%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU702^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 03:29:16 EDT 2024
% Result : Theorem 1.02s 0.59s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 569
% Syntax : Number of formulae : 663 ( 46 unt; 342 typ; 0 def)
% Number of atoms : 2909 ( 653 equ; 0 cnn)
% Maximal formula atoms : 893 ( 9 avg)
% Number of connectives : 11876 ( 796 ~; 888 |; 554 &;7955 @)
% ( 310 <=>;1373 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1010 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 599 ( 599 >; 0 *; 0 +; 0 <<)
% Number of symbols : 346 ( 342 usr; 228 con; 0-4 aty)
% Number of variables : 2512 ( 198 ^2168 !; 146 ?;2512 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
epred1_0: $o ).
thf(decl_278,type,
esk1_2: $i > $i > $i ).
thf(decl_279,type,
esk2_2: $i > $i > $i ).
thf(decl_280,type,
esk3_2: $i > $i > $i ).
thf(decl_281,type,
esk4_1: $i > $i ).
thf(decl_282,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_283,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_284,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_285,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_286,type,
esk9_1: $i > $i ).
thf(decl_287,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_288,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_289,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_290,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_291,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_292,type,
esk15_2: $i > $i > $i ).
thf(decl_293,type,
esk16_2: $i > $i > $i ).
thf(decl_294,type,
esk17_1: $i > $i ).
thf(decl_295,type,
esk18_1: $i > $i ).
thf(decl_296,type,
esk19_1: $i > $i ).
thf(decl_297,type,
esk20_2: $i > $i > $i ).
thf(decl_298,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_299,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_300,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_301,type,
esk24_1: $i > $i ).
thf(decl_302,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_303,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_304,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_305,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_306,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_307,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_308,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_309,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_310,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_311,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_312,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_313,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_314,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_315,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_316,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_317,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_318,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_319,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_320,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_321,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_322,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_323,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_324,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_325,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_326,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_327,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_328,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_329,type,
esk52_2: $i > $i > $i ).
thf(decl_330,type,
esk53_2: $i > $i > $i ).
thf(decl_331,type,
esk54_2: $i > $i > $i ).
thf(decl_332,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_333,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_334,type,
esk57_2: $i > $i > $i ).
thf(decl_335,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_336,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_337,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_338,type,
esk61_2: $i > ( $i > $o ) > $i ).
thf(decl_339,type,
esk62_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_340,type,
esk63_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_341,type,
esk64_2: $i > ( $i > $o ) > $i ).
thf(decl_342,type,
esk65_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk66_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk67_1: $i > $i ).
thf(decl_345,type,
esk68_1: $i > $i ).
thf(decl_346,type,
esk69_4: $i > $i > $i > $i > $i ).
thf(decl_347,type,
esk70_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_348,type,
esk71_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_349,type,
esk72_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_350,type,
esk73_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_351,type,
esk74_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk75_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk76_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_354,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_355,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_356,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_357,type,
esk80_4: $i > $i > $i > $i > $i ).
thf(decl_358,type,
esk81_4: $i > $i > $i > $i > $i ).
thf(decl_359,type,
esk82_4: $i > $i > $i > $i > $i ).
thf(decl_360,type,
esk83_4: $i > $i > $i > $i > $i ).
thf(decl_361,type,
esk84_4: $i > $i > $i > $i > $i ).
thf(decl_362,type,
esk85_4: $i > $i > $i > $i > $i ).
thf(decl_363,type,
esk86_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_364,type,
esk87_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_365,type,
esk88_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_366,type,
esk89_0: $i ).
thf(decl_367,type,
epred2_0: $o ).
thf(decl_368,type,
esk90_0: $i ).
thf(decl_369,type,
esk91_0: $i ).
thf(decl_375,type,
epred3_0: $i > $o ).
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(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(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/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(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
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(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(c_0_224,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X741: $i] :
( ( in @ X741
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X741 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_225,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_226,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_227,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_228,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_229,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_230,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_231,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X741: $i] :
( ( in @ X741
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X741 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_224,c_0_225]) ).
thf(c_0_244,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_245,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_246,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_247,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_248,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_249,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_250,plain,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).
thf(c_0_251,plain,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1E2]) ).
thf(c_0_252,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X712: $i] :
( ( X6 @ X2 @ X712 )
& ! [X713: $i] :
( ( X6 @ X2 @ X713 )
=> ( X712 = X713 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_226,c_0_227]) ).
thf(c_0_253,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X714: $i] :
( ( X1 @ X714 )
& ! [X715: $i] :
( ( X1 @ X715 )
=> ( X714 = X715 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_228,c_0_227]) ).
thf(c_0_254,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_255,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_256,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_257,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X716: $i] :
( ( X1 @ X716 )
& ! [X717: $i] :
( ( X1 @ X717 )
=> ( X716 = X717 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_229,c_0_227]) ).
thf(c_0_258,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X718: $i] :
( ( X1 @ X718 )
& ! [X719: $i] :
( ( X1 @ X719 )
=> ( X718 = X719 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_230,c_0_227]) ).
thf(c_0_259,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_260,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_231]) ).
thf(c_0_261,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_232,c_0_231]) ).
thf(c_0_262,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_231]) ).
thf(c_0_263,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_264,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X720: $i] :
( ( X1 @ X720 )
& ! [X721: $i] :
( ( X1 @ X721 )
=> ( X720 = X721 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_233,c_0_227]) ).
thf(c_0_265,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_231]) ).
thf(c_0_266,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_267,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X722: $i] :
( ( X1 @ X722 )
& ! [X723: $i] :
( ( X1 @ X723 )
=> ( X722 = X723 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_234,c_0_227]) ).
thf(c_0_268,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X724: $i] :
( ( X1 @ X724 )
& ! [X725: $i] :
( ( X1 @ X725 )
=> ( X724 = X725 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_235,c_0_227]) ).
thf(c_0_269,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X726: $i] :
( ( X1 @ X726 )
& ! [X727: $i] :
( ( X1 @ X727 )
=> ( X726 = X727 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_236,c_0_227]) ).
thf(c_0_270,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X728: $i] :
( ( X1 @ X728 )
& ! [X729: $i] :
( ( X1 @ X729 )
=> ( X728 = X729 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_237,c_0_227]) ).
thf(c_0_271,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X730: $i] :
( ( X1 @ X730 )
& ! [X731: $i] :
( ( X1 @ X731 )
=> ( X730 = X731 ) ) )
<=> ? [X732: $i] :
( ( X17 @ X732 )
& ! [X733: $i] :
( ( X17 @ X733 )
=> ( X732 = X733 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_238,c_0_227]) ).
thf(c_0_272,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X734: $i] :
( ( X1 @ X734 )
& ! [X735: $i] :
( ( X1 @ X735 )
=> ( X734 = X735 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_239,c_0_227]) ).
thf(c_0_273,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X736: $i] :
( ( X1 @ X736 )
& ! [X737: $i] :
( ( X1 @ X737 )
=> ( X736 = X737 ) ) )
=> ( ? [X738: $i] :
( ( X17 @ X738 )
& ! [X739: $i] :
( ( X17 @ X739 )
=> ( X738 = X739 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_240,c_0_227]) ).
thf(c_0_274,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_275,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_276,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_277,plain,
( singletonprop
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X740: $i] :
( ( in @ X740
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X740 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_241,c_0_225]) ).
thf(c_0_278,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ? [X742: $i] :
( ( in @ X742
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X742 @ emptyset ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_242,c_0_243]) ).
thf(c_0_279,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ? [X743: $i] :
( ( in @ X743
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X743 @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_244,c_0_243]) ).
thf(c_0_280,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ? [X744: $i] :
( ( in @ X744
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X744 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_245,c_0_243]) ).
thf(c_0_281,plain,
( kfstsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X745: $i] :
( ( in @ X745
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
= ( setadjoin @ X745 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_246,c_0_225]) ).
thf(c_0_282,axiom,
( theprop
= ( ! [X21: $i] :
( ? [X746: $i] :
( ( in @ X746 @ X21 )
& ( X21
= ( setadjoin @ X746 @ emptyset ) ) )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_225]) ).
thf(c_0_283,plain,
( ksndsingleton
= ( ! [X18: $i] :
( ( iskpair @ X18 )
=> ? [X747: $i] :
( ( in @ X747
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X18 )
@ ^ [Z0: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
= ( setadjoin @ X747 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_247,c_0_225]) ).
thf(c_0_284,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_285,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_286,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_248,c_0_249]) ).
thf(c_0_287,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_288,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_289,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_290,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_291,plain,
( funcImageSingleton
= ( ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X748: $i] :
( ( in @ X748
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
& ( ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) )
= ( setadjoin @ X748 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_250,c_0_225]) ).
thf(c_0_292,plain,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
@ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[apProp]) ).
thf(c_0_293,plain,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] :
( ( X30 @ Z0 )
= Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamProp]) ).
thf(c_0_294,plain,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X31 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lamp]) ).
thf(c_0_295,plain,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X32 @ Z0 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2p]) ).
thf(c_0_296,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_249]) ).
thf(c_0_297,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_249]) ).
thf(c_0_298,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ? [X749: $i] :
( ( in @ X749
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( setadjoin @ X749 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_251,c_0_243]) ).
thf(c_0_299,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_249]) ).
thf(c_0_300,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_249]) ).
thf(c_0_301,plain,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X36 @ Z0 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta1]) ).
thf(c_0_302,plain,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta1]) ).
thf(c_0_303,plain,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) )
= ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X37 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[lam2lamEq]) ).
thf(c_0_304,plain,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( X38 @ Z0 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[beta2]) ).
thf(c_0_305,plain,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
= X29 ) ) ),
inference(fof_simplification,[status(thm)],[eta2]) ).
thf(c_0_306,plain,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X39
& ( Z0 = X2 ) )
| ( ~ X39
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp1]) ).
thf(c_0_307,plain,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X40
& ( Z0 = X2 ) )
| ( ~ X40
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iffalseProp2]) ).
thf(c_0_308,plain,
( epred1_0
<=> ! [X779: $i] :
? [X780: $i] :
( ! [X781: $i] :
( ( in @ X781 @ X780 )
=> ! [X782: $i] :
( ( in @ X782 @ X781 )
=> ( in @ X782 @ X779 ) ) )
& ! [X783: $i,X784: $i] :
( ( ( in @ X783 @ X779 )
& ( in @ X784 @ X779 ) )
=> ( ! [X785: $i] :
( ( in @ X785 @ X780 )
=> ( ( in @ X783 @ X785 )
<=> ( in @ X784 @ X785 ) ) )
=> ( X783 = X784 ) ) )
& ! [X786: $i,X787: $i] :
( ( ( in @ X786 @ X780 )
& ( in @ X787 @ X780 ) )
=> ( ! [X788: $i] :
( ( in @ X788 @ X786 )
=> ( in @ X788 @ X787 ) )
| ! [X789: $i] :
( ( in @ X789 @ X787 )
=> ( in @ X789 @ X786 ) ) ) )
& ! [X790: $i] :
( ( ! [X791: $i] :
( ( in @ X791 @ X790 )
=> ( in @ X791 @ X779 ) )
& ? [X792: $i] : ( in @ X792 @ X790 ) )
=> ? [X793: $i,X794: $i] :
( ( in @ X793 @ X780 )
& ( in @ X794 @ X790 )
& ~ ? [X795: $i] :
( ( in @ X795 @ X793 )
& ( in @ X795 @ X790 ) )
& ! [X796: $i] :
( ( in @ X796 @ X780 )
=> ( ! [X797: $i] :
( ( in @ X797 @ X796 )
=> ( in @ X797 @ X793 ) )
| ( in @ X794 @ X796 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_309,negated_conjecture,
~ ( ! [X750: $i,X751: $i] :
( ! [X752: $i] :
( ( in @ X752 @ X750 )
<=> ( in @ X752 @ X751 ) )
=> ( X750 = X751 ) )
=> ( ! [X753: $i] :
~ ( in @ X753 @ emptyset )
=> ( ! [X754: $i,X755: $i,X756: $i] :
( ( in @ X756 @ ( setadjoin @ X754 @ X755 ) )
<=> ( ( X756 = X754 )
| ( in @ X756 @ X755 ) ) )
=> ( ! [X757: $i,X758: $i] :
( ( in @ X758 @ ( powerset @ X757 ) )
<=> ! [X759: $i] :
( ( in @ X759 @ X758 )
=> ( in @ X759 @ X757 ) ) )
=> ( ! [X760: $i,X761: $i] :
( ( in @ X761 @ ( setunion @ X760 ) )
<=> ? [X762: $i] :
( ( in @ X761 @ X762 )
& ( in @ X762 @ X760 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X763: $i] :
( ( in @ X763 @ omega )
=> ( in @ ( setadjoin @ X763 @ X763 ) @ omega ) )
=> ( ! [X764: $i] :
( ( ( in @ emptyset @ X764 )
& ! [X765: $i] :
( ( ( in @ X765 @ omega )
& ( in @ X765 @ X764 ) )
=> ( in @ ( setadjoin @ X765 @ X765 ) @ X764 ) ) )
=> ! [X766: $i] :
( ( in @ X766 @ omega )
=> ( in @ X766 @ X764 ) ) )
=> ( ! [X767: $i > $i > $o,X768: $i] :
( ! [X769: $i] :
( ( in @ X769 @ X768 )
=> ? [X770: $i] :
( ( X767 @ X769 @ X770 )
& ! [X771: $i] :
( ( X767 @ X769 @ X771 )
=> ( X770 = X771 ) ) ) )
=> ? [X772: $i] :
! [X773: $i] :
( ( in @ X773 @ X772 )
<=> ? [X774: $i] :
( ( in @ X774 @ X768 )
& ( X767 @ X774 @ X773 ) ) ) )
=> ( ! [X775: $i] :
( ? [X776: $i] : ( in @ X776 @ X775 )
=> ? [X777: $i] :
( ( in @ X777 @ X775 )
& ~ ? [X778: $i] :
( ( in @ X778 @ X777 )
& ( in @ X778 @ X775 ) ) ) )
=> ( epred1_0
=> ( ! [X798: $i > $o] :
( ? [X799: $i] :
( ( X798 @ X799 )
& ! [X800: $i] :
( ( X798 @ X800 )
=> ( X799 = X800 ) ) )
=> ( X798
@ ( descr
@ ^ [Z0: $i] : ( X798 @ Z0 ) ) ) )
=> ( ! [X801: $i,X802: $i > $o,X803: $i] :
( ( in @ X803 @ X801 )
=> ( ( X802 @ X803 )
=> ( in @ X803 @ ( dsetconstr @ X801 @ X802 ) ) ) )
=> ( ! [X804: $i,X805: $i > $o,X806: $i] :
( ( in @ X806 @ ( dsetconstr @ X804 @ X805 ) )
=> ( in @ X806 @ X804 ) )
=> ( ! [X807: $i,X808: $i > $o,X809: $i] :
( ( in @ X809 @ ( dsetconstr @ X807 @ X808 ) )
=> ( X808 @ X809 ) )
=> ( ! [X810: $i > $o] :
( ? [X811: $i] :
( ( X810 @ X811 )
& ! [X812: $i] :
( ( X810 @ X812 )
=> ( X811 = X812 ) ) )
=> ? [X813: $i] :
( ( X810 @ X813 )
& ! [X814: $i] :
( ( X810 @ X814 )
=> ( X813 = X814 ) ) ) )
=> ( ! [X815: $o,X816: $i] :
( ( in @ X816 @ ( prop2set @ X815 ) )
=> X815 )
=> ( ! [X817: $i] :
( ( in @ X817 @ emptyset )
=> ! [X818: $o] : X818 )
=> ( ! [X819: $i] :
( ( in @ X819 @ emptyset )
=> ~ $true )
=> ( ! [X820: $i] :
~ ( in @ X820 @ emptyset )
=> ( ! [X821: $i > $o] :
( ? [X822: $i] :
( ( X821 @ X822 )
& ! [X823: $i] :
( ( X821 @ X823 )
=> ( X822 = X823 ) ) )
=> ? [X824: $i] : ( X821 @ X824 ) )
=> ( ! [X825: $i,X826: $i] :
( ! [X827: $i] :
( ( in @ X827 @ X825 )
=> ( in @ X827 @ X826 ) )
=> ( ! [X828: $i] :
( ( in @ X828 @ X826 )
=> ( in @ X828 @ X825 ) )
=> ( X825 = X826 ) ) )
=> ( ! [X829: $i] :
( ! [X830: $i] :
~ ( in @ X830 @ X829 )
=> ( X829 = emptyset ) )
=> ( ! [X831: $i] :
( ! [X832: $i] :
~ ( in @ X832 @ X831 )
=> ( X831 = emptyset ) )
=> ( ! [X833: $i,X834: $i > $o,X835: $i] :
( ( in @ X835 @ X833 )
=> ( ( in @ X835 @ ( dsetconstr @ X833 @ X834 ) )
<=> ( X834 @ X835 ) ) )
=> ( ! [X836: $i] :
( ( X836 != emptyset )
=> ? [X837: $i] : ( in @ X837 @ X836 ) )
=> ( ! [X838: $i,X839: $i > $o,X840: $i] :
( ( in @ X840 @ X838 )
=> ( ( X839 @ X840 )
=> ( ( dsetconstr @ X838 @ X839 )
!= emptyset ) ) )
=> ( ! [X841: $i] :
( ? [X842: $i] : ( in @ X842 @ X841 )
=> ( X841 != emptyset ) )
=> ( ! [X843: $i,X844: $i] : ( in @ X843 @ ( setadjoin @ X843 @ X844 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X845: $i,X846: $i,X847: $i] :
( ( in @ X847 @ X846 )
=> ( in @ X847 @ ( setadjoin @ X845 @ X846 ) ) )
=> ( ! [X848: $i,X849: $i,X850: $i] :
( ( in @ X850 @ ( setadjoin @ X848 @ X849 ) )
=> ! [X851: $o] :
( ( ( X850 = X848 )
=> X851 )
=> ( ( ( in @ X850 @ X849 )
=> X851 )
=> X851 ) ) )
=> ( ! [X852: $i,X853: $i,X854: $i] :
( ( in @ X854 @ ( setadjoin @ X852 @ X853 ) )
=> ( ( X854 = X852 )
| ( in @ X854 @ X853 ) ) )
=> ( ! [X855: $i] :
( ( dsetconstr @ X855
@ ^ [Z0: $i] : $true )
= X855 )
=> ( ! [X856: $i,X857: $i] :
( ! [X858: $i] :
( ( in @ X858 @ X857 )
=> ( in @ X858 @ X856 ) )
=> ( in @ X857 @ ( powerset @ X856 ) ) )
=> ( ! [X859: $i] : ( in @ emptyset @ ( powerset @ X859 ) )
=> ( ! [X860: $i] : ( in @ emptyset @ ( powerset @ X860 ) )
=> ( ! [X861: $i,X862: $i,X863: $i] :
( ( in @ X862 @ ( powerset @ X861 ) )
=> ( ( in @ X863 @ X862 )
=> ( in @ X863 @ X861 ) ) )
=> ( ! [X864: $i,X865: $i,X866: $i] :
( ( in @ X865 @ X866 )
=> ( ( in @ X866 @ X864 )
=> ( in @ X865 @ ( setunion @ X864 ) ) ) )
=> ( ! [X867: $i,X868: $i] :
( ( in @ X868 @ ( setunion @ X867 ) )
=> ! [X869: $o] :
( ! [X870: $i] :
( ( in @ X868 @ X870 )
=> ( ( in @ X870 @ X867 )
=> X869 ) )
=> X869 ) )
=> ( ! [X871: $i,X872: $i] :
( ( in @ X872 @ X871 )
=> ( in @ X872 @ ( powerset @ ( setunion @ X871 ) ) ) )
=> ( ! [X873: $i > $o] :
( ? [X874: $i] :
( ( X873 @ X874 )
& ! [X875: $i] :
( ( X873 @ X875 )
=> ( X874 = X875 ) ) )
=> ? [X876: $i] :
! [X877: $i] :
( ( X873 @ X877 )
<=> ( X877 = X876 ) ) )
=> ( ! [X878: $i] :
( ( X878 != emptyset )
=> ? [X879: $i] :
( ( in @ X879 @ X878 )
& $true ) )
=> ( ! [X880: $i,X881: $i] :
( ( in @ X880 @ ( setadjoin @ X881 @ emptyset ) )
=> ( X880 = X881 ) )
=> ( ! [X882: $i,X883: $i] :
( ( X882 != X883 )
=> ~ ( in @ X883 @ ( setadjoin @ X882 @ emptyset ) ) )
=> ( ! [X884: $i,X885: $i] :
( ( X884 = X885 )
=> ( in @ X884 @ ( setadjoin @ X885 @ emptyset ) ) )
=> ( ! [X886: $i,X887: $i] :
( ( in @ X886 @ ( setadjoin @ X887 @ emptyset ) )
=> ( in @ X887 @ ( setadjoin @ X886 @ emptyset ) ) )
=> ( ! [X888: $i,X889: $i,X890: $i] :
( ( in @ X890 @ ( setadjoin @ X888 @ ( setadjoin @ X889 @ emptyset ) ) )
=> ( ( X890 = X888 )
| ( X890 = X889 ) ) )
=> ( ! [X891: $i,X892: $i] : ( in @ X891 @ ( setadjoin @ X891 @ ( setadjoin @ X892 @ emptyset ) ) )
=> ( ! [X893: $i,X894: $i] : ( in @ X894 @ ( setadjoin @ X893 @ ( setadjoin @ X894 @ emptyset ) ) )
=> ( ! [X895: $i,X896: $i > $o] :
( ? [X897: $i] :
( ( in @ X897 @ X895 )
& ( X896 @ X897 ) )
=> ( ( ( dsetconstr @ X895 @ X896 )
= emptyset )
=> ~ $true ) )
=> ( ! [X898: $i > $o,X899: $i] :
( ( in @ X899 @ emptyset )
=> ( X898 @ X899 ) )
=> ( ! [X900: $i,X901: $i > $o] :
( ~ ! [X902: $i] :
( ( in @ X902 @ X900 )
=> ( X901 @ X902 ) )
=> ? [X903: $i] :
( ( in @ X903 @ X900 )
& ~ ( X901 @ X903 ) ) )
=> ( ! [X904: $i,X905: $i > $o] :
( ! [X906: $i] :
( ( in @ X906 @ X904 )
=> ~ ( X905 @ X906 ) )
=> ~ ? [X907: $i] :
( ( in @ X907 @ X904 )
& ( X905 @ X907 ) ) )
=> ( ! [X908: $i,X909: $i > $o] :
( ~ ? [X910: $i] :
( ( in @ X910 @ X908 )
& ( X909 @ X910 ) )
=> ! [X911: $i] :
( ( in @ X911 @ X908 )
=> ~ ( X909 @ X911 ) ) )
=> ( ! [X912: $i,X913: $i > $o] :
( ? [X914: $i] :
( ( in @ X914 @ X912 )
& ~ ( X913 @ X914 ) )
=> ~ ! [X915: $i] :
( ( in @ X915 @ X912 )
=> ( X913 @ X915 ) ) )
=> ( ! [X916: $o] :
( X916
=> ( in @ emptyset @ ( prop2set @ X916 ) ) )
=> ( ! [X917: $o] :
( X917
=> ( set2prop @ ( prop2set @ X917 ) ) )
=> ( ! [X918: $i,X919: $i > $o] :
( ~ ? [X920: $i] :
( ( in @ X920 @ X918 )
& ( X919 @ X920 ) )
=> ! [X921: $i] :
( ( in @ X921 @ X918 )
=> ~ ( X919 @ X921 ) ) )
=> ( ! [X922: $i,X923: $i > $o] :
( ~ ! [X924: $i] :
( ( in @ X924 @ X922 )
=> ( X923 @ X924 ) )
=> ? [X925: $i] :
( ( in @ X925 @ X922 )
& ~ ( X923 @ X925 ) ) )
=> ( ! [X926: $i > $o] :
( ? [X927: $i] :
( ( X926 @ X927 )
& ! [X928: $i] :
( ( X926 @ X928 )
=> ( X927 = X928 ) ) )
=> ? [X929: $i] :
( ( X926 @ X929 )
& ! [X930: $i] :
( ( X926 @ X930 )
=> ( X929 = X930 ) ) ) )
=> ( ! [X931: $i > $o] :
( ? [X932: $i] : ( X931 @ X932 )
=> ( ! [X933: $i,X934: $i] :
( ( X931 @ X933 )
=> ( ( X931 @ X934 )
=> ( X933 = X934 ) ) )
=> ? [X935: $i] :
( ( X931 @ X935 )
& ! [X936: $i] :
( ( X931 @ X936 )
=> ( X935 = X936 ) ) ) ) )
=> ( ! [X937: $i > $o] :
( ? [X938: $i] :
! [X939: $i] :
( ( X937 @ X939 )
<=> ( X939 = X938 ) )
=> ? [X940: $i] :
( ( X937 @ X940 )
& ! [X941: $i] :
( ( X937 @ X941 )
=> ( X940 = X941 ) ) ) )
=> ( ! [X942: $i,X943: $i] :
( ( X942 = X943 )
=> ! [X944: $i,X945: $i] :
( ( X944 = X945 )
=> ( ( in @ X944 @ X942 )
=> ( in @ X945 @ X943 ) ) ) )
=> ( ! [X946: $i,X947: $i] :
( ( X946 = X947 )
=> ! [X948: $i,X949: $i] :
( ( X948 = X949 )
=> ( ( in @ X948 @ X946 )
<=> ( in @ X949 @ X947 ) ) ) )
=> ( ! [X950: $i > $o] :
( ? [X951: $i] :
( ( X950 @ X951 )
& ! [X952: $i] :
( ( X950 @ X952 )
=> ( X951 = X952 ) ) )
=> ! [X953: $i,X954: $i] :
( ( X950 @ X953 )
=> ( ( X950 @ X954 )
=> ( X953 = X954 ) ) ) )
=> ( ! [X955: $i > $o,X956: $i > $o] :
( ! [X957: $i,X958: $i] :
( ( X957 = X958 )
=> ( ( X955 @ X957 )
<=> ( X956 @ X958 ) ) )
=> ( ? [X959: $i] :
( ( X955 @ X959 )
& ! [X960: $i] :
( ( X955 @ X960 )
=> ( X959 = X960 ) ) )
<=> ? [X961: $i] :
( ( X956 @ X961 )
& ! [X962: $i] :
( ( X956 @ X962 )
=> ( X961 = X962 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X963: $i,X964: $i] :
( ( X963 = X964 )
=> ! [X965: $i,X966: $i] :
( ( X965 = X966 )
=> ( ( setadjoin @ X963 @ X965 )
= ( setadjoin @ X964 @ X966 ) ) ) )
=> ( ! [X967: $i,X968: $i] :
( ( X967 = X968 )
=> ( ( powerset @ X967 )
= ( powerset @ X968 ) ) )
=> ( ! [X969: $i,X970: $i] :
( ( X969 = X970 )
=> ( ( setunion @ X969 )
= ( setunion @ X970 ) ) )
=> ( ( omega = omega )
=> ( ! [X971: $i > $o] :
( ? [X972: $i] :
( ( X971 @ X972 )
& ! [X973: $i] :
( ( X971 @ X973 )
=> ( X972 = X973 ) ) )
=> ! [X974: $i,X975: $i] :
( ( X971 @ X974 )
=> ( ( X971 @ X975 )
=> ( X974 = X975 ) ) ) )
=> ( ! [X976: $i > $o,X977: $i > $o] :
( ! [X978: $i,X979: $i] :
( ( X978 = X979 )
=> ( ( X976 @ X978 )
<=> ( X977 @ X979 ) ) )
=> ( ? [X980: $i] :
( ( X976 @ X980 )
& ! [X981: $i] :
( ( X976 @ X981 )
=> ( X980 = X981 ) ) )
=> ( ? [X982: $i] :
( ( X977 @ X982 )
& ! [X983: $i] :
( ( X977 @ X983 )
=> ( X982 = X983 ) ) )
=> ( ( descr @ X976 )
= ( descr @ X977 ) ) ) ) )
=> ( ! [X984: $i,X985: $i] :
( ( X984 = X985 )
=> ! [X986: $i > $o,X987: $i > $o] :
( ! [X988: $i] :
( ( in @ X988 @ X984 )
=> ! [X989: $i] :
( ( in @ X989 @ X985 )
=> ( ( X988 = X989 )
=> ( ( X986 @ X988 )
<=> ( X987 @ X989 ) ) ) ) )
=> ( ( dsetconstr @ X984 @ X986 )
= ( dsetconstr @ X985 @ X987 ) ) ) )
=> ( ! [X990: $i,X991: $i] :
( ! [X992: $i] :
( ( in @ X992 @ X990 )
=> ( in @ X992 @ X991 ) )
=> ( subset @ X990 @ X991 ) )
=> ( ! [X993: $i,X994: $i] :
( ( X993 = X994 )
=> ( subset @ X994 @ X993 ) )
=> ( ! [X995: $i,X996: $i] :
( ( X995 = X996 )
=> ( subset @ X995 @ X996 ) )
=> ( ! [X997: $i,X998: $i] :
( ! [X999: $i] :
( ( in @ X999 @ X997 )
=> ( in @ X999 @ X998 ) )
=> ( subset @ X997 @ X998 ) )
=> ( ! [X1000: $i] : ( subset @ emptyset @ X1000 )
=> ( ! [X1001: $i,X1002: $i,X1003: $i] :
( ( subset @ X1001 @ X1002 )
=> ( ( in @ X1003 @ X1001 )
=> ( in @ X1003 @ X1002 ) ) )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( subset @ X1004 @ X1005 )
=> ( ~ ( in @ X1006 @ X1005 )
=> ~ ( in @ X1006 @ X1004 ) ) )
=> ( ! [X1007: $i,X1008: $i,X1009: $i] :
( ( in @ X1009 @ X1007 )
=> ( ~ ( in @ X1009 @ X1008 )
=> ~ ( subset @ X1007 @ X1008 ) ) )
=> ( ! [X1010: $i,X1011: $i] :
( ~ ( subset @ X1010 @ X1011 )
=> ( X1010 != X1011 ) )
=> ( ! [X1012: $i,X1013: $i,X1014: $i] :
( ( in @ X1014 @ X1012 )
=> ( ~ ( in @ X1014 @ X1013 )
=> ( X1012 != X1013 ) ) )
=> ( ! [X1015: $i] : ( subset @ X1015 @ X1015 )
=> ( ! [X1016: $i,X1017: $i,X1018: $i] :
( ( subset @ X1016 @ X1017 )
=> ( ( subset @ X1017 @ X1018 )
=> ( subset @ X1016 @ X1018 ) ) )
=> ( ! [X1019: $i,X1020: $i] : ( subset @ X1020 @ ( setadjoin @ X1019 @ X1020 ) )
=> ( ! [X1021: $i,X1022: $i,X1023: $i] :
( ( subset @ X1021 @ X1023 )
=> ( subset @ X1021 @ ( setadjoin @ X1022 @ X1023 ) ) )
=> ( ! [X1024: $i,X1025: $i] :
( ( subset @ X1024 @ X1025 )
=> ( in @ X1024 @ ( powerset @ X1025 ) ) )
=> ( ! [X1026: $i,X1027: $i] :
( ( subset @ X1026 @ X1027 )
=> ( ( subset @ X1027 @ X1026 )
=> ( X1026 = X1027 ) ) )
=> ( ! [X1028: $i] :
( ( subset @ X1028 @ emptyset )
=> ( X1028 = emptyset ) )
=> ( ! [X1029: $i,X1030: $i] :
( ( subset @ X1030 @ X1029 )
=> ( in @ X1030 @ ( powerset @ X1029 ) ) )
=> ( ! [X1031: $i,X1032: $i] :
( ( in @ X1032 @ ( powerset @ X1031 ) )
=> ( subset @ X1032 @ X1031 ) )
=> ( ! [X1033: $i] : ( in @ X1033 @ ( powerset @ X1033 ) )
=> ( ! [X1034: $i,X1035: $i] :
( ( subset @ X1034 @ X1035 )
=> ( subset @ ( powerset @ X1034 ) @ ( powerset @ X1035 ) ) )
=> ( ! [X1036: $i,X1037: $i > $o] : ( in @ ( dsetconstr @ X1036 @ X1037 ) @ ( powerset @ X1036 ) )
=> ( ! [X1038: $i,X1039: $i > $o] : ( subset @ ( dsetconstr @ X1038 @ X1039 ) @ X1038 )
=> ( ! [X1040: $i,X1041: $i,X1042: $i] :
( ( in @ X1042 @ X1040 )
=> ( in @ X1042 @ ( binunion @ X1040 @ X1041 ) ) )
=> ( ! [X1043: $i,X1044: $i] : ( in @ X1044 @ ( setadjoin @ X1043 @ ( setadjoin @ X1044 @ emptyset ) ) )
=> ( ! [X1045: $i,X1046: $i,X1047: $i] :
( ( in @ X1047 @ X1046 )
=> ( in @ X1047 @ ( binunion @ X1045 @ X1046 ) ) )
=> ( ! [X1048: $i,X1049: $i,X1050: $i,X1051: $o] :
( ( in @ X1050 @ ( binunion @ X1048 @ X1049 ) )
=> ( ( ( in @ X1050 @ X1048 )
=> X1051 )
=> ( ( ( in @ X1050 @ X1049 )
=> X1051 )
=> X1051 ) ) )
=> ( ! [X1052: $i,X1053: $i,X1054: $i] :
( ( in @ X1054 @ ( binunion @ X1052 @ X1053 ) )
=> ( ( in @ X1054 @ X1052 )
| ( in @ X1054 @ X1053 ) ) )
=> ( ! [X1055: $i,X1056: $i] : ( subset @ X1055 @ ( binunion @ X1055 @ X1056 ) )
=> ( ! [X1057: $i,X1058: $i] : ( subset @ X1058 @ ( binunion @ X1057 @ X1058 ) )
=> ( ! [X1059: $i,X1060: $i,X1061: $i] :
( ( in @ X1061 @ X1059 )
=> ( ( in @ X1061 @ X1060 )
=> ( in @ X1061 @ ( binintersect @ X1059 @ X1060 ) ) ) )
=> ( ! [X1062: $i,X1063: $i,X1064: $i] :
( ( subset @ X1064 @ X1062 )
=> ( ( subset @ X1064 @ X1063 )
=> ( subset @ X1064 @ ( binintersect @ X1062 @ X1063 ) ) ) )
=> ( ! [X1065: $i,X1066: $i,X1067: $i] :
( ( in @ X1067 @ ( binintersect @ X1065 @ X1066 ) )
=> ( in @ X1067 @ X1065 ) )
=> ( ! [X1068: $i,X1069: $i] : ( subset @ ( binintersect @ X1068 @ X1069 ) @ X1068 )
=> ( ! [X1070: $i,X1071: $i] :
( ( subset @ X1070 @ X1071 )
=> ( ( binintersect @ X1070 @ X1071 )
= X1070 ) )
=> ( ! [X1072: $i,X1073: $i] :
( ( ( binintersect @ X1072 @ X1073 )
= X1073 )
=> ( subset @ X1073 @ X1072 ) )
=> ( ! [X1074: $i,X1075: $i,X1076: $i] :
( ( in @ X1076 @ ( binintersect @ X1074 @ X1075 ) )
=> ( in @ X1076 @ X1075 ) )
=> ( ! [X1077: $i,X1078: $i] :
( ~ ? [X1079: $i] :
( ( in @ X1079 @ X1077 )
& ( in @ X1079 @ X1078 ) )
=> ( ( binintersect @ X1077 @ X1078 )
= emptyset ) )
=> ( ! [X1080: $i,X1081: $i] : ( subset @ ( binintersect @ X1080 @ X1081 ) @ X1081 )
=> ( ! [X1082: $i,X1083: $i] :
( ( subset @ X1083 @ X1082 )
=> ( ( binintersect @ X1082 @ X1083 )
= X1083 ) )
=> ( ! [X1084: $i,X1085: $i] :
( ( ( binintersect @ X1084 @ X1085 )
= X1084 )
=> ( subset @ X1084 @ X1085 ) )
=> ( ! [X1086: $i,X1087: $i,X1088: $i] :
( ( binintersect @ X1086 @ ( binunion @ X1087 @ X1088 ) )
= ( binunion @ ( binintersect @ X1086 @ X1087 ) @ ( binintersect @ X1086 @ X1088 ) ) )
=> ( ! [X1089: $i,X1090: $i,X1091: $i] :
( ( in @ X1091 @ X1089 )
=> ( ~ ( in @ X1091 @ X1090 )
=> ( in @ X1091 @ ( setminus @ X1089 @ X1090 ) ) ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i] :
( ( in @ X1094 @ ( setminus @ X1092 @ X1093 ) )
=> ( in @ X1094 @ X1092 ) )
=> ( ! [X1095: $i,X1096: $i,X1097: $i] :
( ( in @ X1097 @ ( setminus @ X1095 @ X1096 ) )
=> ~ ( in @ X1097 @ X1096 ) )
=> ( ! [X1098: $i,X1099: $i] :
( ( subset @ X1098 @ X1099 )
=> ( ( setminus @ X1098 @ X1099 )
= emptyset ) )
=> ( ! [X1100: $i,X1101: $i,X1102: $i] :
( ~ ( in @ X1102 @ ( setminus @ X1100 @ X1101 ) )
=> ( ( in @ X1102 @ X1100 )
=> ( in @ X1102 @ X1101 ) ) )
=> ( ! [X1103: $i,X1104: $i,X1105: $i] :
( ~ ( in @ X1105 @ ( setminus @ X1103 @ X1104 ) )
=> ( ~ ( in @ X1105 @ X1104 )
=> ~ ( in @ X1105 @ X1103 ) ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ~ ( in @ X1108 @ X1106 )
=> ~ ( in @ X1108 @ ( setminus @ X1106 @ X1107 ) ) )
=> ( ! [X1109: $i,X1110: $i,X1111: $i] :
( ( in @ X1111 @ X1110 )
=> ~ ( in @ X1111 @ ( setminus @ X1109 @ X1110 ) ) )
=> ( ! [X1112: $i,X1113: $i] : ( subset @ ( setminus @ X1112 @ X1113 ) @ X1112 )
=> ( ! [X1114: $i,X1115: $i] :
( ( ( setminus @ X1114 @ X1115 )
= emptyset )
=> ( subset @ X1114 @ X1115 ) )
=> ( ! [X1116: $i,X1117: $i,X1118: $i] :
( ( in @ X1118 @ ( symdiff @ X1116 @ X1117 ) )
=> ! [X1119: $o] :
( ( ( in @ X1118 @ X1116 )
=> ( ~ ( in @ X1118 @ X1117 )
=> X1119 ) )
=> ( ( ~ ( in @ X1118 @ X1116 )
=> ( ( in @ X1118 @ X1117 )
=> X1119 ) )
=> X1119 ) ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ( in @ X1122 @ X1120 )
=> ( ~ ( in @ X1122 @ X1121 )
=> ( in @ X1122 @ ( symdiff @ X1120 @ X1121 ) ) ) )
=> ( ! [X1123: $i,X1124: $i,X1125: $i] :
( ~ ( in @ X1125 @ X1123 )
=> ( ( in @ X1125 @ X1124 )
=> ( in @ X1125 @ ( symdiff @ X1123 @ X1124 ) ) ) )
=> ( ! [X1126: $i,X1127: $i,X1128: $i] :
( ( in @ X1128 @ X1126 )
=> ( ( in @ X1128 @ X1127 )
=> ~ ( in @ X1128 @ ( symdiff @ X1126 @ X1127 ) ) ) )
=> ( ! [X1129: $i,X1130: $i,X1131: $i] :
( ~ ( in @ X1131 @ X1129 )
=> ( ~ ( in @ X1131 @ X1130 )
=> ~ ( in @ X1131 @ ( symdiff @ X1129 @ X1130 ) ) ) )
=> ( ! [X1132: $i,X1133: $i] : ( in @ X1133 @ ( setadjoin @ X1132 @ ( setadjoin @ X1133 @ emptyset ) ) )
=> ( ! [X1134: $i,X1135: $i] : ( in @ X1134 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1134 @ ( setadjoin @ X1135 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1136: $i,X1137: $i] : ( in @ X1137 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1136 @ ( setadjoin @ X1137 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1138: $i,X1139: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1138 @ ( setadjoin @ X1139 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1140: $i,X1141: $i] : ( iskpair @ ( kpair @ X1140 @ X1141 ) )
=> ( ! [X1142: $i,X1143: $i] :
( ( in @ X1143 @ X1142 )
=> ( subset @ ( setadjoin @ X1143 @ emptyset ) @ X1142 ) )
=> ( ! [X1144: $i,X1145: $i] :
( ( in @ X1145 @ X1144 )
=> ( in @ ( setadjoin @ X1145 @ emptyset ) @ ( powerset @ X1144 ) ) )
=> ( ! [X1146: $i,X1147: $i,X1148: $i] :
( ( in @ X1148 @ X1146 )
=> ( in @ ( setadjoin @ X1148 @ emptyset ) @ ( powerset @ ( binunion @ X1146 @ X1147 ) ) ) )
=> ( ! [X1149: $i,X1150: $i,X1151: $i] :
( ( in @ X1151 @ ( setadjoin @ X1149 @ ( setadjoin @ X1150 @ emptyset ) ) )
=> ( ( X1151 = X1149 )
| ( X1151 = X1150 ) ) )
=> ( ! [X1152: $i,X1153: $i,X1154: $i] :
( ( in @ X1154 @ X1152 )
=> ! [X1155: $i] :
( ( in @ X1155 @ X1153 )
=> ( subset @ ( setadjoin @ X1154 @ ( setadjoin @ X1155 @ emptyset ) ) @ ( binunion @ X1152 @ X1153 ) ) ) )
=> ( ! [X1156: $i,X1157: $i,X1158: $i] :
( ( in @ X1158 @ X1156 )
=> ! [X1159: $i] :
( ( in @ X1159 @ X1157 )
=> ( in @ ( setadjoin @ X1158 @ ( setadjoin @ X1159 @ emptyset ) ) @ ( powerset @ ( binunion @ X1156 @ X1157 ) ) ) ) )
=> ( ! [X1160: $i,X1161: $i,X1162: $i] :
( ( in @ X1162 @ X1160 )
=> ! [X1163: $i] :
( ( in @ X1163 @ X1161 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1162 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1162 @ ( setadjoin @ X1163 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1160 @ X1161 ) ) ) ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( in @ X1166 @ X1164 )
=> ! [X1167: $i] :
( ( in @ X1167 @ X1165 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1166 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1166 @ ( setadjoin @ X1167 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1164 @ X1165 ) ) ) ) ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ( in @ X1170 @ X1168 )
=> ! [X1171: $i] :
( ( in @ X1171 @ X1169 )
=> ( in @ ( kpair @ X1170 @ X1171 ) @ ( powerset @ ( powerset @ ( binunion @ X1168 @ X1169 ) ) ) ) ) )
=> ( ! [X1172: $i,X1173: $i,X1174: $i] :
( ( in @ X1174 @ X1172 )
=> ! [X1175: $i] :
( ( in @ X1175 @ X1173 )
=> ( in @ ( kpair @ X1174 @ X1175 ) @ ( cartprod @ X1172 @ X1173 ) ) ) )
=> ( ! [X1176: $i,X1177: $i,X1178: $i] :
( ( in @ X1178 @ ( cartprod @ X1176 @ X1177 ) )
=> ? [X1179: $i] :
( ( in @ X1179 @ X1176 )
& ? [X1180: $i] :
( ( in @ X1180 @ X1177 )
& ( X1178
= ( kpair @ X1179 @ X1180 ) ) ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ ( cartprod @ X1181 @ X1182 ) )
=> ( iskpair @ X1183 ) )
=> ( ! [X1184: $i,X1185: $i] :
( ( in @ X1185 @ ( setunion @ X1184 ) )
=> ? [X1186: $i] :
( ( in @ X1186 @ X1184 )
& ( in @ X1185 @ X1186 ) ) )
=> ( ! [X1187: $i] : ( subset @ ( setunion @ ( setadjoin @ X1187 @ emptyset ) ) @ X1187 )
=> ( ! [X1188: $i] : ( subset @ X1188 @ ( setunion @ ( setadjoin @ X1188 @ emptyset ) ) )
=> ( ! [X1189: $i] :
( ( setunion @ ( setadjoin @ X1189 @ emptyset ) )
= X1189 )
=> ( ! [X1190: $i,X1191: $i > $o] :
( ! [X1192: $i] :
( ( in @ X1192 @ X1190 )
=> ! [X1193: $i] :
( ( in @ X1193 @ X1190 )
=> ( ( X1191 @ X1192 )
=> ( ( X1191 @ X1193 )
=> ( X1192 = X1193 ) ) ) ) )
=> ( ? [X1194: $i] :
( ( in @ X1194 @ X1190 )
& ( X1191 @ X1194 ) )
=> ? [X1195: $i] :
( ( in @ X1195 @ ( dsetconstr @ X1190 @ X1191 ) )
& ( ( dsetconstr @ X1190 @ X1191 )
= ( setadjoin @ X1195 @ emptyset ) ) ) ) )
=> ( ! [X1196: $i,X1197: $i > $o] :
( ? [X1198: $i] :
( ( in @ X1198 @ ( dsetconstr @ X1196 @ X1197 ) )
& ( ( dsetconstr @ X1196 @ X1197 )
= ( setadjoin @ X1198 @ emptyset ) ) )
=> ? [X1199: $i] :
( ( in @ X1199 @ X1196 )
& ( X1197 @ X1199 ) ) )
=> ( ! [X1200: $i,X1201: $i > $o,X1202: $i] :
( ( in @ X1202 @ X1200 )
=> ( ( X1201 @ X1202 )
=> ( ! [X1203: $i] :
( ( in @ X1203 @ X1200 )
=> ( ( X1201 @ X1203 )
=> ( X1203 = X1202 ) ) )
=> ? [X1204: $i] :
( ( in @ X1204 @ ( dsetconstr @ X1200 @ X1201 ) )
& ( ( dsetconstr @ X1200 @ X1201 )
= ( setadjoin @ X1204 @ emptyset ) ) ) ) ) )
=> ( ! [X1205: $i,X1206: $i > $o] :
( ! [X1207: $i] :
( ( in @ X1207 @ X1205 )
=> ! [X1208: $i] :
( ( in @ X1208 @ X1205 )
=> ( ( X1206 @ X1207 )
=> ( ( X1206 @ X1208 )
=> ( X1207 = X1208 ) ) ) ) )
=> ( ? [X1209: $i] :
( ( in @ X1209 @ X1205 )
& ( X1206 @ X1209 ) )
=> ? [X1210: $i] :
( ( in @ X1210 @ ( dsetconstr @ X1205 @ X1206 ) )
& ( ( dsetconstr @ X1205 @ X1206 )
= ( setadjoin @ X1210 @ emptyset ) ) ) ) )
=> ( ! [X1211: $i,X1212: $i] :
( ( ( setadjoin @ X1211 @ emptyset )
= ( setadjoin @ X1212 @ emptyset ) )
=> ( X1211 = X1212 ) )
=> ( ! [X1213: $i,X1214: $i,X1215: $i] :
( ( in @ ( setadjoin @ X1215 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1213 @ ( setadjoin @ X1214 @ emptyset ) ) @ emptyset ) ) )
=> ( X1213 = X1215 ) )
=> ( ! [X1216: $i] :
( ( iskpair @ X1216 )
=> ? [X1217: $i] :
( ( in @ X1217
@ ( dsetconstr @ ( setunion @ X1216 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1216 ) ) )
& ( ( dsetconstr @ ( setunion @ X1216 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1216 ) )
= ( setadjoin @ X1217 @ emptyset ) ) ) )
=> ( ! [X1218: $i] :
( ? [X1219: $i] :
( ( in @ X1219 @ X1218 )
& ( X1218
= ( setadjoin @ X1219 @ emptyset ) ) )
=> ( in @ ( setunion @ X1218 ) @ X1218 ) )
=> ( ! [X1220: $i,X1221: $i] :
( ( kfst @ ( kpair @ X1220 @ X1221 ) )
= X1220 )
=> ( ! [X1222: $i,X1223: $i,X1224: $i] :
( ( in @ X1224 @ ( cartprod @ X1222 @ X1223 ) )
=> ( in @ ( kfst @ X1224 ) @ X1222 ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i,X1228: $i] :
( ( ( setadjoin @ ( setadjoin @ X1225 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1225 @ ( setadjoin @ X1226 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1227 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1227 @ ( setadjoin @ X1228 @ emptyset ) ) @ emptyset ) ) )
=> ( X1225 = X1227 ) )
=> ( ! [X1229: $i,X1230: $i,X1231: $i,X1232: $i] :
( ( ( kpair @ X1229 @ X1230 )
= ( kpair @ X1231 @ X1232 ) )
=> ( X1229 = X1231 ) )
=> ( ! [X1233: $i,X1234: $i] :
( ( X1233 = X1234 )
=> ( ( setadjoin @ X1233 @ ( setadjoin @ X1234 @ emptyset ) )
= ( setadjoin @ X1233 @ emptyset ) ) )
=> ( ! [X1235: $i,X1236: $i] :
( ( X1235 = X1236 )
=> ( ( setadjoin @ ( setadjoin @ X1235 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1235 @ ( setadjoin @ X1236 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1235 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1237: $i,X1238: $i,X1239: $i,X1240: $i] :
( ( ( setadjoin @ ( setadjoin @ X1237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1237 @ ( setadjoin @ X1238 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1239 @ ( setadjoin @ X1240 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1239 = X1240 )
=> ( X1238 = X1240 ) ) )
=> ( ! [X1241: $i,X1242: $i,X1243: $i] :
( ( ( setadjoin @ X1241 @ ( setadjoin @ X1242 @ emptyset ) )
= ( setadjoin @ X1243 @ emptyset ) )
=> ( X1241 = X1242 ) )
=> ( ! [X1244: $i,X1245: $i,X1246: $i,X1247: $i] :
( ( ( setadjoin @ ( setadjoin @ X1244 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1244 @ ( setadjoin @ X1245 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) ) @ emptyset ) ) )
=> ( X1245 = X1247 ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i,X1251: $i] :
( ( ( kpair @ X1248 @ X1249 )
= ( kpair @ X1250 @ X1251 ) )
=> ( X1249 = X1251 ) )
=> ( ! [X1252: $i] :
( ( iskpair @ X1252 )
=> ? [X1253: $i] :
( ( in @ X1253
@ ( dsetconstr @ ( setunion @ X1252 )
@ ^ [Z0: $i] :
( X1252
= ( kpair @ ( kfst @ X1252 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X1252 )
@ ^ [Z0: $i] :
( X1252
= ( kpair @ ( kfst @ X1252 ) @ Z0 ) ) )
= ( setadjoin @ X1253 @ emptyset ) ) ) )
=> ( ! [X1254: $i,X1255: $i] :
( ( ksnd @ ( kpair @ X1254 @ X1255 ) )
= X1255 )
=> ( ! [X1256: $i] :
( ( iskpair @ X1256 )
=> ( ( kpair @ ( kfst @ X1256 ) @ ( ksnd @ X1256 ) )
= X1256 ) )
=> ( ! [X1257: $i,X1258: $i,X1259: $i] :
( ( in @ X1259 @ ( cartprod @ X1257 @ X1258 ) )
=> ( in @ ( ksnd @ X1259 ) @ X1258 ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i,X1263: $i] :
( ( in @ ( kpair @ X1262 @ X1263 ) @ ( cartprod @ X1260 @ X1261 ) )
=> ( in @ X1262 @ X1260 ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i,X1267: $i] :
( ( in @ ( kpair @ X1266 @ X1267 ) @ ( cartprod @ X1264 @ X1265 ) )
=> ( in @ X1267 @ X1265 ) )
=> ( ! [X1268: $i,X1269: $i,X1270: $i] :
( ( in @ X1270 @ X1268 )
=> ! [X1271: $i] :
( ( in @ X1271 @ X1269 )
=> ( ( kpair @ X1270 @ X1271 )
= ( kpair @ X1270 @ X1271 ) ) ) )
=> ( ! [X1272: $i,X1273: $i,X1274: $i] :
( ( in @ X1274 @ X1272 )
=> ! [X1275: $i] :
( ( in @ X1275 @ X1273 )
=> ( ( kfst @ ( kpair @ X1274 @ X1275 ) )
= X1274 ) ) )
=> ( ! [X1276: $i,X1277: $i,X1278: $i] :
( ( in @ X1278 @ X1276 )
=> ! [X1279: $i] :
( ( in @ X1279 @ X1277 )
=> ( ( ksnd @ ( kpair @ X1278 @ X1279 ) )
= X1279 ) ) )
=> ( ! [X1280: $i,X1281: $i,X1282: $i] :
( ( in @ X1282 @ ( cartprod @ X1280 @ X1281 ) )
=> ( ( kpair @ ( kfst @ X1282 ) @ ( ksnd @ X1282 ) )
= X1282 ) )
=> ( ! [X1283: $i,X1284: $i,X1285: $i > $i > $o,X1286: $i] :
( ( in @ X1286 @ X1283 )
=> ! [X1287: $i] :
( ( in @ X1287 @ X1284 )
=> ( ( X1285 @ X1286 @ X1287 )
=> ( in @ ( kpair @ X1286 @ X1287 ) @ ( dpsetconstr @ X1283 @ X1284 @ X1285 ) ) ) ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1288 @ X1289 @ X1290 ) @ ( cartprod @ X1288 @ X1289 ) )
=> ( ! [X1291: $i,X1292: $i,X1293: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1291 @ X1292 @ X1293 ) @ ( cartprod @ X1291 @ X1292 ) )
=> ( ! [X1294: $i,X1295: $i,X1296: $i > $i > $o,X1297: $i] :
( ( in @ X1297 @ X1294 )
=> ! [X1298: $i] :
( ( in @ X1298 @ X1295 )
=> ( ( in @ ( kpair @ X1297 @ X1298 ) @ ( dpsetconstr @ X1294 @ X1295 @ X1296 ) )
=> ( X1296 @ X1297 @ X1298 ) ) ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i > $i > $o,X1302: $i,X1303: $i] :
( ( in @ ( kpair @ X1302 @ X1303 ) @ ( dpsetconstr @ X1299 @ X1300 @ X1301 ) )
=> ( in @ X1302 @ X1299 ) )
=> ( ! [X1304: $i,X1305: $i,X1306: $i > $i > $o,X1307: $i,X1308: $i] :
( ( in @ ( kpair @ X1307 @ X1308 ) @ ( dpsetconstr @ X1304 @ X1305 @ X1306 ) )
=> ( in @ X1308 @ X1305 ) )
=> ( ! [X1309: $i,X1310: $i,X1311: $i > $i > $o,X1312: $i,X1313: $i] :
( ( in @ ( kpair @ X1312 @ X1313 ) @ ( dpsetconstr @ X1309 @ X1310 @ X1311 ) )
=> ( X1311 @ X1312 @ X1313 ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( func @ X1314 @ X1315 @ X1316 )
=> ! [X1317: $i] :
( ( in @ X1317 @ X1314 )
=> ? [X1318: $i] :
( ( in @ X1318
@ ( dsetconstr @ X1315
@ ^ [Z0: $i] : ( in @ ( kpair @ X1317 @ Z0 ) @ X1316 ) ) )
& ( ( dsetconstr @ X1315
@ ^ [Z0: $i] : ( in @ ( kpair @ X1317 @ Z0 ) @ X1316 ) )
= ( setadjoin @ X1318 @ emptyset ) ) ) ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i] :
( ( func @ X1319 @ X1320 @ X1321 )
=> ! [X1322: $i] :
( ( in @ X1322 @ X1319 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1320
@ ^ [Z0: $i] : ( in @ ( kpair @ X1322 @ Z0 ) @ X1321 ) ) )
@ X1320 ) ) )
=> ( ! [X1323: $i,X1324: $i,X1325: $i] :
( ( func @ X1323 @ X1324 @ X1325 )
=> ! [X1326: $i] :
( ( in @ X1326 @ X1323 )
=> ( in @ ( ap @ X1323 @ X1324 @ X1325 @ X1326 ) @ X1324 ) ) )
=> ( ! [X1327: $i,X1328: $i,X1329: $i] :
( ( in @ X1329 @ ( funcSet @ X1327 @ X1328 ) )
=> ( func @ X1327 @ X1328 @ X1329 ) )
=> ( ! [X1330: $i,X1331: $i,X1332: $i] :
( ( in @ X1332 @ ( funcSet @ X1330 @ X1331 ) )
=> ! [X1333: $i] :
( ( in @ X1333 @ X1330 )
=> ( in @ ( ap @ X1330 @ X1331 @ X1332 @ X1333 ) @ X1331 ) ) )
=> ( ! [X1334: $i,X1335: $i,X1336: $i] :
( ( func @ X1334 @ X1335 @ X1336 )
=> ( in @ X1336 @ ( funcSet @ X1334 @ X1335 ) ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i > $i] :
( ! [X1340: $i] :
( ( in @ X1340 @ X1337 )
=> ( in @ ( X1339 @ X1340 ) @ X1338 ) )
=> ( func @ X1337 @ X1338
@ ( dpsetconstr @ X1337 @ X1338
@ ^ [Z0: $i] : ( $eq @ ( X1339 @ Z0 ) ) ) ) )
=> ( ! [X1341: $i,X1342: $i,X1343: $i > $i] :
( ! [X1344: $i] :
( ( in @ X1344 @ X1341 )
=> ( in @ ( X1343 @ X1344 ) @ X1342 ) )
=> ( func @ X1341 @ X1342 @ ( lam @ X1341 @ X1342 @ X1343 ) ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i > $i] :
( ! [X1348: $i] :
( ( in @ X1348 @ X1345 )
=> ( in @ ( X1347 @ X1348 ) @ X1346 ) )
=> ( in @ ( lam @ X1345 @ X1346 @ X1347 ) @ ( funcSet @ X1345 @ X1346 ) ) )
=> ( ! [X1349: $i,X1350: $i,X1351: $i] :
( ( subset @ X1351 @ ( cartprod @ X1349 @ X1350 ) )
=> ! [X1352: $i > $o] :
( ! [X1353: $i] :
( ( in @ X1353 @ X1349 )
=> ! [X1354: $i] :
( ( in @ X1354 @ X1350 )
=> ( ( in @ ( kpair @ X1353 @ X1354 ) @ X1351 )
=> ( X1352 @ ( kpair @ X1353 @ X1354 ) ) ) ) )
=> ! [X1355: $i] :
( ( in @ X1355 @ X1351 )
=> ( X1352 @ X1355 ) ) ) )
=> ( ! [X1356: $i,X1357: $i,X1358: $i] :
( ( subset @ X1358 @ ( cartprod @ X1356 @ X1357 ) )
=> ! [X1359: $i > $o] :
( ! [X1360: $i] :
( ( in @ X1360 @ X1356 )
=> ! [X1361: $i] :
( ( in @ X1361 @ X1357 )
=> ( ( in @ ( kpair @ X1360 @ X1361 ) @ X1358 )
=> ( X1359 @ ( kpair @ X1360 @ X1361 ) ) ) ) )
=> ! [X1362: $i] :
( ( in @ X1362 @ X1358 )
=> ( X1359 @ X1362 ) ) ) )
=> ( ! [X1363: $i,X1364: $i > $o] :
( ? [X1365: $i] :
( ( in @ X1365 @ ( dsetconstr @ X1363 @ X1364 ) )
& ( ( dsetconstr @ X1363 @ X1364 )
= ( setadjoin @ X1365 @ emptyset ) ) )
=> ! [X1366: $i] :
( ( in @ X1366 @ X1363 )
=> ! [X1367: $i] :
( ( in @ X1367 @ X1363 )
=> ( ( X1364 @ X1366 )
=> ( ( X1364 @ X1367 )
=> ( X1366 = X1367 ) ) ) ) ) )
=> ( ! [X1368: $i,X1369: $i,X1370: $i] :
( ( func @ X1368 @ X1369 @ X1370 )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1368 )
=> ( in @ ( kpair @ X1371 @ ( ap @ X1368 @ X1369 @ X1370 @ X1371 ) ) @ X1370 ) ) )
=> ( ! [X1372: $i,X1373: $i,X1374: $i] :
( ( in @ X1374 @ ( funcSet @ X1372 @ X1373 ) )
=> ! [X1375: $i] :
( ( in @ X1375 @ X1372 )
=> ( in @ ( kpair @ X1375 @ ( ap @ X1372 @ X1373 @ X1374 @ X1375 ) ) @ X1374 ) ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i] :
( ( func @ X1376 @ X1377 @ X1378 )
=> ! [X1379: $i] :
( ( in @ X1379 @ X1376 )
=> ! [X1380: $i] :
( ( in @ X1380 @ X1377 )
=> ( ( in @ ( kpair @ X1379 @ X1380 ) @ X1378 )
=> ( ( ap @ X1376 @ X1377 @ X1378 @ X1379 )
= X1380 ) ) ) ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i] :
( ( func @ X1381 @ X1382 @ X1383 )
=> ! [X1384: $i] :
( ( func @ X1381 @ X1382 @ X1384 )
=> ( ! [X1385: $i] :
( ( in @ X1385 @ X1381 )
=> ( ( ap @ X1381 @ X1382 @ X1383 @ X1385 )
= ( ap @ X1381 @ X1382 @ X1384 @ X1385 ) ) )
=> ! [X1386: $i] :
( ( in @ X1386 @ X1381 )
=> ! [X1387: $i] :
( ( in @ X1387 @ X1382 )
=> ( ( in @ ( kpair @ X1386 @ X1387 ) @ X1384 )
=> ( in @ ( kpair @ X1386 @ X1387 ) @ X1383 ) ) ) ) ) ) )
=> ( ! [X1388: $i,X1389: $i,X1390: $i] :
( ( in @ X1390 @ ( funcSet @ X1388 @ X1389 ) )
=> ! [X1391: $i] :
( ( in @ X1391 @ X1388 )
=> ! [X1392: $i] :
( ( in @ X1392 @ X1389 )
=> ( ( in @ ( kpair @ X1391 @ X1392 ) @ X1390 )
=> ( ( ap @ X1388 @ X1389 @ X1390 @ X1391 )
= X1392 ) ) ) ) )
=> ( ! [X1393: $i,X1394: $i,X1395: $i] :
( ( subset @ X1395 @ ( cartprod @ X1393 @ X1394 ) )
=> ! [X1396: $i] :
( ( subset @ X1396 @ ( cartprod @ X1393 @ X1394 ) )
=> ( ! [X1397: $i] :
( ( in @ X1397 @ X1393 )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1394 )
=> ( ( in @ ( kpair @ X1397 @ X1398 ) @ X1395 )
=> ( in @ ( kpair @ X1397 @ X1398 ) @ X1396 ) ) ) )
=> ( subset @ X1395 @ X1396 ) ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( subset @ X1401 @ ( cartprod @ X1399 @ X1400 ) )
=> ! [X1402: $i] :
( ( subset @ X1402 @ ( cartprod @ X1399 @ X1400 ) )
=> ( ! [X1403: $i] :
( ( in @ X1403 @ X1399 )
=> ! [X1404: $i] :
( ( in @ X1404 @ X1400 )
=> ( ( in @ ( kpair @ X1403 @ X1404 ) @ X1401 )
=> ( in @ ( kpair @ X1403 @ X1404 ) @ X1402 ) ) ) )
=> ( ! [X1405: $i] :
( ( in @ X1405 @ X1399 )
=> ! [X1406: $i] :
( ( in @ X1406 @ X1400 )
=> ( ( in @ ( kpair @ X1405 @ X1406 ) @ X1402 )
=> ( in @ ( kpair @ X1405 @ X1406 ) @ X1401 ) ) ) )
=> ( X1401 = X1402 ) ) ) ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i] :
( ( func @ X1407 @ X1408 @ X1409 )
=> ! [X1410: $i] :
( ( func @ X1407 @ X1408 @ X1410 )
=> ( ! [X1411: $i] :
( ( in @ X1411 @ X1407 )
=> ( ( ap @ X1407 @ X1408 @ X1409 @ X1411 )
= ( ap @ X1407 @ X1408 @ X1410 @ X1411 ) ) )
=> ( X1409 = X1410 ) ) ) )
=> ( ! [X1412: $i,X1413: $i,X1414: $i] :
( ( in @ X1414 @ ( funcSet @ X1412 @ X1413 ) )
=> ! [X1415: $i] :
( ( in @ X1415 @ ( funcSet @ X1412 @ X1413 ) )
=> ( ! [X1416: $i] :
( ( in @ X1416 @ X1412 )
=> ( ( ap @ X1412 @ X1413 @ X1414 @ X1416 )
= ( ap @ X1412 @ X1413 @ X1415 @ X1416 ) ) )
=> ( X1414 = X1415 ) ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( in @ X1419 @ ( funcSet @ X1417 @ X1418 ) )
=> ! [X1420: $i] :
( ( in @ X1420 @ X1417 )
=> ( ( ap @ X1417 @ X1418 @ X1419 @ X1420 )
= ( ap @ X1417 @ X1418 @ X1419 @ X1420 ) ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i] :
( ( func @ X1421 @ X1422 @ X1423 )
=> ! [X1424: $i] :
( ( in @ X1424 @ X1421 )
=> ( ( ap @ X1421 @ X1422 @ X1423 @ X1424 )
= ( ap @ X1421 @ X1422 @ X1423 @ X1424 ) ) ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i > $i] :
( ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ( in @ ( X1427 @ X1428 ) @ X1426 ) )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1425 )
=> ( ( ap @ X1425 @ X1426 @ ( lam @ X1425 @ X1426 @ X1427 ) @ X1429 )
= ( X1427 @ X1429 ) ) ) )
=> ( ! [X1430: $i,X1431: $i,X1432: $i] :
( ( func @ X1430 @ X1431 @ X1432 )
=> ( ( lam @ X1430 @ X1431 @ ( ap @ X1430 @ X1431 @ X1432 ) )
= X1432 ) )
=> ( ! [X1433: $i,X1434: $i,X1435: $i > $i] :
( ! [X1436: $i] :
( ( in @ X1436 @ X1433 )
=> ( in @ ( X1435 @ X1436 ) @ X1434 ) )
=> ( ( lam @ X1433 @ X1434 @ X1435 )
= ( lam @ X1433 @ X1434 @ X1435 ) ) )
=> ( ! [X1437: $i,X1438: $i,X1439: $i > $i] :
( ! [X1440: $i] :
( ( in @ X1440 @ X1437 )
=> ( in @ ( X1439 @ X1440 ) @ X1438 ) )
=> ! [X1441: $i] :
( ( in @ X1441 @ X1437 )
=> ( ( ap @ X1437 @ X1438 @ ( lam @ X1437 @ X1438 @ X1439 ) @ X1441 )
= ( X1439 @ X1441 ) ) ) )
=> ( ! [X1442: $i,X1443: $i,X1444: $i] :
( ( in @ X1444 @ ( funcSet @ X1442 @ X1443 ) )
=> ( ( lam @ X1442 @ X1443 @ ( ap @ X1442 @ X1443 @ X1444 ) )
= X1444 ) )
=> ( ! [X1445: $i,X1446: $o,X1447: $i] :
( ( in @ X1447 @ X1445 )
=> ! [X1448: $i] :
( ( in @ X1448 @ X1445 )
=> ( ~ X1446
=> ( in @ X1448
@ ( dsetconstr @ X1445
@ ^ [Z0: $i] :
( ( X1446
& ( Z0 = X1447 ) )
| ( ~ X1446
& ( Z0 = X1448 ) ) ) ) ) ) ) )
=> ( ! [X1449: $i,X1450: $o,X1451: $i] :
( ( in @ X1451 @ X1449 )
=> ! [X1452: $i] :
( ( in @ X1452 @ X1449 )
=> ( ~ X1450
=> ( ( dsetconstr @ X1449
@ ^ [Z0: $i] :
( ( X1450
& ( Z0 = X1451 ) )
| ( ~ X1450
& ( Z0 = X1452 ) ) ) )
= ( setadjoin @ X1452 @ emptyset ) ) ) ) )
=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X41
& ( Z0 = X2 ) )
| ( ~ X41
& ( Z0 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[iftrueProp1])]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_252]),foundationAx]),wellorderingAx]),c_0_253]),c_0_254]),c_0_255]),c_0_256]),c_0_257]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_258]),setext]),emptyI]),noeltsimpempty]),c_0_259]),c_0_260]),c_0_261]),c_0_262]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_263]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_264]),c_0_265]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_266]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_267]),c_0_268]),c_0_269]),inCongP]),in__Cong]),c_0_270]),c_0_271]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_272]),c_0_273]),c_0_274]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_275]),c_0_276]),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_277]),c_0_278]),c_0_279]),c_0_280]),singletonsuniq]),setukpairinjL1]),c_0_281]),c_0_282]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_283]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_284]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),c_0_291]),c_0_292]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_293]),c_0_294]),c_0_295]),c_0_296]),c_0_297]),c_0_298]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_299]),c_0_300]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_301]),c_0_302]),c_0_303]),c_0_304]),c_0_305]),c_0_306]),c_0_307])])]),c_0_308]) ).
thf(c_0_310,negated_conjecture,
! [X1453: $i,X1454: $i,X1456: $i,X1457: $i,X1458: $i,X1459: $i,X1460: $i,X1461: $i,X1462: $i,X1463: $i,X1464: $i,X1466: $i,X1467: $i,X1469: $i,X1470: $i,X1471: $i,X1472: $i,X1473: $i,X1475: $i,X1476: $i > $i > $o,X1477: $i,X1479: $i,X1482: $i,X1484: $i,X1485: $i,X1486: $i,X1487: $i,X1489: $i,X1490: $i > $o,X1491: $i,X1493: $i,X1494: $i > $o,X1495: $i,X1496: $i,X1497: $i > $o,X1498: $i,X1499: $i,X1500: $i > $o,X1501: $i,X1502: $i > $o,X1503: $i,X1506: $i,X1507: $o,X1508: $i,X1509: $i,X1510: $o,X1511: $i,X1512: $i,X1513: $i > $o,X1514: $i,X1517: $i,X1518: $i,X1521: $i,X1523: $i,X1525: $i,X1526: $i > $o,X1527: $i,X1528: $i,X1530: $i,X1531: $i > $o,X1532: $i,X1533: $i,X1534: $i,X1535: $i,X1536: $i,X1537: $i,X1538: $i,X1539: $i,X1540: $i,X1541: $i,X1542: $i,X1543: $o,X1544: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1551: $i,X1552: $i,X1553: $i,X1554: $i,X1555: $i,X1556: $i,X1557: $i,X1558: $i,X1559: $i,X1560: $i,X1561: $o,X1563: $i,X1564: $i,X1565: $i > $o,X1566: $i,X1569: $i,X1570: $i,X1571: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $i,X1580: $i,X1581: $i,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $i,X1589: $i > $o,X1590: $i,X1591: $i > $o,X1592: $i,X1593: $i,X1594: $i > $o,X1595: $i,X1597: $i,X1598: $i > $o,X1600: $i,X1601: $i,X1602: $i > $o,X1604: $i,X1605: $i,X1606: $i > $o,X1607: $i,X1609: $o,X1610: $o,X1611: $i,X1612: $i > $o,X1614: $i,X1615: $i,X1616: $i > $o,X1617: $i,X1619: $i > $o,X1620: $i,X1623: $i,X1624: $i > $o,X1625: $i,X1629: $i,X1630: $i > $o,X1631: $i,X1634: $i,X1635: $i,X1636: $i,X1637: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1643: $i > $o,X1644: $i,X1646: $i,X1647: $i,X1648: $i > $o,X1649: $i > $o,X1652: $i,X1655: $i,X1656: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i > $o,X1669: $i,X1671: $i,X1672: $i,X1673: $i > $o,X1674: $i > $o,X1677: $i,X1679: $i,X1681: $i,X1682: $i,X1683: $i > $o,X1684: $i > $o,X1687: $i,X1688: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $i,X1716: $i,X1717: $i,X1718: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1724: $i,X1725: $i,X1726: $i,X1727: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i > $o,X1735: $i,X1736: $i > $o,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $o,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,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $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,X1814: $i,X1815: $i,X1816: $o,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i > $o,X1891: $i,X1893: $i,X1894: $i > $o,X1895: $i,X1897: $i,X1898: $i > $o,X1899: $i,X1902: $i,X1903: $i > $o,X1906: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $i,X1929: $i,X1930: $i,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $i,X1943: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i,X1951: $i,X1952: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i > $i > $o,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i > $i > $o,X1988: $i,X1989: $i,X1990: $i > $i > $o,X1991: $i,X1992: $i,X1993: $i > $i > $o,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i > $i > $o,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i > $i > $o,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i > $i > $o,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i > $i,X2038: $i,X2039: $i,X2040: $i > $i,X2042: $i,X2043: $i,X2044: $i > $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i > $o,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i > $o,X2059: $i,X2060: $i,X2061: $i > $o,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i > $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i > $i,X2134: $i,X2135: $i,X2136: $i > $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $o,X2144: $i,X2145: $i,X2146: $i,X2147: $o,X2148: $i,X2149: $i] :
( ( ~ ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1453 )
| ~ ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1454 )
| ( X1453 = X1454 ) )
& ( ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1453 )
| ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1454 )
| ( X1453 = X1454 ) )
& ~ ( in @ X1456 @ emptyset )
& ( ~ ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) )
| ( X1459 = X1457 )
| ( in @ X1459 @ X1458 ) )
& ( ( X1459 != X1457 )
| ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) ) )
& ( ~ ( in @ X1459 @ X1458 )
| ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) ) )
& ( ~ ( in @ X1461 @ ( powerset @ X1460 ) )
| ~ ( in @ X1462 @ X1461 )
| ( in @ X1462 @ X1460 ) )
& ( ( in @ ( esk2_2 @ X1463 @ X1464 ) @ X1464 )
| ( in @ X1464 @ ( powerset @ X1463 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1463 @ X1464 ) @ X1463 )
| ( in @ X1464 @ ( powerset @ X1463 ) ) )
& ( ( in @ X1467 @ ( esk3_2 @ X1466 @ X1467 ) )
| ~ ( in @ X1467 @ ( setunion @ X1466 ) ) )
& ( ( in @ ( esk3_2 @ X1466 @ X1467 ) @ X1466 )
| ~ ( in @ X1467 @ ( setunion @ X1466 ) ) )
& ( ~ ( in @ X1470 @ X1471 )
| ~ ( in @ X1471 @ X1469 )
| ( in @ X1470 @ ( setunion @ X1469 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1472 @ omega )
| ( in @ ( setadjoin @ X1472 @ X1472 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1473 ) @ omega )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ( in @ ( esk4_1 @ X1473 ) @ X1473 )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1473 ) @ ( esk4_1 @ X1473 ) ) @ X1473 )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ( in @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1477 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ( X1476 @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1482 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ~ ( in @ X1485 @ X1477 )
| ~ ( X1476 @ X1485 @ X1484 )
| ( in @ X1484 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ( in @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1477 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ( X1476 @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1482 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ~ ( in @ X1485 @ X1477 )
| ~ ( X1476 @ X1485 @ X1484 )
| ( in @ X1484 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ( in @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1477 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1479
!= ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ( X1476 @ ( esk8_3 @ X1476 @ X1477 @ X1482 ) @ X1482 )
| ~ ( in @ X1482 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1479
!= ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ~ ( in @ X1485 @ X1477 )
| ~ ( X1476 @ X1485 @ X1484 )
| ( in @ X1484 @ ( esk7_2 @ X1476 @ X1477 ) )
| ( X1479
!= ( esk6_3 @ X1476 @ X1477 @ X1479 ) )
| ~ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) @ X1479 ) )
& ( ( in @ ( esk9_1 @ X1486 ) @ X1486 )
| ~ ( in @ X1487 @ X1486 ) )
& ( ~ ( in @ X1489 @ ( esk9_1 @ X1486 ) )
| ~ ( in @ X1489 @ X1486 )
| ~ ( in @ X1487 @ X1486 ) )
& epred1_0
& ( ( X1490 @ ( esk10_2 @ X1490 @ X1491 ) )
| ~ ( X1490 @ X1491 )
| ( X1490 @ ( descr @ X1490 ) ) )
& ( ( X1491
!= ( esk10_2 @ X1490 @ X1491 ) )
| ~ ( X1490 @ X1491 )
| ( X1490 @ ( descr @ X1490 ) ) )
& ( ~ ( in @ X1495 @ X1493 )
| ~ ( X1494 @ X1495 )
| ( in @ X1495 @ ( dsetconstr @ X1493 @ X1494 ) ) )
& ( ~ ( in @ X1498 @ ( dsetconstr @ X1496 @ X1497 ) )
| ( in @ X1498 @ X1496 ) )
& ( ~ ( in @ X1501 @ ( dsetconstr @ X1499 @ X1500 ) )
| ( X1500 @ X1501 ) )
& ( ( X1502 @ ( esk12_1 @ X1502 ) )
| ( X1502 @ ( esk11_2 @ X1502 @ X1503 ) )
| ~ ( X1502 @ X1503 ) )
& ( ~ ( X1502 @ X1506 )
| ( ( esk12_1 @ X1502 )
= X1506 )
| ( X1502 @ ( esk11_2 @ X1502 @ X1503 ) )
| ~ ( X1502 @ X1503 ) )
& ( ( X1502 @ ( esk12_1 @ X1502 ) )
| ( X1503
!= ( esk11_2 @ X1502 @ X1503 ) )
| ~ ( X1502 @ X1503 ) )
& ( ~ ( X1502 @ X1506 )
| ( ( esk12_1 @ X1502 )
= X1506 )
| ( X1503
!= ( esk11_2 @ X1502 @ X1503 ) )
| ~ ( X1502 @ X1503 ) )
& ( ~ ( in @ X1508 @ ( prop2set @ X1507 ) )
| X1507 )
& ( ~ ( in @ X1509 @ emptyset )
| X1510 )
& ( ~ ( in @ X1511 @ emptyset )
| ~ $true )
& ~ ( in @ X1512 @ emptyset )
& ( ( X1513 @ ( esk13_2 @ X1513 @ X1514 ) )
| ~ ( X1513 @ X1514 )
| ( X1513 @ ( esk14_1 @ X1513 ) ) )
& ( ( X1514
!= ( esk13_2 @ X1513 @ X1514 ) )
| ~ ( X1513 @ X1514 )
| ( X1513 @ ( esk14_1 @ X1513 ) ) )
& ( ( in @ ( esk16_2 @ X1517 @ X1518 ) @ X1518 )
| ( X1517 = X1518 )
| ( in @ ( esk15_2 @ X1517 @ X1518 ) @ X1517 ) )
& ( ~ ( in @ ( esk16_2 @ X1517 @ X1518 ) @ X1517 )
| ( X1517 = X1518 )
| ( in @ ( esk15_2 @ X1517 @ X1518 ) @ X1517 ) )
& ( ( in @ ( esk16_2 @ X1517 @ X1518 ) @ X1518 )
| ( X1517 = X1518 )
| ~ ( in @ ( esk15_2 @ X1517 @ X1518 ) @ X1518 ) )
& ( ~ ( in @ ( esk16_2 @ X1517 @ X1518 ) @ X1517 )
| ( X1517 = X1518 )
| ~ ( in @ ( esk15_2 @ X1517 @ X1518 ) @ X1518 ) )
& ( ( in @ ( esk17_1 @ X1521 ) @ X1521 )
| ( X1521 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1523 ) @ X1523 )
| ( X1523 = emptyset ) )
& ( ~ ( in @ X1527 @ ( dsetconstr @ X1525 @ X1526 ) )
| ( X1526 @ X1527 )
| ~ ( in @ X1527 @ X1525 ) )
& ( ~ ( X1526 @ X1527 )
| ( in @ X1527 @ ( dsetconstr @ X1525 @ X1526 ) )
| ~ ( in @ X1527 @ X1525 ) )
& ( ( X1528 = emptyset )
| ( in @ ( esk19_1 @ X1528 ) @ X1528 ) )
& ( ~ ( in @ X1532 @ X1530 )
| ~ ( X1531 @ X1532 )
| ( ( dsetconstr @ X1530 @ X1531 )
!= emptyset ) )
& ( ~ ( in @ X1534 @ X1533 )
| ( X1533 != emptyset ) )
& ( in @ X1535 @ ( setadjoin @ X1535 @ X1536 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1539 @ X1538 )
| ( in @ X1539 @ ( setadjoin @ X1537 @ X1538 ) ) )
& ( ( in @ X1542 @ X1541 )
| X1543
| ( X1542 = X1540 )
| ~ ( in @ X1542 @ ( setadjoin @ X1540 @ X1541 ) ) )
& ( ~ X1543
| X1543
| ( X1542 = X1540 )
| ~ ( in @ X1542 @ ( setadjoin @ X1540 @ X1541 ) ) )
& ( ( in @ X1542 @ X1541 )
| X1543
| ~ X1543
| ~ ( in @ X1542 @ ( setadjoin @ X1540 @ X1541 ) ) )
& ( ~ X1543
| X1543
| ~ X1543
| ~ ( in @ X1542 @ ( setadjoin @ X1540 @ X1541 ) ) )
& ( ~ ( in @ X1546 @ ( setadjoin @ X1544 @ X1545 ) )
| ( X1546 = X1544 )
| ( in @ X1546 @ X1545 ) )
& ( ( dsetconstr @ X1547
@ ^ [Z0: $i] : $true )
= X1547 )
& ( ( in @ ( esk20_2 @ X1548 @ X1549 ) @ X1549 )
| ( in @ X1549 @ ( powerset @ X1548 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1548 @ X1549 ) @ X1548 )
| ( in @ X1549 @ ( powerset @ X1548 ) ) )
& ( in @ emptyset @ ( powerset @ X1551 ) )
& ( in @ emptyset @ ( powerset @ X1552 ) )
& ( ~ ( in @ X1554 @ ( powerset @ X1553 ) )
| ~ ( in @ X1555 @ X1554 )
| ( in @ X1555 @ X1553 ) )
& ( ~ ( in @ X1557 @ X1558 )
| ~ ( in @ X1558 @ X1556 )
| ( in @ X1557 @ ( setunion @ X1556 ) ) )
& ( ( in @ X1560 @ ( esk21_3 @ X1559 @ X1560 @ X1561 ) )
| X1561
| ~ ( in @ X1560 @ ( setunion @ X1559 ) ) )
& ( ( in @ ( esk21_3 @ X1559 @ X1560 @ X1561 ) @ X1559 )
| X1561
| ~ ( in @ X1560 @ ( setunion @ X1559 ) ) )
& ( ~ X1561
| X1561
| ~ ( in @ X1560 @ ( setunion @ X1559 ) ) )
& ( ~ ( in @ X1564 @ X1563 )
| ( in @ X1564 @ ( powerset @ ( setunion @ X1563 ) ) ) )
& ( ~ ( X1565 @ X1569 )
| ( X1569
= ( esk23_1 @ X1565 ) )
| ( X1565 @ ( esk22_2 @ X1565 @ X1566 ) )
| ~ ( X1565 @ X1566 ) )
& ( ( X1570
!= ( esk23_1 @ X1565 ) )
| ( X1565 @ X1570 )
| ( X1565 @ ( esk22_2 @ X1565 @ X1566 ) )
| ~ ( X1565 @ X1566 ) )
& ( ~ ( X1565 @ X1569 )
| ( X1569
= ( esk23_1 @ X1565 ) )
| ( X1566
!= ( esk22_2 @ X1565 @ X1566 ) )
| ~ ( X1565 @ X1566 ) )
& ( ( X1570
!= ( esk23_1 @ X1565 ) )
| ( X1565 @ X1570 )
| ( X1566
!= ( esk22_2 @ X1565 @ X1566 ) )
| ~ ( X1565 @ X1566 ) )
& ( ( in @ ( esk24_1 @ X1571 ) @ X1571 )
| ( X1571 = emptyset ) )
& ( $true
| ( X1571 = emptyset ) )
& ( ~ ( in @ X1573 @ ( setadjoin @ X1574 @ emptyset ) )
| ( X1573 = X1574 ) )
& ( ( X1575 = X1576 )
| ~ ( in @ X1576 @ ( setadjoin @ X1575 @ emptyset ) ) )
& ( ( X1577 != X1578 )
| ( in @ X1577 @ ( setadjoin @ X1578 @ emptyset ) ) )
& ( ~ ( in @ X1579 @ ( setadjoin @ X1580 @ emptyset ) )
| ( in @ X1580 @ ( setadjoin @ X1579 @ emptyset ) ) )
& ( ~ ( in @ X1583 @ ( setadjoin @ X1581 @ ( setadjoin @ X1582 @ emptyset ) ) )
| ( X1583 = X1581 )
| ( X1583 = X1582 ) )
& ( in @ X1584 @ ( setadjoin @ X1584 @ ( setadjoin @ X1585 @ emptyset ) ) )
& ( in @ X1587 @ ( setadjoin @ X1586 @ ( setadjoin @ X1587 @ emptyset ) ) )
& ( ~ ( in @ X1590 @ X1588 )
| ~ ( X1589 @ X1590 )
| ( ( dsetconstr @ X1588 @ X1589 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1592 @ emptyset )
| ( X1591 @ X1592 ) )
& ( ( in @ ( esk25_2 @ X1593 @ X1594 ) @ X1593 )
| ~ ( in @ X1595 @ X1593 )
| ( X1594 @ X1595 ) )
& ( ~ ( X1594 @ ( esk25_2 @ X1593 @ X1594 ) )
| ~ ( in @ X1595 @ X1593 )
| ( X1594 @ X1595 ) )
& ( ( in @ ( esk26_2 @ X1597 @ X1598 ) @ X1597 )
| ~ ( in @ X1600 @ X1597 )
| ~ ( X1598 @ X1600 ) )
& ( ( X1598 @ ( esk26_2 @ X1597 @ X1598 ) )
| ~ ( in @ X1600 @ X1597 )
| ~ ( X1598 @ X1600 ) )
& ( ( in @ ( esk27_2 @ X1601 @ X1602 ) @ X1601 )
| ~ ( in @ X1604 @ X1601 )
| ~ ( X1602 @ X1604 ) )
& ( ( X1602 @ ( esk27_2 @ X1601 @ X1602 ) )
| ~ ( in @ X1604 @ X1601 )
| ~ ( X1602 @ X1604 ) )
& ( ( in @ ( esk28_2 @ X1605 @ X1606 ) @ X1605 )
| ~ ( in @ X1607 @ X1605 )
| ( X1606 @ X1607 ) )
& ( ~ ( X1606 @ ( esk28_2 @ X1605 @ X1606 ) )
| ~ ( in @ X1607 @ X1605 )
| ( X1606 @ X1607 ) )
& ( ~ X1609
| ( in @ emptyset @ ( prop2set @ X1609 ) ) )
& ( ~ X1610
| ( set2prop @ ( prop2set @ X1610 ) ) )
& ( ( in @ ( esk29_2 @ X1611 @ X1612 ) @ X1611 )
| ~ ( in @ X1614 @ X1611 )
| ~ ( X1612 @ X1614 ) )
& ( ( X1612 @ ( esk29_2 @ X1611 @ X1612 ) )
| ~ ( in @ X1614 @ X1611 )
| ~ ( X1612 @ X1614 ) )
& ( ( in @ ( esk30_2 @ X1615 @ X1616 ) @ X1615 )
| ~ ( in @ X1617 @ X1615 )
| ( X1616 @ X1617 ) )
& ( ~ ( X1616 @ ( esk30_2 @ X1615 @ X1616 ) )
| ~ ( in @ X1617 @ X1615 )
| ( X1616 @ X1617 ) )
& ( ( X1619 @ ( esk32_1 @ X1619 ) )
| ( X1619 @ ( esk31_2 @ X1619 @ X1620 ) )
| ~ ( X1619 @ X1620 ) )
& ( ~ ( X1619 @ X1623 )
| ( ( esk32_1 @ X1619 )
= X1623 )
| ( X1619 @ ( esk31_2 @ X1619 @ X1620 ) )
| ~ ( X1619 @ X1620 ) )
& ( ( X1619 @ ( esk32_1 @ X1619 ) )
| ( X1620
!= ( esk31_2 @ X1619 @ X1620 ) )
| ~ ( X1619 @ X1620 ) )
& ( ~ ( X1619 @ X1623 )
| ( ( esk32_1 @ X1619 )
= X1623 )
| ( X1620
!= ( esk31_2 @ X1619 @ X1620 ) )
| ~ ( X1619 @ X1620 ) )
& ( ( X1624 @ ( esk35_1 @ X1624 ) )
| ( X1624 @ ( esk33_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ~ ( X1624 @ X1629 )
| ( ( esk35_1 @ X1624 )
= X1629 )
| ( X1624 @ ( esk33_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ( X1624 @ ( esk35_1 @ X1624 ) )
| ( X1624 @ ( esk34_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ~ ( X1624 @ X1629 )
| ( ( esk35_1 @ X1624 )
= X1629 )
| ( X1624 @ ( esk34_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ( X1624 @ ( esk35_1 @ X1624 ) )
| ( ( esk33_1 @ X1624 )
!= ( esk34_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ~ ( X1624 @ X1629 )
| ( ( esk35_1 @ X1624 )
= X1629 )
| ( ( esk33_1 @ X1624 )
!= ( esk34_1 @ X1624 ) )
| ~ ( X1624 @ X1625 ) )
& ( ( X1630 @ ( esk37_1 @ X1630 ) )
| ~ ( X1630 @ ( esk36_2 @ X1630 @ X1631 ) )
| ( ( esk36_2 @ X1630 @ X1631 )
!= X1631 ) )
& ( ~ ( X1630 @ X1634 )
| ( ( esk37_1 @ X1630 )
= X1634 )
| ~ ( X1630 @ ( esk36_2 @ X1630 @ X1631 ) )
| ( ( esk36_2 @ X1630 @ X1631 )
!= X1631 ) )
& ( ( X1630 @ ( esk37_1 @ X1630 ) )
| ( X1630 @ ( esk36_2 @ X1630 @ X1631 ) )
| ( ( esk36_2 @ X1630 @ X1631 )
= X1631 ) )
& ( ~ ( X1630 @ X1634 )
| ( ( esk37_1 @ X1630 )
= X1634 )
| ( X1630 @ ( esk36_2 @ X1630 @ X1631 ) )
| ( ( esk36_2 @ X1630 @ X1631 )
= X1631 ) )
& ( ( X1635 != X1636 )
| ( X1637 != X1638 )
| ~ ( in @ X1637 @ X1635 )
| ( in @ X1638 @ X1636 ) )
& ( ~ ( in @ X1641 @ X1639 )
| ( in @ X1642 @ X1640 )
| ( X1641 != X1642 )
| ( X1639 != X1640 ) )
& ( ~ ( in @ X1642 @ X1640 )
| ( in @ X1641 @ X1639 )
| ( X1641 != X1642 )
| ( X1639 != X1640 ) )
& ( ( X1643 @ ( esk38_2 @ X1643 @ X1644 ) )
| ~ ( X1643 @ X1644 )
| ~ ( X1643 @ X1646 )
| ~ ( X1643 @ X1647 )
| ( X1646 = X1647 ) )
& ( ( X1644
!= ( esk38_2 @ X1643 @ X1644 ) )
| ~ ( X1643 @ X1644 )
| ~ ( X1643 @ X1646 )
| ~ ( X1643 @ X1647 )
| ( X1646 = X1647 ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( ( esk39_2 @ X1648 @ X1649 )
= ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ~ ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ~ ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1648 @ ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1649 @ ( esk42_2 @ X1648 @ X1649 ) )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1649 @ X1655 )
| ( ( esk42_2 @ X1648 @ X1649 )
= X1655 )
| ( X1652
!= ( esk41_3 @ X1648 @ X1649 @ X1652 ) )
| ~ ( X1648 @ X1652 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1649 @ ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ( X1648 @ ( esk44_2 @ X1648 @ X1649 ) )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( ~ ( X1648 @ X1659 )
| ( ( esk44_2 @ X1648 @ X1649 )
= X1659 )
| ( X1656
!= ( esk43_3 @ X1648 @ X1649 @ X1656 ) )
| ~ ( X1649 @ X1656 )
| ( X1648 @ ( esk39_2 @ X1648 @ X1649 ) )
| ( X1649 @ ( esk40_2 @ X1648 @ X1649 ) ) )
& ( emptyset = emptyset )
& ( ( X1660 != X1661 )
| ( X1662 != X1663 )
| ( ( setadjoin @ X1660 @ X1662 )
= ( setadjoin @ X1661 @ X1663 ) ) )
& ( ( X1664 != X1665 )
| ( ( powerset @ X1664 )
= ( powerset @ X1665 ) ) )
& ( ( X1666 != X1667 )
| ( ( setunion @ X1666 )
= ( setunion @ X1667 ) ) )
& ( omega = omega )
& ( ( X1668 @ ( esk45_2 @ X1668 @ X1669 ) )
| ~ ( X1668 @ X1669 )
| ~ ( X1668 @ X1671 )
| ~ ( X1668 @ X1672 )
| ( X1671 = X1672 ) )
& ( ( X1669
!= ( esk45_2 @ X1668 @ X1669 ) )
| ~ ( X1668 @ X1669 )
| ~ ( X1668 @ X1671 )
| ~ ( X1668 @ X1672 )
| ( X1671 = X1672 ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( ( esk46_2 @ X1673 @ X1674 )
= ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( ( esk46_2 @ X1673 @ X1674 )
= ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( ( esk46_2 @ X1673 @ X1674 )
= ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( ( esk46_2 @ X1673 @ X1674 )
= ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ~ ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ~ ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ~ ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ~ ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ~ ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ~ ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ~ ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ~ ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1673 @ ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1674 @ ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( X1679
!= ( esk49_3 @ X1673 @ X1674 @ X1679 ) )
| ~ ( X1674 @ X1679 )
| ( ( descr @ X1673 )
= ( descr @ X1674 ) )
| ( X1677
!= ( esk48_3 @ X1673 @ X1674 @ X1677 ) )
| ~ ( X1673 @ X1677 )
| ( X1673 @ ( esk46_2 @ X1673 @ X1674 ) )
| ( X1674 @ ( esk47_2 @ X1673 @ X1674 ) ) )
& ( ( in @ ( esk50_4 @ X1681 @ X1682 @ X1683 @ X1684 ) @ X1681 )
| ( ( dsetconstr @ X1681 @ X1683 )
= ( dsetconstr @ X1682 @ X1684 ) )
| ( X1681 != X1682 ) )
& ( ( in @ ( esk51_4 @ X1681 @ X1682 @ X1683 @ X1684 ) @ X1682 )
| ( ( dsetconstr @ X1681 @ X1683 )
= ( dsetconstr @ X1682 @ X1684 ) )
| ( X1681 != X1682 ) )
& ( ( ( esk50_4 @ X1681 @ X1682 @ X1683 @ X1684 )
= ( esk51_4 @ X1681 @ X1682 @ X1683 @ X1684 ) )
| ( ( dsetconstr @ X1681 @ X1683 )
= ( dsetconstr @ X1682 @ X1684 ) )
| ( X1681 != X1682 ) )
& ( ~ ( X1683 @ ( esk50_4 @ X1681 @ X1682 @ X1683 @ X1684 ) )
| ~ ( X1684 @ ( esk51_4 @ X1681 @ X1682 @ X1683 @ X1684 ) )
| ( ( dsetconstr @ X1681 @ X1683 )
= ( dsetconstr @ X1682 @ X1684 ) )
| ( X1681 != X1682 ) )
& ( ( X1683 @ ( esk50_4 @ X1681 @ X1682 @ X1683 @ X1684 ) )
| ( X1684 @ ( esk51_4 @ X1681 @ X1682 @ X1683 @ X1684 ) )
| ( ( dsetconstr @ X1681 @ X1683 )
= ( dsetconstr @ X1682 @ X1684 ) )
| ( X1681 != X1682 ) )
& ( ( in @ ( esk52_2 @ X1687 @ X1688 ) @ X1687 )
| ( subset @ X1687 @ X1688 ) )
& ( ~ ( in @ ( esk52_2 @ X1687 @ X1688 ) @ X1688 )
| ( subset @ X1687 @ X1688 ) )
& ( ( X1690 != X1691 )
| ( subset @ X1691 @ X1690 ) )
& ( ( X1692 != X1693 )
| ( subset @ X1692 @ X1693 ) )
& ( ( in @ ( esk53_2 @ X1694 @ X1695 ) @ X1694 )
| ( subset @ X1694 @ X1695 ) )
& ( ~ ( in @ ( esk53_2 @ X1694 @ X1695 ) @ X1695 )
| ( subset @ X1694 @ X1695 ) )
& ( subset @ emptyset @ X1697 )
& ( ~ ( subset @ X1698 @ X1699 )
| ~ ( in @ X1700 @ X1698 )
| ( in @ X1700 @ X1699 ) )
& ( ~ ( subset @ X1701 @ X1702 )
| ( in @ X1703 @ X1702 )
| ~ ( in @ X1703 @ X1701 ) )
& ( ~ ( in @ X1706 @ X1704 )
| ( in @ X1706 @ X1705 )
| ~ ( subset @ X1704 @ X1705 ) )
& ( ( subset @ X1707 @ X1708 )
| ( X1707 != X1708 ) )
& ( ~ ( in @ X1711 @ X1709 )
| ( in @ X1711 @ X1710 )
| ( X1709 != X1710 ) )
& ( subset @ X1712 @ X1712 )
& ( ~ ( subset @ X1713 @ X1714 )
| ~ ( subset @ X1714 @ X1715 )
| ( subset @ X1713 @ X1715 ) )
& ( subset @ X1717 @ ( setadjoin @ X1716 @ X1717 ) )
& ( ~ ( subset @ X1718 @ X1720 )
| ( subset @ X1718 @ ( setadjoin @ X1719 @ X1720 ) ) )
& ( ~ ( subset @ X1721 @ X1722 )
| ( in @ X1721 @ ( powerset @ X1722 ) ) )
& ( ~ ( subset @ X1723 @ X1724 )
| ~ ( subset @ X1724 @ X1723 )
| ( X1723 = X1724 ) )
& ( ~ ( subset @ X1725 @ emptyset )
| ( X1725 = emptyset ) )
& ( ~ ( subset @ X1727 @ X1726 )
| ( in @ X1727 @ ( powerset @ X1726 ) ) )
& ( ~ ( in @ X1729 @ ( powerset @ X1728 ) )
| ( subset @ X1729 @ X1728 ) )
& ( in @ X1730 @ ( powerset @ X1730 ) )
& ( ~ ( subset @ X1731 @ X1732 )
| ( subset @ ( powerset @ X1731 ) @ ( powerset @ X1732 ) ) )
& ( in @ ( dsetconstr @ X1733 @ X1734 ) @ ( powerset @ X1733 ) )
& ( subset @ ( dsetconstr @ X1735 @ X1736 ) @ X1735 )
& ( ~ ( in @ X1739 @ X1737 )
| ( in @ X1739 @ ( binunion @ X1737 @ X1738 ) ) )
& ( in @ X1741 @ ( setadjoin @ X1740 @ ( setadjoin @ X1741 @ emptyset ) ) )
& ( ~ ( in @ X1744 @ X1743 )
| ( in @ X1744 @ ( binunion @ X1742 @ X1743 ) ) )
& ( ( in @ X1747 @ X1746 )
| X1748
| ( in @ X1747 @ X1745 )
| ~ ( in @ X1747 @ ( binunion @ X1745 @ X1746 ) ) )
& ( ~ X1748
| X1748
| ( in @ X1747 @ X1745 )
| ~ ( in @ X1747 @ ( binunion @ X1745 @ X1746 ) ) )
& ( ( in @ X1747 @ X1746 )
| X1748
| ~ X1748
| ~ ( in @ X1747 @ ( binunion @ X1745 @ X1746 ) ) )
& ( ~ X1748
| X1748
| ~ X1748
| ~ ( in @ X1747 @ ( binunion @ X1745 @ X1746 ) ) )
& ( ~ ( in @ X1751 @ ( binunion @ X1749 @ X1750 ) )
| ( in @ X1751 @ X1749 )
| ( in @ X1751 @ X1750 ) )
& ( subset @ X1752 @ ( binunion @ X1752 @ X1753 ) )
& ( subset @ X1755 @ ( binunion @ X1754 @ X1755 ) )
& ( ~ ( in @ X1758 @ X1756 )
| ~ ( in @ X1758 @ X1757 )
| ( in @ X1758 @ ( binintersect @ X1756 @ X1757 ) ) )
& ( ~ ( subset @ X1761 @ X1759 )
| ~ ( subset @ X1761 @ X1760 )
| ( subset @ X1761 @ ( binintersect @ X1759 @ X1760 ) ) )
& ( ~ ( in @ X1764 @ ( binintersect @ X1762 @ X1763 ) )
| ( in @ X1764 @ X1762 ) )
& ( subset @ ( binintersect @ X1765 @ X1766 ) @ X1765 )
& ( ~ ( subset @ X1767 @ X1768 )
| ( ( binintersect @ X1767 @ X1768 )
= X1767 ) )
& ( ( ( binintersect @ X1769 @ X1770 )
!= X1770 )
| ( subset @ X1770 @ X1769 ) )
& ( ~ ( in @ X1773 @ ( binintersect @ X1771 @ X1772 ) )
| ( in @ X1773 @ X1772 ) )
& ( ( in @ ( esk54_2 @ X1774 @ X1775 ) @ X1774 )
| ( ( binintersect @ X1774 @ X1775 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1774 @ X1775 ) @ X1775 )
| ( ( binintersect @ X1774 @ X1775 )
= emptyset ) )
& ( subset @ ( binintersect @ X1777 @ X1778 ) @ X1778 )
& ( ~ ( subset @ X1780 @ X1779 )
| ( ( binintersect @ X1779 @ X1780 )
= X1780 ) )
& ( ( ( binintersect @ X1781 @ X1782 )
!= X1781 )
| ( subset @ X1781 @ X1782 ) )
& ( ( binintersect @ X1783 @ ( binunion @ X1784 @ X1785 ) )
= ( binunion @ ( binintersect @ X1783 @ X1784 ) @ ( binintersect @ X1783 @ X1785 ) ) )
& ( ~ ( in @ X1788 @ X1786 )
| ( in @ X1788 @ X1787 )
| ( in @ X1788 @ ( setminus @ X1786 @ X1787 ) ) )
& ( ~ ( in @ X1791 @ ( setminus @ X1789 @ X1790 ) )
| ( in @ X1791 @ X1789 ) )
& ( ~ ( in @ X1794 @ ( setminus @ X1792 @ X1793 ) )
| ~ ( in @ X1794 @ X1793 ) )
& ( ~ ( subset @ X1795 @ X1796 )
| ( ( setminus @ X1795 @ X1796 )
= emptyset ) )
& ( ( in @ X1799 @ ( setminus @ X1797 @ X1798 ) )
| ~ ( in @ X1799 @ X1797 )
| ( in @ X1799 @ X1798 ) )
& ( ( in @ X1802 @ ( setminus @ X1800 @ X1801 ) )
| ( in @ X1802 @ X1801 )
| ~ ( in @ X1802 @ X1800 ) )
& ( ( in @ X1805 @ X1803 )
| ~ ( in @ X1805 @ ( setminus @ X1803 @ X1804 ) ) )
& ( ~ ( in @ X1808 @ X1807 )
| ~ ( in @ X1808 @ ( setminus @ X1806 @ X1807 ) ) )
& ( subset @ ( setminus @ X1809 @ X1810 ) @ X1809 )
& ( ( ( setminus @ X1811 @ X1812 )
!= emptyset )
| ( subset @ X1811 @ X1812 ) )
& ( ~ ( in @ X1815 @ X1813 )
| X1816
| ( in @ X1815 @ X1813 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ( in @ X1815 @ X1814 )
| X1816
| ( in @ X1815 @ X1813 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ X1816
| X1816
| ( in @ X1815 @ X1813 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ ( in @ X1815 @ X1813 )
| X1816
| ~ ( in @ X1815 @ X1814 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ( in @ X1815 @ X1814 )
| X1816
| ~ ( in @ X1815 @ X1814 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ X1816
| X1816
| ~ ( in @ X1815 @ X1814 )
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ ( in @ X1815 @ X1813 )
| X1816
| ~ X1816
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ( in @ X1815 @ X1814 )
| X1816
| ~ X1816
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ X1816
| X1816
| ~ X1816
| ~ ( in @ X1815 @ ( symdiff @ X1813 @ X1814 ) ) )
& ( ~ ( in @ X1819 @ X1817 )
| ( in @ X1819 @ X1818 )
| ( in @ X1819 @ ( symdiff @ X1817 @ X1818 ) ) )
& ( ( in @ X1822 @ X1820 )
| ~ ( in @ X1822 @ X1821 )
| ( in @ X1822 @ ( symdiff @ X1820 @ X1821 ) ) )
& ( ~ ( in @ X1825 @ X1823 )
| ~ ( in @ X1825 @ X1824 )
| ~ ( in @ X1825 @ ( symdiff @ X1823 @ X1824 ) ) )
& ( ( in @ X1828 @ X1826 )
| ( in @ X1828 @ X1827 )
| ~ ( in @ X1828 @ ( symdiff @ X1826 @ X1827 ) ) )
& ( in @ X1830 @ ( setadjoin @ X1829 @ ( setadjoin @ X1830 @ emptyset ) ) )
& ( in @ X1831 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1831 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1831 @ ( setadjoin @ X1832 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1834 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1833 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1833 @ ( setadjoin @ X1834 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1835 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1835 @ ( setadjoin @ X1836 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1837 @ X1838 ) )
& ( ~ ( in @ X1840 @ X1839 )
| ( subset @ ( setadjoin @ X1840 @ emptyset ) @ X1839 ) )
& ( ~ ( in @ X1842 @ X1841 )
| ( in @ ( setadjoin @ X1842 @ emptyset ) @ ( powerset @ X1841 ) ) )
& ( ~ ( in @ X1845 @ X1843 )
| ( in @ ( setadjoin @ X1845 @ emptyset ) @ ( powerset @ ( binunion @ X1843 @ X1844 ) ) ) )
& ( ~ ( in @ X1848 @ ( setadjoin @ X1846 @ ( setadjoin @ X1847 @ emptyset ) ) )
| ( X1848 = X1846 )
| ( X1848 = X1847 ) )
& ( ~ ( in @ X1851 @ X1849 )
| ~ ( in @ X1852 @ X1850 )
| ( subset @ ( setadjoin @ X1851 @ ( setadjoin @ X1852 @ emptyset ) ) @ ( binunion @ X1849 @ X1850 ) ) )
& ( ~ ( in @ X1855 @ X1853 )
| ~ ( in @ X1856 @ X1854 )
| ( in @ ( setadjoin @ X1855 @ ( setadjoin @ X1856 @ emptyset ) ) @ ( powerset @ ( binunion @ X1853 @ X1854 ) ) ) )
& ( ~ ( in @ X1859 @ X1857 )
| ~ ( in @ X1860 @ X1858 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1859 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1859 @ ( setadjoin @ X1860 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1857 @ X1858 ) ) ) )
& ( ~ ( in @ X1863 @ X1861 )
| ~ ( in @ X1864 @ X1862 )
| ( in @ ( setadjoin @ ( setadjoin @ X1863 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1863 @ ( setadjoin @ X1864 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1861 @ X1862 ) ) ) ) )
& ( ~ ( in @ X1867 @ X1865 )
| ~ ( in @ X1868 @ X1866 )
| ( in @ ( kpair @ X1867 @ X1868 ) @ ( powerset @ ( powerset @ ( binunion @ X1865 @ X1866 ) ) ) ) )
& ( ~ ( in @ X1871 @ X1869 )
| ~ ( in @ X1872 @ X1870 )
| ( in @ ( kpair @ X1871 @ X1872 ) @ ( cartprod @ X1869 @ X1870 ) ) )
& ( ( in @ ( esk55_3 @ X1873 @ X1874 @ X1875 ) @ X1873 )
| ~ ( in @ X1875 @ ( cartprod @ X1873 @ X1874 ) ) )
& ( ( in @ ( esk56_3 @ X1873 @ X1874 @ X1875 ) @ X1874 )
| ~ ( in @ X1875 @ ( cartprod @ X1873 @ X1874 ) ) )
& ( ( X1875
= ( kpair @ ( esk55_3 @ X1873 @ X1874 @ X1875 ) @ ( esk56_3 @ X1873 @ X1874 @ X1875 ) ) )
| ~ ( in @ X1875 @ ( cartprod @ X1873 @ X1874 ) ) )
& ( ~ ( in @ X1880 @ ( cartprod @ X1878 @ X1879 ) )
| ( iskpair @ X1880 ) )
& ( ( in @ ( esk57_2 @ X1881 @ X1882 ) @ X1881 )
| ~ ( in @ X1882 @ ( setunion @ X1881 ) ) )
& ( ( in @ X1882 @ ( esk57_2 @ X1881 @ X1882 ) )
| ~ ( in @ X1882 @ ( setunion @ X1881 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1884 @ emptyset ) ) @ X1884 )
& ( subset @ X1885 @ ( setunion @ ( setadjoin @ X1885 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1886 @ emptyset ) )
= X1886 )
& ( ( in @ ( esk60_2 @ X1887 @ X1888 ) @ ( dsetconstr @ X1887 @ X1888 ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( in @ ( esk58_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ( ( dsetconstr @ X1887 @ X1888 )
= ( setadjoin @ ( esk60_2 @ X1887 @ X1888 ) @ emptyset ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( in @ ( esk58_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ( in @ ( esk60_2 @ X1887 @ X1888 ) @ ( dsetconstr @ X1887 @ X1888 ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( in @ ( esk59_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ( ( dsetconstr @ X1887 @ X1888 )
= ( setadjoin @ ( esk60_2 @ X1887 @ X1888 ) @ emptyset ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( in @ ( esk59_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ( in @ ( esk60_2 @ X1887 @ X1888 ) @ ( dsetconstr @ X1887 @ X1888 ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( X1888 @ ( esk58_2 @ X1887 @ X1888 ) ) )
& ( ( ( dsetconstr @ X1887 @ X1888 )
= ( setadjoin @ ( esk60_2 @ X1887 @ X1888 ) @ emptyset ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( X1888 @ ( esk58_2 @ X1887 @ X1888 ) ) )
& ( ( in @ ( esk60_2 @ X1887 @ X1888 ) @ ( dsetconstr @ X1887 @ X1888 ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( X1888 @ ( esk59_2 @ X1887 @ X1888 ) ) )
& ( ( ( dsetconstr @ X1887 @ X1888 )
= ( setadjoin @ ( esk60_2 @ X1887 @ X1888 ) @ emptyset ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( X1888 @ ( esk59_2 @ X1887 @ X1888 ) ) )
& ( ( in @ ( esk60_2 @ X1887 @ X1888 ) @ ( dsetconstr @ X1887 @ X1888 ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( ( esk58_2 @ X1887 @ X1888 )
!= ( esk59_2 @ X1887 @ X1888 ) ) )
& ( ( ( dsetconstr @ X1887 @ X1888 )
= ( setadjoin @ ( esk60_2 @ X1887 @ X1888 ) @ emptyset ) )
| ~ ( in @ X1891 @ X1887 )
| ~ ( X1888 @ X1891 )
| ( ( esk58_2 @ X1887 @ X1888 )
!= ( esk59_2 @ X1887 @ X1888 ) ) )
& ( ( in @ ( esk61_2 @ X1893 @ X1894 ) @ X1893 )
| ~ ( in @ X1895 @ ( dsetconstr @ X1893 @ X1894 ) )
| ( ( dsetconstr @ X1893 @ X1894 )
!= ( setadjoin @ X1895 @ emptyset ) ) )
& ( ( X1894 @ ( esk61_2 @ X1893 @ X1894 ) )
| ~ ( in @ X1895 @ ( dsetconstr @ X1893 @ X1894 ) )
| ( ( dsetconstr @ X1893 @ X1894 )
!= ( setadjoin @ X1895 @ emptyset ) ) )
& ( ( in @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ ( dsetconstr @ X1897 @ X1898 ) )
| ( in @ ( esk62_3 @ X1897 @ X1898 @ X1899 ) @ X1897 )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( ( dsetconstr @ X1897 @ X1898 )
= ( setadjoin @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ emptyset ) )
| ( in @ ( esk62_3 @ X1897 @ X1898 @ X1899 ) @ X1897 )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( in @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ ( dsetconstr @ X1897 @ X1898 ) )
| ( X1898 @ ( esk62_3 @ X1897 @ X1898 @ X1899 ) )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( ( dsetconstr @ X1897 @ X1898 )
= ( setadjoin @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ emptyset ) )
| ( X1898 @ ( esk62_3 @ X1897 @ X1898 @ X1899 ) )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( in @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ ( dsetconstr @ X1897 @ X1898 ) )
| ( ( esk62_3 @ X1897 @ X1898 @ X1899 )
!= X1899 )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( ( dsetconstr @ X1897 @ X1898 )
= ( setadjoin @ ( esk63_3 @ X1897 @ X1898 @ X1899 ) @ emptyset ) )
| ( ( esk62_3 @ X1897 @ X1898 @ X1899 )
!= X1899 )
| ~ ( X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 ) )
& ( ( in @ ( esk66_2 @ X1902 @ X1903 ) @ ( dsetconstr @ X1902 @ X1903 ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( in @ ( esk64_2 @ X1902 @ X1903 ) @ X1902 ) )
& ( ( ( dsetconstr @ X1902 @ X1903 )
= ( setadjoin @ ( esk66_2 @ X1902 @ X1903 ) @ emptyset ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( in @ ( esk64_2 @ X1902 @ X1903 ) @ X1902 ) )
& ( ( in @ ( esk66_2 @ X1902 @ X1903 ) @ ( dsetconstr @ X1902 @ X1903 ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( in @ ( esk65_2 @ X1902 @ X1903 ) @ X1902 ) )
& ( ( ( dsetconstr @ X1902 @ X1903 )
= ( setadjoin @ ( esk66_2 @ X1902 @ X1903 ) @ emptyset ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( in @ ( esk65_2 @ X1902 @ X1903 ) @ X1902 ) )
& ( ( in @ ( esk66_2 @ X1902 @ X1903 ) @ ( dsetconstr @ X1902 @ X1903 ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( X1903 @ ( esk64_2 @ X1902 @ X1903 ) ) )
& ( ( ( dsetconstr @ X1902 @ X1903 )
= ( setadjoin @ ( esk66_2 @ X1902 @ X1903 ) @ emptyset ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( X1903 @ ( esk64_2 @ X1902 @ X1903 ) ) )
& ( ( in @ ( esk66_2 @ X1902 @ X1903 ) @ ( dsetconstr @ X1902 @ X1903 ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( X1903 @ ( esk65_2 @ X1902 @ X1903 ) ) )
& ( ( ( dsetconstr @ X1902 @ X1903 )
= ( setadjoin @ ( esk66_2 @ X1902 @ X1903 ) @ emptyset ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( X1903 @ ( esk65_2 @ X1902 @ X1903 ) ) )
& ( ( in @ ( esk66_2 @ X1902 @ X1903 ) @ ( dsetconstr @ X1902 @ X1903 ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( ( esk64_2 @ X1902 @ X1903 )
!= ( esk65_2 @ X1902 @ X1903 ) ) )
& ( ( ( dsetconstr @ X1902 @ X1903 )
= ( setadjoin @ ( esk66_2 @ X1902 @ X1903 ) @ emptyset ) )
| ~ ( in @ X1906 @ X1902 )
| ~ ( X1903 @ X1906 )
| ( ( esk64_2 @ X1902 @ X1903 )
!= ( esk65_2 @ X1902 @ X1903 ) ) )
& ( ( ( setadjoin @ X1908 @ emptyset )
!= ( setadjoin @ X1909 @ emptyset ) )
| ( X1908 = X1909 ) )
& ( ~ ( in @ ( setadjoin @ X1912 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1910 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1910 @ ( setadjoin @ X1911 @ emptyset ) ) @ emptyset ) ) )
| ( X1910 = X1912 ) )
& ( ( in @ ( esk67_1 @ X1913 )
@ ( dsetconstr @ ( setunion @ X1913 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1913 ) ) )
| ~ ( iskpair @ X1913 ) )
& ( ( ( dsetconstr @ ( setunion @ X1913 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1913 ) )
= ( setadjoin @ ( esk67_1 @ X1913 ) @ emptyset ) )
| ~ ( iskpair @ X1913 ) )
& ( ~ ( in @ X1916 @ X1915 )
| ( X1915
!= ( setadjoin @ X1916 @ emptyset ) )
| ( in @ ( setunion @ X1915 ) @ X1915 ) )
& ( ( kfst @ ( kpair @ X1917 @ X1918 ) )
= X1917 )
& ( ~ ( in @ X1921 @ ( cartprod @ X1919 @ X1920 ) )
| ( in @ ( kfst @ X1921 ) @ X1919 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1922 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1922 @ ( setadjoin @ X1923 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1924 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1924 @ ( setadjoin @ X1925 @ emptyset ) ) @ emptyset ) ) )
| ( X1922 = X1924 ) )
& ( ( ( kpair @ X1926 @ X1927 )
!= ( kpair @ X1928 @ X1929 ) )
| ( X1926 = X1928 ) )
& ( ( X1930 != X1931 )
| ( ( setadjoin @ X1930 @ ( setadjoin @ X1931 @ emptyset ) )
= ( setadjoin @ X1930 @ emptyset ) ) )
& ( ( X1932 != X1933 )
| ( ( setadjoin @ ( setadjoin @ X1932 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1932 @ ( setadjoin @ X1933 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1932 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1934 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1934 @ ( setadjoin @ X1935 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1936 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1936 @ ( setadjoin @ X1937 @ emptyset ) ) @ emptyset ) ) )
| ( X1936 != X1937 )
| ( X1935 = X1937 ) )
& ( ( ( setadjoin @ X1938 @ ( setadjoin @ X1939 @ emptyset ) )
!= ( setadjoin @ X1940 @ emptyset ) )
| ( X1938 = X1939 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1941 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1941 @ ( setadjoin @ X1942 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1943 @ ( setadjoin @ X1944 @ emptyset ) ) @ emptyset ) ) )
| ( X1942 = X1944 ) )
& ( ( ( kpair @ X1945 @ X1946 )
!= ( kpair @ X1947 @ X1948 ) )
| ( X1946 = X1948 ) )
& ( ( in @ ( esk68_1 @ X1949 )
@ ( dsetconstr @ ( setunion @ X1949 )
@ ^ [Z0: $i] :
( X1949
= ( kpair @ ( kfst @ X1949 ) @ Z0 ) ) ) )
| ~ ( iskpair @ X1949 ) )
& ( ( ( dsetconstr @ ( setunion @ X1949 )
@ ^ [Z0: $i] :
( X1949
= ( kpair @ ( kfst @ X1949 ) @ Z0 ) ) )
= ( setadjoin @ ( esk68_1 @ X1949 ) @ emptyset ) )
| ~ ( iskpair @ X1949 ) )
& ( ( ksnd @ ( kpair @ X1951 @ X1952 ) )
= X1952 )
& ( ~ ( iskpair @ X1953 )
| ( ( kpair @ ( kfst @ X1953 ) @ ( ksnd @ X1953 ) )
= X1953 ) )
& ( ~ ( in @ X1956 @ ( cartprod @ X1954 @ X1955 ) )
| ( in @ ( ksnd @ X1956 ) @ X1955 ) )
& ( ~ ( in @ ( kpair @ X1959 @ X1960 ) @ ( cartprod @ X1957 @ X1958 ) )
| ( in @ X1959 @ X1957 ) )
& ( ~ ( in @ ( kpair @ X1963 @ X1964 ) @ ( cartprod @ X1961 @ X1962 ) )
| ( in @ X1964 @ X1962 ) )
& ( ~ ( in @ X1967 @ X1965 )
| ~ ( in @ X1968 @ X1966 )
| ( ( kpair @ X1967 @ X1968 )
= ( kpair @ X1967 @ X1968 ) ) )
& ( ~ ( in @ X1971 @ X1969 )
| ~ ( in @ X1972 @ X1970 )
| ( ( kfst @ ( kpair @ X1971 @ X1972 ) )
= X1971 ) )
& ( ~ ( in @ X1975 @ X1973 )
| ~ ( in @ X1976 @ X1974 )
| ( ( ksnd @ ( kpair @ X1975 @ X1976 ) )
= X1976 ) )
& ( ~ ( in @ X1979 @ ( cartprod @ X1977 @ X1978 ) )
| ( ( kpair @ ( kfst @ X1979 ) @ ( ksnd @ X1979 ) )
= X1979 ) )
& ( ~ ( in @ X1983 @ X1980 )
| ~ ( in @ X1984 @ X1981 )
| ~ ( X1982 @ X1983 @ X1984 )
| ( in @ ( kpair @ X1983 @ X1984 ) @ ( dpsetconstr @ X1980 @ X1981 @ X1982 ) ) )
& ( subset @ ( dpsetconstr @ X1985 @ X1986 @ X1987 ) @ ( cartprod @ X1985 @ X1986 ) )
& ( subset @ ( dpsetconstr @ X1988 @ X1989 @ X1990 ) @ ( cartprod @ X1988 @ X1989 ) )
& ( ~ ( in @ X1994 @ X1991 )
| ~ ( in @ X1995 @ X1992 )
| ~ ( in @ ( kpair @ X1994 @ X1995 ) @ ( dpsetconstr @ X1991 @ X1992 @ X1993 ) )
| ( X1993 @ X1994 @ X1995 ) )
& ( ~ ( in @ ( kpair @ X1999 @ X2000 ) @ ( dpsetconstr @ X1996 @ X1997 @ X1998 ) )
| ( in @ X1999 @ X1996 ) )
& ( ~ ( in @ ( kpair @ X2004 @ X2005 ) @ ( dpsetconstr @ X2001 @ X2002 @ X2003 ) )
| ( in @ X2005 @ X2002 ) )
& ( ~ ( in @ ( kpair @ X2009 @ X2010 ) @ ( dpsetconstr @ X2006 @ X2007 @ X2008 ) )
| ( X2008 @ X2009 @ X2010 ) )
& ( ( in @ ( esk69_4 @ X2011 @ X2012 @ X2013 @ X2014 )
@ ( dsetconstr @ X2012
@ ^ [Z0: $i] : ( in @ ( kpair @ X2014 @ Z0 ) @ X2013 ) ) )
| ~ ( in @ X2014 @ X2011 )
| ~ ( func @ X2011 @ X2012 @ X2013 ) )
& ( ( ( dsetconstr @ X2012
@ ^ [Z0: $i] : ( in @ ( kpair @ X2014 @ Z0 ) @ X2013 ) )
= ( setadjoin @ ( esk69_4 @ X2011 @ X2012 @ X2013 @ X2014 ) @ emptyset ) )
| ~ ( in @ X2014 @ X2011 )
| ~ ( func @ X2011 @ X2012 @ X2013 ) )
& ( ~ ( func @ X2016 @ X2017 @ X2018 )
| ~ ( in @ X2019 @ X2016 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2017
@ ^ [Z0: $i] : ( in @ ( kpair @ X2019 @ Z0 ) @ X2018 ) ) )
@ X2017 ) )
& ( ~ ( func @ X2020 @ X2021 @ X2022 )
| ~ ( in @ X2023 @ X2020 )
| ( in @ ( ap @ X2020 @ X2021 @ X2022 @ X2023 ) @ X2021 ) )
& ( ~ ( in @ X2026 @ ( funcSet @ X2024 @ X2025 ) )
| ( func @ X2024 @ X2025 @ X2026 ) )
& ( ~ ( in @ X2029 @ ( funcSet @ X2027 @ X2028 ) )
| ~ ( in @ X2030 @ X2027 )
| ( in @ ( ap @ X2027 @ X2028 @ X2029 @ X2030 ) @ X2028 ) )
& ( ~ ( func @ X2031 @ X2032 @ X2033 )
| ( in @ X2033 @ ( funcSet @ X2031 @ X2032 ) ) )
& ( ( in @ ( esk70_3 @ X2034 @ X2035 @ X2036 ) @ X2034 )
| ( func @ X2034 @ X2035
@ ( dpsetconstr @ X2034 @ X2035
@ ^ [Z0: $i] : ( $eq @ ( X2036 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2036 @ ( esk70_3 @ X2034 @ X2035 @ X2036 ) ) @ X2035 )
| ( func @ X2034 @ X2035
@ ( dpsetconstr @ X2034 @ X2035
@ ^ [Z0: $i] : ( $eq @ ( X2036 @ Z0 ) ) ) ) )
& ( ( in @ ( esk71_3 @ X2038 @ X2039 @ X2040 ) @ X2038 )
| ( func @ X2038 @ X2039 @ ( lam @ X2038 @ X2039 @ X2040 ) ) )
& ( ~ ( in @ ( X2040 @ ( esk71_3 @ X2038 @ X2039 @ X2040 ) ) @ X2039 )
| ( func @ X2038 @ X2039 @ ( lam @ X2038 @ X2039 @ X2040 ) ) )
& ( ( in @ ( esk72_3 @ X2042 @ X2043 @ X2044 ) @ X2042 )
| ( in @ ( lam @ X2042 @ X2043 @ X2044 ) @ ( funcSet @ X2042 @ X2043 ) ) )
& ( ~ ( in @ ( X2044 @ ( esk72_3 @ X2042 @ X2043 @ X2044 ) ) @ X2043 )
| ( in @ ( lam @ X2042 @ X2043 @ X2044 ) @ ( funcSet @ X2042 @ X2043 ) ) )
& ( ( in @ ( esk73_4 @ X2046 @ X2047 @ X2048 @ X2049 ) @ X2046 )
| ~ ( in @ X2052 @ X2048 )
| ( X2049 @ X2052 )
| ~ ( subset @ X2048 @ ( cartprod @ X2046 @ X2047 ) ) )
& ( ( in @ ( esk74_4 @ X2046 @ X2047 @ X2048 @ X2049 ) @ X2047 )
| ~ ( in @ X2052 @ X2048 )
| ( X2049 @ X2052 )
| ~ ( subset @ X2048 @ ( cartprod @ X2046 @ X2047 ) ) )
& ( ( in @ ( kpair @ ( esk73_4 @ X2046 @ X2047 @ X2048 @ X2049 ) @ ( esk74_4 @ X2046 @ X2047 @ X2048 @ X2049 ) ) @ X2048 )
| ~ ( in @ X2052 @ X2048 )
| ( X2049 @ X2052 )
| ~ ( subset @ X2048 @ ( cartprod @ X2046 @ X2047 ) ) )
& ( ~ ( X2049 @ ( kpair @ ( esk73_4 @ X2046 @ X2047 @ X2048 @ X2049 ) @ ( esk74_4 @ X2046 @ X2047 @ X2048 @ X2049 ) ) )
| ~ ( in @ X2052 @ X2048 )
| ( X2049 @ X2052 )
| ~ ( subset @ X2048 @ ( cartprod @ X2046 @ X2047 ) ) )
& ( ( in @ ( esk75_4 @ X2053 @ X2054 @ X2055 @ X2056 ) @ X2053 )
| ~ ( in @ X2059 @ X2055 )
| ( X2056 @ X2059 )
| ~ ( subset @ X2055 @ ( cartprod @ X2053 @ X2054 ) ) )
& ( ( in @ ( esk76_4 @ X2053 @ X2054 @ X2055 @ X2056 ) @ X2054 )
| ~ ( in @ X2059 @ X2055 )
| ( X2056 @ X2059 )
| ~ ( subset @ X2055 @ ( cartprod @ X2053 @ X2054 ) ) )
& ( ( in @ ( kpair @ ( esk75_4 @ X2053 @ X2054 @ X2055 @ X2056 ) @ ( esk76_4 @ X2053 @ X2054 @ X2055 @ X2056 ) ) @ X2055 )
| ~ ( in @ X2059 @ X2055 )
| ( X2056 @ X2059 )
| ~ ( subset @ X2055 @ ( cartprod @ X2053 @ X2054 ) ) )
& ( ~ ( X2056 @ ( kpair @ ( esk75_4 @ X2053 @ X2054 @ X2055 @ X2056 ) @ ( esk76_4 @ X2053 @ X2054 @ X2055 @ X2056 ) ) )
| ~ ( in @ X2059 @ X2055 )
| ( X2056 @ X2059 )
| ~ ( subset @ X2055 @ ( cartprod @ X2053 @ X2054 ) ) )
& ( ~ ( in @ X2062 @ ( dsetconstr @ X2060 @ X2061 ) )
| ( ( dsetconstr @ X2060 @ X2061 )
!= ( setadjoin @ X2062 @ emptyset ) )
| ~ ( in @ X2063 @ X2060 )
| ~ ( in @ X2064 @ X2060 )
| ~ ( X2061 @ X2063 )
| ~ ( X2061 @ X2064 )
| ( X2063 = X2064 ) )
& ( ~ ( func @ X2065 @ X2066 @ X2067 )
| ~ ( in @ X2068 @ X2065 )
| ( in @ ( kpair @ X2068 @ ( ap @ X2065 @ X2066 @ X2067 @ X2068 ) ) @ X2067 ) )
& ( ~ ( in @ X2071 @ ( funcSet @ X2069 @ X2070 ) )
| ~ ( in @ X2072 @ X2069 )
| ( in @ ( kpair @ X2072 @ ( ap @ X2069 @ X2070 @ X2071 @ X2072 ) ) @ X2071 ) )
& ( ~ ( func @ X2073 @ X2074 @ X2075 )
| ~ ( in @ X2076 @ X2073 )
| ~ ( in @ X2077 @ X2074 )
| ~ ( in @ ( kpair @ X2076 @ X2077 ) @ X2075 )
| ( ( ap @ X2073 @ X2074 @ X2075 @ X2076 )
= X2077 ) )
& ( ( in @ ( esk77_4 @ X2078 @ X2079 @ X2080 @ X2081 ) @ X2078 )
| ~ ( in @ X2083 @ X2078 )
| ~ ( in @ X2084 @ X2079 )
| ~ ( in @ ( kpair @ X2083 @ X2084 ) @ X2081 )
| ( in @ ( kpair @ X2083 @ X2084 ) @ X2080 )
| ~ ( func @ X2078 @ X2079 @ X2081 )
| ~ ( func @ X2078 @ X2079 @ X2080 ) )
& ( ( ( ap @ X2078 @ X2079 @ X2080 @ ( esk77_4 @ X2078 @ X2079 @ X2080 @ X2081 ) )
!= ( ap @ X2078 @ X2079 @ X2081 @ ( esk77_4 @ X2078 @ X2079 @ X2080 @ X2081 ) ) )
| ~ ( in @ X2083 @ X2078 )
| ~ ( in @ X2084 @ X2079 )
| ~ ( in @ ( kpair @ X2083 @ X2084 ) @ X2081 )
| ( in @ ( kpair @ X2083 @ X2084 ) @ X2080 )
| ~ ( func @ X2078 @ X2079 @ X2081 )
| ~ ( func @ X2078 @ X2079 @ X2080 ) )
& ( ~ ( in @ X2087 @ ( funcSet @ X2085 @ X2086 ) )
| ~ ( in @ X2088 @ X2085 )
| ~ ( in @ X2089 @ X2086 )
| ~ ( in @ ( kpair @ X2088 @ X2089 ) @ X2087 )
| ( ( ap @ X2085 @ X2086 @ X2087 @ X2088 )
= X2089 ) )
& ( ( in @ ( esk78_4 @ X2090 @ X2091 @ X2092 @ X2093 ) @ X2090 )
| ( subset @ X2092 @ X2093 )
| ~ ( subset @ X2093 @ ( cartprod @ X2090 @ X2091 ) )
| ~ ( subset @ X2092 @ ( cartprod @ X2090 @ X2091 ) ) )
& ( ( in @ ( esk79_4 @ X2090 @ X2091 @ X2092 @ X2093 ) @ X2091 )
| ( subset @ X2092 @ X2093 )
| ~ ( subset @ X2093 @ ( cartprod @ X2090 @ X2091 ) )
| ~ ( subset @ X2092 @ ( cartprod @ X2090 @ X2091 ) ) )
& ( ( in @ ( kpair @ ( esk78_4 @ X2090 @ X2091 @ X2092 @ X2093 ) @ ( esk79_4 @ X2090 @ X2091 @ X2092 @ X2093 ) ) @ X2092 )
| ( subset @ X2092 @ X2093 )
| ~ ( subset @ X2093 @ ( cartprod @ X2090 @ X2091 ) )
| ~ ( subset @ X2092 @ ( cartprod @ X2090 @ X2091 ) ) )
& ( ~ ( in @ ( kpair @ ( esk78_4 @ X2090 @ X2091 @ X2092 @ X2093 ) @ ( esk79_4 @ X2090 @ X2091 @ X2092 @ X2093 ) ) @ X2093 )
| ( subset @ X2092 @ X2093 )
| ~ ( subset @ X2093 @ ( cartprod @ X2090 @ X2091 ) )
| ~ ( subset @ X2092 @ ( cartprod @ X2090 @ X2091 ) ) )
& ( ( in @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ( X2098 = X2099 )
| ( in @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ( X2098 = X2099 )
| ( in @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ( X2098 = X2099 )
| ( in @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ( X2098 = X2099 )
| ( in @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ( X2098 = X2099 )
| ( in @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ( X2098 = X2099 )
| ( in @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ( X2098 = X2099 )
| ( in @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ( X2098 = X2099 )
| ( in @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ( X2098 = X2099 )
| ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ( X2098 = X2099 )
| ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ( X2098 = X2099 )
| ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ( X2098 = X2099 )
| ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2096 )
| ( X2098 = X2099 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ( X2098 = X2099 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ( X2098 = X2099 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ~ ( in @ ( kpair @ ( esk82_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk83_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ( X2098 = X2099 )
| ~ ( in @ ( kpair @ ( esk80_4 @ X2096 @ X2097 @ X2098 @ X2099 ) @ ( esk81_4 @ X2096 @ X2097 @ X2098 @ X2099 ) ) @ X2099 )
| ~ ( subset @ X2099 @ ( cartprod @ X2096 @ X2097 ) )
| ~ ( subset @ X2098 @ ( cartprod @ X2096 @ X2097 ) ) )
& ( ( in @ ( esk84_4 @ X2104 @ X2105 @ X2106 @ X2107 ) @ X2104 )
| ( X2106 = X2107 )
| ~ ( func @ X2104 @ X2105 @ X2107 )
| ~ ( func @ X2104 @ X2105 @ X2106 ) )
& ( ( ( ap @ X2104 @ X2105 @ X2106 @ ( esk84_4 @ X2104 @ X2105 @ X2106 @ X2107 ) )
!= ( ap @ X2104 @ X2105 @ X2107 @ ( esk84_4 @ X2104 @ X2105 @ X2106 @ X2107 ) ) )
| ( X2106 = X2107 )
| ~ ( func @ X2104 @ X2105 @ X2107 )
| ~ ( func @ X2104 @ X2105 @ X2106 ) )
& ( ( in @ ( esk85_4 @ X2109 @ X2110 @ X2111 @ X2112 ) @ X2109 )
| ( X2111 = X2112 )
| ~ ( in @ X2112 @ ( funcSet @ X2109 @ X2110 ) )
| ~ ( in @ X2111 @ ( funcSet @ X2109 @ X2110 ) ) )
& ( ( ( ap @ X2109 @ X2110 @ X2111 @ ( esk85_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
!= ( ap @ X2109 @ X2110 @ X2112 @ ( esk85_4 @ X2109 @ X2110 @ X2111 @ X2112 ) ) )
| ( X2111 = X2112 )
| ~ ( in @ X2112 @ ( funcSet @ X2109 @ X2110 ) )
| ~ ( in @ X2111 @ ( funcSet @ X2109 @ X2110 ) ) )
& ( ~ ( in @ X2116 @ ( funcSet @ X2114 @ X2115 ) )
| ~ ( in @ X2117 @ X2114 )
| ( ( ap @ X2114 @ X2115 @ X2116 @ X2117 )
= ( ap @ X2114 @ X2115 @ X2116 @ X2117 ) ) )
& ( ~ ( func @ X2118 @ X2119 @ X2120 )
| ~ ( in @ X2121 @ X2118 )
| ( ( ap @ X2118 @ X2119 @ X2120 @ X2121 )
= ( ap @ X2118 @ X2119 @ X2120 @ X2121 ) ) )
& ( ( in @ ( esk86_3 @ X2122 @ X2123 @ X2124 ) @ X2122 )
| ~ ( in @ X2126 @ X2122 )
| ( ( ap @ X2122 @ X2123 @ ( lam @ X2122 @ X2123 @ X2124 ) @ X2126 )
= ( X2124 @ X2126 ) ) )
& ( ~ ( in @ ( X2124 @ ( esk86_3 @ X2122 @ X2123 @ X2124 ) ) @ X2123 )
| ~ ( in @ X2126 @ X2122 )
| ( ( ap @ X2122 @ X2123 @ ( lam @ X2122 @ X2123 @ X2124 ) @ X2126 )
= ( X2124 @ X2126 ) ) )
& ( ~ ( func @ X2127 @ X2128 @ X2129 )
| ( ( lam @ X2127 @ X2128 @ ( ap @ X2127 @ X2128 @ X2129 ) )
= X2129 ) )
& ( ( in @ ( esk87_3 @ X2130 @ X2131 @ X2132 ) @ X2130 )
| ( ( lam @ X2130 @ X2131 @ X2132 )
= ( lam @ X2130 @ X2131 @ X2132 ) ) )
& ( ~ ( in @ ( X2132 @ ( esk87_3 @ X2130 @ X2131 @ X2132 ) ) @ X2131 )
| ( ( lam @ X2130 @ X2131 @ X2132 )
= ( lam @ X2130 @ X2131 @ X2132 ) ) )
& ( ( in @ ( esk88_3 @ X2134 @ X2135 @ X2136 ) @ X2134 )
| ~ ( in @ X2138 @ X2134 )
| ( ( ap @ X2134 @ X2135 @ ( lam @ X2134 @ X2135 @ X2136 ) @ X2138 )
= ( X2136 @ X2138 ) ) )
& ( ~ ( in @ ( X2136 @ ( esk88_3 @ X2134 @ X2135 @ X2136 ) ) @ X2135 )
| ~ ( in @ X2138 @ X2134 )
| ( ( ap @ X2134 @ X2135 @ ( lam @ X2134 @ X2135 @ X2136 ) @ X2138 )
= ( X2136 @ X2138 ) ) )
& ( ~ ( in @ X2141 @ ( funcSet @ X2139 @ X2140 ) )
| ( ( lam @ X2139 @ X2140 @ ( ap @ X2139 @ X2140 @ X2141 ) )
= X2141 ) )
& ( ~ ( in @ X2144 @ X2142 )
| ~ ( in @ X2145 @ X2142 )
| X2143
| ( in @ X2145
@ ( dsetconstr @ X2142
@ ^ [Z0: $i] :
( ( X2143
& ( Z0 = X2144 ) )
| ( ~ X2143
& ( Z0 = X2145 ) ) ) ) ) )
& ( ~ ( in @ X2148 @ X2146 )
| ~ ( in @ X2149 @ X2146 )
| X2147
| ( ( dsetconstr @ X2146
@ ^ [Z0: $i] :
( ( X2147
& ( Z0 = X2148 ) )
| ( ~ X2147
& ( Z0 = X2149 ) ) ) )
= ( setadjoin @ X2149 @ emptyset ) ) )
& ( in @ esk90_0 @ esk89_0 )
& ( in @ esk91_0 @ esk89_0 )
& epred2_0
& ~ ( in @ esk90_0
@ ( dsetconstr @ esk89_0
@ ^ [Z0: $i] :
( ( epred2_0
& ( Z0 = esk90_0 ) )
| ( ~ epred2_0
& ( Z0 = esk91_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_309])])])])])])]) ).
thf(c_0_311,plain,
! [X2173: $i] :
( ( epred3_0 @ X2173 )
<=> ( ( epred2_0
& ( X2173 = esk90_0 ) )
| ( ~ epred2_0
& ( X2173 = esk91_0 ) ) ) ),
introduced(definition) ).
thf(c_0_312,plain,
! [X2186: $i] :
( ( ~ epred2_0
| epred2_0
| ~ ( epred3_0 @ X2186 ) )
& ( ( X2186 = esk91_0 )
| epred2_0
| ~ ( epred3_0 @ X2186 ) )
& ( ~ epred2_0
| ( X2186 = esk90_0 )
| ~ ( epred3_0 @ X2186 ) )
& ( ( X2186 = esk91_0 )
| ( X2186 = esk90_0 )
| ~ ( epred3_0 @ X2186 ) )
& ( ~ epred2_0
| ( X2186 != esk90_0 )
| ( epred3_0 @ X2186 ) )
& ( epred2_0
| ( X2186 != esk91_0 )
| ( epred3_0 @ X2186 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])]) ).
thf(c_0_313,negated_conjecture,
( ( in @ esk90_0 @ ( dsetconstr @ esk89_0 @ epred3_0 ) )
!= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_310]),c_0_311]) ).
thf(c_0_314,plain,
! [X2: $i] :
( ( epred3_0 @ X2 )
| ~ epred2_0
| ( X2 != esk90_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
thf(c_0_315,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_310]) ).
thf(c_0_316,negated_conjecture,
~ ( in @ esk90_0 @ ( dsetconstr @ esk89_0 @ epred3_0 ) ),
inference(cn,[status(thm)],[c_0_313]) ).
thf(c_0_317,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
| ~ ( X1 @ X2 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
thf(c_0_318,negated_conjecture,
in @ esk90_0 @ esk89_0,
inference(split_conjunct,[status(thm)],[c_0_310]) ).
thf(c_0_319,plain,
epred3_0 @ esk90_0,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_314,c_0_315])])]) ).
thf(c_0_320,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_318]),c_0_319])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SEU702^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun May 19 16:13:07 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.15/0.40 Running higher-order theorem proving
% 0.15/0.40 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
% 1.02/0.59 # Version: 3.1.0-ho
% 1.02/0.59 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.02/0.59 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.59 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.02/0.59 # Starting pre_casc_3 with 300s (1) cores
% 1.02/0.59 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.02/0.59 # Starting full_lambda_10 with 300s (1) cores
% 1.02/0.59 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.02/0.59 # ho_unfolding_5 with pid 26820 completed with status 0
% 1.02/0.59 # Result found by ho_unfolding_5
% 1.02/0.59 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.02/0.59 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.59 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.02/0.59 # No SInE strategy applied
% 1.02/0.59 # Search class: HGHSM-FSLM32-MHSMMSBN
% 1.02/0.59 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.02/0.59 # Starting full_lambda_5 with 99s (1) cores
% 1.02/0.59 # Starting ho_unfolding_5 with 121s (1) cores
% 1.02/0.59 # Starting pre_casc_4 with 99s (1) cores
% 1.02/0.59 # Starting pre_casc_3 with 99s (1) cores
% 1.02/0.59 # pre_casc_4 with pid 26831 completed with status 0
% 1.02/0.59 # Result found by pre_casc_4
% 1.02/0.59 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.02/0.59 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.59 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.02/0.59 # No SInE strategy applied
% 1.02/0.59 # Search class: HGHSM-FSLM32-MHSMMSBN
% 1.02/0.59 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.02/0.59 # Starting full_lambda_5 with 99s (1) cores
% 1.02/0.59 # Starting ho_unfolding_5 with 121s (1) cores
% 1.02/0.59 # Starting pre_casc_4 with 99s (1) cores
% 1.02/0.59 # Preprocessing time : 0.006 s
% 1.02/0.59 # Presaturation interreduction done
% 1.02/0.59
% 1.02/0.59 # Proof found!
% 1.02/0.59 # SZS status Theorem
% 1.02/0.59 # SZS output start CNFRefutation
% See solution above
% 1.02/0.59 # Parsed axioms : 479
% 1.02/0.59 # Removed by relevancy pruning/SinE : 0
% 1.02/0.59 # Initial clauses : 683
% 1.02/0.59 # Removed in clause preprocessing : 291
% 1.02/0.59 # Initial clauses in saturation : 392
% 1.02/0.59 # Processed clauses : 647
% 1.02/0.59 # ...of these trivial : 14
% 1.02/0.59 # ...subsumed : 66
% 1.02/0.59 # ...remaining for further processing : 567
% 1.02/0.59 # Other redundant clauses eliminated : 27
% 1.02/0.59 # Clauses deleted for lack of memory : 0
% 1.02/0.59 # Backward-subsumed : 0
% 1.02/0.59 # Backward-rewritten : 5
% 1.02/0.59 # Generated clauses : 1377
% 1.02/0.59 # ...of the previous two non-redundant : 1243
% 1.02/0.59 # ...aggressively subsumed : 0
% 1.02/0.59 # Contextual simplify-reflections : 1
% 1.02/0.59 # Paramodulations : 1324
% 1.02/0.59 # Factorizations : 0
% 1.02/0.59 # NegExts : 10
% 1.02/0.59 # Equation resolutions : 30
% 1.02/0.59 # Disequality decompositions : 0
% 1.02/0.59 # Total rewrite steps : 161
% 1.02/0.59 # ...of those cached : 103
% 1.02/0.59 # Propositional unsat checks : 0
% 1.02/0.59 # Propositional check models : 0
% 1.02/0.59 # Propositional check unsatisfiable : 0
% 1.02/0.59 # Propositional clauses : 0
% 1.02/0.59 # Propositional clauses after purity: 0
% 1.02/0.59 # Propositional unsat core size : 0
% 1.02/0.59 # Propositional preprocessing time : 0.000
% 1.02/0.59 # Propositional encoding time : 0.000
% 1.02/0.59 # Propositional solver time : 0.000
% 1.02/0.59 # Success case prop preproc time : 0.000
% 1.02/0.59 # Success case prop encoding time : 0.000
% 1.02/0.59 # Success case prop solver time : 0.000
% 1.02/0.59 # Current number of processed clauses : 200
% 1.02/0.59 # Positive orientable unit clauses : 52
% 1.02/0.59 # Positive unorientable unit clauses: 0
% 1.02/0.59 # Negative unit clauses : 4
% 1.02/0.59 # Non-unit-clauses : 144
% 1.02/0.59 # Current number of unprocessed clauses: 1325
% 1.02/0.59 # ...number of literals in the above : 3603
% 1.02/0.59 # Current number of archived formulas : 0
% 1.02/0.59 # Current number of archived clauses : 351
% 1.02/0.59 # Clause-clause subsumption calls (NU) : 20010
% 1.02/0.59 # Rec. Clause-clause subsumption calls : 7666
% 1.02/0.59 # Non-unit clause-clause subsumptions : 42
% 1.02/0.59 # Unit Clause-clause subsumption calls : 216
% 1.02/0.59 # Rewrite failures with RHS unbound : 0
% 1.02/0.59 # BW rewrite match attempts : 27
% 1.02/0.59 # BW rewrite match successes : 3
% 1.02/0.59 # Condensation attempts : 0
% 1.02/0.59 # Condensation successes : 0
% 1.02/0.59 # Termbank termtop insertions : 85477
% 1.02/0.59 # Search garbage collected termcells : 23169
% 1.02/0.59
% 1.02/0.59 # -------------------------------------------------
% 1.02/0.59 # User time : 0.145 s
% 1.02/0.59 # System time : 0.018 s
% 1.02/0.59 # Total time : 0.163 s
% 1.02/0.59 # Maximum resident set size: 7284 pages
% 1.02/0.59
% 1.02/0.59 # -------------------------------------------------
% 1.02/0.59 # User time : 0.399 s
% 1.02/0.59 # System time : 0.034 s
% 1.02/0.59 # Total time : 0.433 s
% 1.02/0.59 # Maximum resident set size: 2348 pages
% 1.02/0.59 % E---3.1 exiting
% 1.02/0.59 % E exiting
%------------------------------------------------------------------------------