%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU681^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:05 EDT 2024
% Result : Theorem 1.27s 0.65s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 517
% Syntax : Number of formulae : 612 ( 53 unt; 312 typ; 0 def)
% Number of atoms : 2583 ( 574 equ; 0 cnn)
% Maximal formula atoms : 762 ( 8 avg)
% Number of connectives : 10455 ( 688 ~; 752 |; 520 &;7065 @)
% ( 280 <=>;1150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 895 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 535 ( 535 >; 0 *; 0 +; 0 <<)
% Number of symbols : 316 ( 312 usr; 207 con; 0-4 aty)
% Number of variables : 2285 ( 252 ^1873 !; 160 ?;2285 :)
% 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,
epred1_0: $o ).
thf(decl_257,type,
esk1_2: $i > $i > $i ).
thf(decl_258,type,
esk2_2: $i > $i > $i ).
thf(decl_259,type,
esk3_2: $i > $i > $i ).
thf(decl_260,type,
esk4_1: $i > $i ).
thf(decl_261,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_262,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_263,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_264,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_265,type,
esk9_1: $i > $i ).
thf(decl_266,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_267,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_268,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_269,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_270,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_271,type,
esk15_2: $i > $i > $i ).
thf(decl_272,type,
esk16_2: $i > $i > $i ).
thf(decl_273,type,
esk17_1: $i > $i ).
thf(decl_274,type,
esk18_1: $i > $i ).
thf(decl_275,type,
esk19_1: $i > $i ).
thf(decl_276,type,
esk20_2: $i > $i > $i ).
thf(decl_277,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_278,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_279,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_280,type,
esk24_1: $i > $i ).
thf(decl_281,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_282,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_283,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_284,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_285,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_286,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_287,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_288,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_289,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_290,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_291,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_292,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_293,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_294,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_295,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_296,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_297,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_298,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_299,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_300,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_301,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_302,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_303,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_304,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_305,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_306,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_307,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_308,type,
esk52_2: $i > $i > $i ).
thf(decl_309,type,
esk53_2: $i > $i > $i ).
thf(decl_310,type,
esk54_2: $i > $i > $i ).
thf(decl_311,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_312,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_313,type,
esk57_2: $i > $i > $i ).
thf(decl_314,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_316,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_317,type,
esk61_2: $i > ( $i > $o ) > $i ).
thf(decl_318,type,
esk62_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_319,type,
esk63_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_320,type,
esk64_2: $i > ( $i > $o ) > $i ).
thf(decl_321,type,
esk65_2: $i > ( $i > $o ) > $i ).
thf(decl_322,type,
esk66_2: $i > ( $i > $o ) > $i ).
thf(decl_323,type,
esk67_1: $i > $i ).
thf(decl_324,type,
esk68_1: $i > $i ).
thf(decl_325,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_326,type,
esk70_4: $i > $i > $i > $i > $i ).
thf(decl_327,type,
esk71_3: $i > $i > $i > $i ).
thf(decl_328,type,
esk72_3: $i > $i > $i > $i ).
thf(decl_329,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_330,type,
esk74_3: $i > $i > $i > $i ).
thf(decl_331,type,
esk75_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_332,type,
esk76_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_333,type,
esk77_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_334,type,
esk78_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_335,type,
esk79_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_336,type,
esk80_0: $i ).
thf(decl_337,type,
esk81_0: $i ).
thf(decl_338,type,
esk82_0: $i ).
thf(decl_339,type,
epred2_0: $i > $o ).
thf(decl_340,type,
esk83_0: $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X4: $i] :
? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X4
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
& ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ex1 @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X30 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X31 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X33 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X34 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(brelnall1,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
=> ! [X4: $i,X5: $i,X29: $i] :
( ( breln @ X4 @ X5 @ X29 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(c_0_204,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X634: $i] :
( ( in @ X634
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X634 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_205,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_206,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X641: $i] :
( ( in @ X641
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X641 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_207,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X634: $i] :
( ( in @ X634
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X634 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_204,c_0_205]) ).
thf(c_0_208,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_209,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_210,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_211,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_212,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_213,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_214,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_232,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X641: $i] :
( ( in @ X641
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X641 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_206,c_0_207]),c_0_208]) ).
thf(c_0_233,plain,
( apProp
<=> ! [X4: $i,X5: $i,X30: $i] :
( ( func @ X4 @ X5 @ X30 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_234,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_235,plain,
( lamp
<=> ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_236,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X605: $i] :
( ( X6 @ X2 @ X605 )
& ! [X606: $i] :
( ( X6 @ X2 @ X606 )
=> ( X605 = X606 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_209,c_0_210]) ).
thf(c_0_237,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X607: $i] :
( ( X1 @ X607 )
& ! [X608: $i] :
( ( X1 @ X608 )
=> ( X607 = X608 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_211,c_0_210]) ).
thf(c_0_238,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_239,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_240,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_241,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X609: $i] :
( ( X1 @ X609 )
& ! [X610: $i] :
( ( X1 @ X610 )
=> ( X609 = X610 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_212,c_0_210]) ).
thf(c_0_242,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X611: $i] :
( ( X1 @ X611 )
& ! [X612: $i] :
( ( X1 @ X612 )
=> ( X611 = X612 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_213,c_0_210]) ).
thf(c_0_243,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_244,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_214]) ).
thf(c_0_245,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_215,c_0_214]) ).
thf(c_0_246,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_214]) ).
thf(c_0_247,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_248,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X613: $i] :
( ( X1 @ X613 )
& ! [X614: $i] :
( ( X1 @ X614 )
=> ( X613 = X614 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_216,c_0_210]) ).
thf(c_0_249,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_214]) ).
thf(c_0_250,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_251,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X615: $i] :
( ( X1 @ X615 )
& ! [X616: $i] :
( ( X1 @ X616 )
=> ( X615 = X616 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_217,c_0_210]) ).
thf(c_0_252,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X617: $i] :
( ( X1 @ X617 )
& ! [X618: $i] :
( ( X1 @ X618 )
=> ( X617 = X618 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_218,c_0_210]) ).
thf(c_0_253,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X619: $i] :
( ( X1 @ X619 )
& ! [X620: $i] :
( ( X1 @ X620 )
=> ( X619 = X620 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_219,c_0_210]) ).
thf(c_0_254,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X621: $i] :
( ( X1 @ X621 )
& ! [X622: $i] :
( ( X1 @ X622 )
=> ( X621 = X622 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_220,c_0_210]) ).
thf(c_0_255,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X623: $i] :
( ( X1 @ X623 )
& ! [X624: $i] :
( ( X1 @ X624 )
=> ( X623 = X624 ) ) )
<=> ? [X625: $i] :
( ( X17 @ X625 )
& ! [X626: $i] :
( ( X17 @ X626 )
=> ( X625 = X626 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_221,c_0_210]) ).
thf(c_0_256,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X627: $i] :
( ( X1 @ X627 )
& ! [X628: $i] :
( ( X1 @ X628 )
=> ( X627 = X628 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_222,c_0_210]) ).
thf(c_0_257,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X629: $i] :
( ( X1 @ X629 )
& ! [X630: $i] :
( ( X1 @ X630 )
=> ( X629 = X630 ) ) )
=> ( ? [X631: $i] :
( ( X17 @ X631 )
& ! [X632: $i] :
( ( X17 @ X632 )
=> ( X631 = X632 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_223,c_0_210]) ).
thf(c_0_258,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_259,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_260,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_261,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 ) )
=> ? [X633: $i] :
( ( in @ X633
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X633 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_224,c_0_205]) ).
thf(c_0_262,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X635: $i] :
( ( in @ X635
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X635 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_225,c_0_207]) ).
thf(c_0_263,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X636: $i] :
( ( in @ X636
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X636 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_226,c_0_207]) ).
thf(c_0_264,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 ) )
=> ? [X637: $i] :
( ( in @ X637
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X637 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_227,c_0_207]) ).
thf(c_0_265,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X638: $i] :
( ( in @ X638
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X638 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_228,c_0_205]) ).
thf(c_0_266,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X639: $i] :
( ( in @ X639 @ X21 )
& ( X21
= ( setadjoin @ X639 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_205]) ).
thf(c_0_267,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X640: $i] :
( ( in @ X640
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X640 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_229,c_0_205]) ).
thf(c_0_268,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_269,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_270,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_230,c_0_208]) ).
thf(c_0_271,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_272,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_273,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_274,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_275,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X642: $i] :
( ( in @ X642 @ X4 )
=> ? [X643: $i] :
( ( in @ X643
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X642 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X642 @ Z0 ) @ X30 ) )
= ( setadjoin @ X643 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X644: $i] :
( ( in @ X644
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) )
= ( setadjoin @ X644 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_231,c_0_205]),c_0_232]) ).
thf(c_0_276,plain,
( apProp
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X645: $i] :
( ( in @ X645 @ X4 )
=> ? [X646: $i] :
( ( in @ X646
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X645 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X645 @ Z0 ) @ X30 ) )
= ( setadjoin @ X646 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X30 ) ) )
@ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_233,c_0_232]) ).
thf(c_0_277,axiom,
( app
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X647: $i] :
( ( in @ X647 @ X4 )
=> ? [X648: $i] :
( ( in @ X648
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X647 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X647 @ Z0 ) @ X30 ) )
= ( setadjoin @ X648 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X30 @ X2 ) @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[app,c_0_232]) ).
thf(c_0_278,axiom,
( infuncsetfunc
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( in @ X30 @ ( funcSet @ X4 @ X5 ) )
=> ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X649: $i] :
( ( in @ X649 @ X4 )
=> ? [X650: $i] :
( ( in @ X650
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X649 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X649 @ Z0 ) @ X30 ) )
= ( setadjoin @ X650 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[infuncsetfunc,c_0_232]) ).
thf(c_0_279,axiom,
( funcinfuncset
= ( ! [X4: $i,X5: $i,X30: $i] :
( ( ( subset @ X30 @ ( cartprod @ X4 @ X5 ) )
& ! [X651: $i] :
( ( in @ X651 @ X4 )
=> ? [X652: $i] :
( ( in @ X652
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X651 @ Z0 ) @ X30 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X651 @ Z0 ) @ X30 ) )
= ( setadjoin @ X652 @ emptyset ) ) ) ) )
=> ( in @ X30 @ ( funcSet @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcinfuncset,c_0_232]) ).
thf(c_0_280,plain,
( lamProp
= ( ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X31 @ Z0 )
= Z1 ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X653: $i] :
( ( in @ X653 @ X4 )
=> ? [X654: $i] :
( ( in @ X654
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X653 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i,Z2: $i] :
( ( X31 @ Z1 )
= Z2 ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X653 @ Z0 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z1: $i,Z2: $i] :
( ( X31 @ Z1 )
= Z2 ) ) ) )
= ( setadjoin @ X654 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_234,c_0_232]) ).
thf(c_0_281,plain,
( lamp
= ( ! [X4: $i,X5: $i,X33: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X33 @ X2 ) @ X5 ) )
=> ( ( subset
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X33 @ Z0 ) )
@ ( cartprod @ X4 @ X5 ) )
& ! [X655: $i] :
( ( in @ X655 @ X4 )
=> ? [X656: $i] :
( ( in @ X656
@ ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X655 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] :
( in @ ( kpair @ X655 @ Z0 )
@ ( lam @ X4 @ X5
@ ^ [Z1: $i] : ( X33 @ Z1 ) ) ) )
= ( setadjoin @ X656 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_235,c_0_232]) ).
thf(c_0_282,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X34: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X34 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X34 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_283,plain,
( epred1_0
<=> ! [X686: $i] :
? [X687: $i] :
( ! [X688: $i] :
( ( in @ X688 @ X687 )
=> ! [X689: $i] :
( ( in @ X689 @ X688 )
=> ( in @ X689 @ X686 ) ) )
& ! [X690: $i,X691: $i] :
( ( ( in @ X690 @ X686 )
& ( in @ X691 @ X686 ) )
=> ( ! [X692: $i] :
( ( in @ X692 @ X687 )
=> ( ( in @ X690 @ X692 )
<=> ( in @ X691 @ X692 ) ) )
=> ( X690 = X691 ) ) )
& ! [X693: $i,X694: $i] :
( ( ( in @ X693 @ X687 )
& ( in @ X694 @ X687 ) )
=> ( ! [X695: $i] :
( ( in @ X695 @ X693 )
=> ( in @ X695 @ X694 ) )
| ! [X696: $i] :
( ( in @ X696 @ X694 )
=> ( in @ X696 @ X693 ) ) ) )
& ! [X697: $i] :
( ( ! [X698: $i] :
( ( in @ X698 @ X697 )
=> ( in @ X698 @ X686 ) )
& ? [X699: $i] : ( in @ X699 @ X697 ) )
=> ? [X700: $i,X701: $i] :
( ( in @ X700 @ X687 )
& ( in @ X701 @ X697 )
& ~ ? [X702: $i] :
( ( in @ X702 @ X700 )
& ( in @ X702 @ X697 ) )
& ! [X703: $i] :
( ( in @ X703 @ X687 )
=> ( ! [X704: $i] :
( ( in @ X704 @ X703 )
=> ( in @ X704 @ X700 ) )
| ( in @ X701 @ X703 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_284,negated_conjecture,
~ ( ! [X657: $i,X658: $i] :
( ! [X659: $i] :
( ( in @ X659 @ X657 )
<=> ( in @ X659 @ X658 ) )
=> ( X657 = X658 ) )
=> ( ! [X660: $i] :
~ ( in @ X660 @ emptyset )
=> ( ! [X661: $i,X662: $i,X663: $i] :
( ( in @ X663 @ ( setadjoin @ X661 @ X662 ) )
<=> ( ( X663 = X661 )
| ( in @ X663 @ X662 ) ) )
=> ( ! [X664: $i,X665: $i] :
( ( in @ X665 @ ( powerset @ X664 ) )
<=> ! [X666: $i] :
( ( in @ X666 @ X665 )
=> ( in @ X666 @ X664 ) ) )
=> ( ! [X667: $i,X668: $i] :
( ( in @ X668 @ ( setunion @ X667 ) )
<=> ? [X669: $i] :
( ( in @ X668 @ X669 )
& ( in @ X669 @ X667 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X670: $i] :
( ( in @ X670 @ omega )
=> ( in @ ( setadjoin @ X670 @ X670 ) @ omega ) )
=> ( ! [X671: $i] :
( ( ( in @ emptyset @ X671 )
& ! [X672: $i] :
( ( ( in @ X672 @ omega )
& ( in @ X672 @ X671 ) )
=> ( in @ ( setadjoin @ X672 @ X672 ) @ X671 ) ) )
=> ! [X673: $i] :
( ( in @ X673 @ omega )
=> ( in @ X673 @ X671 ) ) )
=> ( ! [X674: $i > $i > $o,X675: $i] :
( ! [X676: $i] :
( ( in @ X676 @ X675 )
=> ? [X677: $i] :
( ( X674 @ X676 @ X677 )
& ! [X678: $i] :
( ( X674 @ X676 @ X678 )
=> ( X677 = X678 ) ) ) )
=> ? [X679: $i] :
! [X680: $i] :
( ( in @ X680 @ X679 )
<=> ? [X681: $i] :
( ( in @ X681 @ X675 )
& ( X674 @ X681 @ X680 ) ) ) )
=> ( ! [X682: $i] :
( ? [X683: $i] : ( in @ X683 @ X682 )
=> ? [X684: $i] :
( ( in @ X684 @ X682 )
& ~ ? [X685: $i] :
( ( in @ X685 @ X684 )
& ( in @ X685 @ X682 ) ) ) )
=> ( epred1_0
=> ( ! [X705: $i > $o] :
( ? [X706: $i] :
( ( X705 @ X706 )
& ! [X707: $i] :
( ( X705 @ X707 )
=> ( X706 = X707 ) ) )
=> ( X705
@ ( descr
@ ^ [Z0: $i] : ( X705 @ Z0 ) ) ) )
=> ( ! [X708: $i,X709: $i > $o,X710: $i] :
( ( in @ X710 @ X708 )
=> ( ( X709 @ X710 )
=> ( in @ X710 @ ( dsetconstr @ X708 @ X709 ) ) ) )
=> ( ! [X711: $i,X712: $i > $o,X713: $i] :
( ( in @ X713 @ ( dsetconstr @ X711 @ X712 ) )
=> ( in @ X713 @ X711 ) )
=> ( ! [X714: $i,X715: $i > $o,X716: $i] :
( ( in @ X716 @ ( dsetconstr @ X714 @ X715 ) )
=> ( X715 @ X716 ) )
=> ( ! [X717: $i > $o] :
( ? [X718: $i] :
( ( X717 @ X718 )
& ! [X719: $i] :
( ( X717 @ X719 )
=> ( X718 = X719 ) ) )
=> ? [X720: $i] :
( ( X717 @ X720 )
& ! [X721: $i] :
( ( X717 @ X721 )
=> ( X720 = X721 ) ) ) )
=> ( ! [X722: $o,X723: $i] :
( ( in @ X723 @ ( prop2set @ X722 ) )
=> X722 )
=> ( ! [X724: $i] :
( ( in @ X724 @ emptyset )
=> ! [X725: $o] : X725 )
=> ( ! [X726: $i] :
( ( in @ X726 @ emptyset )
=> ~ $true )
=> ( ! [X727: $i] :
~ ( in @ X727 @ emptyset )
=> ( ! [X728: $i > $o] :
( ? [X729: $i] :
( ( X728 @ X729 )
& ! [X730: $i] :
( ( X728 @ X730 )
=> ( X729 = X730 ) ) )
=> ? [X731: $i] : ( X728 @ X731 ) )
=> ( ! [X732: $i,X733: $i] :
( ! [X734: $i] :
( ( in @ X734 @ X732 )
=> ( in @ X734 @ X733 ) )
=> ( ! [X735: $i] :
( ( in @ X735 @ X733 )
=> ( in @ X735 @ X732 ) )
=> ( X732 = X733 ) ) )
=> ( ! [X736: $i] :
( ! [X737: $i] :
~ ( in @ X737 @ X736 )
=> ( X736 = emptyset ) )
=> ( ! [X738: $i] :
( ! [X739: $i] :
~ ( in @ X739 @ X738 )
=> ( X738 = emptyset ) )
=> ( ! [X740: $i,X741: $i > $o,X742: $i] :
( ( in @ X742 @ X740 )
=> ( ( in @ X742 @ ( dsetconstr @ X740 @ X741 ) )
<=> ( X741 @ X742 ) ) )
=> ( ! [X743: $i] :
( ( X743 != emptyset )
=> ? [X744: $i] : ( in @ X744 @ X743 ) )
=> ( ! [X745: $i,X746: $i > $o,X747: $i] :
( ( in @ X747 @ X745 )
=> ( ( X746 @ X747 )
=> ( ( dsetconstr @ X745 @ X746 )
!= emptyset ) ) )
=> ( ! [X748: $i] :
( ? [X749: $i] : ( in @ X749 @ X748 )
=> ( X748 != emptyset ) )
=> ( ! [X750: $i,X751: $i] : ( in @ X750 @ ( setadjoin @ X750 @ X751 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X752: $i,X753: $i,X754: $i] :
( ( in @ X754 @ X753 )
=> ( in @ X754 @ ( setadjoin @ X752 @ X753 ) ) )
=> ( ! [X755: $i,X756: $i,X757: $i] :
( ( in @ X757 @ ( setadjoin @ X755 @ X756 ) )
=> ! [X758: $o] :
( ( ( X757 = X755 )
=> X758 )
=> ( ( ( in @ X757 @ X756 )
=> X758 )
=> X758 ) ) )
=> ( ! [X759: $i,X760: $i,X761: $i] :
( ( in @ X761 @ ( setadjoin @ X759 @ X760 ) )
=> ( ( X761 = X759 )
| ( in @ X761 @ X760 ) ) )
=> ( ! [X762: $i] :
( ( dsetconstr @ X762
@ ^ [Z0: $i] : $true )
= X762 )
=> ( ! [X763: $i,X764: $i] :
( ! [X765: $i] :
( ( in @ X765 @ X764 )
=> ( in @ X765 @ X763 ) )
=> ( in @ X764 @ ( powerset @ X763 ) ) )
=> ( ! [X766: $i] : ( in @ emptyset @ ( powerset @ X766 ) )
=> ( ! [X767: $i] : ( in @ emptyset @ ( powerset @ X767 ) )
=> ( ! [X768: $i,X769: $i,X770: $i] :
( ( in @ X769 @ ( powerset @ X768 ) )
=> ( ( in @ X770 @ X769 )
=> ( in @ X770 @ X768 ) ) )
=> ( ! [X771: $i,X772: $i,X773: $i] :
( ( in @ X772 @ X773 )
=> ( ( in @ X773 @ X771 )
=> ( in @ X772 @ ( setunion @ X771 ) ) ) )
=> ( ! [X774: $i,X775: $i] :
( ( in @ X775 @ ( setunion @ X774 ) )
=> ! [X776: $o] :
( ! [X777: $i] :
( ( in @ X775 @ X777 )
=> ( ( in @ X777 @ X774 )
=> X776 ) )
=> X776 ) )
=> ( ! [X778: $i,X779: $i] :
( ( in @ X779 @ X778 )
=> ( in @ X779 @ ( powerset @ ( setunion @ X778 ) ) ) )
=> ( ! [X780: $i > $o] :
( ? [X781: $i] :
( ( X780 @ X781 )
& ! [X782: $i] :
( ( X780 @ X782 )
=> ( X781 = X782 ) ) )
=> ? [X783: $i] :
! [X784: $i] :
( ( X780 @ X784 )
<=> ( X784 = X783 ) ) )
=> ( ! [X785: $i] :
( ( X785 != emptyset )
=> ? [X786: $i] :
( ( in @ X786 @ X785 )
& $true ) )
=> ( ! [X787: $i,X788: $i] :
( ( in @ X787 @ ( setadjoin @ X788 @ emptyset ) )
=> ( X787 = X788 ) )
=> ( ! [X789: $i,X790: $i] :
( ( X789 != X790 )
=> ~ ( in @ X790 @ ( setadjoin @ X789 @ emptyset ) ) )
=> ( ! [X791: $i,X792: $i] :
( ( X791 = X792 )
=> ( in @ X791 @ ( setadjoin @ X792 @ emptyset ) ) )
=> ( ! [X793: $i,X794: $i] :
( ( in @ X793 @ ( setadjoin @ X794 @ emptyset ) )
=> ( in @ X794 @ ( setadjoin @ X793 @ emptyset ) ) )
=> ( ! [X795: $i,X796: $i,X797: $i] :
( ( in @ X797 @ ( setadjoin @ X795 @ ( setadjoin @ X796 @ emptyset ) ) )
=> ( ( X797 = X795 )
| ( X797 = X796 ) ) )
=> ( ! [X798: $i,X799: $i] : ( in @ X798 @ ( setadjoin @ X798 @ ( setadjoin @ X799 @ emptyset ) ) )
=> ( ! [X800: $i,X801: $i] : ( in @ X801 @ ( setadjoin @ X800 @ ( setadjoin @ X801 @ emptyset ) ) )
=> ( ! [X802: $i,X803: $i > $o] :
( ? [X804: $i] :
( ( in @ X804 @ X802 )
& ( X803 @ X804 ) )
=> ( ( ( dsetconstr @ X802 @ X803 )
= emptyset )
=> ~ $true ) )
=> ( ! [X805: $i > $o,X806: $i] :
( ( in @ X806 @ emptyset )
=> ( X805 @ X806 ) )
=> ( ! [X807: $i,X808: $i > $o] :
( ~ ! [X809: $i] :
( ( in @ X809 @ X807 )
=> ( X808 @ X809 ) )
=> ? [X810: $i] :
( ( in @ X810 @ X807 )
& ~ ( X808 @ X810 ) ) )
=> ( ! [X811: $i,X812: $i > $o] :
( ! [X813: $i] :
( ( in @ X813 @ X811 )
=> ~ ( X812 @ X813 ) )
=> ~ ? [X814: $i] :
( ( in @ X814 @ X811 )
& ( X812 @ X814 ) ) )
=> ( ! [X815: $i,X816: $i > $o] :
( ~ ? [X817: $i] :
( ( in @ X817 @ X815 )
& ( X816 @ X817 ) )
=> ! [X818: $i] :
( ( in @ X818 @ X815 )
=> ~ ( X816 @ X818 ) ) )
=> ( ! [X819: $i,X820: $i > $o] :
( ? [X821: $i] :
( ( in @ X821 @ X819 )
& ~ ( X820 @ X821 ) )
=> ~ ! [X822: $i] :
( ( in @ X822 @ X819 )
=> ( X820 @ X822 ) ) )
=> ( ! [X823: $o] :
( X823
=> ( in @ emptyset @ ( prop2set @ X823 ) ) )
=> ( ! [X824: $o] :
( X824
=> ( set2prop @ ( prop2set @ X824 ) ) )
=> ( ! [X825: $i,X826: $i > $o] :
( ~ ? [X827: $i] :
( ( in @ X827 @ X825 )
& ( X826 @ X827 ) )
=> ! [X828: $i] :
( ( in @ X828 @ X825 )
=> ~ ( X826 @ X828 ) ) )
=> ( ! [X829: $i,X830: $i > $o] :
( ~ ! [X831: $i] :
( ( in @ X831 @ X829 )
=> ( X830 @ X831 ) )
=> ? [X832: $i] :
( ( in @ X832 @ X829 )
& ~ ( X830 @ X832 ) ) )
=> ( ! [X833: $i > $o] :
( ? [X834: $i] :
( ( X833 @ X834 )
& ! [X835: $i] :
( ( X833 @ X835 )
=> ( X834 = X835 ) ) )
=> ? [X836: $i] :
( ( X833 @ X836 )
& ! [X837: $i] :
( ( X833 @ X837 )
=> ( X836 = X837 ) ) ) )
=> ( ! [X838: $i > $o] :
( ? [X839: $i] : ( X838 @ X839 )
=> ( ! [X840: $i,X841: $i] :
( ( X838 @ X840 )
=> ( ( X838 @ X841 )
=> ( X840 = X841 ) ) )
=> ? [X842: $i] :
( ( X838 @ X842 )
& ! [X843: $i] :
( ( X838 @ X843 )
=> ( X842 = X843 ) ) ) ) )
=> ( ! [X844: $i > $o] :
( ? [X845: $i] :
! [X846: $i] :
( ( X844 @ X846 )
<=> ( X846 = X845 ) )
=> ? [X847: $i] :
( ( X844 @ X847 )
& ! [X848: $i] :
( ( X844 @ X848 )
=> ( X847 = X848 ) ) ) )
=> ( ! [X849: $i,X850: $i] :
( ( X849 = X850 )
=> ! [X851: $i,X852: $i] :
( ( X851 = X852 )
=> ( ( in @ X851 @ X849 )
=> ( in @ X852 @ X850 ) ) ) )
=> ( ! [X853: $i,X854: $i] :
( ( X853 = X854 )
=> ! [X855: $i,X856: $i] :
( ( X855 = X856 )
=> ( ( in @ X855 @ X853 )
<=> ( in @ X856 @ X854 ) ) ) )
=> ( ! [X857: $i > $o] :
( ? [X858: $i] :
( ( X857 @ X858 )
& ! [X859: $i] :
( ( X857 @ X859 )
=> ( X858 = X859 ) ) )
=> ! [X860: $i,X861: $i] :
( ( X857 @ X860 )
=> ( ( X857 @ X861 )
=> ( X860 = X861 ) ) ) )
=> ( ! [X862: $i > $o,X863: $i > $o] :
( ! [X864: $i,X865: $i] :
( ( X864 = X865 )
=> ( ( X862 @ X864 )
<=> ( X863 @ X865 ) ) )
=> ( ? [X866: $i] :
( ( X862 @ X866 )
& ! [X867: $i] :
( ( X862 @ X867 )
=> ( X866 = X867 ) ) )
<=> ? [X868: $i] :
( ( X863 @ X868 )
& ! [X869: $i] :
( ( X863 @ X869 )
=> ( X868 = X869 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X870: $i,X871: $i] :
( ( X870 = X871 )
=> ! [X872: $i,X873: $i] :
( ( X872 = X873 )
=> ( ( setadjoin @ X870 @ X872 )
= ( setadjoin @ X871 @ X873 ) ) ) )
=> ( ! [X874: $i,X875: $i] :
( ( X874 = X875 )
=> ( ( powerset @ X874 )
= ( powerset @ X875 ) ) )
=> ( ! [X876: $i,X877: $i] :
( ( X876 = X877 )
=> ( ( setunion @ X876 )
= ( setunion @ X877 ) ) )
=> ( ( omega = omega )
=> ( ! [X878: $i > $o] :
( ? [X879: $i] :
( ( X878 @ X879 )
& ! [X880: $i] :
( ( X878 @ X880 )
=> ( X879 = X880 ) ) )
=> ! [X881: $i,X882: $i] :
( ( X878 @ X881 )
=> ( ( X878 @ X882 )
=> ( X881 = X882 ) ) ) )
=> ( ! [X883: $i > $o,X884: $i > $o] :
( ! [X885: $i,X886: $i] :
( ( X885 = X886 )
=> ( ( X883 @ X885 )
<=> ( X884 @ X886 ) ) )
=> ( ? [X887: $i] :
( ( X883 @ X887 )
& ! [X888: $i] :
( ( X883 @ X888 )
=> ( X887 = X888 ) ) )
=> ( ? [X889: $i] :
( ( X884 @ X889 )
& ! [X890: $i] :
( ( X884 @ X890 )
=> ( X889 = X890 ) ) )
=> ( ( descr @ X883 )
= ( descr @ X884 ) ) ) ) )
=> ( ! [X891: $i,X892: $i] :
( ( X891 = X892 )
=> ! [X893: $i > $o,X894: $i > $o] :
( ! [X895: $i] :
( ( in @ X895 @ X891 )
=> ! [X896: $i] :
( ( in @ X896 @ X892 )
=> ( ( X895 = X896 )
=> ( ( X893 @ X895 )
<=> ( X894 @ X896 ) ) ) ) )
=> ( ( dsetconstr @ X891 @ X893 )
= ( dsetconstr @ X892 @ X894 ) ) ) )
=> ( ! [X897: $i,X898: $i] :
( ! [X899: $i] :
( ( in @ X899 @ X897 )
=> ( in @ X899 @ X898 ) )
=> ( subset @ X897 @ X898 ) )
=> ( ! [X900: $i,X901: $i] :
( ( X900 = X901 )
=> ( subset @ X901 @ X900 ) )
=> ( ! [X902: $i,X903: $i] :
( ( X902 = X903 )
=> ( subset @ X902 @ X903 ) )
=> ( ! [X904: $i,X905: $i] :
( ! [X906: $i] :
( ( in @ X906 @ X904 )
=> ( in @ X906 @ X905 ) )
=> ( subset @ X904 @ X905 ) )
=> ( ! [X907: $i] : ( subset @ emptyset @ X907 )
=> ( ! [X908: $i,X909: $i,X910: $i] :
( ( subset @ X908 @ X909 )
=> ( ( in @ X910 @ X908 )
=> ( in @ X910 @ X909 ) ) )
=> ( ! [X911: $i,X912: $i,X913: $i] :
( ( subset @ X911 @ X912 )
=> ( ~ ( in @ X913 @ X912 )
=> ~ ( in @ X913 @ X911 ) ) )
=> ( ! [X914: $i,X915: $i,X916: $i] :
( ( in @ X916 @ X914 )
=> ( ~ ( in @ X916 @ X915 )
=> ~ ( subset @ X914 @ X915 ) ) )
=> ( ! [X917: $i,X918: $i] :
( ~ ( subset @ X917 @ X918 )
=> ( X917 != X918 ) )
=> ( ! [X919: $i,X920: $i,X921: $i] :
( ( in @ X921 @ X919 )
=> ( ~ ( in @ X921 @ X920 )
=> ( X919 != X920 ) ) )
=> ( ! [X922: $i] : ( subset @ X922 @ X922 )
=> ( ! [X923: $i,X924: $i,X925: $i] :
( ( subset @ X923 @ X924 )
=> ( ( subset @ X924 @ X925 )
=> ( subset @ X923 @ X925 ) ) )
=> ( ! [X926: $i,X927: $i] : ( subset @ X927 @ ( setadjoin @ X926 @ X927 ) )
=> ( ! [X928: $i,X929: $i,X930: $i] :
( ( subset @ X928 @ X930 )
=> ( subset @ X928 @ ( setadjoin @ X929 @ X930 ) ) )
=> ( ! [X931: $i,X932: $i] :
( ( subset @ X931 @ X932 )
=> ( in @ X931 @ ( powerset @ X932 ) ) )
=> ( ! [X933: $i,X934: $i] :
( ( subset @ X933 @ X934 )
=> ( ( subset @ X934 @ X933 )
=> ( X933 = X934 ) ) )
=> ( ! [X935: $i] :
( ( subset @ X935 @ emptyset )
=> ( X935 = emptyset ) )
=> ( ! [X936: $i,X937: $i] :
( ( subset @ X937 @ X936 )
=> ( in @ X937 @ ( powerset @ X936 ) ) )
=> ( ! [X938: $i,X939: $i] :
( ( in @ X939 @ ( powerset @ X938 ) )
=> ( subset @ X939 @ X938 ) )
=> ( ! [X940: $i] : ( in @ X940 @ ( powerset @ X940 ) )
=> ( ! [X941: $i,X942: $i] :
( ( subset @ X941 @ X942 )
=> ( subset @ ( powerset @ X941 ) @ ( powerset @ X942 ) ) )
=> ( ! [X943: $i,X944: $i > $o] : ( in @ ( dsetconstr @ X943 @ X944 ) @ ( powerset @ X943 ) )
=> ( ! [X945: $i,X946: $i > $o] : ( subset @ ( dsetconstr @ X945 @ X946 ) @ X945 )
=> ( ! [X947: $i,X948: $i,X949: $i] :
( ( in @ X949 @ X947 )
=> ( in @ X949 @ ( binunion @ X947 @ X948 ) ) )
=> ( ! [X950: $i,X951: $i] : ( in @ X951 @ ( setadjoin @ X950 @ ( setadjoin @ X951 @ emptyset ) ) )
=> ( ! [X952: $i,X953: $i,X954: $i] :
( ( in @ X954 @ X953 )
=> ( in @ X954 @ ( binunion @ X952 @ X953 ) ) )
=> ( ! [X955: $i,X956: $i,X957: $i,X958: $o] :
( ( in @ X957 @ ( binunion @ X955 @ X956 ) )
=> ( ( ( in @ X957 @ X955 )
=> X958 )
=> ( ( ( in @ X957 @ X956 )
=> X958 )
=> X958 ) ) )
=> ( ! [X959: $i,X960: $i,X961: $i] :
( ( in @ X961 @ ( binunion @ X959 @ X960 ) )
=> ( ( in @ X961 @ X959 )
| ( in @ X961 @ X960 ) ) )
=> ( ! [X962: $i,X963: $i] : ( subset @ X962 @ ( binunion @ X962 @ X963 ) )
=> ( ! [X964: $i,X965: $i] : ( subset @ X965 @ ( binunion @ X964 @ X965 ) )
=> ( ! [X966: $i,X967: $i,X968: $i] :
( ( in @ X968 @ X966 )
=> ( ( in @ X968 @ X967 )
=> ( in @ X968 @ ( binintersect @ X966 @ X967 ) ) ) )
=> ( ! [X969: $i,X970: $i,X971: $i] :
( ( subset @ X971 @ X969 )
=> ( ( subset @ X971 @ X970 )
=> ( subset @ X971 @ ( binintersect @ X969 @ X970 ) ) ) )
=> ( ! [X972: $i,X973: $i,X974: $i] :
( ( in @ X974 @ ( binintersect @ X972 @ X973 ) )
=> ( in @ X974 @ X972 ) )
=> ( ! [X975: $i,X976: $i] : ( subset @ ( binintersect @ X975 @ X976 ) @ X975 )
=> ( ! [X977: $i,X978: $i] :
( ( subset @ X977 @ X978 )
=> ( ( binintersect @ X977 @ X978 )
= X977 ) )
=> ( ! [X979: $i,X980: $i] :
( ( ( binintersect @ X979 @ X980 )
= X980 )
=> ( subset @ X980 @ X979 ) )
=> ( ! [X981: $i,X982: $i,X983: $i] :
( ( in @ X983 @ ( binintersect @ X981 @ X982 ) )
=> ( in @ X983 @ X982 ) )
=> ( ! [X984: $i,X985: $i] :
( ~ ? [X986: $i] :
( ( in @ X986 @ X984 )
& ( in @ X986 @ X985 ) )
=> ( ( binintersect @ X984 @ X985 )
= emptyset ) )
=> ( ! [X987: $i,X988: $i] : ( subset @ ( binintersect @ X987 @ X988 ) @ X988 )
=> ( ! [X989: $i,X990: $i] :
( ( subset @ X990 @ X989 )
=> ( ( binintersect @ X989 @ X990 )
= X990 ) )
=> ( ! [X991: $i,X992: $i] :
( ( ( binintersect @ X991 @ X992 )
= X991 )
=> ( subset @ X991 @ X992 ) )
=> ( ! [X993: $i,X994: $i,X995: $i] :
( ( binintersect @ X993 @ ( binunion @ X994 @ X995 ) )
= ( binunion @ ( binintersect @ X993 @ X994 ) @ ( binintersect @ X993 @ X995 ) ) )
=> ( ! [X996: $i,X997: $i,X998: $i] :
( ( in @ X998 @ X996 )
=> ( ~ ( in @ X998 @ X997 )
=> ( in @ X998 @ ( setminus @ X996 @ X997 ) ) ) )
=> ( ! [X999: $i,X1000: $i,X1001: $i] :
( ( in @ X1001 @ ( setminus @ X999 @ X1000 ) )
=> ( in @ X1001 @ X999 ) )
=> ( ! [X1002: $i,X1003: $i,X1004: $i] :
( ( in @ X1004 @ ( setminus @ X1002 @ X1003 ) )
=> ~ ( in @ X1004 @ X1003 ) )
=> ( ! [X1005: $i,X1006: $i] :
( ( subset @ X1005 @ X1006 )
=> ( ( setminus @ X1005 @ X1006 )
= emptyset ) )
=> ( ! [X1007: $i,X1008: $i,X1009: $i] :
( ~ ( in @ X1009 @ ( setminus @ X1007 @ X1008 ) )
=> ( ( in @ X1009 @ X1007 )
=> ( in @ X1009 @ X1008 ) ) )
=> ( ! [X1010: $i,X1011: $i,X1012: $i] :
( ~ ( in @ X1012 @ ( setminus @ X1010 @ X1011 ) )
=> ( ~ ( in @ X1012 @ X1011 )
=> ~ ( in @ X1012 @ X1010 ) ) )
=> ( ! [X1013: $i,X1014: $i,X1015: $i] :
( ~ ( in @ X1015 @ X1013 )
=> ~ ( in @ X1015 @ ( setminus @ X1013 @ X1014 ) ) )
=> ( ! [X1016: $i,X1017: $i,X1018: $i] :
( ( in @ X1018 @ X1017 )
=> ~ ( in @ X1018 @ ( setminus @ X1016 @ X1017 ) ) )
=> ( ! [X1019: $i,X1020: $i] : ( subset @ ( setminus @ X1019 @ X1020 ) @ X1019 )
=> ( ! [X1021: $i,X1022: $i] :
( ( ( setminus @ X1021 @ X1022 )
= emptyset )
=> ( subset @ X1021 @ X1022 ) )
=> ( ! [X1023: $i,X1024: $i,X1025: $i] :
( ( in @ X1025 @ ( symdiff @ X1023 @ X1024 ) )
=> ! [X1026: $o] :
( ( ( in @ X1025 @ X1023 )
=> ( ~ ( in @ X1025 @ X1024 )
=> X1026 ) )
=> ( ( ~ ( in @ X1025 @ X1023 )
=> ( ( in @ X1025 @ X1024 )
=> X1026 ) )
=> X1026 ) ) )
=> ( ! [X1027: $i,X1028: $i,X1029: $i] :
( ( in @ X1029 @ X1027 )
=> ( ~ ( in @ X1029 @ X1028 )
=> ( in @ X1029 @ ( symdiff @ X1027 @ X1028 ) ) ) )
=> ( ! [X1030: $i,X1031: $i,X1032: $i] :
( ~ ( in @ X1032 @ X1030 )
=> ( ( in @ X1032 @ X1031 )
=> ( in @ X1032 @ ( symdiff @ X1030 @ X1031 ) ) ) )
=> ( ! [X1033: $i,X1034: $i,X1035: $i] :
( ( in @ X1035 @ X1033 )
=> ( ( in @ X1035 @ X1034 )
=> ~ ( in @ X1035 @ ( symdiff @ X1033 @ X1034 ) ) ) )
=> ( ! [X1036: $i,X1037: $i,X1038: $i] :
( ~ ( in @ X1038 @ X1036 )
=> ( ~ ( in @ X1038 @ X1037 )
=> ~ ( in @ X1038 @ ( symdiff @ X1036 @ X1037 ) ) ) )
=> ( ! [X1039: $i,X1040: $i] : ( in @ X1040 @ ( setadjoin @ X1039 @ ( setadjoin @ X1040 @ emptyset ) ) )
=> ( ! [X1041: $i,X1042: $i] : ( in @ X1041 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1041 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1041 @ ( setadjoin @ X1042 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1043: $i,X1044: $i] : ( in @ X1044 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1043 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1043 @ ( setadjoin @ X1044 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1045: $i,X1046: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1045 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1045 @ ( setadjoin @ X1046 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1047: $i,X1048: $i] : ( iskpair @ ( kpair @ X1047 @ X1048 ) )
=> ( ! [X1049: $i,X1050: $i] :
( ( in @ X1050 @ X1049 )
=> ( subset @ ( setadjoin @ X1050 @ emptyset ) @ X1049 ) )
=> ( ! [X1051: $i,X1052: $i] :
( ( in @ X1052 @ X1051 )
=> ( in @ ( setadjoin @ X1052 @ emptyset ) @ ( powerset @ X1051 ) ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i] :
( ( in @ X1055 @ X1053 )
=> ( in @ ( setadjoin @ X1055 @ emptyset ) @ ( powerset @ ( binunion @ X1053 @ X1054 ) ) ) )
=> ( ! [X1056: $i,X1057: $i,X1058: $i] :
( ( in @ X1058 @ ( setadjoin @ X1056 @ ( setadjoin @ X1057 @ emptyset ) ) )
=> ( ( X1058 = X1056 )
| ( X1058 = X1057 ) ) )
=> ( ! [X1059: $i,X1060: $i,X1061: $i] :
( ( in @ X1061 @ X1059 )
=> ! [X1062: $i] :
( ( in @ X1062 @ X1060 )
=> ( subset @ ( setadjoin @ X1061 @ ( setadjoin @ X1062 @ emptyset ) ) @ ( binunion @ X1059 @ X1060 ) ) ) )
=> ( ! [X1063: $i,X1064: $i,X1065: $i] :
( ( in @ X1065 @ X1063 )
=> ! [X1066: $i] :
( ( in @ X1066 @ X1064 )
=> ( in @ ( setadjoin @ X1065 @ ( setadjoin @ X1066 @ emptyset ) ) @ ( powerset @ ( binunion @ X1063 @ X1064 ) ) ) ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i] :
( ( in @ X1069 @ X1067 )
=> ! [X1070: $i] :
( ( in @ X1070 @ X1068 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1069 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1069 @ ( setadjoin @ X1070 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1067 @ X1068 ) ) ) ) )
=> ( ! [X1071: $i,X1072: $i,X1073: $i] :
( ( in @ X1073 @ X1071 )
=> ! [X1074: $i] :
( ( in @ X1074 @ X1072 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1073 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1073 @ ( setadjoin @ X1074 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1071 @ X1072 ) ) ) ) ) )
=> ( ! [X1075: $i,X1076: $i,X1077: $i] :
( ( in @ X1077 @ X1075 )
=> ! [X1078: $i] :
( ( in @ X1078 @ X1076 )
=> ( in @ ( kpair @ X1077 @ X1078 ) @ ( powerset @ ( powerset @ ( binunion @ X1075 @ X1076 ) ) ) ) ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i] :
( ( in @ X1081 @ X1079 )
=> ! [X1082: $i] :
( ( in @ X1082 @ X1080 )
=> ( in @ ( kpair @ X1081 @ X1082 ) @ ( cartprod @ X1079 @ X1080 ) ) ) )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ( in @ X1085 @ ( cartprod @ X1083 @ X1084 ) )
=> ? [X1086: $i] :
( ( in @ X1086 @ X1083 )
& ? [X1087: $i] :
( ( in @ X1087 @ X1084 )
& ( X1085
= ( kpair @ X1086 @ X1087 ) ) ) ) )
=> ( ! [X1088: $i,X1089: $i,X1090: $i] :
( ( in @ X1090 @ ( cartprod @ X1088 @ X1089 ) )
=> ( iskpair @ X1090 ) )
=> ( ! [X1091: $i,X1092: $i] :
( ( in @ X1092 @ ( setunion @ X1091 ) )
=> ? [X1093: $i] :
( ( in @ X1093 @ X1091 )
& ( in @ X1092 @ X1093 ) ) )
=> ( ! [X1094: $i] : ( subset @ ( setunion @ ( setadjoin @ X1094 @ emptyset ) ) @ X1094 )
=> ( ! [X1095: $i] : ( subset @ X1095 @ ( setunion @ ( setadjoin @ X1095 @ emptyset ) ) )
=> ( ! [X1096: $i] :
( ( setunion @ ( setadjoin @ X1096 @ emptyset ) )
= X1096 )
=> ( ! [X1097: $i,X1098: $i > $o] :
( ! [X1099: $i] :
( ( in @ X1099 @ X1097 )
=> ! [X1100: $i] :
( ( in @ X1100 @ X1097 )
=> ( ( X1098 @ X1099 )
=> ( ( X1098 @ X1100 )
=> ( X1099 = X1100 ) ) ) ) )
=> ( ? [X1101: $i] :
( ( in @ X1101 @ X1097 )
& ( X1098 @ X1101 ) )
=> ? [X1102: $i] :
( ( in @ X1102 @ ( dsetconstr @ X1097 @ X1098 ) )
& ( ( dsetconstr @ X1097 @ X1098 )
= ( setadjoin @ X1102 @ emptyset ) ) ) ) )
=> ( ! [X1103: $i,X1104: $i > $o] :
( ? [X1105: $i] :
( ( in @ X1105 @ ( dsetconstr @ X1103 @ X1104 ) )
& ( ( dsetconstr @ X1103 @ X1104 )
= ( setadjoin @ X1105 @ emptyset ) ) )
=> ? [X1106: $i] :
( ( in @ X1106 @ X1103 )
& ( X1104 @ X1106 ) ) )
=> ( ! [X1107: $i,X1108: $i > $o,X1109: $i] :
( ( in @ X1109 @ X1107 )
=> ( ( X1108 @ X1109 )
=> ( ! [X1110: $i] :
( ( in @ X1110 @ X1107 )
=> ( ( X1108 @ X1110 )
=> ( X1110 = X1109 ) ) )
=> ? [X1111: $i] :
( ( in @ X1111 @ ( dsetconstr @ X1107 @ X1108 ) )
& ( ( dsetconstr @ X1107 @ X1108 )
= ( setadjoin @ X1111 @ emptyset ) ) ) ) ) )
=> ( ! [X1112: $i,X1113: $i > $o] :
( ! [X1114: $i] :
( ( in @ X1114 @ X1112 )
=> ! [X1115: $i] :
( ( in @ X1115 @ X1112 )
=> ( ( X1113 @ X1114 )
=> ( ( X1113 @ X1115 )
=> ( X1114 = X1115 ) ) ) ) )
=> ( ? [X1116: $i] :
( ( in @ X1116 @ X1112 )
& ( X1113 @ X1116 ) )
=> ? [X1117: $i] :
( ( in @ X1117 @ ( dsetconstr @ X1112 @ X1113 ) )
& ( ( dsetconstr @ X1112 @ X1113 )
= ( setadjoin @ X1117 @ emptyset ) ) ) ) )
=> ( ! [X1118: $i,X1119: $i] :
( ( ( setadjoin @ X1118 @ emptyset )
= ( setadjoin @ X1119 @ emptyset ) )
=> ( X1118 = X1119 ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ( in @ ( setadjoin @ X1122 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1120 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1120 @ ( setadjoin @ X1121 @ emptyset ) ) @ emptyset ) ) )
=> ( X1120 = X1122 ) )
=> ( ! [X1123: $i] :
( ( iskpair @ X1123 )
=> ? [X1124: $i] :
( ( in @ X1124
@ ( dsetconstr @ ( setunion @ X1123 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1123 ) ) )
& ( ( dsetconstr @ ( setunion @ X1123 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1123 ) )
= ( setadjoin @ X1124 @ emptyset ) ) ) )
=> ( ! [X1125: $i] :
( ? [X1126: $i] :
( ( in @ X1126 @ X1125 )
& ( X1125
= ( setadjoin @ X1126 @ emptyset ) ) )
=> ( in @ ( setunion @ X1125 ) @ X1125 ) )
=> ( ! [X1127: $i,X1128: $i] :
( ( kfst @ ( kpair @ X1127 @ X1128 ) )
= X1127 )
=> ( ! [X1129: $i,X1130: $i,X1131: $i] :
( ( in @ X1131 @ ( cartprod @ X1129 @ X1130 ) )
=> ( in @ ( kfst @ X1131 ) @ X1129 ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i,X1135: $i] :
( ( ( setadjoin @ ( setadjoin @ X1132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1132 @ ( setadjoin @ X1133 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1134 @ ( setadjoin @ X1135 @ emptyset ) ) @ emptyset ) ) )
=> ( X1132 = X1134 ) )
=> ( ! [X1136: $i,X1137: $i,X1138: $i,X1139: $i] :
( ( ( kpair @ X1136 @ X1137 )
= ( kpair @ X1138 @ X1139 ) )
=> ( X1136 = X1138 ) )
=> ( ! [X1140: $i,X1141: $i] :
( ( X1140 = X1141 )
=> ( ( setadjoin @ X1140 @ ( setadjoin @ X1141 @ emptyset ) )
= ( setadjoin @ X1140 @ emptyset ) ) )
=> ( ! [X1142: $i,X1143: $i] :
( ( X1142 = X1143 )
=> ( ( setadjoin @ ( setadjoin @ X1142 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1142 @ ( setadjoin @ X1143 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1142 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1144: $i,X1145: $i,X1146: $i,X1147: $i] :
( ( ( setadjoin @ ( setadjoin @ X1144 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1144 @ ( setadjoin @ X1145 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1146 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1146 @ ( setadjoin @ X1147 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1146 = X1147 )
=> ( X1145 = X1147 ) ) )
=> ( ! [X1148: $i,X1149: $i,X1150: $i] :
( ( ( setadjoin @ X1148 @ ( setadjoin @ X1149 @ emptyset ) )
= ( setadjoin @ X1150 @ emptyset ) )
=> ( X1148 = X1149 ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i,X1154: $i] :
( ( ( setadjoin @ ( setadjoin @ X1151 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1151 @ ( setadjoin @ X1152 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1153 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1153 @ ( setadjoin @ X1154 @ emptyset ) ) @ emptyset ) ) )
=> ( X1152 = X1154 ) )
=> ( ! [X1155: $i,X1156: $i,X1157: $i,X1158: $i] :
( ( ( kpair @ X1155 @ X1156 )
= ( kpair @ X1157 @ X1158 ) )
=> ( X1156 = X1158 ) )
=> ( ! [X1159: $i] :
( ( iskpair @ X1159 )
=> ? [X1160: $i] :
( ( in @ X1160
@ ( dsetconstr @ ( setunion @ X1159 )
@ ^ [Z0: $i] :
( X1159
= ( kpair @ ( kfst @ X1159 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X1159 )
@ ^ [Z0: $i] :
( X1159
= ( kpair @ ( kfst @ X1159 ) @ Z0 ) ) )
= ( setadjoin @ X1160 @ emptyset ) ) ) )
=> ( ! [X1161: $i,X1162: $i] :
( ( ksnd @ ( kpair @ X1161 @ X1162 ) )
= X1162 )
=> ( ! [X1163: $i] :
( ( iskpair @ X1163 )
=> ( ( kpair @ ( kfst @ X1163 ) @ ( ksnd @ X1163 ) )
= X1163 ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( in @ X1166 @ ( cartprod @ X1164 @ X1165 ) )
=> ( in @ ( ksnd @ X1166 ) @ X1165 ) )
=> ( ! [X1167: $i,X1168: $i,X1169: $i,X1170: $i] :
( ( in @ ( kpair @ X1169 @ X1170 ) @ ( cartprod @ X1167 @ X1168 ) )
=> ( in @ X1169 @ X1167 ) )
=> ( ! [X1171: $i,X1172: $i,X1173: $i,X1174: $i] :
( ( in @ ( kpair @ X1173 @ X1174 ) @ ( cartprod @ X1171 @ X1172 ) )
=> ( in @ X1174 @ X1172 ) )
=> ( ! [X1175: $i,X1176: $i,X1177: $i] :
( ( in @ X1177 @ X1175 )
=> ! [X1178: $i] :
( ( in @ X1178 @ X1176 )
=> ( ( kpair @ X1177 @ X1178 )
= ( kpair @ X1177 @ X1178 ) ) ) )
=> ( ! [X1179: $i,X1180: $i,X1181: $i] :
( ( in @ X1181 @ X1179 )
=> ! [X1182: $i] :
( ( in @ X1182 @ X1180 )
=> ( ( kfst @ ( kpair @ X1181 @ X1182 ) )
= X1181 ) ) )
=> ( ! [X1183: $i,X1184: $i,X1185: $i] :
( ( in @ X1185 @ X1183 )
=> ! [X1186: $i] :
( ( in @ X1186 @ X1184 )
=> ( ( ksnd @ ( kpair @ X1185 @ X1186 ) )
= X1186 ) ) )
=> ( ! [X1187: $i,X1188: $i,X1189: $i] :
( ( in @ X1189 @ ( cartprod @ X1187 @ X1188 ) )
=> ( ( kpair @ ( kfst @ X1189 ) @ ( ksnd @ X1189 ) )
= X1189 ) )
=> ( ! [X1190: $i,X1191: $i,X1192: $i > $i > $o,X1193: $i] :
( ( in @ X1193 @ X1190 )
=> ! [X1194: $i] :
( ( in @ X1194 @ X1191 )
=> ( ( X1192 @ X1193 @ X1194 )
=> ( in @ ( kpair @ X1193 @ X1194 ) @ ( dpsetconstr @ X1190 @ X1191 @ X1192 ) ) ) ) )
=> ( ! [X1195: $i,X1196: $i,X1197: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1195 @ X1196 @ X1197 ) @ ( cartprod @ X1195 @ X1196 ) )
=> ( ! [X1198: $i,X1199: $i,X1200: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1198 @ X1199 @ X1200 ) @ ( cartprod @ X1198 @ X1199 ) )
=> ( ! [X1201: $i,X1202: $i,X1203: $i > $i > $o,X1204: $i] :
( ( in @ X1204 @ X1201 )
=> ! [X1205: $i] :
( ( in @ X1205 @ X1202 )
=> ( ( in @ ( kpair @ X1204 @ X1205 ) @ ( dpsetconstr @ X1201 @ X1202 @ X1203 ) )
=> ( X1203 @ X1204 @ X1205 ) ) ) )
=> ( ! [X1206: $i,X1207: $i,X1208: $i > $i > $o,X1209: $i,X1210: $i] :
( ( in @ ( kpair @ X1209 @ X1210 ) @ ( dpsetconstr @ X1206 @ X1207 @ X1208 ) )
=> ( in @ X1209 @ X1206 ) )
=> ( ! [X1211: $i,X1212: $i,X1213: $i > $i > $o,X1214: $i,X1215: $i] :
( ( in @ ( kpair @ X1214 @ X1215 ) @ ( dpsetconstr @ X1211 @ X1212 @ X1213 ) )
=> ( in @ X1215 @ X1212 ) )
=> ( ! [X1216: $i,X1217: $i,X1218: $i > $i > $o,X1219: $i,X1220: $i] :
( ( in @ ( kpair @ X1219 @ X1220 ) @ ( dpsetconstr @ X1216 @ X1217 @ X1218 ) )
=> ( X1218 @ X1219 @ X1220 ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i] :
( ( ( subset @ X1223 @ ( cartprod @ X1221 @ X1222 ) )
& ! [X1224: $i] :
( ( in @ X1224 @ X1221 )
=> ? [X1225: $i] :
( ( in @ X1225
@ ( dsetconstr @ X1222
@ ^ [Z0: $i] : ( in @ ( kpair @ X1224 @ Z0 ) @ X1223 ) ) )
& ( ( dsetconstr @ X1222
@ ^ [Z0: $i] : ( in @ ( kpair @ X1224 @ Z0 ) @ X1223 ) )
= ( setadjoin @ X1225 @ emptyset ) ) ) ) )
=> ! [X1226: $i] :
( ( in @ X1226 @ X1221 )
=> ? [X1227: $i] :
( ( in @ X1227
@ ( dsetconstr @ X1222
@ ^ [Z0: $i] : ( in @ ( kpair @ X1226 @ Z0 ) @ X1223 ) ) )
& ( ( dsetconstr @ X1222
@ ^ [Z0: $i] : ( in @ ( kpair @ X1226 @ Z0 ) @ X1223 ) )
= ( setadjoin @ X1227 @ emptyset ) ) ) ) )
=> ( ! [X1228: $i,X1229: $i,X1230: $i] :
( ( ( subset @ X1230 @ ( cartprod @ X1228 @ X1229 ) )
& ! [X1231: $i] :
( ( in @ X1231 @ X1228 )
=> ? [X1232: $i] :
( ( in @ X1232
@ ( dsetconstr @ X1229
@ ^ [Z0: $i] : ( in @ ( kpair @ X1231 @ Z0 ) @ X1230 ) ) )
& ( ( dsetconstr @ X1229
@ ^ [Z0: $i] : ( in @ ( kpair @ X1231 @ Z0 ) @ X1230 ) )
= ( setadjoin @ X1232 @ emptyset ) ) ) ) )
=> ! [X1233: $i] :
( ( in @ X1233 @ X1228 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1229
@ ^ [Z0: $i] : ( in @ ( kpair @ X1233 @ Z0 ) @ X1230 ) ) )
@ X1229 ) ) )
=> ( ! [X1234: $i,X1235: $i,X1236: $i] :
( ( ( subset @ X1236 @ ( cartprod @ X1234 @ X1235 ) )
& ! [X1237: $i] :
( ( in @ X1237 @ X1234 )
=> ? [X1238: $i] :
( ( in @ X1238
@ ( dsetconstr @ X1235
@ ^ [Z0: $i] : ( in @ ( kpair @ X1237 @ Z0 ) @ X1236 ) ) )
& ( ( dsetconstr @ X1235
@ ^ [Z0: $i] : ( in @ ( kpair @ X1237 @ Z0 ) @ X1236 ) )
= ( setadjoin @ X1238 @ emptyset ) ) ) ) )
=> ! [X1239: $i] :
( ( in @ X1239 @ X1234 )
=> ( in @ ( ap @ X1234 @ X1235 @ X1236 @ X1239 ) @ X1235 ) ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i] :
( ( in @ X1242 @ ( funcSet @ X1240 @ X1241 ) )
=> ( ( subset @ X1242 @ ( cartprod @ X1240 @ X1241 ) )
& ! [X1243: $i] :
( ( in @ X1243 @ X1240 )
=> ? [X1244: $i] :
( ( in @ X1244
@ ( dsetconstr @ X1241
@ ^ [Z0: $i] : ( in @ ( kpair @ X1243 @ Z0 ) @ X1242 ) ) )
& ( ( dsetconstr @ X1241
@ ^ [Z0: $i] : ( in @ ( kpair @ X1243 @ Z0 ) @ X1242 ) )
= ( setadjoin @ X1244 @ emptyset ) ) ) ) ) )
=> ( ! [X1245: $i,X1246: $i,X1247: $i] :
( ( in @ X1247 @ ( funcSet @ X1245 @ X1246 ) )
=> ! [X1248: $i] :
( ( in @ X1248 @ X1245 )
=> ( in @ ( ap @ X1245 @ X1246 @ X1247 @ X1248 ) @ X1246 ) ) )
=> ( ! [X1249: $i,X1250: $i,X1251: $i] :
( ( ( subset @ X1251 @ ( cartprod @ X1249 @ X1250 ) )
& ! [X1252: $i] :
( ( in @ X1252 @ X1249 )
=> ? [X1253: $i] :
( ( in @ X1253
@ ( dsetconstr @ X1250
@ ^ [Z0: $i] : ( in @ ( kpair @ X1252 @ Z0 ) @ X1251 ) ) )
& ( ( dsetconstr @ X1250
@ ^ [Z0: $i] : ( in @ ( kpair @ X1252 @ Z0 ) @ X1251 ) )
= ( setadjoin @ X1253 @ emptyset ) ) ) ) )
=> ( in @ X1251 @ ( funcSet @ X1249 @ X1250 ) ) )
=> ( ! [X1254: $i,X1255: $i,X1256: $i > $i] :
( ! [X1257: $i] :
( ( in @ X1257 @ X1254 )
=> ( in @ ( X1256 @ X1257 ) @ X1255 ) )
=> ( ( subset
@ ( dpsetconstr @ X1254 @ X1255
@ ^ [Z0: $i] : ( $eq @ ( X1256 @ Z0 ) ) )
@ ( cartprod @ X1254 @ X1255 ) )
& ! [X1258: $i] :
( ( in @ X1258 @ X1254 )
=> ? [X1259: $i] :
( ( in @ X1259
@ ( dsetconstr @ X1255
@ ^ [Z0: $i] :
( in @ ( kpair @ X1258 @ Z0 )
@ ( dpsetconstr @ X1254 @ X1255
@ ^ [Z1: $i] : ( $eq @ ( X1256 @ Z1 ) ) ) ) ) )
& ( ( dsetconstr @ X1255
@ ^ [Z0: $i] :
( in @ ( kpair @ X1258 @ Z0 )
@ ( dpsetconstr @ X1254 @ X1255
@ ^ [Z1: $i] : ( $eq @ ( X1256 @ Z1 ) ) ) ) )
= ( setadjoin @ X1259 @ emptyset ) ) ) ) ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i > $i] :
( ! [X1263: $i] :
( ( in @ X1263 @ X1260 )
=> ( in @ ( X1262 @ X1263 ) @ X1261 ) )
=> ( ( subset @ ( lam @ X1260 @ X1261 @ X1262 ) @ ( cartprod @ X1260 @ X1261 ) )
& ! [X1264: $i] :
( ( in @ X1264 @ X1260 )
=> ? [X1265: $i] :
( ( in @ X1265
@ ( dsetconstr @ X1261
@ ^ [Z0: $i] : ( in @ ( kpair @ X1264 @ Z0 ) @ ( lam @ X1260 @ X1261 @ X1262 ) ) ) )
& ( ( dsetconstr @ X1261
@ ^ [Z0: $i] : ( in @ ( kpair @ X1264 @ Z0 ) @ ( lam @ X1260 @ X1261 @ X1262 ) ) )
= ( setadjoin @ X1265 @ emptyset ) ) ) ) ) )
=> ( ! [X1266: $i,X1267: $i,X1268: $i > $i] :
( ! [X1269: $i] :
( ( in @ X1269 @ X1266 )
=> ( in @ ( X1268 @ X1269 ) @ X1267 ) )
=> ( in @ ( lam @ X1266 @ X1267 @ X1268 ) @ ( funcSet @ X1266 @ X1267 ) ) )
=> ! [X4: $i,X5: $i,X29: $i] :
( ( subset @ X29 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X29 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[brelnall1]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_236]),foundationAx]),wellorderingAx]),c_0_237]),c_0_238]),c_0_239]),c_0_240]),c_0_241]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_242]),setext]),emptyI]),noeltsimpempty]),c_0_243]),c_0_244]),c_0_245]),c_0_246]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_247]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_248]),c_0_249]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_250]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_251]),c_0_252]),c_0_253]),inCongP]),in__Cong]),c_0_254]),c_0_255]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_256]),c_0_257]),c_0_258]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_259]),c_0_260]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_261]),c_0_262]),c_0_263]),c_0_264]),singletonsuniq]),setukpairinjL1]),c_0_265]),c_0_266]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_267]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_208]),c_0_268]),c_0_269]),c_0_270]),c_0_271]),c_0_272]),c_0_273]),c_0_274]),c_0_275]),c_0_276]),c_0_277]),c_0_278]),ap2p]),c_0_279]),c_0_280]),c_0_281]),c_0_282])])]),c_0_283]) ).
thf(c_0_285,negated_conjecture,
! [X1284: $i,X1285: $i,X1287: $i,X1288: $i,X1289: $i,X1290: $i,X1291: $i,X1292: $i,X1293: $i,X1294: $i,X1295: $i,X1297: $i,X1298: $i,X1300: $i,X1301: $i,X1302: $i,X1303: $i,X1304: $i,X1306: $i,X1307: $i > $i > $o,X1308: $i,X1310: $i,X1313: $i,X1315: $i,X1316: $i,X1317: $i,X1318: $i,X1320: $i,X1321: $i > $o,X1322: $i,X1324: $i,X1325: $i > $o,X1326: $i,X1327: $i,X1328: $i > $o,X1329: $i,X1330: $i,X1331: $i > $o,X1332: $i,X1333: $i > $o,X1334: $i,X1337: $i,X1338: $o,X1339: $i,X1340: $i,X1341: $o,X1342: $i,X1343: $i,X1344: $i > $o,X1345: $i,X1348: $i,X1349: $i,X1352: $i,X1354: $i,X1356: $i,X1357: $i > $o,X1358: $i,X1359: $i,X1361: $i,X1362: $i > $o,X1363: $i,X1364: $i,X1365: $i,X1366: $i,X1367: $i,X1368: $i,X1369: $i,X1370: $i,X1371: $i,X1372: $i,X1373: $i,X1374: $o,X1375: $i,X1376: $i,X1377: $i,X1378: $i,X1379: $i,X1380: $i,X1382: $i,X1383: $i,X1384: $i,X1385: $i,X1386: $i,X1387: $i,X1388: $i,X1389: $i,X1390: $i,X1391: $i,X1392: $o,X1394: $i,X1395: $i,X1396: $i > $o,X1397: $i,X1400: $i,X1401: $i,X1402: $i,X1404: $i,X1405: $i,X1406: $i,X1407: $i,X1408: $i,X1409: $i,X1410: $i,X1411: $i,X1412: $i,X1413: $i,X1414: $i,X1415: $i,X1416: $i,X1417: $i,X1418: $i,X1419: $i,X1420: $i > $o,X1421: $i,X1422: $i > $o,X1423: $i,X1424: $i,X1425: $i > $o,X1426: $i,X1428: $i,X1429: $i > $o,X1431: $i,X1432: $i,X1433: $i > $o,X1435: $i,X1436: $i,X1437: $i > $o,X1438: $i,X1440: $o,X1441: $o,X1442: $i,X1443: $i > $o,X1445: $i,X1446: $i,X1447: $i > $o,X1448: $i,X1450: $i > $o,X1451: $i,X1454: $i,X1455: $i > $o,X1456: $i,X1460: $i,X1461: $i > $o,X1462: $i,X1465: $i,X1466: $i,X1467: $i,X1468: $i,X1469: $i,X1470: $i,X1471: $i,X1472: $i,X1473: $i,X1474: $i > $o,X1475: $i,X1477: $i,X1478: $i,X1479: $i > $o,X1480: $i > $o,X1483: $i,X1486: $i,X1487: $i,X1490: $i,X1491: $i,X1492: $i,X1493: $i,X1494: $i,X1495: $i,X1496: $i,X1497: $i,X1498: $i,X1499: $i > $o,X1500: $i,X1502: $i,X1503: $i,X1504: $i > $o,X1505: $i > $o,X1508: $i,X1510: $i,X1512: $i,X1513: $i,X1514: $i > $o,X1515: $i > $o,X1518: $i,X1519: $i,X1521: $i,X1522: $i,X1523: $i,X1524: $i,X1525: $i,X1526: $i,X1528: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $i,X1535: $i,X1536: $i,X1537: $i,X1538: $i,X1539: $i,X1540: $i,X1541: $i,X1542: $i,X1543: $i,X1544: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1550: $i,X1551: $i,X1552: $i,X1553: $i,X1554: $i,X1555: $i,X1556: $i,X1557: $i,X1558: $i,X1559: $i,X1560: $i,X1561: $i,X1562: $i,X1563: $i,X1564: $i,X1565: $i > $o,X1566: $i,X1567: $i > $o,X1568: $i,X1569: $i,X1570: $i,X1571: $i,X1572: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $o,X1580: $i,X1581: $i,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $i,X1589: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $i,X1605: $i,X1606: $i,X1608: $i,X1609: $i,X1610: $i,X1611: $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,X1629: $i,X1630: $i,X1631: $i,X1632: $i,X1633: $i,X1634: $i,X1635: $i,X1636: $i,X1637: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1643: $i,X1644: $i,X1645: $i,X1646: $i,X1647: $o,X1648: $i,X1649: $i,X1650: $i,X1651: $i,X1652: $i,X1653: $i,X1654: $i,X1655: $i,X1656: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1715: $i,X1716: $i,X1717: $i,X1718: $i,X1719: $i > $o,X1722: $i,X1724: $i,X1725: $i > $o,X1726: $i,X1728: $i,X1729: $i > $o,X1730: $i,X1733: $i,X1734: $i > $o,X1737: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $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,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i,X1787: $i,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 > $i > $o,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i > $i > $o,X1819: $i,X1820: $i,X1821: $i > $i > $o,X1822: $i,X1823: $i,X1824: $i > $i > $o,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i > $i > $o,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i > $i > $o,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i > $i > $o,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1846: $i,X1847: $i,X1849: $i,X1850: $i,X1851: $i,X1853: $i,X1854: $i,X1855: $i,X1856: $i,X1857: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i > $i,X1879: $i,X1881: $i,X1882: $i,X1883: $i > $i,X1885: $i,X1887: $i,X1888: $i,X1889: $i > $i,X1895: $i,X1896: $i] :
( ( ~ ( in @ ( esk1_2 @ X1284 @ X1285 ) @ X1284 )
| ~ ( in @ ( esk1_2 @ X1284 @ X1285 ) @ X1285 )
| ( X1284 = X1285 ) )
& ( ( in @ ( esk1_2 @ X1284 @ X1285 ) @ X1284 )
| ( in @ ( esk1_2 @ X1284 @ X1285 ) @ X1285 )
| ( X1284 = X1285 ) )
& ~ ( in @ X1287 @ emptyset )
& ( ~ ( in @ X1290 @ ( setadjoin @ X1288 @ X1289 ) )
| ( X1290 = X1288 )
| ( in @ X1290 @ X1289 ) )
& ( ( X1290 != X1288 )
| ( in @ X1290 @ ( setadjoin @ X1288 @ X1289 ) ) )
& ( ~ ( in @ X1290 @ X1289 )
| ( in @ X1290 @ ( setadjoin @ X1288 @ X1289 ) ) )
& ( ~ ( in @ X1292 @ ( powerset @ X1291 ) )
| ~ ( in @ X1293 @ X1292 )
| ( in @ X1293 @ X1291 ) )
& ( ( in @ ( esk2_2 @ X1294 @ X1295 ) @ X1295 )
| ( in @ X1295 @ ( powerset @ X1294 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1294 @ X1295 ) @ X1294 )
| ( in @ X1295 @ ( powerset @ X1294 ) ) )
& ( ( in @ X1298 @ ( esk3_2 @ X1297 @ X1298 ) )
| ~ ( in @ X1298 @ ( setunion @ X1297 ) ) )
& ( ( in @ ( esk3_2 @ X1297 @ X1298 ) @ X1297 )
| ~ ( in @ X1298 @ ( setunion @ X1297 ) ) )
& ( ~ ( in @ X1301 @ X1302 )
| ~ ( in @ X1302 @ X1300 )
| ( in @ X1301 @ ( setunion @ X1300 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1303 @ omega )
| ( in @ ( setadjoin @ X1303 @ X1303 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1304 ) @ omega )
| ~ ( in @ emptyset @ X1304 )
| ~ ( in @ X1306 @ omega )
| ( in @ X1306 @ X1304 ) )
& ( ( in @ ( esk4_1 @ X1304 ) @ X1304 )
| ~ ( in @ emptyset @ X1304 )
| ~ ( in @ X1306 @ omega )
| ( in @ X1306 @ X1304 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1304 ) @ ( esk4_1 @ X1304 ) ) @ X1304 )
| ~ ( in @ emptyset @ X1304 )
| ~ ( in @ X1306 @ omega )
| ( in @ X1306 @ X1304 ) )
& ( ( in @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1308 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( in @ ( esk5_2 @ X1307 @ X1308 ) @ X1308 ) )
& ( ( X1307 @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1313 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( in @ ( esk5_2 @ X1307 @ X1308 ) @ X1308 ) )
& ( ~ ( in @ X1316 @ X1308 )
| ~ ( X1307 @ X1316 @ X1315 )
| ( in @ X1315 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( in @ ( esk5_2 @ X1307 @ X1308 ) @ X1308 ) )
& ( ( in @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1308 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ( X1307 @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1313 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ~ ( in @ X1316 @ X1308 )
| ~ ( X1307 @ X1316 @ X1315 )
| ( in @ X1315 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ( in @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1308 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1310
!= ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ( X1307 @ ( esk8_3 @ X1307 @ X1308 @ X1313 ) @ X1313 )
| ~ ( in @ X1313 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1310
!= ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ~ ( in @ X1316 @ X1308 )
| ~ ( X1307 @ X1316 @ X1315 )
| ( in @ X1315 @ ( esk7_2 @ X1307 @ X1308 ) )
| ( X1310
!= ( esk6_3 @ X1307 @ X1308 @ X1310 ) )
| ~ ( X1307 @ ( esk5_2 @ X1307 @ X1308 ) @ X1310 ) )
& ( ( in @ ( esk9_1 @ X1317 ) @ X1317 )
| ~ ( in @ X1318 @ X1317 ) )
& ( ~ ( in @ X1320 @ ( esk9_1 @ X1317 ) )
| ~ ( in @ X1320 @ X1317 )
| ~ ( in @ X1318 @ X1317 ) )
& epred1_0
& ( ( X1321 @ ( esk10_2 @ X1321 @ X1322 ) )
| ~ ( X1321 @ X1322 )
| ( X1321 @ ( descr @ X1321 ) ) )
& ( ( X1322
!= ( esk10_2 @ X1321 @ X1322 ) )
| ~ ( X1321 @ X1322 )
| ( X1321 @ ( descr @ X1321 ) ) )
& ( ~ ( in @ X1326 @ X1324 )
| ~ ( X1325 @ X1326 )
| ( in @ X1326 @ ( dsetconstr @ X1324 @ X1325 ) ) )
& ( ~ ( in @ X1329 @ ( dsetconstr @ X1327 @ X1328 ) )
| ( in @ X1329 @ X1327 ) )
& ( ~ ( in @ X1332 @ ( dsetconstr @ X1330 @ X1331 ) )
| ( X1331 @ X1332 ) )
& ( ( X1333 @ ( esk12_1 @ X1333 ) )
| ( X1333 @ ( esk11_2 @ X1333 @ X1334 ) )
| ~ ( X1333 @ X1334 ) )
& ( ~ ( X1333 @ X1337 )
| ( ( esk12_1 @ X1333 )
= X1337 )
| ( X1333 @ ( esk11_2 @ X1333 @ X1334 ) )
| ~ ( X1333 @ X1334 ) )
& ( ( X1333 @ ( esk12_1 @ X1333 ) )
| ( X1334
!= ( esk11_2 @ X1333 @ X1334 ) )
| ~ ( X1333 @ X1334 ) )
& ( ~ ( X1333 @ X1337 )
| ( ( esk12_1 @ X1333 )
= X1337 )
| ( X1334
!= ( esk11_2 @ X1333 @ X1334 ) )
| ~ ( X1333 @ X1334 ) )
& ( ~ ( in @ X1339 @ ( prop2set @ X1338 ) )
| X1338 )
& ( ~ ( in @ X1340 @ emptyset )
| X1341 )
& ( ~ ( in @ X1342 @ emptyset )
| ~ $true )
& ~ ( in @ X1343 @ emptyset )
& ( ( X1344 @ ( esk13_2 @ X1344 @ X1345 ) )
| ~ ( X1344 @ X1345 )
| ( X1344 @ ( esk14_1 @ X1344 ) ) )
& ( ( X1345
!= ( esk13_2 @ X1344 @ X1345 ) )
| ~ ( X1344 @ X1345 )
| ( X1344 @ ( esk14_1 @ X1344 ) ) )
& ( ( in @ ( esk16_2 @ X1348 @ X1349 ) @ X1349 )
| ( X1348 = X1349 )
| ( in @ ( esk15_2 @ X1348 @ X1349 ) @ X1348 ) )
& ( ~ ( in @ ( esk16_2 @ X1348 @ X1349 ) @ X1348 )
| ( X1348 = X1349 )
| ( in @ ( esk15_2 @ X1348 @ X1349 ) @ X1348 ) )
& ( ( in @ ( esk16_2 @ X1348 @ X1349 ) @ X1349 )
| ( X1348 = X1349 )
| ~ ( in @ ( esk15_2 @ X1348 @ X1349 ) @ X1349 ) )
& ( ~ ( in @ ( esk16_2 @ X1348 @ X1349 ) @ X1348 )
| ( X1348 = X1349 )
| ~ ( in @ ( esk15_2 @ X1348 @ X1349 ) @ X1349 ) )
& ( ( in @ ( esk17_1 @ X1352 ) @ X1352 )
| ( X1352 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1354 ) @ X1354 )
| ( X1354 = emptyset ) )
& ( ~ ( in @ X1358 @ ( dsetconstr @ X1356 @ X1357 ) )
| ( X1357 @ X1358 )
| ~ ( in @ X1358 @ X1356 ) )
& ( ~ ( X1357 @ X1358 )
| ( in @ X1358 @ ( dsetconstr @ X1356 @ X1357 ) )
| ~ ( in @ X1358 @ X1356 ) )
& ( ( X1359 = emptyset )
| ( in @ ( esk19_1 @ X1359 ) @ X1359 ) )
& ( ~ ( in @ X1363 @ X1361 )
| ~ ( X1362 @ X1363 )
| ( ( dsetconstr @ X1361 @ X1362 )
!= emptyset ) )
& ( ~ ( in @ X1365 @ X1364 )
| ( X1364 != emptyset ) )
& ( in @ X1366 @ ( setadjoin @ X1366 @ X1367 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1370 @ X1369 )
| ( in @ X1370 @ ( setadjoin @ X1368 @ X1369 ) ) )
& ( ( in @ X1373 @ X1372 )
| X1374
| ( X1373 = X1371 )
| ~ ( in @ X1373 @ ( setadjoin @ X1371 @ X1372 ) ) )
& ( ~ X1374
| X1374
| ( X1373 = X1371 )
| ~ ( in @ X1373 @ ( setadjoin @ X1371 @ X1372 ) ) )
& ( ( in @ X1373 @ X1372 )
| X1374
| ~ X1374
| ~ ( in @ X1373 @ ( setadjoin @ X1371 @ X1372 ) ) )
& ( ~ X1374
| X1374
| ~ X1374
| ~ ( in @ X1373 @ ( setadjoin @ X1371 @ X1372 ) ) )
& ( ~ ( in @ X1377 @ ( setadjoin @ X1375 @ X1376 ) )
| ( X1377 = X1375 )
| ( in @ X1377 @ X1376 ) )
& ( ( dsetconstr @ X1378
@ ^ [Z0: $i] : $true )
= X1378 )
& ( ( in @ ( esk20_2 @ X1379 @ X1380 ) @ X1380 )
| ( in @ X1380 @ ( powerset @ X1379 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1379 @ X1380 ) @ X1379 )
| ( in @ X1380 @ ( powerset @ X1379 ) ) )
& ( in @ emptyset @ ( powerset @ X1382 ) )
& ( in @ emptyset @ ( powerset @ X1383 ) )
& ( ~ ( in @ X1385 @ ( powerset @ X1384 ) )
| ~ ( in @ X1386 @ X1385 )
| ( in @ X1386 @ X1384 ) )
& ( ~ ( in @ X1388 @ X1389 )
| ~ ( in @ X1389 @ X1387 )
| ( in @ X1388 @ ( setunion @ X1387 ) ) )
& ( ( in @ X1391 @ ( esk21_3 @ X1390 @ X1391 @ X1392 ) )
| X1392
| ~ ( in @ X1391 @ ( setunion @ X1390 ) ) )
& ( ( in @ ( esk21_3 @ X1390 @ X1391 @ X1392 ) @ X1390 )
| X1392
| ~ ( in @ X1391 @ ( setunion @ X1390 ) ) )
& ( ~ X1392
| X1392
| ~ ( in @ X1391 @ ( setunion @ X1390 ) ) )
& ( ~ ( in @ X1395 @ X1394 )
| ( in @ X1395 @ ( powerset @ ( setunion @ X1394 ) ) ) )
& ( ~ ( X1396 @ X1400 )
| ( X1400
= ( esk23_1 @ X1396 ) )
| ( X1396 @ ( esk22_2 @ X1396 @ X1397 ) )
| ~ ( X1396 @ X1397 ) )
& ( ( X1401
!= ( esk23_1 @ X1396 ) )
| ( X1396 @ X1401 )
| ( X1396 @ ( esk22_2 @ X1396 @ X1397 ) )
| ~ ( X1396 @ X1397 ) )
& ( ~ ( X1396 @ X1400 )
| ( X1400
= ( esk23_1 @ X1396 ) )
| ( X1397
!= ( esk22_2 @ X1396 @ X1397 ) )
| ~ ( X1396 @ X1397 ) )
& ( ( X1401
!= ( esk23_1 @ X1396 ) )
| ( X1396 @ X1401 )
| ( X1397
!= ( esk22_2 @ X1396 @ X1397 ) )
| ~ ( X1396 @ X1397 ) )
& ( ( in @ ( esk24_1 @ X1402 ) @ X1402 )
| ( X1402 = emptyset ) )
& ( $true
| ( X1402 = emptyset ) )
& ( ~ ( in @ X1404 @ ( setadjoin @ X1405 @ emptyset ) )
| ( X1404 = X1405 ) )
& ( ( X1406 = X1407 )
| ~ ( in @ X1407 @ ( setadjoin @ X1406 @ emptyset ) ) )
& ( ( X1408 != X1409 )
| ( in @ X1408 @ ( setadjoin @ X1409 @ emptyset ) ) )
& ( ~ ( in @ X1410 @ ( setadjoin @ X1411 @ emptyset ) )
| ( in @ X1411 @ ( setadjoin @ X1410 @ emptyset ) ) )
& ( ~ ( in @ X1414 @ ( setadjoin @ X1412 @ ( setadjoin @ X1413 @ emptyset ) ) )
| ( X1414 = X1412 )
| ( X1414 = X1413 ) )
& ( in @ X1415 @ ( setadjoin @ X1415 @ ( setadjoin @ X1416 @ emptyset ) ) )
& ( in @ X1418 @ ( setadjoin @ X1417 @ ( setadjoin @ X1418 @ emptyset ) ) )
& ( ~ ( in @ X1421 @ X1419 )
| ~ ( X1420 @ X1421 )
| ( ( dsetconstr @ X1419 @ X1420 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1423 @ emptyset )
| ( X1422 @ X1423 ) )
& ( ( in @ ( esk25_2 @ X1424 @ X1425 ) @ X1424 )
| ~ ( in @ X1426 @ X1424 )
| ( X1425 @ X1426 ) )
& ( ~ ( X1425 @ ( esk25_2 @ X1424 @ X1425 ) )
| ~ ( in @ X1426 @ X1424 )
| ( X1425 @ X1426 ) )
& ( ( in @ ( esk26_2 @ X1428 @ X1429 ) @ X1428 )
| ~ ( in @ X1431 @ X1428 )
| ~ ( X1429 @ X1431 ) )
& ( ( X1429 @ ( esk26_2 @ X1428 @ X1429 ) )
| ~ ( in @ X1431 @ X1428 )
| ~ ( X1429 @ X1431 ) )
& ( ( in @ ( esk27_2 @ X1432 @ X1433 ) @ X1432 )
| ~ ( in @ X1435 @ X1432 )
| ~ ( X1433 @ X1435 ) )
& ( ( X1433 @ ( esk27_2 @ X1432 @ X1433 ) )
| ~ ( in @ X1435 @ X1432 )
| ~ ( X1433 @ X1435 ) )
& ( ( in @ ( esk28_2 @ X1436 @ X1437 ) @ X1436 )
| ~ ( in @ X1438 @ X1436 )
| ( X1437 @ X1438 ) )
& ( ~ ( X1437 @ ( esk28_2 @ X1436 @ X1437 ) )
| ~ ( in @ X1438 @ X1436 )
| ( X1437 @ X1438 ) )
& ( ~ X1440
| ( in @ emptyset @ ( prop2set @ X1440 ) ) )
& ( ~ X1441
| ( set2prop @ ( prop2set @ X1441 ) ) )
& ( ( in @ ( esk29_2 @ X1442 @ X1443 ) @ X1442 )
| ~ ( in @ X1445 @ X1442 )
| ~ ( X1443 @ X1445 ) )
& ( ( X1443 @ ( esk29_2 @ X1442 @ X1443 ) )
| ~ ( in @ X1445 @ X1442 )
| ~ ( X1443 @ X1445 ) )
& ( ( in @ ( esk30_2 @ X1446 @ X1447 ) @ X1446 )
| ~ ( in @ X1448 @ X1446 )
| ( X1447 @ X1448 ) )
& ( ~ ( X1447 @ ( esk30_2 @ X1446 @ X1447 ) )
| ~ ( in @ X1448 @ X1446 )
| ( X1447 @ X1448 ) )
& ( ( X1450 @ ( esk32_1 @ X1450 ) )
| ( X1450 @ ( esk31_2 @ X1450 @ X1451 ) )
| ~ ( X1450 @ X1451 ) )
& ( ~ ( X1450 @ X1454 )
| ( ( esk32_1 @ X1450 )
= X1454 )
| ( X1450 @ ( esk31_2 @ X1450 @ X1451 ) )
| ~ ( X1450 @ X1451 ) )
& ( ( X1450 @ ( esk32_1 @ X1450 ) )
| ( X1451
!= ( esk31_2 @ X1450 @ X1451 ) )
| ~ ( X1450 @ X1451 ) )
& ( ~ ( X1450 @ X1454 )
| ( ( esk32_1 @ X1450 )
= X1454 )
| ( X1451
!= ( esk31_2 @ X1450 @ X1451 ) )
| ~ ( X1450 @ X1451 ) )
& ( ( X1455 @ ( esk35_1 @ X1455 ) )
| ( X1455 @ ( esk33_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ~ ( X1455 @ X1460 )
| ( ( esk35_1 @ X1455 )
= X1460 )
| ( X1455 @ ( esk33_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ( X1455 @ ( esk35_1 @ X1455 ) )
| ( X1455 @ ( esk34_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ~ ( X1455 @ X1460 )
| ( ( esk35_1 @ X1455 )
= X1460 )
| ( X1455 @ ( esk34_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ( X1455 @ ( esk35_1 @ X1455 ) )
| ( ( esk33_1 @ X1455 )
!= ( esk34_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ~ ( X1455 @ X1460 )
| ( ( esk35_1 @ X1455 )
= X1460 )
| ( ( esk33_1 @ X1455 )
!= ( esk34_1 @ X1455 ) )
| ~ ( X1455 @ X1456 ) )
& ( ( X1461 @ ( esk37_1 @ X1461 ) )
| ~ ( X1461 @ ( esk36_2 @ X1461 @ X1462 ) )
| ( ( esk36_2 @ X1461 @ X1462 )
!= X1462 ) )
& ( ~ ( X1461 @ X1465 )
| ( ( esk37_1 @ X1461 )
= X1465 )
| ~ ( X1461 @ ( esk36_2 @ X1461 @ X1462 ) )
| ( ( esk36_2 @ X1461 @ X1462 )
!= X1462 ) )
& ( ( X1461 @ ( esk37_1 @ X1461 ) )
| ( X1461 @ ( esk36_2 @ X1461 @ X1462 ) )
| ( ( esk36_2 @ X1461 @ X1462 )
= X1462 ) )
& ( ~ ( X1461 @ X1465 )
| ( ( esk37_1 @ X1461 )
= X1465 )
| ( X1461 @ ( esk36_2 @ X1461 @ X1462 ) )
| ( ( esk36_2 @ X1461 @ X1462 )
= X1462 ) )
& ( ( X1466 != X1467 )
| ( X1468 != X1469 )
| ~ ( in @ X1468 @ X1466 )
| ( in @ X1469 @ X1467 ) )
& ( ~ ( in @ X1472 @ X1470 )
| ( in @ X1473 @ X1471 )
| ( X1472 != X1473 )
| ( X1470 != X1471 ) )
& ( ~ ( in @ X1473 @ X1471 )
| ( in @ X1472 @ X1470 )
| ( X1472 != X1473 )
| ( X1470 != X1471 ) )
& ( ( X1474 @ ( esk38_2 @ X1474 @ X1475 ) )
| ~ ( X1474 @ X1475 )
| ~ ( X1474 @ X1477 )
| ~ ( X1474 @ X1478 )
| ( X1477 = X1478 ) )
& ( ( X1475
!= ( esk38_2 @ X1474 @ X1475 ) )
| ~ ( X1474 @ X1475 )
| ~ ( X1474 @ X1477 )
| ~ ( X1474 @ X1478 )
| ( X1477 = X1478 ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( ( esk39_2 @ X1479 @ X1480 )
= ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ~ ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ~ ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1479 @ ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1480 @ ( esk42_2 @ X1479 @ X1480 ) )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1480 @ X1486 )
| ( ( esk42_2 @ X1479 @ X1480 )
= X1486 )
| ( X1483
!= ( esk41_3 @ X1479 @ X1480 @ X1483 ) )
| ~ ( X1479 @ X1483 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1480 @ ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ( X1479 @ ( esk44_2 @ X1479 @ X1480 ) )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( ~ ( X1479 @ X1490 )
| ( ( esk44_2 @ X1479 @ X1480 )
= X1490 )
| ( X1487
!= ( esk43_3 @ X1479 @ X1480 @ X1487 ) )
| ~ ( X1480 @ X1487 )
| ( X1479 @ ( esk39_2 @ X1479 @ X1480 ) )
| ( X1480 @ ( esk40_2 @ X1479 @ X1480 ) ) )
& ( emptyset = emptyset )
& ( ( X1491 != X1492 )
| ( X1493 != X1494 )
| ( ( setadjoin @ X1491 @ X1493 )
= ( setadjoin @ X1492 @ X1494 ) ) )
& ( ( X1495 != X1496 )
| ( ( powerset @ X1495 )
= ( powerset @ X1496 ) ) )
& ( ( X1497 != X1498 )
| ( ( setunion @ X1497 )
= ( setunion @ X1498 ) ) )
& ( omega = omega )
& ( ( X1499 @ ( esk45_2 @ X1499 @ X1500 ) )
| ~ ( X1499 @ X1500 )
| ~ ( X1499 @ X1502 )
| ~ ( X1499 @ X1503 )
| ( X1502 = X1503 ) )
& ( ( X1500
!= ( esk45_2 @ X1499 @ X1500 ) )
| ~ ( X1499 @ X1500 )
| ~ ( X1499 @ X1502 )
| ~ ( X1499 @ X1503 )
| ( X1502 = X1503 ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( ( esk46_2 @ X1504 @ X1505 )
= ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( ( esk46_2 @ X1504 @ X1505 )
= ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( ( esk46_2 @ X1504 @ X1505 )
= ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( ( esk46_2 @ X1504 @ X1505 )
= ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ~ ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ~ ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ~ ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ~ ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ~ ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ~ ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ~ ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ~ ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1504 @ ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1505 @ ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( X1510
!= ( esk49_3 @ X1504 @ X1505 @ X1510 ) )
| ~ ( X1505 @ X1510 )
| ( ( descr @ X1504 )
= ( descr @ X1505 ) )
| ( X1508
!= ( esk48_3 @ X1504 @ X1505 @ X1508 ) )
| ~ ( X1504 @ X1508 )
| ( X1504 @ ( esk46_2 @ X1504 @ X1505 ) )
| ( X1505 @ ( esk47_2 @ X1504 @ X1505 ) ) )
& ( ( in @ ( esk50_4 @ X1512 @ X1513 @ X1514 @ X1515 ) @ X1512 )
| ( ( dsetconstr @ X1512 @ X1514 )
= ( dsetconstr @ X1513 @ X1515 ) )
| ( X1512 != X1513 ) )
& ( ( in @ ( esk51_4 @ X1512 @ X1513 @ X1514 @ X1515 ) @ X1513 )
| ( ( dsetconstr @ X1512 @ X1514 )
= ( dsetconstr @ X1513 @ X1515 ) )
| ( X1512 != X1513 ) )
& ( ( ( esk50_4 @ X1512 @ X1513 @ X1514 @ X1515 )
= ( esk51_4 @ X1512 @ X1513 @ X1514 @ X1515 ) )
| ( ( dsetconstr @ X1512 @ X1514 )
= ( dsetconstr @ X1513 @ X1515 ) )
| ( X1512 != X1513 ) )
& ( ~ ( X1514 @ ( esk50_4 @ X1512 @ X1513 @ X1514 @ X1515 ) )
| ~ ( X1515 @ ( esk51_4 @ X1512 @ X1513 @ X1514 @ X1515 ) )
| ( ( dsetconstr @ X1512 @ X1514 )
= ( dsetconstr @ X1513 @ X1515 ) )
| ( X1512 != X1513 ) )
& ( ( X1514 @ ( esk50_4 @ X1512 @ X1513 @ X1514 @ X1515 ) )
| ( X1515 @ ( esk51_4 @ X1512 @ X1513 @ X1514 @ X1515 ) )
| ( ( dsetconstr @ X1512 @ X1514 )
= ( dsetconstr @ X1513 @ X1515 ) )
| ( X1512 != X1513 ) )
& ( ( in @ ( esk52_2 @ X1518 @ X1519 ) @ X1518 )
| ( subset @ X1518 @ X1519 ) )
& ( ~ ( in @ ( esk52_2 @ X1518 @ X1519 ) @ X1519 )
| ( subset @ X1518 @ X1519 ) )
& ( ( X1521 != X1522 )
| ( subset @ X1522 @ X1521 ) )
& ( ( X1523 != X1524 )
| ( subset @ X1523 @ X1524 ) )
& ( ( in @ ( esk53_2 @ X1525 @ X1526 ) @ X1525 )
| ( subset @ X1525 @ X1526 ) )
& ( ~ ( in @ ( esk53_2 @ X1525 @ X1526 ) @ X1526 )
| ( subset @ X1525 @ X1526 ) )
& ( subset @ emptyset @ X1528 )
& ( ~ ( subset @ X1529 @ X1530 )
| ~ ( in @ X1531 @ X1529 )
| ( in @ X1531 @ X1530 ) )
& ( ~ ( subset @ X1532 @ X1533 )
| ( in @ X1534 @ X1533 )
| ~ ( in @ X1534 @ X1532 ) )
& ( ~ ( in @ X1537 @ X1535 )
| ( in @ X1537 @ X1536 )
| ~ ( subset @ X1535 @ X1536 ) )
& ( ( subset @ X1538 @ X1539 )
| ( X1538 != X1539 ) )
& ( ~ ( in @ X1542 @ X1540 )
| ( in @ X1542 @ X1541 )
| ( X1540 != X1541 ) )
& ( subset @ X1543 @ X1543 )
& ( ~ ( subset @ X1544 @ X1545 )
| ~ ( subset @ X1545 @ X1546 )
| ( subset @ X1544 @ X1546 ) )
& ( subset @ X1548 @ ( setadjoin @ X1547 @ X1548 ) )
& ( ~ ( subset @ X1549 @ X1551 )
| ( subset @ X1549 @ ( setadjoin @ X1550 @ X1551 ) ) )
& ( ~ ( subset @ X1552 @ X1553 )
| ( in @ X1552 @ ( powerset @ X1553 ) ) )
& ( ~ ( subset @ X1554 @ X1555 )
| ~ ( subset @ X1555 @ X1554 )
| ( X1554 = X1555 ) )
& ( ~ ( subset @ X1556 @ emptyset )
| ( X1556 = emptyset ) )
& ( ~ ( subset @ X1558 @ X1557 )
| ( in @ X1558 @ ( powerset @ X1557 ) ) )
& ( ~ ( in @ X1560 @ ( powerset @ X1559 ) )
| ( subset @ X1560 @ X1559 ) )
& ( in @ X1561 @ ( powerset @ X1561 ) )
& ( ~ ( subset @ X1562 @ X1563 )
| ( subset @ ( powerset @ X1562 ) @ ( powerset @ X1563 ) ) )
& ( in @ ( dsetconstr @ X1564 @ X1565 ) @ ( powerset @ X1564 ) )
& ( subset @ ( dsetconstr @ X1566 @ X1567 ) @ X1566 )
& ( ~ ( in @ X1570 @ X1568 )
| ( in @ X1570 @ ( binunion @ X1568 @ X1569 ) ) )
& ( in @ X1572 @ ( setadjoin @ X1571 @ ( setadjoin @ X1572 @ emptyset ) ) )
& ( ~ ( in @ X1575 @ X1574 )
| ( in @ X1575 @ ( binunion @ X1573 @ X1574 ) ) )
& ( ( in @ X1578 @ X1577 )
| X1579
| ( in @ X1578 @ X1576 )
| ~ ( in @ X1578 @ ( binunion @ X1576 @ X1577 ) ) )
& ( ~ X1579
| X1579
| ( in @ X1578 @ X1576 )
| ~ ( in @ X1578 @ ( binunion @ X1576 @ X1577 ) ) )
& ( ( in @ X1578 @ X1577 )
| X1579
| ~ X1579
| ~ ( in @ X1578 @ ( binunion @ X1576 @ X1577 ) ) )
& ( ~ X1579
| X1579
| ~ X1579
| ~ ( in @ X1578 @ ( binunion @ X1576 @ X1577 ) ) )
& ( ~ ( in @ X1582 @ ( binunion @ X1580 @ X1581 ) )
| ( in @ X1582 @ X1580 )
| ( in @ X1582 @ X1581 ) )
& ( subset @ X1583 @ ( binunion @ X1583 @ X1584 ) )
& ( subset @ X1586 @ ( binunion @ X1585 @ X1586 ) )
& ( ~ ( in @ X1589 @ X1587 )
| ~ ( in @ X1589 @ X1588 )
| ( in @ X1589 @ ( binintersect @ X1587 @ X1588 ) ) )
& ( ~ ( subset @ X1592 @ X1590 )
| ~ ( subset @ X1592 @ X1591 )
| ( subset @ X1592 @ ( binintersect @ X1590 @ X1591 ) ) )
& ( ~ ( in @ X1595 @ ( binintersect @ X1593 @ X1594 ) )
| ( in @ X1595 @ X1593 ) )
& ( subset @ ( binintersect @ X1596 @ X1597 ) @ X1596 )
& ( ~ ( subset @ X1598 @ X1599 )
| ( ( binintersect @ X1598 @ X1599 )
= X1598 ) )
& ( ( ( binintersect @ X1600 @ X1601 )
!= X1601 )
| ( subset @ X1601 @ X1600 ) )
& ( ~ ( in @ X1604 @ ( binintersect @ X1602 @ X1603 ) )
| ( in @ X1604 @ X1603 ) )
& ( ( in @ ( esk54_2 @ X1605 @ X1606 ) @ X1605 )
| ( ( binintersect @ X1605 @ X1606 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1605 @ X1606 ) @ X1606 )
| ( ( binintersect @ X1605 @ X1606 )
= emptyset ) )
& ( subset @ ( binintersect @ X1608 @ X1609 ) @ X1609 )
& ( ~ ( subset @ X1611 @ X1610 )
| ( ( binintersect @ X1610 @ X1611 )
= X1611 ) )
& ( ( ( binintersect @ X1612 @ X1613 )
!= X1612 )
| ( subset @ X1612 @ X1613 ) )
& ( ( binintersect @ X1614 @ ( binunion @ X1615 @ X1616 ) )
= ( binunion @ ( binintersect @ X1614 @ X1615 ) @ ( binintersect @ X1614 @ X1616 ) ) )
& ( ~ ( in @ X1619 @ X1617 )
| ( in @ X1619 @ X1618 )
| ( in @ X1619 @ ( setminus @ X1617 @ X1618 ) ) )
& ( ~ ( in @ X1622 @ ( setminus @ X1620 @ X1621 ) )
| ( in @ X1622 @ X1620 ) )
& ( ~ ( in @ X1625 @ ( setminus @ X1623 @ X1624 ) )
| ~ ( in @ X1625 @ X1624 ) )
& ( ~ ( subset @ X1626 @ X1627 )
| ( ( setminus @ X1626 @ X1627 )
= emptyset ) )
& ( ( in @ X1630 @ ( setminus @ X1628 @ X1629 ) )
| ~ ( in @ X1630 @ X1628 )
| ( in @ X1630 @ X1629 ) )
& ( ( in @ X1633 @ ( setminus @ X1631 @ X1632 ) )
| ( in @ X1633 @ X1632 )
| ~ ( in @ X1633 @ X1631 ) )
& ( ( in @ X1636 @ X1634 )
| ~ ( in @ X1636 @ ( setminus @ X1634 @ X1635 ) ) )
& ( ~ ( in @ X1639 @ X1638 )
| ~ ( in @ X1639 @ ( setminus @ X1637 @ X1638 ) ) )
& ( subset @ ( setminus @ X1640 @ X1641 ) @ X1640 )
& ( ( ( setminus @ X1642 @ X1643 )
!= emptyset )
| ( subset @ X1642 @ X1643 ) )
& ( ~ ( in @ X1646 @ X1644 )
| X1647
| ( in @ X1646 @ X1644 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ( in @ X1646 @ X1645 )
| X1647
| ( in @ X1646 @ X1644 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ X1647
| X1647
| ( in @ X1646 @ X1644 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ ( in @ X1646 @ X1644 )
| X1647
| ~ ( in @ X1646 @ X1645 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ( in @ X1646 @ X1645 )
| X1647
| ~ ( in @ X1646 @ X1645 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ X1647
| X1647
| ~ ( in @ X1646 @ X1645 )
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ ( in @ X1646 @ X1644 )
| X1647
| ~ X1647
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ( in @ X1646 @ X1645 )
| X1647
| ~ X1647
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ X1647
| X1647
| ~ X1647
| ~ ( in @ X1646 @ ( symdiff @ X1644 @ X1645 ) ) )
& ( ~ ( in @ X1650 @ X1648 )
| ( in @ X1650 @ X1649 )
| ( in @ X1650 @ ( symdiff @ X1648 @ X1649 ) ) )
& ( ( in @ X1653 @ X1651 )
| ~ ( in @ X1653 @ X1652 )
| ( in @ X1653 @ ( symdiff @ X1651 @ X1652 ) ) )
& ( ~ ( in @ X1656 @ X1654 )
| ~ ( in @ X1656 @ X1655 )
| ~ ( in @ X1656 @ ( symdiff @ X1654 @ X1655 ) ) )
& ( ( in @ X1659 @ X1657 )
| ( in @ X1659 @ X1658 )
| ~ ( in @ X1659 @ ( symdiff @ X1657 @ X1658 ) ) )
& ( in @ X1661 @ ( setadjoin @ X1660 @ ( setadjoin @ X1661 @ emptyset ) ) )
& ( in @ X1662 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1662 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1662 @ ( setadjoin @ X1663 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1665 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1664 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1664 @ ( setadjoin @ X1665 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1666 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1666 @ ( setadjoin @ X1667 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1668 @ X1669 ) )
& ( ~ ( in @ X1671 @ X1670 )
| ( subset @ ( setadjoin @ X1671 @ emptyset ) @ X1670 ) )
& ( ~ ( in @ X1673 @ X1672 )
| ( in @ ( setadjoin @ X1673 @ emptyset ) @ ( powerset @ X1672 ) ) )
& ( ~ ( in @ X1676 @ X1674 )
| ( in @ ( setadjoin @ X1676 @ emptyset ) @ ( powerset @ ( binunion @ X1674 @ X1675 ) ) ) )
& ( ~ ( in @ X1679 @ ( setadjoin @ X1677 @ ( setadjoin @ X1678 @ emptyset ) ) )
| ( X1679 = X1677 )
| ( X1679 = X1678 ) )
& ( ~ ( in @ X1682 @ X1680 )
| ~ ( in @ X1683 @ X1681 )
| ( subset @ ( setadjoin @ X1682 @ ( setadjoin @ X1683 @ emptyset ) ) @ ( binunion @ X1680 @ X1681 ) ) )
& ( ~ ( in @ X1686 @ X1684 )
| ~ ( in @ X1687 @ X1685 )
| ( in @ ( setadjoin @ X1686 @ ( setadjoin @ X1687 @ emptyset ) ) @ ( powerset @ ( binunion @ X1684 @ X1685 ) ) ) )
& ( ~ ( in @ X1690 @ X1688 )
| ~ ( in @ X1691 @ X1689 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1690 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1690 @ ( setadjoin @ X1691 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1688 @ X1689 ) ) ) )
& ( ~ ( in @ X1694 @ X1692 )
| ~ ( in @ X1695 @ X1693 )
| ( in @ ( setadjoin @ ( setadjoin @ X1694 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1694 @ ( setadjoin @ X1695 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1692 @ X1693 ) ) ) ) )
& ( ~ ( in @ X1698 @ X1696 )
| ~ ( in @ X1699 @ X1697 )
| ( in @ ( kpair @ X1698 @ X1699 ) @ ( powerset @ ( powerset @ ( binunion @ X1696 @ X1697 ) ) ) ) )
& ( ~ ( in @ X1702 @ X1700 )
| ~ ( in @ X1703 @ X1701 )
| ( in @ ( kpair @ X1702 @ X1703 ) @ ( cartprod @ X1700 @ X1701 ) ) )
& ( ( in @ ( esk55_3 @ X1704 @ X1705 @ X1706 ) @ X1704 )
| ~ ( in @ X1706 @ ( cartprod @ X1704 @ X1705 ) ) )
& ( ( in @ ( esk56_3 @ X1704 @ X1705 @ X1706 ) @ X1705 )
| ~ ( in @ X1706 @ ( cartprod @ X1704 @ X1705 ) ) )
& ( ( X1706
= ( kpair @ ( esk55_3 @ X1704 @ X1705 @ X1706 ) @ ( esk56_3 @ X1704 @ X1705 @ X1706 ) ) )
| ~ ( in @ X1706 @ ( cartprod @ X1704 @ X1705 ) ) )
& ( ~ ( in @ X1711 @ ( cartprod @ X1709 @ X1710 ) )
| ( iskpair @ X1711 ) )
& ( ( in @ ( esk57_2 @ X1712 @ X1713 ) @ X1712 )
| ~ ( in @ X1713 @ ( setunion @ X1712 ) ) )
& ( ( in @ X1713 @ ( esk57_2 @ X1712 @ X1713 ) )
| ~ ( in @ X1713 @ ( setunion @ X1712 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1715 @ emptyset ) ) @ X1715 )
& ( subset @ X1716 @ ( setunion @ ( setadjoin @ X1716 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1717 @ emptyset ) )
= X1717 )
& ( ( in @ ( esk60_2 @ X1718 @ X1719 ) @ ( dsetconstr @ X1718 @ X1719 ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( in @ ( esk58_2 @ X1718 @ X1719 ) @ X1718 ) )
& ( ( ( dsetconstr @ X1718 @ X1719 )
= ( setadjoin @ ( esk60_2 @ X1718 @ X1719 ) @ emptyset ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( in @ ( esk58_2 @ X1718 @ X1719 ) @ X1718 ) )
& ( ( in @ ( esk60_2 @ X1718 @ X1719 ) @ ( dsetconstr @ X1718 @ X1719 ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( in @ ( esk59_2 @ X1718 @ X1719 ) @ X1718 ) )
& ( ( ( dsetconstr @ X1718 @ X1719 )
= ( setadjoin @ ( esk60_2 @ X1718 @ X1719 ) @ emptyset ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( in @ ( esk59_2 @ X1718 @ X1719 ) @ X1718 ) )
& ( ( in @ ( esk60_2 @ X1718 @ X1719 ) @ ( dsetconstr @ X1718 @ X1719 ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( X1719 @ ( esk58_2 @ X1718 @ X1719 ) ) )
& ( ( ( dsetconstr @ X1718 @ X1719 )
= ( setadjoin @ ( esk60_2 @ X1718 @ X1719 ) @ emptyset ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( X1719 @ ( esk58_2 @ X1718 @ X1719 ) ) )
& ( ( in @ ( esk60_2 @ X1718 @ X1719 ) @ ( dsetconstr @ X1718 @ X1719 ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( X1719 @ ( esk59_2 @ X1718 @ X1719 ) ) )
& ( ( ( dsetconstr @ X1718 @ X1719 )
= ( setadjoin @ ( esk60_2 @ X1718 @ X1719 ) @ emptyset ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( X1719 @ ( esk59_2 @ X1718 @ X1719 ) ) )
& ( ( in @ ( esk60_2 @ X1718 @ X1719 ) @ ( dsetconstr @ X1718 @ X1719 ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( ( esk58_2 @ X1718 @ X1719 )
!= ( esk59_2 @ X1718 @ X1719 ) ) )
& ( ( ( dsetconstr @ X1718 @ X1719 )
= ( setadjoin @ ( esk60_2 @ X1718 @ X1719 ) @ emptyset ) )
| ~ ( in @ X1722 @ X1718 )
| ~ ( X1719 @ X1722 )
| ( ( esk58_2 @ X1718 @ X1719 )
!= ( esk59_2 @ X1718 @ X1719 ) ) )
& ( ( in @ ( esk61_2 @ X1724 @ X1725 ) @ X1724 )
| ~ ( in @ X1726 @ ( dsetconstr @ X1724 @ X1725 ) )
| ( ( dsetconstr @ X1724 @ X1725 )
!= ( setadjoin @ X1726 @ emptyset ) ) )
& ( ( X1725 @ ( esk61_2 @ X1724 @ X1725 ) )
| ~ ( in @ X1726 @ ( dsetconstr @ X1724 @ X1725 ) )
| ( ( dsetconstr @ X1724 @ X1725 )
!= ( setadjoin @ X1726 @ emptyset ) ) )
& ( ( in @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ ( dsetconstr @ X1728 @ X1729 ) )
| ( in @ ( esk62_3 @ X1728 @ X1729 @ X1730 ) @ X1728 )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( ( dsetconstr @ X1728 @ X1729 )
= ( setadjoin @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ emptyset ) )
| ( in @ ( esk62_3 @ X1728 @ X1729 @ X1730 ) @ X1728 )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( in @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ ( dsetconstr @ X1728 @ X1729 ) )
| ( X1729 @ ( esk62_3 @ X1728 @ X1729 @ X1730 ) )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( ( dsetconstr @ X1728 @ X1729 )
= ( setadjoin @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ emptyset ) )
| ( X1729 @ ( esk62_3 @ X1728 @ X1729 @ X1730 ) )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( in @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ ( dsetconstr @ X1728 @ X1729 ) )
| ( ( esk62_3 @ X1728 @ X1729 @ X1730 )
!= X1730 )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( ( dsetconstr @ X1728 @ X1729 )
= ( setadjoin @ ( esk63_3 @ X1728 @ X1729 @ X1730 ) @ emptyset ) )
| ( ( esk62_3 @ X1728 @ X1729 @ X1730 )
!= X1730 )
| ~ ( X1729 @ X1730 )
| ~ ( in @ X1730 @ X1728 ) )
& ( ( in @ ( esk66_2 @ X1733 @ X1734 ) @ ( dsetconstr @ X1733 @ X1734 ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( in @ ( esk64_2 @ X1733 @ X1734 ) @ X1733 ) )
& ( ( ( dsetconstr @ X1733 @ X1734 )
= ( setadjoin @ ( esk66_2 @ X1733 @ X1734 ) @ emptyset ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( in @ ( esk64_2 @ X1733 @ X1734 ) @ X1733 ) )
& ( ( in @ ( esk66_2 @ X1733 @ X1734 ) @ ( dsetconstr @ X1733 @ X1734 ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( in @ ( esk65_2 @ X1733 @ X1734 ) @ X1733 ) )
& ( ( ( dsetconstr @ X1733 @ X1734 )
= ( setadjoin @ ( esk66_2 @ X1733 @ X1734 ) @ emptyset ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( in @ ( esk65_2 @ X1733 @ X1734 ) @ X1733 ) )
& ( ( in @ ( esk66_2 @ X1733 @ X1734 ) @ ( dsetconstr @ X1733 @ X1734 ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( X1734 @ ( esk64_2 @ X1733 @ X1734 ) ) )
& ( ( ( dsetconstr @ X1733 @ X1734 )
= ( setadjoin @ ( esk66_2 @ X1733 @ X1734 ) @ emptyset ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( X1734 @ ( esk64_2 @ X1733 @ X1734 ) ) )
& ( ( in @ ( esk66_2 @ X1733 @ X1734 ) @ ( dsetconstr @ X1733 @ X1734 ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( X1734 @ ( esk65_2 @ X1733 @ X1734 ) ) )
& ( ( ( dsetconstr @ X1733 @ X1734 )
= ( setadjoin @ ( esk66_2 @ X1733 @ X1734 ) @ emptyset ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( X1734 @ ( esk65_2 @ X1733 @ X1734 ) ) )
& ( ( in @ ( esk66_2 @ X1733 @ X1734 ) @ ( dsetconstr @ X1733 @ X1734 ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( ( esk64_2 @ X1733 @ X1734 )
!= ( esk65_2 @ X1733 @ X1734 ) ) )
& ( ( ( dsetconstr @ X1733 @ X1734 )
= ( setadjoin @ ( esk66_2 @ X1733 @ X1734 ) @ emptyset ) )
| ~ ( in @ X1737 @ X1733 )
| ~ ( X1734 @ X1737 )
| ( ( esk64_2 @ X1733 @ X1734 )
!= ( esk65_2 @ X1733 @ X1734 ) ) )
& ( ( ( setadjoin @ X1739 @ emptyset )
!= ( setadjoin @ X1740 @ emptyset ) )
| ( X1739 = X1740 ) )
& ( ~ ( in @ ( setadjoin @ X1743 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1741 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1741 @ ( setadjoin @ X1742 @ emptyset ) ) @ emptyset ) ) )
| ( X1741 = X1743 ) )
& ( ( in @ ( esk67_1 @ X1744 )
@ ( dsetconstr @ ( setunion @ X1744 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1744 ) ) )
| ~ ( iskpair @ X1744 ) )
& ( ( ( dsetconstr @ ( setunion @ X1744 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1744 ) )
= ( setadjoin @ ( esk67_1 @ X1744 ) @ emptyset ) )
| ~ ( iskpair @ X1744 ) )
& ( ~ ( in @ X1747 @ X1746 )
| ( X1746
!= ( setadjoin @ X1747 @ emptyset ) )
| ( in @ ( setunion @ X1746 ) @ X1746 ) )
& ( ( kfst @ ( kpair @ X1748 @ X1749 ) )
= X1748 )
& ( ~ ( in @ X1752 @ ( cartprod @ X1750 @ X1751 ) )
| ( in @ ( kfst @ X1752 ) @ X1750 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1753 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1753 @ ( setadjoin @ X1754 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1755 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1755 @ ( setadjoin @ X1756 @ emptyset ) ) @ emptyset ) ) )
| ( X1753 = X1755 ) )
& ( ( ( kpair @ X1757 @ X1758 )
!= ( kpair @ X1759 @ X1760 ) )
| ( X1757 = X1759 ) )
& ( ( X1761 != X1762 )
| ( ( setadjoin @ X1761 @ ( setadjoin @ X1762 @ emptyset ) )
= ( setadjoin @ X1761 @ emptyset ) ) )
& ( ( X1763 != X1764 )
| ( ( setadjoin @ ( setadjoin @ X1763 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1763 @ ( setadjoin @ X1764 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1763 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1765 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1765 @ ( setadjoin @ X1766 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1767 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1767 @ ( setadjoin @ X1768 @ emptyset ) ) @ emptyset ) ) )
| ( X1767 != X1768 )
| ( X1766 = X1768 ) )
& ( ( ( setadjoin @ X1769 @ ( setadjoin @ X1770 @ emptyset ) )
!= ( setadjoin @ X1771 @ emptyset ) )
| ( X1769 = X1770 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1772 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1772 @ ( setadjoin @ X1773 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1774 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1774 @ ( setadjoin @ X1775 @ emptyset ) ) @ emptyset ) ) )
| ( X1773 = X1775 ) )
& ( ( ( kpair @ X1776 @ X1777 )
!= ( kpair @ X1778 @ X1779 ) )
| ( X1777 = X1779 ) )
& ( ( in @ ( esk68_1 @ X1780 )
@ ( dsetconstr @ ( setunion @ X1780 )
@ ^ [Z0: $i] :
( X1780
= ( kpair @ ( kfst @ X1780 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X1780 ) )
& ( ( ( dsetconstr @ ( setunion @ X1780 )
@ ^ [Z0: $i] :
( X1780
= ( kpair @ ( kfst @ X1780 ) @ Z0 ) ) )
= ( setadjoin @ ( esk68_1 @ X1780 ) @ emptyset ) )
| ~ ( iskpair @ X1780 ) )
& ( ( ksnd @ ( kpair @ X1782 @ X1783 ) )
= X1783 )
& ( ~ ( iskpair @ X1784 )
| ( ( kpair @ ( kfst @ X1784 ) @ ( ksnd @ X1784 ) )
= X1784 ) )
& ( ~ ( in @ X1787 @ ( cartprod @ X1785 @ X1786 ) )
| ( in @ ( ksnd @ X1787 ) @ X1786 ) )
& ( ~ ( in @ ( kpair @ X1790 @ X1791 ) @ ( cartprod @ X1788 @ X1789 ) )
| ( in @ X1790 @ X1788 ) )
& ( ~ ( in @ ( kpair @ X1794 @ X1795 ) @ ( cartprod @ X1792 @ X1793 ) )
| ( in @ X1795 @ X1793 ) )
& ( ~ ( in @ X1798 @ X1796 )
| ~ ( in @ X1799 @ X1797 )
| ( ( kpair @ X1798 @ X1799 )
= ( kpair @ X1798 @ X1799 ) ) )
& ( ~ ( in @ X1802 @ X1800 )
| ~ ( in @ X1803 @ X1801 )
| ( ( kfst @ ( kpair @ X1802 @ X1803 ) )
= X1802 ) )
& ( ~ ( in @ X1806 @ X1804 )
| ~ ( in @ X1807 @ X1805 )
| ( ( ksnd @ ( kpair @ X1806 @ X1807 ) )
= X1807 ) )
& ( ~ ( in @ X1810 @ ( cartprod @ X1808 @ X1809 ) )
| ( ( kpair @ ( kfst @ X1810 ) @ ( ksnd @ X1810 ) )
= X1810 ) )
& ( ~ ( in @ X1814 @ X1811 )
| ~ ( in @ X1815 @ X1812 )
| ~ ( X1813 @ X1814 @ X1815 )
| ( in @ ( kpair @ X1814 @ X1815 ) @ ( dpsetconstr @ X1811 @ X1812 @ X1813 ) ) )
& ( subset @ ( dpsetconstr @ X1816 @ X1817 @ X1818 ) @ ( cartprod @ X1816 @ X1817 ) )
& ( subset @ ( dpsetconstr @ X1819 @ X1820 @ X1821 ) @ ( cartprod @ X1819 @ X1820 ) )
& ( ~ ( in @ X1825 @ X1822 )
| ~ ( in @ X1826 @ X1823 )
| ~ ( in @ ( kpair @ X1825 @ X1826 ) @ ( dpsetconstr @ X1822 @ X1823 @ X1824 ) )
| ( X1824 @ X1825 @ X1826 ) )
& ( ~ ( in @ ( kpair @ X1830 @ X1831 ) @ ( dpsetconstr @ X1827 @ X1828 @ X1829 ) )
| ( in @ X1830 @ X1827 ) )
& ( ~ ( in @ ( kpair @ X1835 @ X1836 ) @ ( dpsetconstr @ X1832 @ X1833 @ X1834 ) )
| ( in @ X1836 @ X1833 ) )
& ( ~ ( in @ ( kpair @ X1840 @ X1841 ) @ ( dpsetconstr @ X1837 @ X1838 @ X1839 ) )
| ( X1839 @ X1840 @ X1841 ) )
& ( ( in @ ( esk70_4 @ X1842 @ X1843 @ X1844 @ X1847 )
@ ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ X1847 @ Z0 ) @ X1844 ) ) )
| ~ ( in @ X1847 @ X1842 )
| ( in @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ X1842 )
| ~ ( subset @ X1844 @ ( cartprod @ X1842 @ X1843 ) ) )
& ( ( ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ X1847 @ Z0 ) @ X1844 ) )
= ( setadjoin @ ( esk70_4 @ X1842 @ X1843 @ X1844 @ X1847 ) @ emptyset ) )
| ~ ( in @ X1847 @ X1842 )
| ( in @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ X1842 )
| ~ ( subset @ X1844 @ ( cartprod @ X1842 @ X1843 ) ) )
& ( ( in @ ( esk70_4 @ X1842 @ X1843 @ X1844 @ X1847 )
@ ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ X1847 @ Z0 ) @ X1844 ) ) )
| ~ ( in @ X1847 @ X1842 )
| ~ ( in @ X1846
@ ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ Z0 ) @ X1844 ) ) )
| ( ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ Z0 ) @ X1844 ) )
!= ( setadjoin @ X1846 @ emptyset ) )
| ~ ( subset @ X1844 @ ( cartprod @ X1842 @ X1843 ) ) )
& ( ( ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ X1847 @ Z0 ) @ X1844 ) )
= ( setadjoin @ ( esk70_4 @ X1842 @ X1843 @ X1844 @ X1847 ) @ emptyset ) )
| ~ ( in @ X1847 @ X1842 )
| ~ ( in @ X1846
@ ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ Z0 ) @ X1844 ) ) )
| ( ( dsetconstr @ X1843
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk69_3 @ X1842 @ X1843 @ X1844 ) @ Z0 ) @ X1844 ) )
!= ( setadjoin @ X1846 @ emptyset ) )
| ~ ( subset @ X1844 @ ( cartprod @ X1842 @ X1843 ) ) )
& ( ( in @ ( esk71_3 @ X1849 @ X1850 @ X1851 ) @ X1849 )
| ~ ( subset @ X1851 @ ( cartprod @ X1849 @ X1850 ) )
| ~ ( in @ X1854 @ X1849 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1850
@ ^ [Z0: $i] : ( in @ ( kpair @ X1854 @ Z0 ) @ X1851 ) ) )
@ X1850 ) )
& ( ~ ( in @ X1853
@ ( dsetconstr @ X1850
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk71_3 @ X1849 @ X1850 @ X1851 ) @ Z0 ) @ X1851 ) ) )
| ( ( dsetconstr @ X1850
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk71_3 @ X1849 @ X1850 @ X1851 ) @ Z0 ) @ X1851 ) )
!= ( setadjoin @ X1853 @ emptyset ) )
| ~ ( subset @ X1851 @ ( cartprod @ X1849 @ X1850 ) )
| ~ ( in @ X1854 @ X1849 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1850
@ ^ [Z0: $i] : ( in @ ( kpair @ X1854 @ Z0 ) @ X1851 ) ) )
@ X1850 ) )
& ( ( in @ ( esk72_3 @ X1855 @ X1856 @ X1857 ) @ X1855 )
| ~ ( subset @ X1857 @ ( cartprod @ X1855 @ X1856 ) )
| ~ ( in @ X1860 @ X1855 )
| ( in @ ( ap @ X1855 @ X1856 @ X1857 @ X1860 ) @ X1856 ) )
& ( ~ ( in @ X1859
@ ( dsetconstr @ X1856
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk72_3 @ X1855 @ X1856 @ X1857 ) @ Z0 ) @ X1857 ) ) )
| ( ( dsetconstr @ X1856
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk72_3 @ X1855 @ X1856 @ X1857 ) @ Z0 ) @ X1857 ) )
!= ( setadjoin @ X1859 @ emptyset ) )
| ~ ( subset @ X1857 @ ( cartprod @ X1855 @ X1856 ) )
| ~ ( in @ X1860 @ X1855 )
| ( in @ ( ap @ X1855 @ X1856 @ X1857 @ X1860 ) @ X1856 ) )
& ( ( subset @ X1863 @ ( cartprod @ X1861 @ X1862 ) )
| ~ ( in @ X1863 @ ( funcSet @ X1861 @ X1862 ) ) )
& ( ( in @ ( esk73_4 @ X1861 @ X1862 @ X1863 @ X1864 )
@ ( dsetconstr @ X1862
@ ^ [Z0: $i] : ( in @ ( kpair @ X1864 @ Z0 ) @ X1863 ) ) )
| ~ ( in @ X1864 @ X1861 )
| ~ ( in @ X1863 @ ( funcSet @ X1861 @ X1862 ) ) )
& ( ( ( dsetconstr @ X1862
@ ^ [Z0: $i] : ( in @ ( kpair @ X1864 @ Z0 ) @ X1863 ) )
= ( setadjoin @ ( esk73_4 @ X1861 @ X1862 @ X1863 @ X1864 ) @ emptyset ) )
| ~ ( in @ X1864 @ X1861 )
| ~ ( in @ X1863 @ ( funcSet @ X1861 @ X1862 ) ) )
& ( ~ ( in @ X1868 @ ( funcSet @ X1866 @ X1867 ) )
| ~ ( in @ X1869 @ X1866 )
| ( in @ ( ap @ X1866 @ X1867 @ X1868 @ X1869 ) @ X1867 ) )
& ( ( in @ ( esk74_3 @ X1870 @ X1871 @ X1872 ) @ X1870 )
| ~ ( subset @ X1872 @ ( cartprod @ X1870 @ X1871 ) )
| ( in @ X1872 @ ( funcSet @ X1870 @ X1871 ) ) )
& ( ~ ( in @ X1874
@ ( dsetconstr @ X1871
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk74_3 @ X1870 @ X1871 @ X1872 ) @ Z0 ) @ X1872 ) ) )
| ( ( dsetconstr @ X1871
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk74_3 @ X1870 @ X1871 @ X1872 ) @ Z0 ) @ X1872 ) )
!= ( setadjoin @ X1874 @ emptyset ) )
| ~ ( subset @ X1872 @ ( cartprod @ X1870 @ X1871 ) )
| ( in @ X1872 @ ( funcSet @ X1870 @ X1871 ) ) )
& ( ( subset
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z0: $i] : ( $eq @ ( X1877 @ Z0 ) ) )
@ ( cartprod @ X1875 @ X1876 ) )
| ( in @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) @ X1875 ) )
& ( ( in @ ( esk76_4 @ X1875 @ X1876 @ X1877 @ X1879 )
@ ( dsetconstr @ X1876
@ ^ [Z0: $i] :
( in @ ( kpair @ X1879 @ Z0 )
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z1: $i] : ( $eq @ ( X1877 @ Z1 ) ) ) ) ) )
| ~ ( in @ X1879 @ X1875 )
| ( in @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) @ X1875 ) )
& ( ( ( dsetconstr @ X1876
@ ^ [Z0: $i] :
( in @ ( kpair @ X1879 @ Z0 )
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z1: $i] : ( $eq @ ( X1877 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk76_4 @ X1875 @ X1876 @ X1877 @ X1879 ) @ emptyset ) )
| ~ ( in @ X1879 @ X1875 )
| ( in @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) @ X1875 ) )
& ( ( subset
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z0: $i] : ( $eq @ ( X1877 @ Z0 ) ) )
@ ( cartprod @ X1875 @ X1876 ) )
| ~ ( in @ ( X1877 @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) ) @ X1876 ) )
& ( ( in @ ( esk76_4 @ X1875 @ X1876 @ X1877 @ X1879 )
@ ( dsetconstr @ X1876
@ ^ [Z0: $i] :
( in @ ( kpair @ X1879 @ Z0 )
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z1: $i] : ( $eq @ ( X1877 @ Z1 ) ) ) ) ) )
| ~ ( in @ X1879 @ X1875 )
| ~ ( in @ ( X1877 @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) ) @ X1876 ) )
& ( ( ( dsetconstr @ X1876
@ ^ [Z0: $i] :
( in @ ( kpair @ X1879 @ Z0 )
@ ( dpsetconstr @ X1875 @ X1876
@ ^ [Z1: $i] : ( $eq @ ( X1877 @ Z1 ) ) ) ) )
= ( setadjoin @ ( esk76_4 @ X1875 @ X1876 @ X1877 @ X1879 ) @ emptyset ) )
| ~ ( in @ X1879 @ X1875 )
| ~ ( in @ ( X1877 @ ( esk75_3 @ X1875 @ X1876 @ X1877 ) ) @ X1876 ) )
& ( ( subset @ ( lam @ X1881 @ X1882 @ X1883 ) @ ( cartprod @ X1881 @ X1882 ) )
| ( in @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) @ X1881 ) )
& ( ( in @ ( esk78_4 @ X1881 @ X1882 @ X1883 @ X1885 )
@ ( dsetconstr @ X1882
@ ^ [Z0: $i] : ( in @ ( kpair @ X1885 @ Z0 ) @ ( lam @ X1881 @ X1882 @ X1883 ) ) ) )
| ~ ( in @ X1885 @ X1881 )
| ( in @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) @ X1881 ) )
& ( ( ( dsetconstr @ X1882
@ ^ [Z0: $i] : ( in @ ( kpair @ X1885 @ Z0 ) @ ( lam @ X1881 @ X1882 @ X1883 ) ) )
= ( setadjoin @ ( esk78_4 @ X1881 @ X1882 @ X1883 @ X1885 ) @ emptyset ) )
| ~ ( in @ X1885 @ X1881 )
| ( in @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) @ X1881 ) )
& ( ( subset @ ( lam @ X1881 @ X1882 @ X1883 ) @ ( cartprod @ X1881 @ X1882 ) )
| ~ ( in @ ( X1883 @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) ) @ X1882 ) )
& ( ( in @ ( esk78_4 @ X1881 @ X1882 @ X1883 @ X1885 )
@ ( dsetconstr @ X1882
@ ^ [Z0: $i] : ( in @ ( kpair @ X1885 @ Z0 ) @ ( lam @ X1881 @ X1882 @ X1883 ) ) ) )
| ~ ( in @ X1885 @ X1881 )
| ~ ( in @ ( X1883 @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) ) @ X1882 ) )
& ( ( ( dsetconstr @ X1882
@ ^ [Z0: $i] : ( in @ ( kpair @ X1885 @ Z0 ) @ ( lam @ X1881 @ X1882 @ X1883 ) ) )
= ( setadjoin @ ( esk78_4 @ X1881 @ X1882 @ X1883 @ X1885 ) @ emptyset ) )
| ~ ( in @ X1885 @ X1881 )
| ~ ( in @ ( X1883 @ ( esk77_3 @ X1881 @ X1882 @ X1883 ) ) @ X1882 ) )
& ( ( in @ ( esk79_3 @ X1887 @ X1888 @ X1889 ) @ X1887 )
| ( in @ ( lam @ X1887 @ X1888 @ X1889 ) @ ( funcSet @ X1887 @ X1888 ) ) )
& ( ~ ( in @ ( X1889 @ ( esk79_3 @ X1887 @ X1888 @ X1889 ) ) @ X1888 )
| ( in @ ( lam @ X1887 @ X1888 @ X1889 ) @ ( funcSet @ X1887 @ X1888 ) ) )
& ( subset @ esk82_0 @ ( cartprod @ esk80_0 @ esk81_0 ) )
& ( ~ ( in @ X1895 @ esk80_0 )
| ~ ( in @ X1896 @ esk81_0 )
| ~ ( in @ ( kpair @ X1895 @ X1896 ) @ esk82_0 )
| ( epred2_0 @ ( kpair @ X1895 @ X1896 ) ) )
& ( in @ esk83_0 @ esk82_0 )
& ~ ( epred2_0 @ esk83_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_284])])])])])])]) ).
thf(c_0_286,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_287,negated_conjecture,
in @ esk83_0 @ esk82_0,
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_288,negated_conjecture,
! [X2: $i] :
( ( in @ esk83_0 @ X2 )
| ~ ( subset @ esk82_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_286,c_0_287]) ).
thf(c_0_289,negated_conjecture,
subset @ esk82_0 @ ( cartprod @ esk80_0 @ esk81_0 ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_290,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_291,negated_conjecture,
in @ esk83_0 @ ( cartprod @ esk80_0 @ esk81_0 ),
inference(spm,[status(thm)],[c_0_288,c_0_289]) ).
thf(c_0_292,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ ( ksnd @ X2 ) @ X4 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_293,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ ( kfst @ X2 ) @ X3 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_294,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_0 @ ( kpair @ X2 @ X3 ) )
| ~ ( in @ X2 @ esk80_0 )
| ~ ( in @ X3 @ esk81_0 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ esk82_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_295,negated_conjecture,
( ( kpair @ ( kfst @ esk83_0 ) @ ( ksnd @ esk83_0 ) )
= esk83_0 ),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
thf(c_0_296,negated_conjecture,
in @ ( ksnd @ esk83_0 ) @ esk81_0,
inference(spm,[status(thm)],[c_0_292,c_0_291]) ).
thf(c_0_297,negated_conjecture,
in @ ( kfst @ esk83_0 ) @ esk80_0,
inference(spm,[status(thm)],[c_0_293,c_0_291]) ).
thf(c_0_298,negated_conjecture,
~ ( epred2_0 @ esk83_0 ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
thf(c_0_299,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_295]),c_0_287]),c_0_296]),c_0_297])]),c_0_298]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU681^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:56:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running higher-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.27/0.65 # Version: 3.1.0-ho
% 1.27/0.65 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.27/0.65 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.27/0.65 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.27/0.65 # Starting pre_casc_3 with 300s (1) cores
% 1.27/0.65 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.27/0.65 # Starting full_lambda_10 with 300s (1) cores
% 1.27/0.65 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.27/0.65 # ho_unfolding_5 with pid 17504 completed with status 0
% 1.27/0.65 # Result found by ho_unfolding_5
% 1.27/0.65 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.27/0.65 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.27/0.65 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.27/0.65 # No SInE strategy applied
% 1.27/0.65 # Search class: HGHSM-FSLM32-DHSMMSBN
% 1.27/0.65 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 1.27/0.65 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.27/0.65 # Starting full_lambda_5 with 99s (1) cores
% 1.27/0.65 # Starting ho_unfolding_5 with 121s (1) cores
% 1.27/0.65 # Starting pre_casc_4 with 99s (1) cores
% 1.27/0.65 # Starting pre_casc_3 with 99s (1) cores
% 1.27/0.65 # ho_unfolding_5 with pid 17514 completed with status 0
% 1.27/0.65 # Result found by ho_unfolding_5
% 1.27/0.65 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.27/0.65 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.27/0.65 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.27/0.65 # No SInE strategy applied
% 1.27/0.65 # Search class: HGHSM-FSLM32-DHSMMSBN
% 1.27/0.65 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 1.27/0.65 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.27/0.65 # Starting full_lambda_5 with 99s (1) cores
% 1.27/0.65 # Starting ho_unfolding_5 with 121s (1) cores
% 1.27/0.65 # Preprocessing time : 0.008 s
% 1.27/0.65 # Presaturation interreduction done
% 1.27/0.65
% 1.27/0.65 # Proof found!
% 1.27/0.65 # SZS status Theorem
% 1.27/0.65 # SZS output start CNFRefutation
% See solution above
% 1.27/0.65 # Parsed axioms : 440
% 1.27/0.65 # Removed by relevancy pruning/SinE : 0
% 1.27/0.65 # Initial clauses : 616
% 1.27/0.65 # Removed in clause preprocessing : 264
% 1.27/0.65 # Initial clauses in saturation : 352
% 1.27/0.65 # Processed clauses : 733
% 1.27/0.65 # ...of these trivial : 21
% 1.27/0.65 # ...subsumed : 124
% 1.27/0.65 # ...remaining for further processing : 588
% 1.27/0.65 # Other redundant clauses eliminated : 36
% 1.27/0.65 # Clauses deleted for lack of memory : 0
% 1.27/0.65 # Backward-subsumed : 1
% 1.27/0.65 # Backward-rewritten : 4
% 1.27/0.65 # Generated clauses : 2125
% 1.27/0.65 # ...of the previous two non-redundant : 1929
% 1.27/0.65 # ...aggressively subsumed : 0
% 1.27/0.65 # Contextual simplify-reflections : 1
% 1.27/0.65 # Paramodulations : 2070
% 1.27/0.65 # Factorizations : 0
% 1.27/0.65 # NegExts : 0
% 1.27/0.65 # Equation resolutions : 39
% 1.27/0.65 # Disequality decompositions : 0
% 1.27/0.65 # Total rewrite steps : 261
% 1.27/0.65 # ...of those cached : 190
% 1.27/0.65 # Propositional unsat checks : 0
% 1.27/0.65 # Propositional check models : 0
% 1.27/0.65 # Propositional check unsatisfiable : 0
% 1.27/0.65 # Propositional clauses : 0
% 1.27/0.65 # Propositional clauses after purity: 0
% 1.27/0.65 # Propositional unsat core size : 0
% 1.27/0.65 # Propositional preprocessing time : 0.000
% 1.27/0.65 # Propositional encoding time : 0.000
% 1.27/0.65 # Propositional solver time : 0.000
% 1.27/0.65 # Success case prop preproc time : 0.000
% 1.27/0.65 # Success case prop encoding time : 0.000
% 1.27/0.65 # Success case prop solver time : 0.000
% 1.27/0.65 # Current number of processed clauses : 259
% 1.27/0.65 # Positive orientable unit clauses : 60
% 1.27/0.65 # Positive unorientable unit clauses: 0
% 1.27/0.65 # Negative unit clauses : 5
% 1.27/0.65 # Non-unit-clauses : 194
% 1.27/0.65 # Current number of unprocessed clauses: 1827
% 1.27/0.65 # ...number of literals in the above : 4849
% 1.27/0.65 # Current number of archived formulas : 0
% 1.27/0.65 # Current number of archived clauses : 317
% 1.27/0.65 # Clause-clause subsumption calls (NU) : 22161
% 1.27/0.65 # Rec. Clause-clause subsumption calls : 10916
% 1.27/0.65 # Non-unit clause-clause subsumptions : 86
% 1.27/0.65 # Unit Clause-clause subsumption calls : 312
% 1.27/0.65 # Rewrite failures with RHS unbound : 0
% 1.27/0.65 # BW rewrite match attempts : 18
% 1.27/0.65 # BW rewrite match successes : 3
% 1.27/0.65 # Condensation attempts : 0
% 1.27/0.65 # Condensation successes : 0
% 1.27/0.65 # Termbank termtop insertions : 90863
% 1.27/0.65 # Search garbage collected termcells : 20491
% 1.27/0.65
% 1.27/0.65 # -------------------------------------------------
% 1.27/0.65 # User time : 0.139 s
% 1.27/0.65 # System time : 0.017 s
% 1.27/0.65 # Total time : 0.156 s
% 1.27/0.65 # Maximum resident set size: 6660 pages
% 1.27/0.65
% 1.27/0.65 # -------------------------------------------------
% 1.27/0.65 # User time : 0.374 s
% 1.27/0.65 # System time : 0.037 s
% 1.27/0.65 # Total time : 0.411 s
% 1.27/0.65 # Maximum resident set size: 2468 pages
% 1.27/0.65 % E---3.1 exiting
% 1.27/0.66 % E exiting
%------------------------------------------------------------------------------