod @ X2017 @ X2018 ) )
& ( subset @ ( dpsetconstr @ X2020 @ X2021 @ X2022 ) @ ( cartprod @ X2020 @ X2021 ) )
& ( ~ ( in @ X2026 @ X2023 )
| ~ ( in @ X2027 @ X2024 )
| ~ ( in @ ( kpair @ X2026 @ X2027 ) @ ( dpsetconstr @ X2023 @ X2024 @ X2025 ) )
| ( X2025 @ X2026 @ X2027 ) )
& ( ~ ( in @ ( kpair @ X2031 @ X2032 ) @ ( dpsetconstr @ X2028 @ X2029 @ X2030 ) )
| ( in @ X2031 @ X2028 ) )
& ( ~ ( in @ ( kpair @ X2036 @ X2037 ) @ ( dpsetconstr @ X2033 @ X2034 @ X2035 ) )
| ( in @ X2037 @ X2034 ) )
& ( ~ ( in @ ( kpair @ X2041 @ X2042 ) @ ( dpsetconstr @ X2038 @ X2039 @ X2040 ) )
| ( X2040 @ X2041 @ X2042 ) )
& ( ~ ( func @ X2043 @ X2044 @ X2045 )
| ~ ( in @ X2046 @ X2043 )
| ( singleton
@ ( dsetconstr @ X2044
@ ^ [Z0: $i] : ( in @ ( kpair @ X2046 @ Z0 ) @ X2045 ) ) ) )
& ( ~ ( func @ X2047 @ X2048 @ X2049 )
| ~ ( in @ X2050 @ X2047 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2048
@ ^ [Z0: $i] : ( in @ ( kpair @ X2050 @ Z0 ) @ X2049 ) ) )
@ X2048 ) )
& ( ~ ( func @ X2051 @ X2052 @ X2053 )
| ~ ( in @ X2054 @ X2051 )
| ( in @ ( ap @ X2051 @ X2052 @ X2053 @ X2054 ) @ X2052 ) )
& ( ~ ( in @ X2057 @ ( funcSet @ X2055 @ X2056 ) )
| ( func @ X2055 @ X2056 @ X2057 ) )
& ( ~ ( in @ X2060 @ ( funcSet @ X2058 @ X2059 ) )
| ~ ( in @ X2061 @ X2058 )
| ( in @ ( ap @ X2058 @ X2059 @ X2060 @ X2061 ) @ X2059 ) )
& ( ~ ( func @ X2062 @ X2063 @ X2064 )
| ( in @ X2064 @ ( funcSet @ X2062 @ X2063 ) ) )
& ( ( in @ ( esk64_3 @ X2065 @ X2066 @ X2067 ) @ X2065 )
| ( func @ X2065 @ X2066
@ ( dpsetconstr @ X2065 @ X2066
@ ^ [Z0: $i] : ( $eq @ ( X2067 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2067 @ ( esk64_3 @ X2065 @ X2066 @ X2067 ) ) @ X2066 )
| ( func @ X2065 @ X2066
@ ( dpsetconstr @ X2065 @ X2066
@ ^ [Z0: $i] : ( $eq @ ( X2067 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2069 @ X2070 @ X2071 ) @ X2069 )
| ( func @ X2069 @ X2070 @ ( lam @ X2069 @ X2070 @ X2071 ) ) )
& ( ~ ( in @ ( X2071 @ ( esk65_3 @ X2069 @ X2070 @ X2071 ) ) @ X2070 )
| ( func @ X2069 @ X2070 @ ( lam @ X2069 @ X2070 @ X2071 ) ) )
& ( ( in @ ( esk66_3 @ X2073 @ X2074 @ X2075 ) @ X2073 )
| ( in @ ( lam @ X2073 @ X2074 @ X2075 ) @ ( funcSet @ X2073 @ X2074 ) ) )
& ( ~ ( in @ ( X2075 @ ( esk66_3 @ X2073 @ X2074 @ X2075 ) ) @ X2074 )
| ( in @ ( lam @ X2073 @ X2074 @ X2075 ) @ ( funcSet @ X2073 @ X2074 ) ) )
& ( ( in @ ( esk67_4 @ X2077 @ X2078 @ X2079 @ X2080 ) @ X2077 )
| ~ ( in @ X2083 @ X2079 )
| ( X2080 @ X2083 )
| ~ ( subset @ X2079 @ ( cartprod @ X2077 @ X2078 ) ) )
& ( ( in @ ( esk68_4 @ X2077 @ X2078 @ X2079 @ X2080 ) @ X2078 )
| ~ ( in @ X2083 @ X2079 )
| ( X2080 @ X2083 )
| ~ ( subset @ X2079 @ ( cartprod @ X2077 @ X2078 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2077 @ X2078 @ X2079 @ X2080 ) @ ( esk68_4 @ X2077 @ X2078 @ X2079 @ X2080 ) ) @ X2079 )
| ~ ( in @ X2083 @ X2079 )
| ( X2080 @ X2083 )
| ~ ( subset @ X2079 @ ( cartprod @ X2077 @ X2078 ) ) )
& ( ~ ( X2080 @ ( kpair @ ( esk67_4 @ X2077 @ X2078 @ X2079 @ X2080 ) @ ( esk68_4 @ X2077 @ X2078 @ X2079 @ X2080 ) ) )
| ~ ( in @ X2083 @ X2079 )
| ( X2080 @ X2083 )
| ~ ( subset @ X2079 @ ( cartprod @ X2077 @ X2078 ) ) )
& ( ( in @ ( esk69_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ X2084 )
| ~ ( in @ X2090 @ X2086 )
| ( X2087 @ X2090 )
| ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
& ( ( in @ ( esk70_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ X2085 )
| ~ ( in @ X2090 @ X2086 )
| ( X2087 @ X2090 )
| ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ ( esk70_4 @ X2084 @ X2085 @ X2086 @ X2087 ) ) @ X2086 )
| ~ ( in @ X2090 @ X2086 )
| ( X2087 @ X2090 )
| ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
& ( ~ ( X2087 @ ( kpair @ ( esk69_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ ( esk70_4 @ X2084 @ X2085 @ X2086 @ X2087 ) ) )
| ~ ( in @ X2090 @ X2086 )
| ( X2087 @ X2090 )
| ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2091 @ X2092 ) )
| ~ ( in @ X2093 @ X2091 )
| ~ ( in @ X2094 @ X2091 )
| ~ ( X2092 @ X2093 )
| ~ ( X2092 @ X2094 )
| ( X2093 = X2094 ) )
& ( ~ ( func @ X2095 @ X2096 @ X2097 )
| ~ ( in @ X2098 @ X2095 )
| ( in @ ( kpair @ X2098 @ ( ap @ X2095 @ X2096 @ X2097 @ X2098 ) ) @ X2097 ) )
& ( ~ ( in @ X2101 @ ( funcSet @ X2099 @ X2100 ) )
| ~ ( in @ X2102 @ X2099 )
| ( in @ ( kpair @ X2102 @ ( ap @ X2099 @ X2100 @ X2101 @ X2102 ) ) @ X2101 ) )
& ( ~ ( func @ X2103 @ X2104 @ X2105 )
| ~ ( in @ X2106 @ X2103 )
| ~ ( in @ X2107 @ X2104 )
| ~ ( in @ ( kpair @ X2106 @ X2107 ) @ X2105 )
| ( ( ap @ X2103 @ X2104 @ X2105 @ X2106 )
= X2107 ) )
& ( ( in @ ( esk71_4 @ X2108 @ X2109 @ X2110 @ X2111 ) @ X2108 )
| ~ ( in @ X2113 @ X2108 )
| ~ ( in @ X2114 @ X2109 )
| ~ ( in @ ( kpair @ X2113 @ X2114 ) @ X2111 )
| ( in @ ( kpair @ X2113 @ X2114 ) @ X2110 )
| ~ ( func @ X2108 @ X2109 @ X2111 )
| ~ ( func @ X2108 @ X2109 @ X2110 ) )
& ( ( ( ap @ X2108 @ X2109 @ X2110 @ ( esk71_4 @ X2108 @ X2109 @ X2110 @ X2111 ) )
!= ( ap @ X2108 @ X2109 @ X2111 @ ( esk71_4 @ X2108 @ X2109 @ X2110 @ X2111 ) ) )
| ~ ( in @ X2113 @ X2108 )
| ~ ( in @ X2114 @ X2109 )
| ~ ( in @ ( kpair @ X2113 @ X2114 ) @ X2111 )
| ( in @ ( kpair @ X2113 @ X2114 ) @ X2110 )
| ~ ( func @ X2108 @ X2109 @ X2111 )
| ~ ( func @ X2108 @ X2109 @ X2110 ) )
& ( ~ ( in @ X2117 @ ( funcSet @ X2115 @ X2116 ) )
| ~ ( in @ X2118 @ X2115 )
| ~ ( in @ X2119 @ X2116 )
| ~ ( in @ ( kpair @ X2118 @ X2119 ) @ X2117 )
| ( ( ap @ X2115 @ X2116 @ X2117 @ X2118 )
= X2119 ) )
& ( ( in @ ( esk72_4 @ X2120 @ X2121 @ X2122 @ X2123 ) @ X2120 )
| ( subset @ X2122 @ X2123 )
| ~ ( subset @ X2123 @ ( cartprod @ X2120 @ X2121 ) )
| ~ ( subset @ X2122 @ ( cartprod @ X2120 @ X2121 ) ) )
& ( ( in @ ( esk73_4 @ X2120 @ X2121 @ X2122 @ X2123 ) @ X2121 )
| ( subset @ X2122 @ X2123 )
| ~ ( subset @ X2123 @ ( cartprod @ X2120 @ X2121 ) )
| ~ ( subset @ X2122 @ ( cartprod @ X2120 @ X2121 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2120 @ X2121 @ X2122 @ X2123 ) @ ( esk73_4 @ X2120 @ X2121 @ X2122 @ X2123 ) ) @ X2122 )
| ( subset @ X2122 @ X2123 )
| ~ ( subset @ X2123 @ ( cartprod @ X2120 @ X2121 ) )
| ~ ( subset @ X2122 @ ( cartprod @ X2120 @ X2121 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2120 @ X2121 @ X2122 @ X2123 ) @ ( esk73_4 @ X2120 @ X2121 @ X2122 @ X2123 ) ) @ X2123 )
| ( subset @ X2122 @ X2123 )
| ~ ( subset @ X2123 @ ( cartprod @ X2120 @ X2121 ) )
| ~ ( subset @ X2122 @ ( cartprod @ X2120 @ X2121 ) ) )
& ( ( in @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ( X2128 = X2129 )
| ( in @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ( X2128 = X2129 )
| ( in @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ( X2128 = X2129 )
| ( in @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ( X2128 = X2129 )
| ( in @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ( X2128 = X2129 )
| ( in @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ( X2128 = X2129 )
| ( in @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ( X2128 = X2129 )
| ( in @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ( X2128 = X2129 )
| ( in @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ( X2128 = X2129 )
| ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ( X2128 = X2129 )
| ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ( X2128 = X2129 )
| ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ( X2128 = X2129 )
| ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2126 )
| ( X2128 = X2129 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ X2127 )
| ( X2128 = X2129 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ( X2128 = X2129 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk77_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2128 )
| ( X2128 = X2129 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2126 @ X2127 @ X2128 @ X2129 ) @ ( esk75_4 @ X2126 @ X2127 @ X2128 @ X2129 ) ) @ X2129 )
| ~ ( subset @ X2129 @ ( cartprod @ X2126 @ X2127 ) )
| ~ ( subset @ X2128 @ ( cartprod @ X2126 @ X2127 ) ) )
& ( ( in @ ( esk78_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
| ( X2136 = X2137 )
| ~ ( func @ X2134 @ X2135 @ X2137 )
| ~ ( func @ X2134 @ X2135 @ X2136 ) )
& ( ( ( ap @ X2134 @ X2135 @ X2136 @ ( esk78_4 @ X2134 @ X2135 @ X2136 @ X2137 ) )
!= ( ap @ X2134 @ X2135 @ X2137 @ ( esk78_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) )
| ( X2136 = X2137 )
| ~ ( func @ X2134 @ X2135 @ X2137 )
| ~ ( func @ X2134 @ X2135 @ X2136 ) )
& ( ( in @ ( esk79_4 @ X2139 @ X2140 @ X2141 @ X2142 ) @ X2139 )
| ( X2141 = X2142 )
| ~ ( in @ X2142 @ ( funcSet @ X2139 @ X2140 ) )
| ~ ( in @ X2141 @ ( funcSet @ X2139 @ X2140 ) ) )
& ( ( ( ap @ X2139 @ X2140 @ X2141 @ ( esk79_4 @ X2139 @ X2140 @ X2141 @ X2142 ) )
!= ( ap @ X2139 @ X2140 @ X2142 @ ( esk79_4 @ X2139 @ X2140 @ X2141 @ X2142 ) ) )
| ( X2141 = X2142 )
| ~ ( in @ X2142 @ ( funcSet @ X2139 @ X2140 ) )
| ~ ( in @ X2141 @ ( funcSet @ X2139 @ X2140 ) ) )
& ( ~ ( in @ X2146 @ ( funcSet @ X2144 @ X2145 ) )
| ~ ( in @ X2147 @ X2144 )
| ( ( ap @ X2144 @ X2145 @ X2146 @ X2147 )
= ( ap @ X2144 @ X2145 @ X2146 @ X2147 ) ) )
& ( ~ ( func @ X2148 @ X2149 @ X2150 )
| ~ ( in @ X2151 @ X2148 )
| ( ( ap @ X2148 @ X2149 @ X2150 @ X2151 )
= ( ap @ X2148 @ X2149 @ X2150 @ X2151 ) ) )
& ( ( in @ ( esk80_3 @ X2152 @ X2153 @ X2154 ) @ X2152 )
| ~ ( in @ X2156 @ X2152 )
| ( ( ap @ X2152 @ X2153 @ ( lam @ X2152 @ X2153 @ X2154 ) @ X2156 )
= ( X2154 @ X2156 ) ) )
& ( ~ ( in @ ( X2154 @ ( esk80_3 @ X2152 @ X2153 @ X2154 ) ) @ X2153 )
| ~ ( in @ X2156 @ X2152 )
| ( ( ap @ X2152 @ X2153 @ ( lam @ X2152 @ X2153 @ X2154 ) @ X2156 )
= ( X2154 @ X2156 ) ) )
& ( ~ ( func @ X2157 @ X2158 @ X2159 )
| ( ( lam @ X2157 @ X2158 @ ( ap @ X2157 @ X2158 @ X2159 ) )
= X2159 ) )
& ( ( in @ ( esk81_3 @ X2160 @ X2161 @ X2162 ) @ X2160 )
| ( ( lam @ X2160 @ X2161 @ X2162 )
= ( lam @ X2160 @ X2161 @ X2162 ) ) )
& ( ~ ( in @ ( X2162 @ ( esk81_3 @ X2160 @ X2161 @ X2162 ) ) @ X2161 )
| ( ( lam @ X2160 @ X2161 @ X2162 )
= ( lam @ X2160 @ X2161 @ X2162 ) ) )
& ( ( in @ ( esk82_3 @ X2164 @ X2165 @ X2166 ) @ X2164 )
| ~ ( in @ X2168 @ X2164 )
| ( ( ap @ X2164 @ X2165 @ ( lam @ X2164 @ X2165 @ X2166 ) @ X2168 )
= ( X2166 @ X2168 ) ) )
& ( ~ ( in @ ( X2166 @ ( esk82_3 @ X2164 @ X2165 @ X2166 ) ) @ X2165 )
| ~ ( in @ X2168 @ X2164 )
| ( ( ap @ X2164 @ X2165 @ ( lam @ X2164 @ X2165 @ X2166 ) @ X2168 )
= ( X2166 @ X2168 ) ) )
& ( ~ ( in @ X2171 @ ( funcSet @ X2169 @ X2170 ) )
| ( ( lam @ X2169 @ X2170 @ ( ap @ X2169 @ X2170 @ X2171 ) )
= X2171 ) )
& ( ~ ( in @ X2174 @ X2172 )
| ~ ( in @ X2175 @ X2172 )
| X2173
| ( in @ X2175
@ ( dsetconstr @ X2172
@ ^ [Z0: $i] :
( ( X2173
& ( Z0 = X2174 ) )
| ( ~ X2173
& ( Z0 = X2175 ) ) ) ) ) )
& ( ~ ( in @ X2178 @ X2176 )
| ~ ( in @ X2179 @ X2176 )
| X2177
| ( ( dsetconstr @ X2176
@ ^ [Z0: $i] :
( ( X2177
& ( Z0 = X2178 ) )
| ( ~ X2177
& ( Z0 = X2179 ) ) ) )
= ( setadjoin @ X2179 @ emptyset ) ) )
& ( ~ ( in @ X2182 @ X2180 )
| ~ ( in @ X2183 @ X2180 )
| ~ X2181
| ( in @ X2182
@ ( dsetconstr @ X2180
@ ^ [Z0: $i] :
( ( X2181
& ( Z0 = X2182 ) )
| ( ~ X2181
& ( Z0 = X2183 ) ) ) ) ) )
& ( ~ ( in @ X2186 @ X2184 )
| ~ ( in @ X2187 @ X2184 )
| ~ X2185
| ( ( dsetconstr @ X2184
@ ^ [Z0: $i] :
( ( X2185
& ( Z0 = X2186 ) )
| ( ~ X2185
& ( Z0 = X2187 ) ) ) )
= ( setadjoin @ X2186 @ emptyset ) ) )
& ( ~ ( in @ X2190 @ X2188 )
| ~ ( in @ X2191 @ X2188 )
| ( singleton
@ ( dsetconstr @ X2188
@ ^ [Z0: $i] :
( ( X2189
& ( Z0 = X2190 ) )
| ( ~ X2189
& ( Z0 = X2191 ) ) ) ) ) )
& ( ~ ( in @ X2194 @ X2192 )
| ~ ( in @ X2195 @ X2192 )
| ( in @ ( if @ X2192 @ X2193 @ X2194 @ X2195 ) @ X2192 ) )
& ( ~ ( singleton @ X2196 )
| ~ ( in @ X2197 @ X2196 )
| ( ( setunion @ X2196 )
= X2197 ) )
& ( ~ ( in @ X2200 @ X2198 )
| ~ ( in @ X2201 @ X2198 )
| ~ X2199
| ( ( if @ X2198 @ X2199 @ X2200 @ X2201 )
= X2200 ) )
& ( in @ esk84_0 @ esk83_0 )
& ( in @ esk85_0 @ esk83_0 )
& ~ epred2_0
& ( ~ epred2_0
| epred2_0 )
& ( ( ( if @ esk83_0 @ $false @ esk84_0 @ esk85_0 )
!= esk85_0 )
| epred2_0 )
& ( ~ epred2_0
| ( ( if @ esk83_0 @ $true @ esk84_0 @ esk85_0 )
!= esk85_0 ) )
& ( ( ( if @ esk83_0 @ $false @ esk84_0 @ esk85_0 )
!= esk85_0 )
| ( ( if @ esk83_0 @ $true @ esk84_0 @ esk85_0 )
!= esk85_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[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_314,plain,
! [X1488: $i,X1489: $o,X1490: $i,X1491: $i] :
( ( if @ X1488 @ X1489 @ X1490 @ X1491 )
= ( setunion
@ ( dsetconstr @ X1488
@ ^ [Z0: $i] :
( ( X1489
& ( Z0 = X1490 ) )
| ( ~ X1489
& ( Z0 = X1491 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_312]) ).
thf(c_0_315,negated_conjecture,
( epred2_0
| ( ( if @ esk83_0 @ ~ $true @ esk84_0 @ esk85_0 )
!= esk85_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
thf(c_0_316,plain,
! [X2: $i,X3: $i,X10: $o,X4: $i] :
( ( if @ X2 @ X10 @ X3 @ X4 )
= ( setunion
@ ( dsetconstr @ X2
@ ^ [Z0: $i] :
( ( X10
& ( Z0 = X3 ) )
| ( ~ X10
& ( Z0 = X4 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_317,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( if @ X3 @ $true @ X2 @ X4 )
= X2 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X4 @ X3 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_313])])]) ).
thf(c_0_318,negated_conjecture,
( epred2_0
| ( ( setunion
@ ( dsetconstr @ esk83_0
@ ^ [Z0: $i] :
( ( ~ $true
& ( Z0 = esk84_0 ) )
| ( ~ ~ $true
& ( Z0 = esk85_0 ) ) ) ) )
!= esk85_0 ) ),
inference(rw,[status(thm)],[c_0_315,c_0_316]) ).
thf(c_0_319,negated_conjecture,
~ epred2_0,
inference(split_conjunct,[status(thm)],[c_0_313]) ).
thf(c_0_320,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( ( setunion
@ ( dsetconstr @ X3
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = X2 ) )
| ( ~ $true
& ( Z0 = X4 ) ) ) ) )
= X2 )
| ~ ( in @ X4 @ X3 )
| ~ ( in @ X2 @ X3 ) ),
inference(rw,[status(thm)],[c_0_317,c_0_316]) ).
thf(c_0_321,negated_conjecture,
( ( setunion
@ ( dsetconstr @ esk83_0
@ ^ [Z0: $i] : ( Z0 = esk85_0 ) ) )
!= esk85_0 ),
inference(cn,[status(thm)],[inference(sr,[status(thm)],[c_0_318,c_0_319])]) ).
thf(c_0_322,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( ( setunion
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( Z0 = X3 ) ) )
= X3 )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X3 @ X2 ) ),
inference(cn,[status(thm)],[c_0_320]) ).
thf(c_0_323,negated_conjecture,
in @ esk85_0 @ esk83_0,
inference(split_conjunct,[status(thm)],[c_0_313]) ).
thf(c_0_324,negated_conjecture,
in @ esk84_0 @ esk83_0,
inference(split_conjunct,[status(thm)],[c_0_313]) ).
thf(c_0_325,plain,
! [X2: $i] :
~ ( in @ X2 @ esk83_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_321,c_0_322])])]),c_0_323])]) ).
thf(c_0_326,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_324,c_0_325]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU708^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 12:35:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.52 Running higher-order theorem proving
% 0.20/0.52 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.27b97WYxb4/E---3.1_30776.p
% 2.16/1.04 # Version: 3.2.0-ho
% 2.16/1.04 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/1.04 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/1.04 # Starting ehoh_best5 with 300s (1) cores
% 2.16/1.04 # Starting almost_fo_3_lam with 300s (1) cores
% 2.16/1.04 # Starting new_bool_5 with 300s (1) cores
% 2.16/1.04 # Starting pre_casc_3 with 300s (1) cores
% 2.16/1.04 # Starting ho_unfolding_8 with 300s (1) cores
% 2.16/1.04 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.16/1.04 # Starting new_bool_3 with 300s (1) cores
% 2.16/1.04 # Starting new_ho_5 with 300s (1) cores
% 2.16/1.04 # ho_unfolding_8 with pid 30858 completed with status 0
% 2.16/1.04 # Result found by ho_unfolding_8
% 2.16/1.04 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/1.04 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/1.04 # Starting ehoh_best5 with 300s (1) cores
% 2.16/1.04 # Starting almost_fo_3_lam with 300s (1) cores
% 2.16/1.04 # Starting new_bool_5 with 300s (1) cores
% 2.16/1.04 # Starting pre_casc_3 with 300s (1) cores
% 2.16/1.04 # Starting ho_unfolding_8 with 300s (1) cores
% 2.16/1.04 # No SInE strategy applied
% 2.16/1.04 # Search class: HGHSM-FSLM32-DHFMMSBN
% 2.16/1.04 # partial match(1): HGHSM-FSLM32-MHFMMSBN
% 2.16/1.04 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.16/1.04 # Starting ho_unfolding_8 with 61s (1) cores
% 2.16/1.04 # ho_unfolding_8 with pid 30869 completed with status 0
% 2.16/1.04 # Result found by ho_unfolding_8
% 2.16/1.04 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.16/1.04 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/1.04 # Starting ehoh_best5 with 300s (1) cores
% 2.16/1.04 # Starting almost_fo_3_lam with 300s (1) cores
% 2.16/1.04 # Starting new_bool_5 with 300s (1) cores
% 2.16/1.04 # Starting pre_casc_3 with 300s (1) cores
% 2.16/1.04 # Starting ho_unfolding_8 with 300s (1) cores
% 2.16/1.04 # No SInE strategy applied
% 2.16/1.04 # Search class: HGHSM-FSLM32-DHFMMSBN
% 2.16/1.04 # partial match(1): HGHSM-FSLM32-MHFMMSBN
% 2.16/1.04 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 2.16/1.04 # Starting ho_unfolding_8 with 61s (1) cores
% 2.16/1.04 # Preprocessing time : 0.110 s
% 2.16/1.04 # Presaturation interreduction done
% 2.16/1.04
% 2.16/1.04 # Proof found!
% 2.16/1.04 # SZS status Theorem
% 2.16/1.04 # SZS output start CNFRefutation
% See solution above
% 2.16/1.04 # Parsed axioms : 492
% 2.16/1.04 # Removed by relevancy pruning/SinE : 0
% 2.16/1.04 # Initial clauses : 663
% 2.16/1.04 # Removed in clause preprocessing : 293
% 2.16/1.04 # Initial clauses in saturation : 370
% 2.16/1.04 # Processed clauses : 710
% 2.16/1.04 # ...of these trivial : 10
% 2.16/1.04 # ...subsumed : 31
% 2.16/1.04 # ...remaining for further processing : 669
% 2.16/1.04 # Other redundant clauses eliminated : 52
% 2.16/1.04 # Clauses deleted for lack of memory : 0
% 2.16/1.04 # Backward-subsumed : 2
% 2.16/1.04 # Backward-rewritten : 2
% 2.16/1.04 # Generated clauses : 8168
% 2.16/1.04 # ...of the previous two non-redundant : 7941
% 2.16/1.04 # ...aggressively subsumed : 0
% 2.16/1.04 # Contextual simplify-reflections : 0
% 2.16/1.04 # Paramodulations : 8079
% 2.16/1.04 # Factorizations : 2
% 2.16/1.04 # NegExts : 1
% 2.16/1.04 # Equation resolutions : 59
% 2.16/1.04 # Disequality decompositions : 0
% 2.16/1.04 # Total rewrite steps : 199
% 2.16/1.04 # ...of those cached : 136
% 2.16/1.04 # Propositional unsat checks : 0
% 2.16/1.04 # Propositional check models : 0
% 2.16/1.04 # Propositional check unsatisfiable : 0
% 2.16/1.04 # Propositional clauses : 0
% 2.16/1.04 # Propositional clauses after purity: 0
% 2.16/1.04 # Propositional unsat core size : 0
% 2.16/1.04 # Propositional preprocessing time : 0.000
% 2.16/1.04 # Propositional encoding time : 0.000
% 2.16/1.04 # Propositional solver time : 0.000
% 2.16/1.04 # Success case prop preproc time : 0.000
% 2.16/1.04 # Success case prop encoding time : 0.000
% 2.16/1.04 # Success case prop solver time : 0.000
% 2.16/1.04 # Current number of processed clauses : 325
% 2.16/1.04 # Positive orientable unit clauses : 30
% 2.16/1.04 # Positive unorientable unit clauses: 0
% 2.16/1.04 # Negative unit clauses : 4
% 2.16/1.04 # Non-unit-clauses : 291
% 2.16/1.04 # Current number of unprocessed clauses: 7921
% 2.16/1.04 # ...number of literals in the above : 35000
% 2.16/1.04 # Current number of archived formulas : 0
% 2.16/1.04 # Current number of archived clauses : 330
% 2.16/1.04 # Clause-clause subsumption calls (NU) : 46944
% 2.16/1.04 # Rec. Clause-clause subsumption calls : 16927
% 2.16/1.04 # Non-unit clause-clause subsumptions : 25
% 2.16/1.04 # Unit Clause-clause subsumption calls : 93
% 2.16/1.04 # Rewrite failures with RHS unbound : 0
% 2.16/1.04 # BW rewrite match attempts : 23
% 2.16/1.04 # BW rewrite match successes : 2
% 2.16/1.04 # Condensation attempts : 0
% 2.16/1.04 # Condensation successes : 0
% 2.16/1.04 # Termbank termtop insertions : 222039
% 2.16/1.04 # Search garbage collected termcells : 24631
% 2.16/1.04
% 2.16/1.04 # -------------------------------------------------
% 2.16/1.04 # User time : 0.412 s
% 2.16/1.04 # System time : 0.037 s
% 2.16/1.04 # Total time : 0.448 s
% 2.16/1.04 # Maximum resident set size: 7508 pages
% 2.16/1.04
% 2.16/1.04 # -------------------------------------------------
% 2.16/1.04 # User time : 0.424 s
% 2.16/1.04 # System time : 0.040 s
% 2.16/1.04 # Total time : 0.464 s
% 2.16/1.04 # Maximum resident set size: 2348 pages
% 2.16/1.04 % E---3.1 exiting
% 2.16/1.04 % E exiting
%------------------------------------------------------------------------------