%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU747^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.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 03:29:49 EDT 2024
% Result : Theorem 1.22s 0.71s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 632
% Syntax : Number of formulae : 690 ( 4 unt; 368 typ; 0 def)
% Number of atoms : 3318 ( 457 equ; 0 cnn)
% Maximal formula atoms : 1052 ( 10 avg)
% Number of connectives : 12773 ( 831 ~; 832 |; 507 &;8593 @)
% ( 350 <=>;1660 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1145 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 372 ( 368 usr; 273 con; 0-4 aty)
% Number of variables : 2747 ( 156 ^2511 !; 80 ?;2747 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
epred1_0: $o ).
thf(decl_324,type,
esk1_2: $i > $i > $i ).
thf(decl_325,type,
esk2_2: $i > $i > $i ).
thf(decl_326,type,
esk3_2: $i > $i > $i ).
thf(decl_327,type,
esk4_1: $i > $i ).
thf(decl_328,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_329,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_330,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_331,type,
esk8_1: $i > $i ).
thf(decl_332,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_333,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_334,type,
esk11_2: $i > $i > $i ).
thf(decl_335,type,
esk12_2: $i > $i > $i ).
thf(decl_336,type,
esk13_1: $i > $i ).
thf(decl_337,type,
esk14_1: $i > $i ).
thf(decl_338,type,
esk15_1: $i > $i ).
thf(decl_339,type,
esk16_2: $i > $i > $i ).
thf(decl_340,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_341,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_342,type,
esk19_1: $i > $i ).
thf(decl_343,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_346,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_347,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_349,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_350,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_351,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_352,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_353,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_354,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_355,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_356,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_357,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_358,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_359,type,
esk36_2: $i > $i > $i ).
thf(decl_360,type,
esk37_2: $i > $i > $i ).
thf(decl_361,type,
esk38_2: $i > $i > $i ).
thf(decl_362,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_363,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_364,type,
esk41_2: $i > $i > $i ).
thf(decl_365,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_366,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_367,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_368,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_369,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_370,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_371,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_372,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_373,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_374,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_375,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_376,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_377,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_378,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_379,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_380,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_381,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_382,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_383,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_384,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_385,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_386,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_387,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_388,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_389,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_390,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_391,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_392,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_393,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_394,type,
esk71_0: $i ).
thf(decl_395,type,
esk72_0: $i ).
thf(decl_396,type,
esk73_0: $i ).
thf(decl_397,type,
esk74_0: $i ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',iffalseProp2) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(binunionTEcontra,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).
thf(binunionTE,axiom,
( binunionTE
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X50: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ( ( ( in @ X2 @ X21 )
=> X50 )
=> ( ( ( in @ X2 @ X48 )
=> X50 )
=> X50 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifp) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(intersectInPowersetIntersectUnions,axiom,
( intersectInPowersetIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(inComplementUnionImpNotIn1,axiom,
( inComplementUnionImpNotIn1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inComplementUnionImpInComplement1,axiom,
( inComplementUnionImpInComplement1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_263,plain,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X41
& ( Z0 = X2 ) )
| ( ~ X41
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_264,plain,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X42
& ( Z0 = X2 ) )
| ( ~ X42
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp2]) ).
thf(c_0_265,plain,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifSingleton]) ).
thf(c_0_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_305,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_306,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_307,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_308,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_309,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_310,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_311,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_312,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_313,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_314,plain,
( epred1_0
<=> ! [X908: $i] :
? [X909: $i] :
( ! [X910: $i] :
( ( in @ X910 @ X909 )
=> ! [X911: $i] :
( ( in @ X911 @ X910 )
=> ( in @ X911 @ X908 ) ) )
& ! [X912: $i,X913: $i] :
( ( ( in @ X912 @ X908 )
& ( in @ X913 @ X908 ) )
=> ( ! [X914: $i] :
( ( in @ X914 @ X909 )
=> ( ( in @ X912 @ X914 )
<=> ( in @ X913 @ X914 ) ) )
=> ( X912 = X913 ) ) )
& ! [X915: $i,X916: $i] :
( ( ( in @ X915 @ X909 )
& ( in @ X916 @ X909 ) )
=> ( ! [X917: $i] :
( ( in @ X917 @ X915 )
=> ( in @ X917 @ X916 ) )
| ! [X918: $i] :
( ( in @ X918 @ X916 )
=> ( in @ X918 @ X915 ) ) ) )
& ! [X919: $i] :
( ( ! [X920: $i] :
( ( in @ X920 @ X919 )
=> ( in @ X920 @ X908 ) )
& ? [X921: $i] : ( in @ X921 @ X919 ) )
=> ? [X922: $i,X923: $i] :
( ( in @ X922 @ X909 )
& ( in @ X923 @ X919 )
& ~ ? [X924: $i] :
( ( in @ X924 @ X922 )
& ( in @ X924 @ X919 ) )
& ! [X925: $i] :
( ( in @ X925 @ X909 )
=> ( ! [X926: $i] :
( ( in @ X926 @ X925 )
=> ( in @ X926 @ X922 ) )
| ( in @ X923 @ X925 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_315,negated_conjecture,
~ ( ! [X881: $i,X882: $i] :
( ! [X883: $i] :
( ( in @ X883 @ X881 )
<=> ( in @ X883 @ X882 ) )
=> ( X881 = X882 ) )
=> ( ! [X884: $i] :
~ ( in @ X884 @ emptyset )
=> ( ! [X885: $i,X886: $i,X887: $i] :
( ( in @ X887 @ ( setadjoin @ X885 @ X886 ) )
<=> ( ( X887 = X885 )
| ( in @ X887 @ X886 ) ) )
=> ( ! [X888: $i,X889: $i] :
( ( in @ X889 @ ( powerset @ X888 ) )
<=> ! [X890: $i] :
( ( in @ X890 @ X889 )
=> ( in @ X890 @ X888 ) ) )
=> ( ! [X891: $i,X892: $i] :
( ( in @ X892 @ ( setunion @ X891 ) )
<=> ? [X893: $i] :
( ( in @ X892 @ X893 )
& ( in @ X893 @ X891 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X894: $i] :
( ( in @ X894 @ omega )
=> ( in @ ( setadjoin @ X894 @ X894 ) @ omega ) )
=> ( ! [X895: $i] :
( ( ( in @ emptyset @ X895 )
& ! [X896: $i] :
( ( ( in @ X896 @ omega )
& ( in @ X896 @ X895 ) )
=> ( in @ ( setadjoin @ X896 @ X896 ) @ X895 ) ) )
=> ! [X897: $i] :
( ( in @ X897 @ omega )
=> ( in @ X897 @ X895 ) ) )
=> ( ! [X898: $i > $i > $o,X899: $i] :
( ! [X900: $i] :
( ( in @ X900 @ X899 )
=> ( exu @ ( X898 @ X900 ) ) )
=> ? [X901: $i] :
! [X902: $i] :
( ( in @ X902 @ X901 )
<=> ? [X903: $i] :
( ( in @ X903 @ X899 )
& ( X898 @ X903 @ X902 ) ) ) )
=> ( ! [X904: $i] :
( ? [X905: $i] : ( in @ X905 @ X904 )
=> ? [X906: $i] :
( ( in @ X906 @ X904 )
& ~ ? [X907: $i] :
( ( in @ X907 @ X906 )
& ( in @ X907 @ X904 ) ) ) )
=> ( epred1_0
=> ( ! [X927: $i > $o] :
( ( exu @ X927 )
=> ( X927
@ ( descr
@ ^ [Z0: $i] : ( X927 @ Z0 ) ) ) )
=> ( ! [X928: $i,X929: $i > $o,X930: $i] :
( ( in @ X930 @ X928 )
=> ( ( X929 @ X930 )
=> ( in @ X930 @ ( dsetconstr @ X928 @ X929 ) ) ) )
=> ( ! [X931: $i,X932: $i > $o,X933: $i] :
( ( in @ X933 @ ( dsetconstr @ X931 @ X932 ) )
=> ( in @ X933 @ X931 ) )
=> ( ! [X934: $i,X935: $i > $o,X936: $i] :
( ( in @ X936 @ ( dsetconstr @ X934 @ X935 ) )
=> ( X935 @ X936 ) )
=> ( ! [X937: $i > $o] :
( ( exu @ X937 )
=> ? [X938: $i] :
( ( X937 @ X938 )
& ! [X939: $i] :
( ( X937 @ X939 )
=> ( X938 = X939 ) ) ) )
=> ( ! [X940: $o,X941: $i] :
( ( in @ X941 @ ( prop2set @ X940 ) )
=> X940 )
=> ( ! [X942: $i] :
( ( in @ X942 @ emptyset )
=> ! [X943: $o] : X943 )
=> ( ! [X944: $i] :
( ( in @ X944 @ emptyset )
=> ~ $true )
=> ( ! [X945: $i] :
~ ( in @ X945 @ emptyset )
=> ( ! [X946: $i > $o] :
( ( exu @ X946 )
=> ? [X947: $i] : ( X946 @ X947 ) )
=> ( ! [X948: $i,X949: $i] :
( ! [X950: $i] :
( ( in @ X950 @ X948 )
=> ( in @ X950 @ X949 ) )
=> ( ! [X951: $i] :
( ( in @ X951 @ X949 )
=> ( in @ X951 @ X948 ) )
=> ( X948 = X949 ) ) )
=> ( ! [X952: $i] :
( ! [X953: $i] :
~ ( in @ X953 @ X952 )
=> ( X952 = emptyset ) )
=> ( ! [X954: $i] :
( ! [X955: $i] :
~ ( in @ X955 @ X954 )
=> ( X954 = emptyset ) )
=> ( ! [X956: $i,X957: $i > $o,X958: $i] :
( ( in @ X958 @ X956 )
=> ( ( in @ X958 @ ( dsetconstr @ X956 @ X957 ) )
<=> ( X957 @ X958 ) ) )
=> ( ! [X959: $i] :
( ( nonempty @ X959 )
=> ? [X960: $i] : ( in @ X960 @ X959 ) )
=> ( ! [X961: $i,X962: $i > $o,X963: $i] :
( ( in @ X963 @ X961 )
=> ( ( X962 @ X963 )
=> ( nonempty @ ( dsetconstr @ X961 @ X962 ) ) ) )
=> ( ! [X964: $i] :
( ? [X965: $i] : ( in @ X965 @ X964 )
=> ( nonempty @ X964 ) )
=> ( ! [X966: $i,X967: $i] : ( in @ X966 @ ( setadjoin @ X966 @ X967 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X968: $i,X969: $i,X970: $i] :
( ( in @ X970 @ X969 )
=> ( in @ X970 @ ( setadjoin @ X968 @ X969 ) ) )
=> ( ! [X971: $i,X972: $i,X973: $i] :
( ( in @ X973 @ ( setadjoin @ X971 @ X972 ) )
=> ! [X974: $o] :
( ( ( X973 = X971 )
=> X974 )
=> ( ( ( in @ X973 @ X972 )
=> X974 )
=> X974 ) ) )
=> ( ! [X975: $i,X976: $i,X977: $i] :
( ( in @ X977 @ ( setadjoin @ X975 @ X976 ) )
=> ( ( X977 = X975 )
| ( in @ X977 @ X976 ) ) )
=> ( ! [X978: $i] :
( ( dsetconstr @ X978
@ ^ [Z0: $i] : $true )
= X978 )
=> ( ! [X979: $i,X980: $i] :
( ! [X981: $i] :
( ( in @ X981 @ X980 )
=> ( in @ X981 @ X979 ) )
=> ( in @ X980 @ ( powerset @ X979 ) ) )
=> ( ! [X982: $i] : ( in @ emptyset @ ( powerset @ X982 ) )
=> ( ! [X983: $i] : ( in @ emptyset @ ( powerset @ X983 ) )
=> ( ! [X984: $i,X985: $i,X986: $i] :
( ( in @ X985 @ ( powerset @ X984 ) )
=> ( ( in @ X986 @ X985 )
=> ( in @ X986 @ X984 ) ) )
=> ( ! [X987: $i,X988: $i,X989: $i] :
( ( in @ X988 @ X989 )
=> ( ( in @ X989 @ X987 )
=> ( in @ X988 @ ( setunion @ X987 ) ) ) )
=> ( ! [X990: $i,X991: $i] :
( ( in @ X991 @ ( setunion @ X990 ) )
=> ! [X992: $o] :
( ! [X993: $i] :
( ( in @ X991 @ X993 )
=> ( ( in @ X993 @ X990 )
=> X992 ) )
=> X992 ) )
=> ( ! [X994: $i,X995: $i] :
( ( in @ X995 @ X994 )
=> ( in @ X995 @ ( powerset @ ( setunion @ X994 ) ) ) )
=> ( ! [X996: $i > $o] :
( ( exu @ X996 )
=> ? [X997: $i] :
! [X998: $i] :
( ( X996 @ X998 )
<=> ( X998 = X997 ) ) )
=> ( ! [X999: $i] :
( ( nonempty @ X999 )
=> ? [X1000: $i] :
( ( in @ X1000 @ X999 )
& $true ) )
=> ( ! [X1001: $i,X1002: $i] :
( ( in @ X1001 @ ( setadjoin @ X1002 @ emptyset ) )
=> ( X1001 = X1002 ) )
=> ( ! [X1003: $i,X1004: $i] :
( ( X1003 != X1004 )
=> ~ ( in @ X1004 @ ( setadjoin @ X1003 @ emptyset ) ) )
=> ( ! [X1005: $i,X1006: $i] :
( ( X1005 = X1006 )
=> ( in @ X1005 @ ( setadjoin @ X1006 @ emptyset ) ) )
=> ( ! [X1007: $i,X1008: $i] :
( ( in @ X1007 @ ( setadjoin @ X1008 @ emptyset ) )
=> ( in @ X1008 @ ( setadjoin @ X1007 @ emptyset ) ) )
=> ( ! [X1009: $i,X1010: $i,X1011: $i] :
( ( in @ X1011 @ ( setadjoin @ X1009 @ ( setadjoin @ X1010 @ emptyset ) ) )
=> ( ( X1011 = X1009 )
| ( X1011 = X1010 ) ) )
=> ( ! [X1012: $i,X1013: $i] : ( in @ X1012 @ ( setadjoin @ X1012 @ ( setadjoin @ X1013 @ emptyset ) ) )
=> ( ! [X1014: $i,X1015: $i] : ( in @ X1015 @ ( setadjoin @ X1014 @ ( setadjoin @ X1015 @ emptyset ) ) )
=> ( ! [X1016: $i,X1017: $i > $o] :
( ? [X1018: $i] :
( ( in @ X1018 @ X1016 )
& ( X1017 @ X1018 ) )
=> ( ( ( dsetconstr @ X1016 @ X1017 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1019: $i > $o,X1020: $i] :
( ( in @ X1020 @ emptyset )
=> ( X1019 @ X1020 ) )
=> ( ! [X1021: $i,X1022: $i > $o] :
( ~ ! [X1023: $i] :
( ( in @ X1023 @ X1021 )
=> ( X1022 @ X1023 ) )
=> ? [X1024: $i] :
( ( in @ X1024 @ X1021 )
& ~ ( X1022 @ X1024 ) ) )
=> ( ! [X1025: $i,X1026: $i > $o] :
( ! [X1027: $i] :
( ( in @ X1027 @ X1025 )
=> ~ ( X1026 @ X1027 ) )
=> ~ ? [X1028: $i] :
( ( in @ X1028 @ X1025 )
& ( X1026 @ X1028 ) ) )
=> ( ! [X1029: $i,X1030: $i > $o] :
( ~ ? [X1031: $i] :
( ( in @ X1031 @ X1029 )
& ( X1030 @ X1031 ) )
=> ! [X1032: $i] :
( ( in @ X1032 @ X1029 )
=> ~ ( X1030 @ X1032 ) ) )
=> ( ! [X1033: $i,X1034: $i > $o] :
( ? [X1035: $i] :
( ( in @ X1035 @ X1033 )
& ~ ( X1034 @ X1035 ) )
=> ~ ! [X1036: $i] :
( ( in @ X1036 @ X1033 )
=> ( X1034 @ X1036 ) ) )
=> ( ! [X1037: $o] :
( X1037
=> ( in @ emptyset @ ( prop2set @ X1037 ) ) )
=> ( prop2set2propI
=> ( ! [X1038: $i,X1039: $i > $o] :
( ~ ? [X1040: $i] :
( ( in @ X1040 @ X1038 )
& ( X1039 @ X1040 ) )
=> ! [X1041: $i] :
( ( in @ X1041 @ X1038 )
=> ~ ( X1039 @ X1041 ) ) )
=> ( ! [X1042: $i,X1043: $i > $o] :
( ~ ! [X1044: $i] :
( ( in @ X1044 @ X1042 )
=> ( X1043 @ X1044 ) )
=> ? [X1045: $i] :
( ( in @ X1045 @ X1042 )
& ~ ( X1043 @ X1045 ) ) )
=> ( ! [X1046: $i > $o] :
( ? [X1047: $i] :
( ( X1046 @ X1047 )
& ! [X1048: $i] :
( ( X1046 @ X1048 )
=> ( X1047 = X1048 ) ) )
=> ( exu @ X1046 ) )
=> ( ! [X1049: $i > $o] :
( ? [X1050: $i] : ( X1049 @ X1050 )
=> ( ! [X1051: $i,X1052: $i] :
( ( X1049 @ X1051 )
=> ( ( X1049 @ X1052 )
=> ( X1051 = X1052 ) ) )
=> ( exu @ X1049 ) ) )
=> ( ! [X1053: $i > $o] :
( ? [X1054: $i] :
! [X1055: $i] :
( ( X1053 @ X1055 )
<=> ( X1055 = X1054 ) )
=> ( exu @ X1053 ) )
=> ( ! [X1056: $i,X1057: $i] :
( ( X1056 = X1057 )
=> ! [X1058: $i,X1059: $i] :
( ( X1058 = X1059 )
=> ( ( in @ X1058 @ X1056 )
=> ( in @ X1059 @ X1057 ) ) ) )
=> ( ! [X1060: $i,X1061: $i] :
( ( X1060 = X1061 )
=> ! [X1062: $i,X1063: $i] :
( ( X1062 = X1063 )
=> ( ( in @ X1062 @ X1060 )
<=> ( in @ X1063 @ X1061 ) ) ) )
=> ( ! [X1064: $i > $o] :
( ( exu @ X1064 )
=> ! [X1065: $i,X1066: $i] :
( ( X1064 @ X1065 )
=> ( ( X1064 @ X1066 )
=> ( X1065 = X1066 ) ) ) )
=> ( ! [X1067: $i > $o,X1068: $i > $o] :
( ! [X1069: $i,X1070: $i] :
( ( X1069 = X1070 )
=> ( ( X1067 @ X1069 )
<=> ( X1068 @ X1070 ) ) )
=> ( ( exu @ X1067 )
<=> ( exu @ X1068 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1071: $i,X1072: $i] :
( ( X1071 = X1072 )
=> ! [X1073: $i,X1074: $i] :
( ( X1073 = X1074 )
=> ( ( setadjoin @ X1071 @ X1073 )
= ( setadjoin @ X1072 @ X1074 ) ) ) )
=> ( ! [X1075: $i,X1076: $i] :
( ( X1075 = X1076 )
=> ( ( powerset @ X1075 )
= ( powerset @ X1076 ) ) )
=> ( ! [X1077: $i,X1078: $i] :
( ( X1077 = X1078 )
=> ( ( setunion @ X1077 )
= ( setunion @ X1078 ) ) )
=> ( ( omega = omega )
=> ( ! [X1079: $i > $o] :
( ( exu @ X1079 )
=> ! [X1080: $i,X1081: $i] :
( ( X1079 @ X1080 )
=> ( ( X1079 @ X1081 )
=> ( X1080 = X1081 ) ) ) )
=> ( ! [X1082: $i > $o,X1083: $i > $o] :
( ! [X1084: $i,X1085: $i] :
( ( X1084 = X1085 )
=> ( ( X1082 @ X1084 )
<=> ( X1083 @ X1085 ) ) )
=> ( ( exu @ X1082 )
=> ( ( exu @ X1083 )
=> ( ( descr @ X1082 )
= ( descr @ X1083 ) ) ) ) )
=> ( ! [X1086: $i,X1087: $i] :
( ( X1086 = X1087 )
=> ! [X1088: $i > $o,X1089: $i > $o] :
( ! [X1090: $i] :
( ( in @ X1090 @ X1086 )
=> ! [X1091: $i] :
( ( in @ X1091 @ X1087 )
=> ( ( X1090 = X1091 )
=> ( ( X1088 @ X1090 )
<=> ( X1089 @ X1091 ) ) ) ) )
=> ( ( dsetconstr @ X1086 @ X1088 )
= ( dsetconstr @ X1087 @ X1089 ) ) ) )
=> ( ! [X1092: $i,X1093: $i] :
( ! [X1094: $i] :
( ( in @ X1094 @ X1092 )
=> ( in @ X1094 @ X1093 ) )
=> ( subset @ X1092 @ X1093 ) )
=> ( ! [X1095: $i,X1096: $i] :
( ( X1095 = X1096 )
=> ( subset @ X1096 @ X1095 ) )
=> ( ! [X1097: $i,X1098: $i] :
( ( X1097 = X1098 )
=> ( subset @ X1097 @ X1098 ) )
=> ( ! [X1099: $i,X1100: $i] :
( ! [X1101: $i] :
( ( in @ X1101 @ X1099 )
=> ( in @ X1101 @ X1100 ) )
=> ( subset @ X1099 @ X1100 ) )
=> ( ! [X1102: $i] : ( subset @ emptyset @ X1102 )
=> ( ! [X1103: $i,X1104: $i,X1105: $i] :
( ( subset @ X1103 @ X1104 )
=> ( ( in @ X1105 @ X1103 )
=> ( in @ X1105 @ X1104 ) ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ( subset @ X1106 @ X1107 )
=> ( ~ ( in @ X1108 @ X1107 )
=> ~ ( in @ X1108 @ X1106 ) ) )
=> ( ! [X1109: $i,X1110: $i,X1111: $i] :
( ( in @ X1111 @ X1109 )
=> ( ~ ( in @ X1111 @ X1110 )
=> ~ ( subset @ X1109 @ X1110 ) ) )
=> ( ! [X1112: $i,X1113: $i] :
( ~ ( subset @ X1112 @ X1113 )
=> ( X1112 != X1113 ) )
=> ( ! [X1114: $i,X1115: $i,X1116: $i] :
( ( in @ X1116 @ X1114 )
=> ( ~ ( in @ X1116 @ X1115 )
=> ( X1114 != X1115 ) ) )
=> ( ! [X1117: $i] : ( subset @ X1117 @ X1117 )
=> ( ! [X1118: $i,X1119: $i,X1120: $i] :
( ( subset @ X1118 @ X1119 )
=> ( ( subset @ X1119 @ X1120 )
=> ( subset @ X1118 @ X1120 ) ) )
=> ( ! [X1121: $i,X1122: $i] : ( subset @ X1122 @ ( setadjoin @ X1121 @ X1122 ) )
=> ( ! [X1123: $i,X1124: $i,X1125: $i] :
( ( subset @ X1123 @ X1125 )
=> ( subset @ X1123 @ ( setadjoin @ X1124 @ X1125 ) ) )
=> ( ! [X1126: $i,X1127: $i] :
( ( subset @ X1126 @ X1127 )
=> ( in @ X1126 @ ( powerset @ X1127 ) ) )
=> ( ! [X1128: $i,X1129: $i] :
( ( subset @ X1128 @ X1129 )
=> ( ( subset @ X1129 @ X1128 )
=> ( X1128 = X1129 ) ) )
=> ( ! [X1130: $i] :
( ( subset @ X1130 @ emptyset )
=> ( X1130 = emptyset ) )
=> ( ! [X1131: $i,X1132: $i] :
( ( subset @ X1132 @ X1131 )
=> ( in @ X1132 @ ( powerset @ X1131 ) ) )
=> ( ! [X1133: $i,X1134: $i] :
( ( in @ X1134 @ ( powerset @ X1133 ) )
=> ( subset @ X1134 @ X1133 ) )
=> ( ! [X1135: $i] : ( in @ X1135 @ ( powerset @ X1135 ) )
=> ( ! [X1136: $i,X1137: $i] :
( ( subset @ X1136 @ X1137 )
=> ( subset @ ( powerset @ X1136 ) @ ( powerset @ X1137 ) ) )
=> ( ! [X1138: $i,X1139: $i > $o] : ( in @ ( dsetconstr @ X1138 @ X1139 ) @ ( powerset @ X1138 ) )
=> ( ! [X1140: $i,X1141: $i > $o] : ( subset @ ( dsetconstr @ X1140 @ X1141 ) @ X1140 )
=> ( ! [X1142: $i,X1143: $i,X1144: $i] :
( ( in @ X1144 @ X1142 )
=> ( in @ X1144 @ ( binunion @ X1142 @ X1143 ) ) )
=> ( ! [X1145: $i,X1146: $i] : ( in @ X1146 @ ( setadjoin @ X1145 @ ( setadjoin @ X1146 @ emptyset ) ) )
=> ( ! [X1147: $i,X1148: $i,X1149: $i] :
( ( in @ X1149 @ X1148 )
=> ( in @ X1149 @ ( binunion @ X1147 @ X1148 ) ) )
=> ( ! [X1150: $i,X1151: $i,X1152: $i,X1153: $o] :
( ( in @ X1152 @ ( binunion @ X1150 @ X1151 ) )
=> ( ( ( in @ X1152 @ X1150 )
=> X1153 )
=> ( ( ( in @ X1152 @ X1151 )
=> X1153 )
=> X1153 ) ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ ( binunion @ X1154 @ X1155 ) )
=> ( ( in @ X1156 @ X1154 )
| ( in @ X1156 @ X1155 ) ) )
=> ( ! [X1157: $i,X1158: $i] : ( subset @ X1157 @ ( binunion @ X1157 @ X1158 ) )
=> ( ! [X1159: $i,X1160: $i] : ( subset @ X1160 @ ( binunion @ X1159 @ X1160 ) )
=> ( ! [X1161: $i,X1162: $i,X1163: $i] :
( ( in @ X1163 @ X1161 )
=> ( ( in @ X1163 @ X1162 )
=> ( in @ X1163 @ ( binintersect @ X1161 @ X1162 ) ) ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( subset @ X1166 @ X1164 )
=> ( ( subset @ X1166 @ X1165 )
=> ( subset @ X1166 @ ( binintersect @ X1164 @ X1165 ) ) ) )
=> ( ! [X1167: $i,X1168: $i,X1169: $i] :
( ( in @ X1169 @ ( binintersect @ X1167 @ X1168 ) )
=> ( in @ X1169 @ X1167 ) )
=> ( ! [X1170: $i,X1171: $i] : ( subset @ ( binintersect @ X1170 @ X1171 ) @ X1170 )
=> ( ! [X1172: $i,X1173: $i] :
( ( subset @ X1172 @ X1173 )
=> ( ( binintersect @ X1172 @ X1173 )
= X1172 ) )
=> ( ! [X1174: $i,X1175: $i] :
( ( ( binintersect @ X1174 @ X1175 )
= X1175 )
=> ( subset @ X1175 @ X1174 ) )
=> ( ! [X1176: $i,X1177: $i,X1178: $i] :
( ( in @ X1178 @ ( binintersect @ X1176 @ X1177 ) )
=> ( in @ X1178 @ X1177 ) )
=> ( ! [X1179: $i,X1180: $i] :
( ~ ? [X1181: $i] :
( ( in @ X1181 @ X1179 )
& ( in @ X1181 @ X1180 ) )
=> ( ( binintersect @ X1179 @ X1180 )
= emptyset ) )
=> ( ! [X1182: $i,X1183: $i] : ( subset @ ( binintersect @ X1182 @ X1183 ) @ X1183 )
=> ( ! [X1184: $i,X1185: $i] :
( ( subset @ X1185 @ X1184 )
=> ( ( binintersect @ X1184 @ X1185 )
= X1185 ) )
=> ( ! [X1186: $i,X1187: $i] :
( ( ( binintersect @ X1186 @ X1187 )
= X1186 )
=> ( subset @ X1186 @ X1187 ) )
=> ( ! [X1188: $i,X1189: $i,X1190: $i] :
( ( binintersect @ X1188 @ ( binunion @ X1189 @ X1190 ) )
= ( binunion @ ( binintersect @ X1188 @ X1189 ) @ ( binintersect @ X1188 @ X1190 ) ) )
=> ( ! [X1191: $i,X1192: $i,X1193: $i] :
( ( in @ X1193 @ X1191 )
=> ( ~ ( in @ X1193 @ X1192 )
=> ( in @ X1193 @ ( setminus @ X1191 @ X1192 ) ) ) )
=> ( ! [X1194: $i,X1195: $i,X1196: $i] :
( ( in @ X1196 @ ( setminus @ X1194 @ X1195 ) )
=> ( in @ X1196 @ X1194 ) )
=> ( ! [X1197: $i,X1198: $i,X1199: $i] :
( ( in @ X1199 @ ( setminus @ X1197 @ X1198 ) )
=> ~ ( in @ X1199 @ X1198 ) )
=> ( ! [X1200: $i,X1201: $i] :
( ( subset @ X1200 @ X1201 )
=> ( ( setminus @ X1200 @ X1201 )
= emptyset ) )
=> ( ! [X1202: $i,X1203: $i,X1204: $i] :
( ~ ( in @ X1204 @ ( setminus @ X1202 @ X1203 ) )
=> ( ( in @ X1204 @ X1202 )
=> ( in @ X1204 @ X1203 ) ) )
=> ( ! [X1205: $i,X1206: $i,X1207: $i] :
( ~ ( in @ X1207 @ ( setminus @ X1205 @ X1206 ) )
=> ( ~ ( in @ X1207 @ X1206 )
=> ~ ( in @ X1207 @ X1205 ) ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ~ ( in @ X1210 @ X1208 )
=> ~ ( in @ X1210 @ ( setminus @ X1208 @ X1209 ) ) )
=> ( ! [X1211: $i,X1212: $i,X1213: $i] :
( ( in @ X1213 @ X1212 )
=> ~ ( in @ X1213 @ ( setminus @ X1211 @ X1212 ) ) )
=> ( ! [X1214: $i,X1215: $i] : ( subset @ ( setminus @ X1214 @ X1215 ) @ X1214 )
=> ( ! [X1216: $i,X1217: $i] :
( ( ( setminus @ X1216 @ X1217 )
= emptyset )
=> ( subset @ X1216 @ X1217 ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( in @ X1220 @ ( symdiff @ X1218 @ X1219 ) )
=> ! [X1221: $o] :
( ( ( in @ X1220 @ X1218 )
=> ( ~ ( in @ X1220 @ X1219 )
=> X1221 ) )
=> ( ( ~ ( in @ X1220 @ X1218 )
=> ( ( in @ X1220 @ X1219 )
=> X1221 ) )
=> X1221 ) ) )
=> ( ! [X1222: $i,X1223: $i,X1224: $i] :
( ( in @ X1224 @ X1222 )
=> ( ~ ( in @ X1224 @ X1223 )
=> ( in @ X1224 @ ( symdiff @ X1222 @ X1223 ) ) ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i] :
( ~ ( in @ X1227 @ X1225 )
=> ( ( in @ X1227 @ X1226 )
=> ( in @ X1227 @ ( symdiff @ X1225 @ X1226 ) ) ) )
=> ( ! [X1228: $i,X1229: $i,X1230: $i] :
( ( in @ X1230 @ X1228 )
=> ( ( in @ X1230 @ X1229 )
=> ~ ( in @ X1230 @ ( symdiff @ X1228 @ X1229 ) ) ) )
=> ( ! [X1231: $i,X1232: $i,X1233: $i] :
( ~ ( in @ X1233 @ X1231 )
=> ( ~ ( in @ X1233 @ X1232 )
=> ~ ( in @ X1233 @ ( symdiff @ X1231 @ X1232 ) ) ) )
=> ( ! [X1234: $i,X1235: $i] : ( in @ X1235 @ ( setadjoin @ X1234 @ ( setadjoin @ X1235 @ emptyset ) ) )
=> ( ! [X1236: $i,X1237: $i] : ( in @ X1236 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1236 @ ( setadjoin @ X1237 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1238: $i,X1239: $i] : ( in @ X1239 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1238 @ ( setadjoin @ X1239 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1240: $i,X1241: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1240 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1240 @ ( setadjoin @ X1241 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1242: $i,X1243: $i] : ( iskpair @ ( kpair @ X1242 @ X1243 ) )
=> ( ! [X1244: $i,X1245: $i] :
( ( in @ X1245 @ X1244 )
=> ( subset @ ( setadjoin @ X1245 @ emptyset ) @ X1244 ) )
=> ( ! [X1246: $i,X1247: $i] :
( ( in @ X1247 @ X1246 )
=> ( in @ ( setadjoin @ X1247 @ emptyset ) @ ( powerset @ X1246 ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ( in @ ( setadjoin @ X1250 @ emptyset ) @ ( powerset @ ( binunion @ X1248 @ X1249 ) ) ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i] :
( ( in @ X1253 @ ( setadjoin @ X1251 @ ( setadjoin @ X1252 @ emptyset ) ) )
=> ( ( X1253 = X1251 )
| ( X1253 = X1252 ) ) )
=> ( ! [X1254: $i,X1255: $i,X1256: $i] :
( ( in @ X1256 @ X1254 )
=> ! [X1257: $i] :
( ( in @ X1257 @ X1255 )
=> ( subset @ ( setadjoin @ X1256 @ ( setadjoin @ X1257 @ emptyset ) ) @ ( binunion @ X1254 @ X1255 ) ) ) )
=> ( ! [X1258: $i,X1259: $i,X1260: $i] :
( ( in @ X1260 @ X1258 )
=> ! [X1261: $i] :
( ( in @ X1261 @ X1259 )
=> ( in @ ( setadjoin @ X1260 @ ( setadjoin @ X1261 @ emptyset ) ) @ ( powerset @ ( binunion @ X1258 @ X1259 ) ) ) ) )
=> ( ! [X1262: $i,X1263: $i,X1264: $i] :
( ( in @ X1264 @ X1262 )
=> ! [X1265: $i] :
( ( in @ X1265 @ X1263 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1264 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1264 @ ( setadjoin @ X1265 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1262 @ X1263 ) ) ) ) )
=> ( ! [X1266: $i,X1267: $i,X1268: $i] :
( ( in @ X1268 @ X1266 )
=> ! [X1269: $i] :
( ( in @ X1269 @ X1267 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1268 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1268 @ ( setadjoin @ X1269 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1266 @ X1267 ) ) ) ) ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i] :
( ( in @ X1272 @ X1270 )
=> ! [X1273: $i] :
( ( in @ X1273 @ X1271 )
=> ( in @ ( kpair @ X1272 @ X1273 ) @ ( powerset @ ( powerset @ ( binunion @ X1270 @ X1271 ) ) ) ) ) )
=> ( ! [X1274: $i,X1275: $i,X1276: $i] :
( ( in @ X1276 @ X1274 )
=> ! [X1277: $i] :
( ( in @ X1277 @ X1275 )
=> ( in @ ( kpair @ X1276 @ X1277 ) @ ( cartprod @ X1274 @ X1275 ) ) ) )
=> ( ! [X1278: $i,X1279: $i,X1280: $i] :
( ( in @ X1280 @ ( cartprod @ X1278 @ X1279 ) )
=> ? [X1281: $i] :
( ( in @ X1281 @ X1278 )
& ? [X1282: $i] :
( ( in @ X1282 @ X1279 )
& ( X1280
= ( kpair @ X1281 @ X1282 ) ) ) ) )
=> ( ! [X1283: $i,X1284: $i,X1285: $i] :
( ( in @ X1285 @ ( cartprod @ X1283 @ X1284 ) )
=> ( iskpair @ X1285 ) )
=> ( ! [X1286: $i,X1287: $i] :
( ( in @ X1287 @ ( setunion @ X1286 ) )
=> ? [X1288: $i] :
( ( in @ X1288 @ X1286 )
& ( in @ X1287 @ X1288 ) ) )
=> ( ! [X1289: $i] : ( subset @ ( setunion @ ( setadjoin @ X1289 @ emptyset ) ) @ X1289 )
=> ( ! [X1290: $i] : ( subset @ X1290 @ ( setunion @ ( setadjoin @ X1290 @ emptyset ) ) )
=> ( ! [X1291: $i] :
( ( setunion @ ( setadjoin @ X1291 @ emptyset ) )
= X1291 )
=> ( ! [X1292: $i,X1293: $i > $o] :
( ! [X1294: $i] :
( ( in @ X1294 @ X1292 )
=> ! [X1295: $i] :
( ( in @ X1295 @ X1292 )
=> ( ( X1293 @ X1294 )
=> ( ( X1293 @ X1295 )
=> ( X1294 = X1295 ) ) ) ) )
=> ( ? [X1296: $i] :
( ( in @ X1296 @ X1292 )
& ( X1293 @ X1296 ) )
=> ( singleton @ ( dsetconstr @ X1292 @ X1293 ) ) ) )
=> ( ! [X1297: $i,X1298: $i > $o] :
( ( ex1 @ X1297 @ X1298 )
=> ? [X1299: $i] :
( ( in @ X1299 @ X1297 )
& ( X1298 @ X1299 ) ) )
=> ( ! [X1300: $i,X1301: $i > $o,X1302: $i] :
( ( in @ X1302 @ X1300 )
=> ( ( X1301 @ X1302 )
=> ( ! [X1303: $i] :
( ( in @ X1303 @ X1300 )
=> ( ( X1301 @ X1303 )
=> ( X1303 = X1302 ) ) )
=> ( ex1 @ X1300 @ X1301 ) ) ) )
=> ( ! [X1304: $i,X1305: $i > $o] :
( ! [X1306: $i] :
( ( in @ X1306 @ X1304 )
=> ! [X1307: $i] :
( ( in @ X1307 @ X1304 )
=> ( ( X1305 @ X1306 )
=> ( ( X1305 @ X1307 )
=> ( X1306 = X1307 ) ) ) ) )
=> ( ? [X1308: $i] :
( ( in @ X1308 @ X1304 )
& ( X1305 @ X1308 ) )
=> ( ex1 @ X1304 @ X1305 ) ) )
=> ( ! [X1309: $i,X1310: $i] :
( ( ( setadjoin @ X1309 @ emptyset )
= ( setadjoin @ X1310 @ emptyset ) )
=> ( X1309 = X1310 ) )
=> ( ! [X1311: $i,X1312: $i,X1313: $i] :
( ( in @ ( setadjoin @ X1313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1311 @ ( setadjoin @ X1312 @ emptyset ) ) @ emptyset ) ) )
=> ( X1311 = X1313 ) )
=> ( ! [X1314: $i] :
( ( iskpair @ X1314 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1314 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1314 ) ) ) )
=> ( ! [X1315: $i] :
( ( singleton @ X1315 )
=> ( in @ ( setunion @ X1315 ) @ X1315 ) )
=> ( ! [X1316: $i,X1317: $i] :
( ( kfst @ ( kpair @ X1316 @ X1317 ) )
= X1316 )
=> ( ! [X1318: $i,X1319: $i,X1320: $i] :
( ( in @ X1320 @ ( cartprod @ X1318 @ X1319 ) )
=> ( in @ ( kfst @ X1320 ) @ X1318 ) )
=> ( ! [X1321: $i,X1322: $i,X1323: $i,X1324: $i] :
( ( ( setadjoin @ ( setadjoin @ X1321 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1321 @ ( setadjoin @ X1322 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1323 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1323 @ ( setadjoin @ X1324 @ emptyset ) ) @ emptyset ) ) )
=> ( X1321 = X1323 ) )
=> ( ! [X1325: $i,X1326: $i,X1327: $i,X1328: $i] :
( ( ( kpair @ X1325 @ X1326 )
= ( kpair @ X1327 @ X1328 ) )
=> ( X1325 = X1327 ) )
=> ( ! [X1329: $i,X1330: $i] :
( ( X1329 = X1330 )
=> ( ( setadjoin @ X1329 @ ( setadjoin @ X1330 @ emptyset ) )
= ( setadjoin @ X1329 @ emptyset ) ) )
=> ( ! [X1331: $i,X1332: $i] :
( ( X1331 = X1332 )
=> ( ( setadjoin @ ( setadjoin @ X1331 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1331 @ ( setadjoin @ X1332 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1331 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1333: $i,X1334: $i,X1335: $i,X1336: $i] :
( ( ( setadjoin @ ( setadjoin @ X1333 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1333 @ ( setadjoin @ X1334 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1335 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1335 @ ( setadjoin @ X1336 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1335 = X1336 )
=> ( X1334 = X1336 ) ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i] :
( ( ( setadjoin @ X1337 @ ( setadjoin @ X1338 @ emptyset ) )
= ( setadjoin @ X1339 @ emptyset ) )
=> ( X1337 = X1338 ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i,X1343: $i] :
( ( ( setadjoin @ ( setadjoin @ X1340 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1340 @ ( setadjoin @ X1341 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1342 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1342 @ ( setadjoin @ X1343 @ emptyset ) ) @ emptyset ) ) )
=> ( X1341 = X1343 ) )
=> ( ! [X1344: $i,X1345: $i,X1346: $i,X1347: $i] :
( ( ( kpair @ X1344 @ X1345 )
= ( kpair @ X1346 @ X1347 ) )
=> ( X1345 = X1347 ) )
=> ( ! [X1348: $i] :
( ( iskpair @ X1348 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1348 )
@ ^ [Z0: $i] :
( X1348
= ( kpair @ ( kfst @ X1348 ) @ Z0 ) ) ) ) )
=> ( ! [X1349: $i,X1350: $i] :
( ( ksnd @ ( kpair @ X1349 @ X1350 ) )
= X1350 )
=> ( ! [X1351: $i] :
( ( iskpair @ X1351 )
=> ( ( kpair @ ( kfst @ X1351 ) @ ( ksnd @ X1351 ) )
= X1351 ) )
=> ( ! [X1352: $i,X1353: $i,X1354: $i] :
( ( in @ X1354 @ ( cartprod @ X1352 @ X1353 ) )
=> ( in @ ( ksnd @ X1354 ) @ X1353 ) )
=> ( ! [X1355: $i,X1356: $i,X1357: $i,X1358: $i] :
( ( in @ ( kpair @ X1357 @ X1358 ) @ ( cartprod @ X1355 @ X1356 ) )
=> ( in @ X1357 @ X1355 ) )
=> ( ! [X1359: $i,X1360: $i,X1361: $i,X1362: $i] :
( ( in @ ( kpair @ X1361 @ X1362 ) @ ( cartprod @ X1359 @ X1360 ) )
=> ( in @ X1362 @ X1360 ) )
=> ( ! [X1363: $i,X1364: $i,X1365: $i] :
( ( in @ X1365 @ X1363 )
=> ! [X1366: $i] :
( ( in @ X1366 @ X1364 )
=> ( ( kpair @ X1365 @ X1366 )
= ( kpair @ X1365 @ X1366 ) ) ) )
=> ( ! [X1367: $i,X1368: $i,X1369: $i] :
( ( in @ X1369 @ X1367 )
=> ! [X1370: $i] :
( ( in @ X1370 @ X1368 )
=> ( ( kfst @ ( kpair @ X1369 @ X1370 ) )
= X1369 ) ) )
=> ( ! [X1371: $i,X1372: $i,X1373: $i] :
( ( in @ X1373 @ X1371 )
=> ! [X1374: $i] :
( ( in @ X1374 @ X1372 )
=> ( ( ksnd @ ( kpair @ X1373 @ X1374 ) )
= X1374 ) ) )
=> ( ! [X1375: $i,X1376: $i,X1377: $i] :
( ( in @ X1377 @ ( cartprod @ X1375 @ X1376 ) )
=> ( ( kpair @ ( kfst @ X1377 ) @ ( ksnd @ X1377 ) )
= X1377 ) )
=> ( ! [X1378: $i,X1379: $i,X1380: $i > $i > $o,X1381: $i] :
( ( in @ X1381 @ X1378 )
=> ! [X1382: $i] :
( ( in @ X1382 @ X1379 )
=> ( ( X1380 @ X1381 @ X1382 )
=> ( in @ ( kpair @ X1381 @ X1382 ) @ ( dpsetconstr @ X1378 @ X1379 @ X1380 ) ) ) ) )
=> ( ! [X1383: $i,X1384: $i,X1385: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1383 @ X1384 @ X1385 ) @ ( cartprod @ X1383 @ X1384 ) )
=> ( ! [X1386: $i,X1387: $i,X1388: $i > $i > $o] : ( breln @ X1386 @ X1387 @ ( dpsetconstr @ X1386 @ X1387 @ X1388 ) )
=> ( ! [X1389: $i,X1390: $i,X1391: $i > $i > $o,X1392: $i] :
( ( in @ X1392 @ X1389 )
=> ! [X1393: $i] :
( ( in @ X1393 @ X1390 )
=> ( ( in @ ( kpair @ X1392 @ X1393 ) @ ( dpsetconstr @ X1389 @ X1390 @ X1391 ) )
=> ( X1391 @ X1392 @ X1393 ) ) ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i > $i > $o,X1397: $i,X1398: $i] :
( ( in @ ( kpair @ X1397 @ X1398 ) @ ( dpsetconstr @ X1394 @ X1395 @ X1396 ) )
=> ( in @ X1397 @ X1394 ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i > $i > $o,X1402: $i,X1403: $i] :
( ( in @ ( kpair @ X1402 @ X1403 ) @ ( dpsetconstr @ X1399 @ X1400 @ X1401 ) )
=> ( in @ X1403 @ X1400 ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i > $i > $o,X1407: $i,X1408: $i] :
( ( in @ ( kpair @ X1407 @ X1408 ) @ ( dpsetconstr @ X1404 @ X1405 @ X1406 ) )
=> ( X1406 @ X1407 @ X1408 ) )
=> ( ! [X1409: $i,X1410: $i,X1411: $i] :
( ( func @ X1409 @ X1410 @ X1411 )
=> ! [X1412: $i] :
( ( in @ X1412 @ X1409 )
=> ( singleton
@ ( dsetconstr @ X1410
@ ^ [Z0: $i] : ( in @ ( kpair @ X1412 @ Z0 ) @ X1411 ) ) ) ) )
=> ( ! [X1413: $i,X1414: $i,X1415: $i] :
( ( func @ X1413 @ X1414 @ X1415 )
=> ! [X1416: $i] :
( ( in @ X1416 @ X1413 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1414
@ ^ [Z0: $i] : ( in @ ( kpair @ X1416 @ Z0 ) @ X1415 ) ) )
@ X1414 ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( func @ X1417 @ X1418 @ X1419 )
=> ! [X1420: $i] :
( ( in @ X1420 @ X1417 )
=> ( in @ ( ap @ X1417 @ X1418 @ X1419 @ X1420 ) @ X1418 ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i] :
( ( in @ X1423 @ ( funcSet @ X1421 @ X1422 ) )
=> ( func @ X1421 @ X1422 @ X1423 ) )
=> ( ! [X1424: $i,X1425: $i,X1426: $i] :
( ( in @ X1426 @ ( funcSet @ X1424 @ X1425 ) )
=> ! [X1427: $i] :
( ( in @ X1427 @ X1424 )
=> ( in @ ( ap @ X1424 @ X1425 @ X1426 @ X1427 ) @ X1425 ) ) )
=> ( ! [X1428: $i,X1429: $i,X1430: $i] :
( ( func @ X1428 @ X1429 @ X1430 )
=> ( in @ X1430 @ ( funcSet @ X1428 @ X1429 ) ) )
=> ( ! [X1431: $i,X1432: $i,X1433: $i > $i] :
( ! [X1434: $i] :
( ( in @ X1434 @ X1431 )
=> ( in @ ( X1433 @ X1434 ) @ X1432 ) )
=> ( func @ X1431 @ X1432
@ ( dpsetconstr @ X1431 @ X1432
@ ^ [Z0: $i] : ( $eq @ ( X1433 @ Z0 ) ) ) ) )
=> ( ! [X1435: $i,X1436: $i,X1437: $i > $i] :
( ! [X1438: $i] :
( ( in @ X1438 @ X1435 )
=> ( in @ ( X1437 @ X1438 ) @ X1436 ) )
=> ( func @ X1435 @ X1436 @ ( lam @ X1435 @ X1436 @ X1437 ) ) )
=> ( ! [X1439: $i,X1440: $i,X1441: $i > $i] :
( ! [X1442: $i] :
( ( in @ X1442 @ X1439 )
=> ( in @ ( X1441 @ X1442 ) @ X1440 ) )
=> ( in @ ( lam @ X1439 @ X1440 @ X1441 ) @ ( funcSet @ X1439 @ X1440 ) ) )
=> ( ! [X1443: $i,X1444: $i,X1445: $i] :
( ( breln @ X1443 @ X1444 @ X1445 )
=> ! [X1446: $i > $o] :
( ! [X1447: $i] :
( ( in @ X1447 @ X1443 )
=> ! [X1448: $i] :
( ( in @ X1448 @ X1444 )
=> ( ( in @ ( kpair @ X1447 @ X1448 ) @ X1445 )
=> ( X1446 @ ( kpair @ X1447 @ X1448 ) ) ) ) )
=> ! [X1449: $i] :
( ( in @ X1449 @ X1445 )
=> ( X1446 @ X1449 ) ) ) )
=> ( ! [X1450: $i,X1451: $i,X1452: $i] :
( ( breln @ X1450 @ X1451 @ X1452 )
=> ! [X1453: $i > $o] :
( ! [X1454: $i] :
( ( in @ X1454 @ X1450 )
=> ! [X1455: $i] :
( ( in @ X1455 @ X1451 )
=> ( ( in @ ( kpair @ X1454 @ X1455 ) @ X1452 )
=> ( X1453 @ ( kpair @ X1454 @ X1455 ) ) ) ) )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1452 )
=> ( X1453 @ X1456 ) ) ) )
=> ( ! [X1457: $i,X1458: $i > $o] :
( ( ex1 @ X1457 @ X1458 )
=> ! [X1459: $i] :
( ( in @ X1459 @ X1457 )
=> ! [X1460: $i] :
( ( in @ X1460 @ X1457 )
=> ( ( X1458 @ X1459 )
=> ( ( X1458 @ X1460 )
=> ( X1459 = X1460 ) ) ) ) ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i] :
( ( func @ X1461 @ X1462 @ X1463 )
=> ! [X1464: $i] :
( ( in @ X1464 @ X1461 )
=> ( in @ ( kpair @ X1464 @ ( ap @ X1461 @ X1462 @ X1463 @ X1464 ) ) @ X1463 ) ) )
=> ( ! [X1465: $i,X1466: $i,X1467: $i] :
( ( in @ X1467 @ ( funcSet @ X1465 @ X1466 ) )
=> ! [X1468: $i] :
( ( in @ X1468 @ X1465 )
=> ( in @ ( kpair @ X1468 @ ( ap @ X1465 @ X1466 @ X1467 @ X1468 ) ) @ X1467 ) ) )
=> ( ! [X1469: $i,X1470: $i,X1471: $i] :
( ( func @ X1469 @ X1470 @ X1471 )
=> ! [X1472: $i] :
( ( in @ X1472 @ X1469 )
=> ! [X1473: $i] :
( ( in @ X1473 @ X1470 )
=> ( ( in @ ( kpair @ X1472 @ X1473 ) @ X1471 )
=> ( ( ap @ X1469 @ X1470 @ X1471 @ X1472 )
= X1473 ) ) ) ) )
=> ( ! [X1474: $i,X1475: $i,X1476: $i] :
( ( func @ X1474 @ X1475 @ X1476 )
=> ! [X1477: $i] :
( ( func @ X1474 @ X1475 @ X1477 )
=> ( ! [X1478: $i] :
( ( in @ X1478 @ X1474 )
=> ( ( ap @ X1474 @ X1475 @ X1476 @ X1478 )
= ( ap @ X1474 @ X1475 @ X1477 @ X1478 ) ) )
=> ! [X1479: $i] :
( ( in @ X1479 @ X1474 )
=> ! [X1480: $i] :
( ( in @ X1480 @ X1475 )
=> ( ( in @ ( kpair @ X1479 @ X1480 ) @ X1477 )
=> ( in @ ( kpair @ X1479 @ X1480 ) @ X1476 ) ) ) ) ) ) )
=> ( ! [X1481: $i,X1482: $i,X1483: $i] :
( ( in @ X1483 @ ( funcSet @ X1481 @ X1482 ) )
=> ! [X1484: $i] :
( ( in @ X1484 @ X1481 )
=> ! [X1485: $i] :
( ( in @ X1485 @ X1482 )
=> ( ( in @ ( kpair @ X1484 @ X1485 ) @ X1483 )
=> ( ( ap @ X1481 @ X1482 @ X1483 @ X1484 )
= X1485 ) ) ) ) )
=> ( ! [X1486: $i,X1487: $i,X1488: $i] :
( ( breln @ X1486 @ X1487 @ X1488 )
=> ! [X1489: $i] :
( ( breln @ X1486 @ X1487 @ X1489 )
=> ( ! [X1490: $i] :
( ( in @ X1490 @ X1486 )
=> ! [X1491: $i] :
( ( in @ X1491 @ X1487 )
=> ( ( in @ ( kpair @ X1490 @ X1491 ) @ X1488 )
=> ( in @ ( kpair @ X1490 @ X1491 ) @ X1489 ) ) ) )
=> ( subset @ X1488 @ X1489 ) ) ) )
=> ( ! [X1492: $i,X1493: $i,X1494: $i] :
( ( breln @ X1492 @ X1493 @ X1494 )
=> ! [X1495: $i] :
( ( breln @ X1492 @ X1493 @ X1495 )
=> ( ! [X1496: $i] :
( ( in @ X1496 @ X1492 )
=> ! [X1497: $i] :
( ( in @ X1497 @ X1493 )
=> ( ( in @ ( kpair @ X1496 @ X1497 ) @ X1494 )
=> ( in @ ( kpair @ X1496 @ X1497 ) @ X1495 ) ) ) )
=> ( ! [X1498: $i] :
( ( in @ X1498 @ X1492 )
=> ! [X1499: $i] :
( ( in @ X1499 @ X1493 )
=> ( ( in @ ( kpair @ X1498 @ X1499 ) @ X1495 )
=> ( in @ ( kpair @ X1498 @ X1499 ) @ X1494 ) ) ) )
=> ( X1494 = X1495 ) ) ) ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i] :
( ( func @ X1500 @ X1501 @ X1502 )
=> ! [X1503: $i] :
( ( func @ X1500 @ X1501 @ X1503 )
=> ( ! [X1504: $i] :
( ( in @ X1504 @ X1500 )
=> ( ( ap @ X1500 @ X1501 @ X1502 @ X1504 )
= ( ap @ X1500 @ X1501 @ X1503 @ X1504 ) ) )
=> ( X1502 = X1503 ) ) ) )
=> ( ! [X1505: $i,X1506: $i,X1507: $i] :
( ( in @ X1507 @ ( funcSet @ X1505 @ X1506 ) )
=> ! [X1508: $i] :
( ( in @ X1508 @ ( funcSet @ X1505 @ X1506 ) )
=> ( ! [X1509: $i] :
( ( in @ X1509 @ X1505 )
=> ( ( ap @ X1505 @ X1506 @ X1507 @ X1509 )
= ( ap @ X1505 @ X1506 @ X1508 @ X1509 ) ) )
=> ( X1507 = X1508 ) ) ) )
=> ( ! [X1510: $i,X1511: $i,X1512: $i] :
( ( in @ X1512 @ ( funcSet @ X1510 @ X1511 ) )
=> ! [X1513: $i] :
( ( in @ X1513 @ X1510 )
=> ( ( ap @ X1510 @ X1511 @ X1512 @ X1513 )
= ( ap @ X1510 @ X1511 @ X1512 @ X1513 ) ) ) )
=> ( ! [X1514: $i,X1515: $i,X1516: $i] :
( ( func @ X1514 @ X1515 @ X1516 )
=> ! [X1517: $i] :
( ( in @ X1517 @ X1514 )
=> ( ( ap @ X1514 @ X1515 @ X1516 @ X1517 )
= ( ap @ X1514 @ X1515 @ X1516 @ X1517 ) ) ) )
=> ( ! [X1518: $i,X1519: $i,X1520: $i > $i] :
( ! [X1521: $i] :
( ( in @ X1521 @ X1518 )
=> ( in @ ( X1520 @ X1521 ) @ X1519 ) )
=> ! [X1522: $i] :
( ( in @ X1522 @ X1518 )
=> ( ( ap @ X1518 @ X1519 @ ( lam @ X1518 @ X1519 @ X1520 ) @ X1522 )
= ( X1520 @ X1522 ) ) ) )
=> ( ! [X1523: $i,X1524: $i,X1525: $i] :
( ( func @ X1523 @ X1524 @ X1525 )
=> ( ( lam @ X1523 @ X1524 @ ( ap @ X1523 @ X1524 @ X1525 ) )
= X1525 ) )
=> ( ! [X1526: $i,X1527: $i,X1528: $i > $i] :
( ! [X1529: $i] :
( ( in @ X1529 @ X1526 )
=> ( in @ ( X1528 @ X1529 ) @ X1527 ) )
=> ( ( lam @ X1526 @ X1527 @ X1528 )
= ( lam @ X1526 @ X1527 @ X1528 ) ) )
=> ( ! [X1530: $i,X1531: $i,X1532: $i > $i] :
( ! [X1533: $i] :
( ( in @ X1533 @ X1530 )
=> ( in @ ( X1532 @ X1533 ) @ X1531 ) )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1530 )
=> ( ( ap @ X1530 @ X1531 @ ( lam @ X1530 @ X1531 @ X1532 ) @ X1534 )
= ( X1532 @ X1534 ) ) ) )
=> ( ! [X1535: $i,X1536: $i,X1537: $i] :
( ( in @ X1537 @ ( funcSet @ X1535 @ X1536 ) )
=> ( ( lam @ X1535 @ X1536 @ ( ap @ X1535 @ X1536 @ X1537 ) )
= X1537 ) )
=> ( ! [X1538: $i,X1539: $o,X1540: $i] :
( ( in @ X1540 @ X1538 )
=> ! [X1541: $i] :
( ( in @ X1541 @ X1538 )
=> ( ~ X1539
=> ( in @ X1541
@ ( dsetconstr @ X1538
@ ^ [Z0: $i] :
( ( X1539
& ( Z0 = X1540 ) )
| ( ~ X1539
& ( Z0 = X1541 ) ) ) ) ) ) ) )
=> ( ! [X1542: $i,X1543: $o,X1544: $i] :
( ( in @ X1544 @ X1542 )
=> ! [X1545: $i] :
( ( in @ X1545 @ X1542 )
=> ( ~ X1543
=> ( ( dsetconstr @ X1542
@ ^ [Z0: $i] :
( ( X1543
& ( Z0 = X1544 ) )
| ( ~ X1543
& ( Z0 = X1545 ) ) ) )
= ( setadjoin @ X1545 @ emptyset ) ) ) ) )
=> ( ! [X1546: $i,X1547: $o,X1548: $i] :
( ( in @ X1548 @ X1546 )
=> ! [X1549: $i] :
( ( in @ X1549 @ X1546 )
=> ( X1547
=> ( in @ X1548
@ ( dsetconstr @ X1546
@ ^ [Z0: $i] :
( ( X1547
& ( Z0 = X1548 ) )
| ( ~ X1547
& ( Z0 = X1549 ) ) ) ) ) ) ) )
=> ( ! [X1550: $i,X1551: $o,X1552: $i] :
( ( in @ X1552 @ X1550 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1550 )
=> ( X1551
=> ( ( dsetconstr @ X1550
@ ^ [Z0: $i] :
( ( X1551
& ( Z0 = X1552 ) )
| ( ~ X1551
& ( Z0 = X1553 ) ) ) )
= ( setadjoin @ X1552 @ emptyset ) ) ) ) )
=> ( ! [X1554: $i,X1555: $o,X1556: $i] :
( ( in @ X1556 @ X1554 )
=> ! [X1557: $i] :
( ( in @ X1557 @ X1554 )
=> ( singleton
@ ( dsetconstr @ X1554
@ ^ [Z0: $i] :
( ( X1555
& ( Z0 = X1556 ) )
| ( ~ X1555
& ( Z0 = X1557 ) ) ) ) ) ) )
=> ( ! [X1558: $i,X1559: $o,X1560: $i] :
( ( in @ X1560 @ X1558 )
=> ! [X1561: $i] :
( ( in @ X1561 @ X1558 )
=> ( in @ ( if @ X1558 @ X1559 @ X1560 @ X1561 ) @ X1558 ) ) )
=> ( ! [X1562: $i] :
( ( singleton @ X1562 )
=> ! [X1563: $i] :
( ( in @ X1563 @ X1562 )
=> ( ( setunion @ X1562 )
= X1563 ) ) )
=> ( ! [X1564: $i,X1565: $o,X1566: $i] :
( ( in @ X1566 @ X1564 )
=> ! [X1567: $i] :
( ( in @ X1567 @ X1564 )
=> ( X1565
=> ( ( if @ X1564 @ X1565 @ X1566 @ X1567 )
= X1566 ) ) ) )
=> ( ! [X1568: $i,X1569: $o,X1570: $i] :
( ( in @ X1570 @ X1568 )
=> ! [X1571: $i] :
( ( in @ X1571 @ X1568 )
=> ( ~ X1569
=> ( ( if @ X1568 @ X1569 @ X1570 @ X1571 )
= X1571 ) ) ) )
=> ( ! [X1572: $i,X1573: $o,X1574: $i] :
( ( in @ X1574 @ X1572 )
=> ! [X1575: $i] :
( ( in @ X1575 @ X1572 )
=> ( in @ ( if @ X1572 @ X1573 @ X1574 @ X1575 ) @ ( setadjoin @ X1574 @ ( setadjoin @ X1575 @ emptyset ) ) ) ) )
=> ( ! [X1576: $i,X1577: $i] :
( ( in @ X1577 @ ( powerset @ X1576 ) )
=> ! [X1578: $i] :
( ( in @ X1578 @ ( powerset @ X1576 ) )
=> ( in @ ( binintersect @ X1577 @ X1578 ) @ ( powerset @ X1576 ) ) ) )
=> ( ! [X1579: $i,X1580: $i] :
( ( in @ X1580 @ ( powerset @ X1579 ) )
=> ! [X1581: $i] :
( ( in @ X1581 @ ( powerset @ X1579 ) )
=> ( in @ ( binunion @ X1580 @ X1581 ) @ ( powerset @ X1579 ) ) ) )
=> ( ! [X1582: $i,X1583: $i] :
( ( in @ X1583 @ ( powerset @ X1582 ) )
=> ( in @ ( powerset @ X1583 ) @ ( powerset @ ( powerset @ X1582 ) ) ) )
=> ( ! [X1584: $i,X1585: $i] :
( ( in @ X1585 @ ( powerset @ X1584 ) )
=> ! [X1586: $i] :
( ( in @ X1586 @ ( powerset @ X1584 ) )
=> ( in @ ( setminus @ X1585 @ X1586 ) @ ( powerset @ X1584 ) ) ) )
=> ( ! [X1587: $i,X1588: $i] :
( ( in @ X1588 @ ( powerset @ X1587 ) )
=> ( in @ ( setminus @ X1587 @ X1588 ) @ ( powerset @ X1587 ) ) )
=> ( ! [X1589: $i,X1590: $i] :
( ( in @ X1590 @ ( powerset @ X1589 ) )
=> ! [X1591: $i] :
( ( in @ X1591 @ ( powerset @ X1589 ) )
=> ( ! [X1592: $i] :
( ( in @ X1592 @ X1589 )
=> ( ( in @ X1592 @ X1590 )
=> ( in @ X1592 @ X1591 ) ) )
=> ( ! [X1593: $i] :
( ( in @ X1593 @ X1589 )
=> ( ( in @ X1593 @ X1591 )
=> ( in @ X1593 @ X1590 ) ) )
=> ( X1590 = X1591 ) ) ) ) )
=> ( ! [X1594: $i,X1595: $i] :
( ( in @ X1595 @ ( powerset @ X1594 ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ ( powerset @ X1594 ) )
=> ( ! [X1597: $i] :
( ( in @ X1597 @ X1594 )
=> ( ( in @ X1597 @ X1595 )
=> ( in @ X1597 @ X1596 ) ) )
=> ( subset @ X1595 @ X1596 ) ) ) )
=> ( ! [X1598: $i,X1599: $i] :
( ( in @ X1599 @ ( powerset @ X1598 ) )
=> ! [X1600: $i] :
( ( in @ X1600 @ ( powerset @ X1598 ) )
=> ( ! [X1601: $i] :
( ( in @ X1601 @ X1598 )
=> ( ( in @ X1601 @ X1599 )
=> ( in @ X1601 @ X1600 ) ) )
=> ( in @ X1599 @ ( powerset @ X1600 ) ) ) ) )
=> ( ! [X1602: $i,X1603: $i] :
( ( in @ X1603 @ ( powerset @ X1602 ) )
=> ! [X1604: $i] :
( ( in @ X1604 @ ( powerset @ X1602 ) )
=> ! [X1605: $i] :
( ( in @ X1605 @ X1602 )
=> ( ( in @ X1603 @ ( powerset @ X1604 ) )
=> ( ( in @ X1605 @ X1603 )
=> ( in @ X1605 @ X1604 ) ) ) ) ) )
=> ( ! [X1606: $i,X1607: $i] :
( ( in @ X1607 @ ( powerset @ X1606 ) )
=> ! [X1608: $i] :
( ( in @ X1608 @ X1606 )
=> ( ( in @ X1608 @ X1607 )
=> ~ ( in @ X1608 @ ( setminus @ X1606 @ X1607 ) ) ) ) )
=> ( ! [X1609: $i,X1610: $i] :
( ( in @ X1610 @ ( powerset @ X1609 ) )
=> ! [X1611: $i] :
( ( in @ X1611 @ X1609 )
=> ( ~ ( in @ X1611 @ ( setminus @ X1609 @ X1610 ) )
=> ( in @ X1611 @ X1610 ) ) ) )
=> ( ! [X1612: $i,X1613: $i] :
( ( in @ X1613 @ ( powerset @ X1612 ) )
=> ! [X1614: $i] :
( ( in @ X1614 @ ( powerset @ X1612 ) )
=> ! [X1615: $i] :
( ( in @ X1615 @ X1612 )
=> ( ~ ( in @ X1615 @ X1613 )
=> ~ ( in @ X1615 @ ( binintersect @ X1613 @ X1614 ) ) ) ) ) )
=> ( ! [X1616: $i,X1617: $i] :
( ( in @ X1617 @ ( powerset @ X1616 ) )
=> ! [X1618: $i] :
( ( in @ X1618 @ ( powerset @ X1616 ) )
=> ! [X1619: $i] :
( ( in @ X1619 @ X1616 )
=> ( ~ ( in @ X1619 @ X1618 )
=> ~ ( in @ X1619 @ ( binintersect @ X1617 @ X1618 ) ) ) ) ) )
=> ( ! [X1620: $i,X1621: $i] :
( ( in @ X1621 @ ( powerset @ X1620 ) )
=> ! [X1622: $i] :
( ( in @ X1622 @ ( powerset @ X1620 ) )
=> ! [X1623: $i] :
( ( in @ X1623 @ X1620 )
=> ( ( subset @ X1621 @ ( setminus @ X1620 @ X1622 ) )
=> ( ( in @ X1623 @ X1622 )
=> ~ ( in @ X1623 @ X1621 ) ) ) ) ) )
=> ( ! [X1624: $i,X1625: $i] :
( ( in @ X1625 @ ( powerset @ X1624 ) )
=> ! [X1626: $i] :
( ( in @ X1626 @ ( powerset @ X1624 ) )
=> ! [X1627: $i] :
( ( in @ X1627 @ X1624 )
=> ( ( subset @ X1625 @ X1626 )
=> ( ~ ( in @ X1627 @ X1626 )
=> ~ ( in @ X1627 @ X1625 ) ) ) ) ) )
=> ( ! [X1628: $i,X1629: $i] :
( ( in @ X1629 @ ( powerset @ X1628 ) )
=> ! [X1630: $i] :
( ( in @ X1630 @ ( powerset @ X1628 ) )
=> ( ( subset @ X1629 @ X1630 )
=> ( subset @ ( setminus @ X1628 @ X1630 ) @ ( setminus @ X1628 @ X1629 ) ) ) ) )
=> ( ! [X1631: $i,X1632: $i] :
( ( in @ X1632 @ ( powerset @ X1631 ) )
=> ! [X1633: $i] :
( ( in @ X1633 @ ( powerset @ X1631 ) )
=> ( ( subset @ ( setminus @ X1631 @ X1633 ) @ ( setminus @ X1631 @ X1632 ) )
=> ( subset @ X1632 @ X1633 ) ) ) )
=> ( ! [X1634: $i,X1635: $i] :
( ( in @ X1635 @ ( powerset @ X1634 ) )
=> ! [X1636: $i] :
( ( in @ X1636 @ X1634 )
=> ( ( in @ X1636 @ X1635 )
=> ( in @ X1636 @ ( setminus @ X1634 @ ( setminus @ X1634 @ X1635 ) ) ) ) ) )
=> ( ! [X1637: $i,X1638: $i] :
( ( in @ X1638 @ ( powerset @ X1637 ) )
=> ! [X1639: $i] :
( ( in @ X1639 @ X1637 )
=> ( ( in @ X1639 @ ( setminus @ X1637 @ ( setminus @ X1637 @ X1638 ) ) )
=> ( in @ X1639 @ X1638 ) ) ) )
=> ( ! [X1640: $i,X1641: $i] :
( ( in @ X1641 @ ( powerset @ X1640 ) )
=> ( subset @ X1641 @ ( setminus @ X1640 @ ( setminus @ X1640 @ X1641 ) ) ) )
=> ( ! [X1642: $i,X1643: $i] :
( ( in @ X1643 @ ( powerset @ X1642 ) )
=> ( subset @ ( setminus @ X1642 @ ( setminus @ X1642 @ X1643 ) ) @ X1643 ) )
=> ( ! [X1644: $i,X1645: $i] :
( ( in @ X1645 @ ( powerset @ X1644 ) )
=> ( X1645
= ( setminus @ X1644 @ ( setminus @ X1644 @ X1645 ) ) ) )
=> ( ! [X1646: $i,X1647: $i] :
( ( in @ X1647 @ ( powerset @ X1646 ) )
=> ! [X1648: $i] :
( ( in @ X1648 @ ( powerset @ X1646 ) )
=> ! [X1649: $i] :
( ( in @ X1649 @ X1646 )
=> ( ( in @ X1649 @ ( setminus @ X1646 @ X1647 ) )
=> ~ ( in @ X1649 @ ( binintersect @ X1647 @ X1648 ) ) ) ) ) )
=> ( ! [X1650: $i,X1651: $i] :
( ( in @ X1651 @ ( powerset @ X1650 ) )
=> ! [X1652: $i] :
( ( in @ X1652 @ ( powerset @ X1650 ) )
=> ! [X1653: $i] :
( ( in @ X1653 @ X1650 )
=> ( ( in @ X1653 @ ( setminus @ X1650 @ X1651 ) )
=> ( in @ X1653 @ ( setminus @ X1650 @ ( binintersect @ X1651 @ X1652 ) ) ) ) ) ) )
=> ( ! [X1654: $i,X1655: $i] :
( ( in @ X1655 @ ( powerset @ X1654 ) )
=> ! [X1656: $i] :
( ( in @ X1656 @ ( powerset @ X1654 ) )
=> ( subset @ ( setminus @ X1654 @ X1655 ) @ ( setminus @ X1654 @ ( binintersect @ X1655 @ X1656 ) ) ) ) )
=> ( ! [X1657: $i,X1658: $i] :
( ( in @ X1658 @ ( powerset @ X1657 ) )
=> ! [X1659: $i] :
( ( in @ X1659 @ ( powerset @ X1657 ) )
=> ( in @ ( setminus @ X1657 @ X1658 ) @ ( powerset @ ( setminus @ X1657 @ ( binintersect @ X1658 @ X1659 ) ) ) ) ) )
=> ( ! [X1660: $i,X1661: $i] :
( ( in @ X1661 @ ( powerset @ X1660 ) )
=> ! [X1662: $i] :
( ( in @ X1662 @ ( powerset @ X1660 ) )
=> ( ( subset @ X1661 @ ( setminus @ X1660 @ X1662 ) )
=> ! [X1663: $i] :
( ( in @ X1663 @ X1660 )
=> ( ( in @ X1663 @ X1662 )
=> ( in @ X1663 @ ( setminus @ X1660 @ X1661 ) ) ) ) ) ) )
=> ( ! [X1664: $i,X1665: $i] :
( ( in @ X1665 @ ( powerset @ X1664 ) )
=> ! [X1666: $i] :
( ( in @ X1666 @ ( powerset @ X1664 ) )
=> ( ( subset @ X1665 @ ( setminus @ X1664 @ X1666 ) )
=> ( subset @ X1666 @ ( setminus @ X1664 @ X1665 ) ) ) ) )
=> ( ! [X1667: $i,X1668: $i] :
( ( in @ X1668 @ ( powerset @ X1667 ) )
=> ! [X1669: $i] :
( ( in @ X1669 @ ( powerset @ X1667 ) )
=> ! [X1670: $i] :
( ( in @ X1670 @ X1667 )
=> ( ~ ( in @ X1670 @ ( binunion @ X1668 @ X1669 ) )
=> ~ ( in @ X1670 @ X1668 ) ) ) ) )
=> ( ! [X1671: $i,X1672: $i] :
( ( in @ X1672 @ ( powerset @ X1671 ) )
=> ! [X1673: $i] :
( ( in @ X1673 @ ( powerset @ X1671 ) )
=> ! [X1674: $i] :
( ( in @ X1674 @ X1671 )
=> ( ~ ( in @ X1674 @ ( binunion @ X1672 @ X1673 ) )
=> ~ ( in @ X1674 @ X1673 ) ) ) ) )
=> ( ! [X1675: $i,X1676: $i] :
( ( in @ X1676 @ ( powerset @ X1675 ) )
=> ! [X1677: $i] :
( ( in @ X1677 @ ( powerset @ X1675 ) )
=> ! [X1678: $i] :
( ( in @ X1678 @ ( powerset @ X1675 ) )
=> ! [X1679: $i] :
( ( in @ X1679 @ X1675 )
=> ( ( in @ X1679 @ ( binintersect @ X1676 @ X1677 ) )
=> ( in @ X1679 @ ( binunion @ X1676 @ X1678 ) ) ) ) ) ) )
=> ( ! [X1680: $i,X1681: $i] :
( ( in @ X1681 @ ( powerset @ X1680 ) )
=> ! [X1682: $i] :
( ( in @ X1682 @ ( powerset @ X1680 ) )
=> ! [X1683: $i] :
( ( in @ X1683 @ ( powerset @ X1680 ) )
=> ! [X1684: $i] :
( ( in @ X1684 @ X1680 )
=> ( ( in @ X1684 @ ( binintersect @ X1681 @ X1682 ) )
=> ( in @ X1684 @ ( binunion @ X1682 @ X1683 ) ) ) ) ) ) )
=> ( ! [X1685: $i,X1686: $i] :
( ( in @ X1686 @ ( powerset @ X1685 ) )
=> ! [X1687: $i] :
( ( in @ X1687 @ ( powerset @ X1685 ) )
=> ! [X1688: $i] :
( ( in @ X1688 @ ( powerset @ X1685 ) )
=> ! [X1689: $i] :
( ( in @ X1689 @ X1685 )
=> ( ( in @ X1689 @ ( binintersect @ X1686 @ X1687 ) )
=> ( in @ X1689 @ ( binintersect @ ( binunion @ X1686 @ X1688 ) @ ( binunion @ X1687 @ X1688 ) ) ) ) ) ) ) )
=> ( ! [X1690: $i,X1691: $i] :
( ( in @ X1691 @ ( powerset @ X1690 ) )
=> ! [X1692: $i] :
( ( in @ X1692 @ ( powerset @ X1690 ) )
=> ! [X1693: $i] :
( ( in @ X1693 @ ( powerset @ X1690 ) )
=> ( in @ ( binintersect @ X1691 @ X1692 ) @ ( powerset @ ( binintersect @ ( binunion @ X1691 @ X1693 ) @ ( binunion @ X1692 @ X1693 ) ) ) ) ) ) )
=> ( ! [X1694: $i,X1695: $i] :
( ( in @ X1695 @ ( powerset @ X1694 ) )
=> ! [X1696: $i] :
( ( in @ X1696 @ ( powerset @ X1694 ) )
=> ! [X1697: $i] :
( ( in @ X1697 @ X1694 )
=> ( ( in @ X1697 @ ( setminus @ X1694 @ ( binunion @ X1695 @ X1696 ) ) )
=> ~ ( in @ X1697 @ X1695 ) ) ) ) )
=> ( ! [X1698: $i,X1699: $i] :
( ( in @ X1699 @ ( powerset @ X1698 ) )
=> ! [X1700: $i] :
( ( in @ X1700 @ ( powerset @ X1698 ) )
=> ! [X1701: $i] :
( ( in @ X1701 @ X1698 )
=> ( ( in @ X1701 @ ( setminus @ X1698 @ ( binunion @ X1699 @ X1700 ) ) )
=> ( in @ X1701 @ ( setminus @ X1698 @ X1699 ) ) ) ) ) )
=> ( ! [X1702: $i,X1703: $i] :
( ( in @ X1703 @ ( powerset @ X1702 ) )
=> ! [X1704: $i] :
( ( in @ X1704 @ ( powerset @ X1702 ) )
=> ! [X1705: $o,X1706: $i] :
( ( in @ X1706 @ X1702 )
=> ( ( in @ X1706 @ ( binunion @ X1703 @ X1704 ) )
=> ( ( ( in @ X1706 @ X1703 )
=> X1705 )
=> ( ( ( in @ X1706 @ X1704 )
=> X1705 )
=> X1705 ) ) ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binunionTEcontra]),contrasubsetT]),binunionTE]),c_0_263]),binunionIL]),c_0_264]),c_0_265]),ifp]),upairset2IR]),theeq]),iftrue]),binunionIR]),iffalse]),iftrueorfalse]),binunionEcases]),binintersectT_lem]),binunionT_lem]),binunionE]),powersetT_lem]),setminusT_lem]),binunionLsub]),complementT_lem]),setextT]),binunionRsub]),subsetTI]),binintersectI]),powersetTI1]),powersetTE1]),complementTI1]),binintersectSubset5]),complementTE1]),binintersectTELcontra]),binintersectTERcontra]),binintersectEL]),setminusSubset1]),contrasubsetT1]),contrasubsetT2]),binintersectLsub]),contrasubsetT3]),doubleComplementI1]),binintersectSubset2]),doubleComplementE1]),doubleComplementSub1]),binintersectSubset3]),doubleComplementSub2]),doubleComplementEq]),complementTnotintersectT]),complementImpComplementIntersect]),binintersectER]),complementSubsetComplementIntersect]),complementInPowersetComplementIntersect]),disjointsetsI1]),contraSubsetComplement]),complementTcontraSubset]),binintersectRsub]),binunionTILcontra]),binunionTIRcontra]),binintersectSubset4]),inIntersectImpInUnion]),inIntersectImpInUnion2]),binintersectSubset1]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),bs114d]),inComplementUnionImpNotIn1]),inComplementUnionImpInComplement1]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),cartprodfstin]),setukpairinjL2]),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_266]),c_0_267]),c_0_268]),setadjoinSub]),c_0_269]),setadjoinSub2]),singletonsuniq]),setukpairinjL1]),subset2powerset]),c_0_270]),theprop]),kfstpairEq]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_271]),setextsub]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_272]),c_0_273]),c_0_274]),c_0_275]),c_0_276]),c_0_277]),c_0_278]),c_0_279]),c_0_280]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_281]),c_0_282]),c_0_283]),brelnall1]),brelnall2]),c_0_284]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),subsetemptysetimpeq]),powersetI1]),c_0_291]),powersetE1]),inPowerset]),powersetsubset]),c_0_292]),c_0_293]),subsetTrans]),subsetRefl]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_294]),c_0_295]),c_0_296]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_297]),c_0_298]),in__Cong]),inCongP]),c_0_299]),c_0_300]),c_0_301]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_302]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_303]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_304]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_305]),nonemptyE1]),c_0_306]),noeltsimpempty]),emptyI]),setext]),c_0_307]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_308]),c_0_309]),c_0_310]),c_0_311]),c_0_312]),wellorderingAx]),foundationAx]),c_0_313]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_314]) ).
thf(c_0_316,negated_conjecture,
! 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$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 > $o,X1834: $i,X1835: $i > $o,X1836: $i,X1837: $i,X1838: $i > $o,X1839: $i,X1841: $i,X1842: $i > $o,X1844: $i,X1845: $i,X1846: $i > $o,X1848: $i,X1849: $i,X1850: $i > $o,X1851: $i,X1853: $o,X1854: $i,X1855: $i > $o,X1857: $i,X1858: $i,X1859: $i > $o,X1860: $i,X1862: $i > $o,X1863: $i,X1865: $i > $o,X1866: $i,X1869: $i > $o,X1870: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i > $o,X1881: $i,X1882: $i,X1883: $i > $o,X1884: $i > $o,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i > $o,X1896: $i,X1897: $i,X1898: $i > $o,X1899: $i > $o,X1902: $i,X1903: $i,X1904: $i > $o,X1905: $i > $o,X1908: $i,X1909: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1915: $i,X1916: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: 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$i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2037: $o,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,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,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i > $o,X2112: $i,X2113: $i,X2114: $i > $o,X2116: $i,X2117: $i > $o,X2118: $i,X2120: $i,X2121: $i > $o,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i > $i > $o,X2197: $i,X2198: $i,X2199: $i,X2200: $i,X2201: $i > $i > $o,X2202: $i,X2203: $i,X2204: $i > $i > $o,X2205: $i,X2206: $i,X2207: $i > $i > $o,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i > $i > $o,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i > $i > $o,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i > $i > $o,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2245: $i,X2246: $i,X2247: $i,X2248: $i,X2249: $i > $i,X2251: $i,X2252: $i,X2253: $i > $i,X2255: $i,X2256: $i,X2257: $i > $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i > $o,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i > $o,X2272: $i,X2273: $i,X2274: $i > $o,X2275: $i,X2276: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2287: $i,X2288: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i,X2293: $i,X2295: $i,X2296: $i,X2297: $i,X2298: $i,X2299: $i,X2300: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i,X2308: $i,X2309: $i,X2310: $i,X2311: $i,X2316: $i,X2317: $i,X2318: $i,X2319: $i,X2321: $i,X2322: $i,X2323: $i,X2324: $i,X2326: $i,X2327: $i,X2328: $i,X2329: $i,X2330: $i,X2331: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i > $i,X2338: $i,X2339: $i,X2340: $i,X2341: $i,X2342: $i,X2343: $i,X2344: $i > $i,X2346: $i,X2347: $i,X2348: $i > $i,X2350: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $o,X2356: $i,X2357: $i,X2358: $i,X2359: $o,X2360: $i,X2361: $i,X2362: $i,X2363: $o,X2364: $i,X2365: $i,X2366: $i,X2367: $o,X2368: $i,X2369: $i,X2370: $i,X2371: $o,X2372: $i,X2373: $i,X2374: $i,X2375: $o,X2376: $i,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2381: $o,X2382: $i,X2383: $i,X2384: $i,X2385: $o,X2386: $i,X2387: $i,X2388: $i,X2389: $o,X2390: $i,X2391: $i,X2392: $i,X2393: $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2410: $i,X2411: $i,X2412: $i,X2414: $i,X2415: $i,X2416: $i,X2418: $i,X2419: $i,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i,X2425: $i,X2426: $i,X2427: $i,X2428: $i,X2429: $i,X2430: $i,X2431: $i,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2436: $i,X2437: $i,X2438: $i,X2439: $i,X2440: $i,X2441: $i,X2442: $i,X2443: $i,X2444: $i,X2445: $i,X2446: $i,X2447: $i,X2448: $i,X2449: $i,X2450: $i,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i,X2456: $i,X2457: $i,X2458: $i,X2459: $i,X2460: $i,X2461: $i,X2462: $i,X2463: $i,X2464: $i,X2465: $i,X2466: $i,X2467: $i,X2468: $i,X2469: $i,X2470: $i,X2471: $i,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2490: $i,X2491: $i,X2492: $i,X2493: $i,X2494: $i,X2495: $i,X2496: $i,X2497: $i,X2498: $i,X2499: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i,X2517: $i,X2518: $i,X2519: $i,X2520: $i,X2521: $o,X2522: $i] :
( ( ~ ( in @ ( esk1_2 @ X1707 @ X1708 ) @ X1707 )
| ~ ( in @ ( esk1_2 @ X1707 @ X1708 ) @ X1708 )
| ( X1707 = X1708 ) )
& ( ( in @ ( esk1_2 @ X1707 @ X1708 ) @ X1707 )
| ( in @ ( esk1_2 @ X1707 @ X1708 ) @ X1708 )
| ( X1707 = X1708 ) )
& ~ ( in @ X1710 @ emptyset )
& ( ~ ( in @ X1713 @ ( setadjoin @ X1711 @ X1712 ) )
| ( X1713 = X1711 )
| ( in @ X1713 @ X1712 ) )
& ( ( X1713 != X1711 )
| ( in @ X1713 @ ( setadjoin @ X1711 @ X1712 ) ) )
& ( ~ ( in @ X1713 @ X1712 )
| ( in @ X1713 @ ( setadjoin @ X1711 @ X1712 ) ) )
& ( ~ ( in @ X1715 @ ( powerset @ X1714 ) )
| ~ ( in @ X1716 @ X1715 )
| ( in @ X1716 @ X1714 ) )
& ( ( in @ ( esk2_2 @ X1717 @ X1718 ) @ X1718 )
| ( in @ X1718 @ ( powerset @ X1717 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1717 @ X1718 ) @ X1717 )
| ( in @ X1718 @ ( powerset @ X1717 ) ) )
& ( ( in @ X1721 @ ( esk3_2 @ X1720 @ X1721 ) )
| ~ ( in @ X1721 @ ( setunion @ X1720 ) ) )
& ( ( in @ ( esk3_2 @ X1720 @ X1721 ) @ X1720 )
| ~ ( in @ X1721 @ ( setunion @ X1720 ) ) )
& ( ~ ( in @ X1724 @ X1725 )
| ~ ( in @ X1725 @ X1723 )
| ( in @ X1724 @ ( setunion @ X1723 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1726 @ omega )
| ( in @ ( setadjoin @ X1726 @ X1726 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1727 ) @ omega )
| ~ ( in @ emptyset @ X1727 )
| ~ ( in @ X1729 @ omega )
| ( in @ X1729 @ X1727 ) )
& ( ( in @ ( esk4_1 @ X1727 ) @ X1727 )
| ~ ( in @ emptyset @ X1727 )
| ~ ( in @ X1729 @ omega )
| ( in @ X1729 @ X1727 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1727 ) @ ( esk4_1 @ X1727 ) ) @ X1727 )
| ~ ( in @ emptyset @ X1727 )
| ~ ( in @ X1729 @ omega )
| ( in @ X1729 @ X1727 ) )
& ( ( in @ ( esk7_3 @ X1730 @ X1731 @ X1734 ) @ X1731 )
| ~ ( in @ X1734 @ ( esk6_2 @ X1730 @ X1731 ) )
| ( in @ ( esk5_2 @ X1730 @ X1731 ) @ X1731 ) )
& ( ( X1730 @ ( esk7_3 @ X1730 @ X1731 @ X1734 ) @ X1734 )
| ~ ( in @ X1734 @ ( esk6_2 @ X1730 @ X1731 ) )
| ( in @ ( esk5_2 @ X1730 @ X1731 ) @ X1731 ) )
& ( ~ ( in @ X1737 @ X1731 )
| ~ ( X1730 @ X1737 @ X1736 )
| ( in @ X1736 @ ( esk6_2 @ X1730 @ X1731 ) )
| ( in @ ( esk5_2 @ X1730 @ X1731 ) @ X1731 ) )
& ( ( in @ ( esk7_3 @ X1730 @ X1731 @ X1734 ) @ X1731 )
| ~ ( in @ X1734 @ ( esk6_2 @ X1730 @ X1731 ) )
| ~ ( exu @ ( X1730 @ ( esk5_2 @ X1730 @ X1731 ) ) ) )
& ( ( X1730 @ ( esk7_3 @ X1730 @ X1731 @ X1734 ) @ X1734 )
| ~ ( in @ X1734 @ ( esk6_2 @ X1730 @ X1731 ) )
| ~ ( exu @ ( X1730 @ ( esk5_2 @ X1730 @ X1731 ) ) ) )
& ( ~ ( in @ X1737 @ X1731 )
| ~ ( X1730 @ X1737 @ X1736 )
| ( in @ X1736 @ ( esk6_2 @ X1730 @ X1731 ) )
| ~ ( exu @ ( X1730 @ ( esk5_2 @ X1730 @ X1731 ) ) ) )
& ( ( in @ ( esk8_1 @ X1738 ) @ X1738 )
| ~ ( in @ X1739 @ X1738 ) )
& ( ~ ( in @ X1741 @ ( esk8_1 @ X1738 ) )
| ~ ( in @ X1741 @ X1738 )
| ~ ( in @ X1739 @ X1738 ) )
& epred1_0
& ( ~ ( exu @ X1742 )
| ( X1742 @ ( descr @ X1742 ) ) )
& ( ~ ( in @ X1745 @ X1743 )
| ~ ( X1744 @ X1745 )
| ( in @ X1745 @ ( dsetconstr @ X1743 @ X1744 ) ) )
& ( ~ ( in @ X1748 @ ( dsetconstr @ X1746 @ X1747 ) )
| ( in @ X1748 @ X1746 ) )
& ( ~ ( in @ X1751 @ ( dsetconstr @ X1749 @ X1750 ) )
| ( X1750 @ X1751 ) )
& ( ( X1752 @ ( esk9_1 @ X1752 ) )
| ~ ( exu @ X1752 ) )
& ( ~ ( X1752 @ X1754 )
| ( ( esk9_1 @ X1752 )
= X1754 )
| ~ ( exu @ X1752 ) )
& ( ~ ( in @ X1756 @ ( prop2set @ X1755 ) )
| X1755 )
& ( ~ ( in @ X1757 @ emptyset )
| X1758 )
& ( ~ ( in @ X1759 @ emptyset )
| ~ $true )
& ~ ( in @ X1760 @ emptyset )
& ( ~ ( exu @ X1761 )
| ( X1761 @ ( esk10_1 @ X1761 ) ) )
& ( ( in @ ( esk12_2 @ X1763 @ X1764 ) @ X1764 )
| ( X1763 = X1764 )
| ( in @ ( esk11_2 @ X1763 @ X1764 ) @ X1763 ) )
& ( ~ ( in @ ( esk12_2 @ X1763 @ X1764 ) @ X1763 )
| ( X1763 = X1764 )
| ( in @ ( esk11_2 @ X1763 @ X1764 ) @ X1763 ) )
& ( ( in @ ( esk12_2 @ X1763 @ X1764 ) @ X1764 )
| ( X1763 = X1764 )
| ~ ( in @ ( esk11_2 @ X1763 @ X1764 ) @ X1764 ) )
& ( ~ ( in @ ( esk12_2 @ X1763 @ X1764 ) @ X1763 )
| ( X1763 = X1764 )
| ~ ( in @ ( esk11_2 @ X1763 @ X1764 ) @ X1764 ) )
& ( ( in @ ( esk13_1 @ X1767 ) @ X1767 )
| ( X1767 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1769 ) @ X1769 )
| ( X1769 = emptyset ) )
& ( ~ ( in @ X1773 @ ( dsetconstr @ X1771 @ X1772 ) )
| ( X1772 @ X1773 )
| ~ ( in @ X1773 @ X1771 ) )
& ( ~ ( X1772 @ X1773 )
| ( in @ X1773 @ ( dsetconstr @ X1771 @ X1772 ) )
| ~ ( in @ X1773 @ X1771 ) )
& ( ~ ( nonempty @ X1774 )
| ( in @ ( esk15_1 @ X1774 ) @ X1774 ) )
& ( ~ ( in @ X1778 @ X1776 )
| ~ ( X1777 @ X1778 )
| ( nonempty @ ( dsetconstr @ X1776 @ X1777 ) ) )
& ( ~ ( in @ X1780 @ X1779 )
| ( nonempty @ X1779 ) )
& ( in @ X1781 @ ( setadjoin @ X1781 @ X1782 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1785 @ X1784 )
| ( in @ X1785 @ ( setadjoin @ X1783 @ X1784 ) ) )
& ( ( in @ X1788 @ X1787 )
| X1789
| ( X1788 = X1786 )
| ~ ( in @ X1788 @ ( setadjoin @ X1786 @ X1787 ) ) )
& ( ~ X1789
| X1789
| ( X1788 = X1786 )
| ~ ( in @ X1788 @ ( setadjoin @ X1786 @ X1787 ) ) )
& ( ( in @ X1788 @ X1787 )
| X1789
| ~ X1789
| ~ ( in @ X1788 @ ( setadjoin @ X1786 @ X1787 ) ) )
& ( ~ X1789
| X1789
| ~ X1789
| ~ ( in @ X1788 @ ( setadjoin @ X1786 @ X1787 ) ) )
& ( ~ ( in @ X1792 @ ( setadjoin @ X1790 @ X1791 ) )
| ( X1792 = X1790 )
| ( in @ X1792 @ X1791 ) )
& ( ( dsetconstr @ X1793
@ ^ [Z0: $i] : $true )
= X1793 )
& ( ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1795 )
| ( in @ X1795 @ ( powerset @ X1794 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1794 )
| ( in @ X1795 @ ( powerset @ X1794 ) ) )
& ( in @ emptyset @ ( powerset @ X1797 ) )
& ( in @ emptyset @ ( powerset @ X1798 ) )
& ( ~ ( in @ X1800 @ ( powerset @ X1799 ) )
| ~ ( in @ X1801 @ X1800 )
| ( in @ X1801 @ X1799 ) )
& ( ~ ( in @ X1803 @ X1804 )
| ~ ( in @ X1804 @ X1802 )
| ( in @ X1803 @ ( setunion @ X1802 ) ) )
& ( ( in @ X1806 @ ( esk17_3 @ X1805 @ X1806 @ X1807 ) )
| X1807
| ~ ( in @ X1806 @ ( setunion @ X1805 ) ) )
& ( ( in @ ( esk17_3 @ X1805 @ X1806 @ X1807 ) @ X1805 )
| X1807
| ~ ( in @ X1806 @ ( setunion @ X1805 ) ) )
& ( ~ X1807
| X1807
| ~ ( in @ X1806 @ ( setunion @ X1805 ) ) )
& ( ~ ( in @ X1810 @ X1809 )
| ( in @ X1810 @ ( powerset @ ( setunion @ X1809 ) ) ) )
& ( ~ ( X1811 @ X1813 )
| ( X1813
= ( esk18_1 @ X1811 ) )
| ~ ( exu @ X1811 ) )
& ( ( X1814
!= ( esk18_1 @ X1811 ) )
| ( X1811 @ X1814 )
| ~ ( exu @ X1811 ) )
& ( ( in @ ( esk19_1 @ X1815 ) @ X1815 )
| ~ ( nonempty @ X1815 ) )
& ( $true
| ~ ( nonempty @ X1815 ) )
& ( ~ ( in @ X1817 @ ( setadjoin @ X1818 @ emptyset ) )
| ( X1817 = X1818 ) )
& ( ( X1819 = X1820 )
| ~ ( in @ X1820 @ ( setadjoin @ X1819 @ emptyset ) ) )
& ( ( X1821 != X1822 )
| ( in @ X1821 @ ( setadjoin @ X1822 @ emptyset ) ) )
& ( ~ ( in @ X1823 @ ( setadjoin @ X1824 @ emptyset ) )
| ( in @ X1824 @ ( setadjoin @ X1823 @ emptyset ) ) )
& ( ~ ( in @ X1827 @ ( setadjoin @ X1825 @ ( setadjoin @ X1826 @ emptyset ) ) )
| ( X1827 = X1825 )
| ( X1827 = X1826 ) )
& ( in @ X1828 @ ( setadjoin @ X1828 @ ( setadjoin @ X1829 @ emptyset ) ) )
& ( in @ X1831 @ ( setadjoin @ X1830 @ ( setadjoin @ X1831 @ emptyset ) ) )
& ( ~ ( in @ X1834 @ X1832 )
| ~ ( X1833 @ X1834 )
| ( ( dsetconstr @ X1832 @ X1833 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1836 @ emptyset )
| ( X1835 @ X1836 ) )
& ( ( in @ ( esk20_2 @ X1837 @ X1838 ) @ X1837 )
| ~ ( in @ X1839 @ X1837 )
| ( X1838 @ X1839 ) )
& ( ~ ( X1838 @ ( esk20_2 @ X1837 @ X1838 ) )
| ~ ( in @ X1839 @ X1837 )
| ( X1838 @ X1839 ) )
& ( ( in @ ( esk21_2 @ X1841 @ X1842 ) @ X1841 )
| ~ ( in @ X1844 @ X1841 )
| ~ ( X1842 @ X1844 ) )
& ( ( X1842 @ ( esk21_2 @ X1841 @ X1842 ) )
| ~ ( in @ X1844 @ X1841 )
| ~ ( X1842 @ X1844 ) )
& ( ( in @ ( esk22_2 @ X1845 @ X1846 ) @ X1845 )
| ~ ( in @ X1848 @ X1845 )
| ~ ( X1846 @ X1848 ) )
& ( ( X1846 @ ( esk22_2 @ X1845 @ X1846 ) )
| ~ ( in @ X1848 @ X1845 )
| ~ ( X1846 @ X1848 ) )
& ( ( in @ ( esk23_2 @ X1849 @ X1850 ) @ X1849 )
| ~ ( in @ X1851 @ X1849 )
| ( X1850 @ X1851 ) )
& ( ~ ( X1850 @ ( esk23_2 @ X1849 @ X1850 ) )
| ~ ( in @ X1851 @ X1849 )
| ( X1850 @ X1851 ) )
& ( ~ X1853
| ( in @ emptyset @ ( prop2set @ X1853 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1854 @ X1855 ) @ X1854 )
| ~ ( in @ X1857 @ X1854 )
| ~ ( X1855 @ X1857 ) )
& ( ( X1855 @ ( esk24_2 @ X1854 @ X1855 ) )
| ~ ( in @ X1857 @ X1854 )
| ~ ( X1855 @ X1857 ) )
& ( ( in @ ( esk25_2 @ X1858 @ X1859 ) @ X1858 )
| ~ ( in @ X1860 @ X1858 )
| ( X1859 @ X1860 ) )
& ( ~ ( X1859 @ ( esk25_2 @ X1858 @ X1859 ) )
| ~ ( in @ X1860 @ X1858 )
| ( X1859 @ X1860 ) )
& ( ( X1862 @ ( esk26_2 @ X1862 @ X1863 ) )
| ~ ( X1862 @ X1863 )
| ( exu @ X1862 ) )
& ( ( X1863
!= ( esk26_2 @ X1862 @ X1863 ) )
| ~ ( X1862 @ X1863 )
| ( exu @ X1862 ) )
& ( ( X1865 @ ( esk27_1 @ X1865 ) )
| ( exu @ X1865 )
| ~ ( X1865 @ X1866 ) )
& ( ( X1865 @ ( esk28_1 @ X1865 ) )
| ( exu @ X1865 )
| ~ ( X1865 @ X1866 ) )
& ( ( ( esk27_1 @ X1865 )
!= ( esk28_1 @ X1865 ) )
| ( exu @ X1865 )
| ~ ( X1865 @ X1866 ) )
& ( ~ ( X1869 @ ( esk29_2 @ X1869 @ X1870 ) )
| ( ( esk29_2 @ X1869 @ X1870 )
!= X1870 )
| ( exu @ X1869 ) )
& ( ( X1869 @ ( esk29_2 @ X1869 @ X1870 ) )
| ( ( esk29_2 @ X1869 @ X1870 )
= X1870 )
| ( exu @ X1869 ) )
& ( ( X1872 != X1873 )
| ( X1874 != X1875 )
| ~ ( in @ X1874 @ X1872 )
| ( in @ X1875 @ X1873 ) )
& ( ~ ( in @ X1878 @ X1876 )
| ( in @ X1879 @ X1877 )
| ( X1878 != X1879 )
| ( X1876 != X1877 ) )
& ( ~ ( in @ X1879 @ X1877 )
| ( in @ X1878 @ X1876 )
| ( X1878 != X1879 )
| ( X1876 != X1877 ) )
& ( ~ ( exu @ X1880 )
| ~ ( X1880 @ X1881 )
| ~ ( X1880 @ X1882 )
| ( X1881 = X1882 ) )
& ( ~ ( exu @ X1883 )
| ( exu @ X1884 )
| ( ( esk30_2 @ X1883 @ X1884 )
= ( esk31_2 @ X1883 @ X1884 ) ) )
& ( ~ ( exu @ X1884 )
| ( exu @ X1883 )
| ( ( esk30_2 @ X1883 @ X1884 )
= ( esk31_2 @ X1883 @ X1884 ) ) )
& ( ~ ( exu @ X1883 )
| ( exu @ X1884 )
| ~ ( X1883 @ ( esk30_2 @ X1883 @ X1884 ) )
| ~ ( X1884 @ ( esk31_2 @ X1883 @ X1884 ) ) )
& ( ~ ( exu @ X1884 )
| ( exu @ X1883 )
| ~ ( X1883 @ ( esk30_2 @ X1883 @ X1884 ) )
| ~ ( X1884 @ ( esk31_2 @ X1883 @ X1884 ) ) )
& ( ~ ( exu @ X1883 )
| ( exu @ X1884 )
| ( X1883 @ ( esk30_2 @ X1883 @ X1884 ) )
| ( X1884 @ ( esk31_2 @ X1883 @ X1884 ) ) )
& ( ~ ( exu @ X1884 )
| ( exu @ X1883 )
| ( X1883 @ ( esk30_2 @ X1883 @ X1884 ) )
| ( X1884 @ ( esk31_2 @ X1883 @ X1884 ) ) )
& ( emptyset = emptyset )
& ( ( X1887 != X1888 )
| ( X1889 != X1890 )
| ( ( setadjoin @ X1887 @ X1889 )
= ( setadjoin @ X1888 @ X1890 ) ) )
& ( ( X1891 != X1892 )
| ( ( powerset @ X1891 )
= ( powerset @ X1892 ) ) )
& ( ( X1893 != X1894 )
| ( ( setunion @ X1893 )
= ( setunion @ X1894 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1895 )
| ~ ( X1895 @ X1896 )
| ~ ( X1895 @ X1897 )
| ( X1896 = X1897 ) )
& ( ( ( esk32_2 @ X1898 @ X1899 )
= ( esk33_2 @ X1898 @ X1899 ) )
| ~ ( exu @ X1898 )
| ~ ( exu @ X1899 )
| ( ( descr @ X1898 )
= ( descr @ X1899 ) ) )
& ( ~ ( X1898 @ ( esk32_2 @ X1898 @ X1899 ) )
| ~ ( X1899 @ ( esk33_2 @ X1898 @ X1899 ) )
| ~ ( exu @ X1898 )
| ~ ( exu @ X1899 )
| ( ( descr @ X1898 )
= ( descr @ X1899 ) ) )
& ( ( X1898 @ ( esk32_2 @ X1898 @ X1899 ) )
| ( X1899 @ ( esk33_2 @ X1898 @ X1899 ) )
| ~ ( exu @ X1898 )
| ~ ( exu @ X1899 )
| ( ( descr @ X1898 )
= ( descr @ X1899 ) ) )
& ( ( in @ ( esk34_4 @ X1902 @ X1903 @ X1904 @ X1905 ) @ X1902 )
| ( ( dsetconstr @ X1902 @ X1904 )
= ( dsetconstr @ X1903 @ X1905 ) )
| ( X1902 != X1903 ) )
& ( ( in @ ( esk35_4 @ X1902 @ X1903 @ X1904 @ X1905 ) @ X1903 )
| ( ( dsetconstr @ X1902 @ X1904 )
= ( dsetconstr @ X1903 @ X1905 ) )
| ( X1902 != X1903 ) )
& ( ( ( esk34_4 @ X1902 @ X1903 @ X1904 @ X1905 )
= ( esk35_4 @ X1902 @ X1903 @ X1904 @ X1905 ) )
| ( ( dsetconstr @ X1902 @ X1904 )
= ( dsetconstr @ X1903 @ X1905 ) )
| ( X1902 != X1903 ) )
& ( ~ ( X1904 @ ( esk34_4 @ X1902 @ X1903 @ X1904 @ X1905 ) )
| ~ ( X1905 @ ( esk35_4 @ X1902 @ X1903 @ X1904 @ X1905 ) )
| ( ( dsetconstr @ X1902 @ X1904 )
= ( dsetconstr @ X1903 @ X1905 ) )
| ( X1902 != X1903 ) )
& ( ( X1904 @ ( esk34_4 @ X1902 @ X1903 @ X1904 @ X1905 ) )
| ( X1905 @ ( esk35_4 @ X1902 @ X1903 @ X1904 @ X1905 ) )
| ( ( dsetconstr @ X1902 @ X1904 )
= ( dsetconstr @ X1903 @ X1905 ) )
| ( X1902 != X1903 ) )
& ( ( in @ ( esk36_2 @ X1908 @ X1909 ) @ X1908 )
| ( subset @ X1908 @ X1909 ) )
& ( ~ ( in @ ( esk36_2 @ X1908 @ X1909 ) @ X1909 )
| ( subset @ X1908 @ X1909 ) )
& ( ( X1911 != X1912 )
| ( subset @ X1912 @ X1911 ) )
& ( ( X1913 != X1914 )
| ( subset @ X1913 @ X1914 ) )
& ( ( in @ ( esk37_2 @ X1915 @ X1916 ) @ X1915 )
| ( subset @ X1915 @ X1916 ) )
& ( ~ ( in @ ( esk37_2 @ X1915 @ X1916 ) @ X1916 )
| ( subset @ X1915 @ X1916 ) )
& ( subset @ emptyset @ X1918 )
& ( ~ ( subset @ X1919 @ X1920 )
| ~ ( in @ X1921 @ X1919 )
| ( in @ X1921 @ X1920 ) )
& ( ~ ( subset @ X1922 @ X1923 )
| ( in @ X1924 @ X1923 )
| ~ ( in @ X1924 @ X1922 ) )
& ( ~ ( in @ X1927 @ X1925 )
| ( in @ X1927 @ X1926 )
| ~ ( subset @ X1925 @ X1926 ) )
& ( ( subset @ X1928 @ X1929 )
| ( X1928 != X1929 ) )
& ( ~ ( in @ X1932 @ X1930 )
| ( in @ X1932 @ X1931 )
| ( X1930 != X1931 ) )
& ( subset @ X1933 @ X1933 )
& ( ~ ( subset @ X1934 @ X1935 )
| ~ ( subset @ X1935 @ X1936 )
| ( subset @ X1934 @ X1936 ) )
& ( subset @ X1938 @ ( setadjoin @ X1937 @ X1938 ) )
& ( ~ ( subset @ X1939 @ X1941 )
| ( subset @ X1939 @ ( setadjoin @ X1940 @ X1941 ) ) )
& ( ~ ( subset @ X1942 @ X1943 )
| ( in @ X1942 @ ( powerset @ X1943 ) ) )
& ( ~ ( subset @ X1944 @ X1945 )
| ~ ( subset @ X1945 @ X1944 )
| ( X1944 = X1945 ) )
& ( ~ ( subset @ X1946 @ emptyset )
| ( X1946 = emptyset ) )
& ( ~ ( subset @ X1948 @ X1947 )
| ( in @ X1948 @ ( powerset @ X1947 ) ) )
& ( ~ ( in @ X1950 @ ( powerset @ X1949 ) )
| ( subset @ X1950 @ X1949 ) )
& ( in @ X1951 @ ( powerset @ X1951 ) )
& ( ~ ( subset @ X1952 @ X1953 )
| ( subset @ ( powerset @ X1952 ) @ ( powerset @ X1953 ) ) )
& ( in @ ( dsetconstr @ X1954 @ X1955 ) @ ( powerset @ X1954 ) )
& ( subset @ ( dsetconstr @ X1956 @ X1957 ) @ X1956 )
& ( ~ ( in @ X1960 @ X1958 )
| ( in @ X1960 @ ( binunion @ X1958 @ X1959 ) ) )
& ( in @ X1962 @ ( setadjoin @ X1961 @ ( setadjoin @ X1962 @ emptyset ) ) )
& ( ~ ( in @ X1965 @ X1964 )
| ( in @ X1965 @ ( binunion @ X1963 @ X1964 ) ) )
& ( ( in @ X1968 @ X1967 )
| X1969
| ( in @ X1968 @ X1966 )
| ~ ( in @ X1968 @ ( binunion @ X1966 @ X1967 ) ) )
& ( ~ X1969
| X1969
| ( in @ X1968 @ X1966 )
| ~ ( in @ X1968 @ ( binunion @ X1966 @ X1967 ) ) )
& ( ( in @ X1968 @ X1967 )
| X1969
| ~ X1969
| ~ ( in @ X1968 @ ( binunion @ X1966 @ X1967 ) ) )
& ( ~ X1969
| X1969
| ~ X1969
| ~ ( in @ X1968 @ ( binunion @ X1966 @ X1967 ) ) )
& ( ~ ( in @ X1972 @ ( binunion @ X1970 @ X1971 ) )
| ( in @ X1972 @ X1970 )
| ( in @ X1972 @ X1971 ) )
& ( subset @ X1973 @ ( binunion @ X1973 @ X1974 ) )
& ( subset @ X1976 @ ( binunion @ X1975 @ X1976 ) )
& ( ~ ( in @ X1979 @ X1977 )
| ~ ( in @ X1979 @ X1978 )
| ( in @ X1979 @ ( binintersect @ X1977 @ X1978 ) ) )
& ( ~ ( subset @ X1982 @ X1980 )
| ~ ( subset @ X1982 @ X1981 )
| ( subset @ X1982 @ ( binintersect @ X1980 @ X1981 ) ) )
& ( ~ ( in @ X1985 @ ( binintersect @ X1983 @ X1984 ) )
| ( in @ X1985 @ X1983 ) )
& ( subset @ ( binintersect @ X1986 @ X1987 ) @ X1986 )
& ( ~ ( subset @ X1988 @ X1989 )
| ( ( binintersect @ X1988 @ X1989 )
= X1988 ) )
& ( ( ( binintersect @ X1990 @ X1991 )
!= X1991 )
| ( subset @ X1991 @ X1990 ) )
& ( ~ ( in @ X1994 @ ( binintersect @ X1992 @ X1993 ) )
| ( in @ X1994 @ X1993 ) )
& ( ( in @ ( esk38_2 @ X1995 @ X1996 ) @ X1995 )
| ( ( binintersect @ X1995 @ X1996 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1995 @ X1996 ) @ X1996 )
| ( ( binintersect @ X1995 @ X1996 )
= emptyset ) )
& ( subset @ ( binintersect @ X1998 @ X1999 ) @ X1999 )
& ( ~ ( subset @ X2001 @ X2000 )
| ( ( binintersect @ X2000 @ X2001 )
= X2001 ) )
& ( ( ( binintersect @ X2002 @ X2003 )
!= X2002 )
| ( subset @ X2002 @ X2003 ) )
& ( ( binintersect @ X2004 @ ( binunion @ X2005 @ X2006 ) )
= ( binunion @ ( binintersect @ X2004 @ X2005 ) @ ( binintersect @ X2004 @ X2006 ) ) )
& ( ~ ( in @ X2009 @ X2007 )
| ( in @ X2009 @ X2008 )
| ( in @ X2009 @ ( setminus @ X2007 @ X2008 ) ) )
& ( ~ ( in @ X2012 @ ( setminus @ X2010 @ X2011 ) )
| ( in @ X2012 @ X2010 ) )
& ( ~ ( in @ X2015 @ ( setminus @ X2013 @ X2014 ) )
| ~ ( in @ X2015 @ X2014 ) )
& ( ~ ( subset @ X2016 @ X2017 )
| ( ( setminus @ X2016 @ X2017 )
= emptyset ) )
& ( ( in @ X2020 @ ( setminus @ X2018 @ X2019 ) )
| ~ ( in @ X2020 @ X2018 )
| ( in @ X2020 @ X2019 ) )
& ( ( in @ X2023 @ ( setminus @ X2021 @ X2022 ) )
| ( in @ X2023 @ X2022 )
| ~ ( in @ X2023 @ X2021 ) )
& ( ( in @ X2026 @ X2024 )
| ~ ( in @ X2026 @ ( setminus @ X2024 @ X2025 ) ) )
& ( ~ ( in @ X2029 @ X2028 )
| ~ ( in @ X2029 @ ( setminus @ X2027 @ X2028 ) ) )
& ( subset @ ( setminus @ X2030 @ X2031 ) @ X2030 )
& ( ( ( setminus @ X2032 @ X2033 )
!= emptyset )
| ( subset @ X2032 @ X2033 ) )
& ( ~ ( in @ X2036 @ X2034 )
| X2037
| ( in @ X2036 @ X2034 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ( in @ X2036 @ X2035 )
| X2037
| ( in @ X2036 @ X2034 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ X2037
| X2037
| ( in @ X2036 @ X2034 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ ( in @ X2036 @ X2034 )
| X2037
| ~ ( in @ X2036 @ X2035 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ( in @ X2036 @ X2035 )
| X2037
| ~ ( in @ X2036 @ X2035 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ X2037
| X2037
| ~ ( in @ X2036 @ X2035 )
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ ( in @ X2036 @ X2034 )
| X2037
| ~ X2037
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ( in @ X2036 @ X2035 )
| X2037
| ~ X2037
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ X2037
| X2037
| ~ X2037
| ~ ( in @ X2036 @ ( symdiff @ X2034 @ X2035 ) ) )
& ( ~ ( in @ X2040 @ X2038 )
| ( in @ X2040 @ X2039 )
| ( in @ X2040 @ ( symdiff @ X2038 @ X2039 ) ) )
& ( ( in @ X2043 @ X2041 )
| ~ ( in @ X2043 @ X2042 )
| ( in @ X2043 @ ( symdiff @ X2041 @ X2042 ) ) )
& ( ~ ( in @ X2046 @ X2044 )
| ~ ( in @ X2046 @ X2045 )
| ~ ( in @ X2046 @ ( symdiff @ X2044 @ X2045 ) ) )
& ( ( in @ X2049 @ X2047 )
| ( in @ X2049 @ X2048 )
| ~ ( in @ X2049 @ ( symdiff @ X2047 @ X2048 ) ) )
& ( in @ X2051 @ ( setadjoin @ X2050 @ ( setadjoin @ X2051 @ emptyset ) ) )
& ( in @ X2052 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2052 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2052 @ ( setadjoin @ X2053 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2055 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2054 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2054 @ ( setadjoin @ X2055 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2056 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2056 @ ( setadjoin @ X2057 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2058 @ X2059 ) )
& ( ~ ( in @ X2061 @ X2060 )
| ( subset @ ( setadjoin @ X2061 @ emptyset ) @ X2060 ) )
& ( ~ ( in @ X2063 @ X2062 )
| ( in @ ( setadjoin @ X2063 @ emptyset ) @ ( powerset @ X2062 ) ) )
& ( ~ ( in @ X2066 @ X2064 )
| ( in @ ( setadjoin @ X2066 @ emptyset ) @ ( powerset @ ( binunion @ X2064 @ X2065 ) ) ) )
& ( ~ ( in @ X2069 @ ( setadjoin @ X2067 @ ( setadjoin @ X2068 @ emptyset ) ) )
| ( X2069 = X2067 )
| ( X2069 = X2068 ) )
& ( ~ ( in @ X2072 @ X2070 )
| ~ ( in @ X2073 @ X2071 )
| ( subset @ ( setadjoin @ X2072 @ ( setadjoin @ X2073 @ emptyset ) ) @ ( binunion @ X2070 @ X2071 ) ) )
& ( ~ ( in @ X2076 @ X2074 )
| ~ ( in @ X2077 @ X2075 )
| ( in @ ( setadjoin @ X2076 @ ( setadjoin @ X2077 @ emptyset ) ) @ ( powerset @ ( binunion @ X2074 @ X2075 ) ) ) )
& ( ~ ( in @ X2080 @ X2078 )
| ~ ( in @ X2081 @ X2079 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2080 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2080 @ ( setadjoin @ X2081 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2078 @ X2079 ) ) ) )
& ( ~ ( in @ X2084 @ X2082 )
| ~ ( in @ X2085 @ X2083 )
| ( in @ ( setadjoin @ ( setadjoin @ X2084 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2084 @ ( setadjoin @ X2085 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2082 @ X2083 ) ) ) ) )
& ( ~ ( in @ X2088 @ X2086 )
| ~ ( in @ X2089 @ X2087 )
| ( in @ ( kpair @ X2088 @ X2089 ) @ ( powerset @ ( powerset @ ( binunion @ X2086 @ X2087 ) ) ) ) )
& ( ~ ( in @ X2092 @ X2090 )
| ~ ( in @ X2093 @ X2091 )
| ( in @ ( kpair @ X2092 @ X2093 ) @ ( cartprod @ X2090 @ X2091 ) ) )
& ( ( in @ ( esk39_3 @ X2094 @ X2095 @ X2096 ) @ X2094 )
| ~ ( in @ X2096 @ ( cartprod @ X2094 @ X2095 ) ) )
& ( ( in @ ( esk40_3 @ X2094 @ X2095 @ X2096 ) @ X2095 )
| ~ ( in @ X2096 @ ( cartprod @ X2094 @ X2095 ) ) )
& ( ( X2096
= ( kpair @ ( esk39_3 @ X2094 @ X2095 @ X2096 ) @ ( esk40_3 @ X2094 @ X2095 @ X2096 ) ) )
| ~ ( in @ X2096 @ ( cartprod @ X2094 @ X2095 ) ) )
& ( ~ ( in @ X2101 @ ( cartprod @ X2099 @ X2100 ) )
| ( iskpair @ X2101 ) )
& ( ( in @ ( esk41_2 @ X2102 @ X2103 ) @ X2102 )
| ~ ( in @ X2103 @ ( setunion @ X2102 ) ) )
& ( ( in @ X2103 @ ( esk41_2 @ X2102 @ X2103 ) )
| ~ ( in @ X2103 @ ( setunion @ X2102 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2105 @ emptyset ) ) @ X2105 )
& ( subset @ X2106 @ ( setunion @ ( setadjoin @ X2106 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2107 @ emptyset ) )
= X2107 )
& ( ( in @ ( esk42_2 @ X2108 @ X2109 ) @ X2108 )
| ~ ( in @ X2112 @ X2108 )
| ~ ( X2109 @ X2112 )
| ( singleton @ ( dsetconstr @ X2108 @ X2109 ) ) )
& ( ( in @ ( esk43_2 @ X2108 @ X2109 ) @ X2108 )
| ~ ( in @ X2112 @ X2108 )
| ~ ( X2109 @ X2112 )
| ( singleton @ ( dsetconstr @ X2108 @ X2109 ) ) )
& ( ( X2109 @ ( esk42_2 @ X2108 @ X2109 ) )
| ~ ( in @ X2112 @ X2108 )
| ~ ( X2109 @ X2112 )
| ( singleton @ ( dsetconstr @ X2108 @ X2109 ) ) )
& ( ( X2109 @ ( esk43_2 @ X2108 @ X2109 ) )
| ~ ( in @ X2112 @ X2108 )
| ~ ( X2109 @ X2112 )
| ( singleton @ ( dsetconstr @ X2108 @ X2109 ) ) )
& ( ( ( esk42_2 @ X2108 @ X2109 )
!= ( esk43_2 @ X2108 @ X2109 ) )
| ~ ( in @ X2112 @ X2108 )
| ~ ( X2109 @ X2112 )
| ( singleton @ ( dsetconstr @ X2108 @ X2109 ) ) )
& ( ( in @ ( esk44_2 @ X2113 @ X2114 ) @ X2113 )
| ~ ( ex1 @ X2113 @ X2114 ) )
& ( ( X2114 @ ( esk44_2 @ X2113 @ X2114 ) )
| ~ ( ex1 @ X2113 @ X2114 ) )
& ( ( in @ ( esk45_3 @ X2116 @ X2117 @ X2118 ) @ X2116 )
| ( ex1 @ X2116 @ X2117 )
| ~ ( X2117 @ X2118 )
| ~ ( in @ X2118 @ X2116 ) )
& ( ( X2117 @ ( esk45_3 @ X2116 @ X2117 @ X2118 ) )
| ( ex1 @ X2116 @ X2117 )
| ~ ( X2117 @ X2118 )
| ~ ( in @ X2118 @ X2116 ) )
& ( ( ( esk45_3 @ X2116 @ X2117 @ X2118 )
!= X2118 )
| ( ex1 @ X2116 @ X2117 )
| ~ ( X2117 @ X2118 )
| ~ ( in @ X2118 @ X2116 ) )
& ( ( in @ ( esk46_2 @ X2120 @ X2121 ) @ X2120 )
| ~ ( in @ X2124 @ X2120 )
| ~ ( X2121 @ X2124 )
| ( ex1 @ X2120 @ X2121 ) )
& ( ( in @ ( esk47_2 @ X2120 @ X2121 ) @ X2120 )
| ~ ( in @ X2124 @ X2120 )
| ~ ( X2121 @ X2124 )
| ( ex1 @ X2120 @ X2121 ) )
& ( ( X2121 @ ( esk46_2 @ X2120 @ X2121 ) )
| ~ ( in @ X2124 @ X2120 )
| ~ ( X2121 @ X2124 )
| ( ex1 @ X2120 @ X2121 ) )
& ( ( X2121 @ ( esk47_2 @ X2120 @ X2121 ) )
| ~ ( in @ X2124 @ X2120 )
| ~ ( X2121 @ X2124 )
| ( ex1 @ X2120 @ X2121 ) )
& ( ( ( esk46_2 @ X2120 @ X2121 )
!= ( esk47_2 @ X2120 @ X2121 ) )
| ~ ( in @ X2124 @ X2120 )
| ~ ( X2121 @ X2124 )
| ( ex1 @ X2120 @ X2121 ) )
& ( ( ( setadjoin @ X2125 @ emptyset )
!= ( setadjoin @ X2126 @ emptyset ) )
| ( X2125 = X2126 ) )
& ( ~ ( in @ ( setadjoin @ X2129 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2127 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2127 @ ( setadjoin @ X2128 @ emptyset ) ) @ emptyset ) ) )
| ( X2127 = X2129 ) )
& ( ~ ( iskpair @ X2130 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2130 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2130 ) ) ) )
& ( ~ ( singleton @ X2131 )
| ( in @ ( setunion @ X2131 ) @ X2131 ) )
& ( ( kfst @ ( kpair @ X2132 @ X2133 ) )
= X2132 )
& ( ~ ( in @ X2136 @ ( cartprod @ X2134 @ X2135 ) )
| ( in @ ( kfst @ X2136 ) @ X2134 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2137 @ ( setadjoin @ X2138 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2139 @ ( setadjoin @ X2140 @ emptyset ) ) @ emptyset ) ) )
| ( X2137 = X2139 ) )
& ( ( ( kpair @ X2141 @ X2142 )
!= ( kpair @ X2143 @ X2144 ) )
| ( X2141 = X2143 ) )
& ( ( X2145 != X2146 )
| ( ( setadjoin @ X2145 @ ( setadjoin @ X2146 @ emptyset ) )
= ( setadjoin @ X2145 @ emptyset ) ) )
& ( ( X2147 != X2148 )
| ( ( setadjoin @ ( setadjoin @ X2147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2147 @ ( setadjoin @ X2148 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2147 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2149 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2149 @ ( setadjoin @ X2150 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2151 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2151 @ ( setadjoin @ X2152 @ emptyset ) ) @ emptyset ) ) )
| ( X2151 != X2152 )
| ( X2150 = X2152 ) )
& ( ( ( setadjoin @ X2153 @ ( setadjoin @ X2154 @ emptyset ) )
!= ( setadjoin @ X2155 @ emptyset ) )
| ( X2153 = X2154 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2156 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2156 @ ( setadjoin @ X2157 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2158 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2158 @ ( setadjoin @ X2159 @ emptyset ) ) @ emptyset ) ) )
| ( X2157 = X2159 ) )
& ( ( ( kpair @ X2160 @ X2161 )
!= ( kpair @ X2162 @ X2163 ) )
| ( X2161 = X2163 ) )
& ( ~ ( iskpair @ X2164 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2164 )
@ ^ [Z0: $i] :
( X2164
= ( kpair @ ( kfst @ X2164 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2165 @ X2166 ) )
= X2166 )
& ( ~ ( iskpair @ X2167 )
| ( ( kpair @ ( kfst @ X2167 ) @ ( ksnd @ X2167 ) )
= X2167 ) )
& ( ~ ( in @ X2170 @ ( cartprod @ X2168 @ X2169 ) )
| ( in @ ( ksnd @ X2170 ) @ X2169 ) )
& ( ~ ( in @ ( kpair @ X2173 @ X2174 ) @ ( cartprod @ X2171 @ X2172 ) )
| ( in @ X2173 @ X2171 ) )
& ( ~ ( in @ ( kpair @ X2177 @ X2178 ) @ ( cartprod @ X2175 @ X2176 ) )
| ( in @ X2178 @ X2176 ) )
& ( ~ ( in @ X2181 @ X2179 )
| ~ ( in @ X2182 @ X2180 )
| ( ( kpair @ X2181 @ X2182 )
= ( kpair @ X2181 @ X2182 ) ) )
& ( ~ ( in @ X2185 @ X2183 )
| ~ ( in @ X2186 @ X2184 )
| ( ( kfst @ ( kpair @ X2185 @ X2186 ) )
= X2185 ) )
& ( ~ ( in @ X2189 @ X2187 )
| ~ ( in @ X2190 @ X2188 )
| ( ( ksnd @ ( kpair @ X2189 @ X2190 ) )
= X2190 ) )
& ( ~ ( in @ X2193 @ ( cartprod @ X2191 @ X2192 ) )
| ( ( kpair @ ( kfst @ X2193 ) @ ( ksnd @ X2193 ) )
= X2193 ) )
& ( ~ ( in @ X2197 @ X2194 )
| ~ ( in @ X2198 @ X2195 )
| ~ ( X2196 @ X2197 @ X2198 )
| ( in @ ( kpair @ X2197 @ X2198 ) @ ( dpsetconstr @ X2194 @ X2195 @ X2196 ) ) )
& ( subset @ ( dpsetconstr @ X2199 @ X2200 @ X2201 ) @ ( cartprod @ X2199 @ X2200 ) )
& ( breln @ X2202 @ X2203 @ ( dpsetconstr @ X2202 @ X2203 @ X2204 ) )
& ( ~ ( in @ X2208 @ X2205 )
| ~ ( in @ X2209 @ X2206 )
| ~ ( in @ ( kpair @ X2208 @ X2209 ) @ ( dpsetconstr @ X2205 @ X2206 @ X2207 ) )
| ( X2207 @ X2208 @ X2209 ) )
& ( ~ ( in @ ( kpair @ X2213 @ X2214 ) @ ( dpsetconstr @ X2210 @ X2211 @ X2212 ) )
| ( in @ X2213 @ X2210 ) )
& ( ~ ( in @ ( kpair @ X2218 @ X2219 ) @ ( dpsetconstr @ X2215 @ X2216 @ X2217 ) )
| ( in @ X2219 @ X2216 ) )
& ( ~ ( in @ ( kpair @ X2223 @ X2224 ) @ ( dpsetconstr @ X2220 @ X2221 @ X2222 ) )
| ( X2222 @ X2223 @ X2224 ) )
& ( ~ ( func @ X2225 @ X2226 @ X2227 )
| ~ ( in @ X2228 @ X2225 )
| ( singleton
@ ( dsetconstr @ X2226
@ ^ [Z0: $i] : ( in @ ( kpair @ X2228 @ Z0 ) @ X2227 ) ) ) )
& ( ~ ( func @ X2229 @ X2230 @ X2231 )
| ~ ( in @ X2232 @ X2229 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2230
@ ^ [Z0: $i] : ( in @ ( kpair @ X2232 @ Z0 ) @ X2231 ) ) )
@ X2230 ) )
& ( ~ ( func @ X2233 @ X2234 @ X2235 )
| ~ ( in @ X2236 @ X2233 )
| ( in @ ( ap @ X2233 @ X2234 @ X2235 @ X2236 ) @ X2234 ) )
& ( ~ ( in @ X2239 @ ( funcSet @ X2237 @ X2238 ) )
| ( func @ X2237 @ X2238 @ X2239 ) )
& ( ~ ( in @ X2242 @ ( funcSet @ X2240 @ X2241 ) )
| ~ ( in @ X2243 @ X2240 )
| ( in @ ( ap @ X2240 @ X2241 @ X2242 @ X2243 ) @ X2241 ) )
& ( ~ ( func @ X2244 @ X2245 @ X2246 )
| ( in @ X2246 @ ( funcSet @ X2244 @ X2245 ) ) )
& ( ( in @ ( esk48_3 @ X2247 @ X2248 @ X2249 ) @ X2247 )
| ( func @ X2247 @ X2248
@ ( dpsetconstr @ X2247 @ X2248
@ ^ [Z0: $i] : ( $eq @ ( X2249 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2249 @ ( esk48_3 @ X2247 @ X2248 @ X2249 ) ) @ X2248 )
| ( func @ X2247 @ X2248
@ ( dpsetconstr @ X2247 @ X2248
@ ^ [Z0: $i] : ( $eq @ ( X2249 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2251 @ X2252 @ X2253 ) @ X2251 )
| ( func @ X2251 @ X2252 @ ( lam @ X2251 @ X2252 @ X2253 ) ) )
& ( ~ ( in @ ( X2253 @ ( esk49_3 @ X2251 @ X2252 @ X2253 ) ) @ X2252 )
| ( func @ X2251 @ X2252 @ ( lam @ X2251 @ X2252 @ X2253 ) ) )
& ( ( in @ ( esk50_3 @ X2255 @ X2256 @ X2257 ) @ X2255 )
| ( in @ ( lam @ X2255 @ X2256 @ X2257 ) @ ( funcSet @ X2255 @ X2256 ) ) )
& ( ~ ( in @ ( X2257 @ ( esk50_3 @ X2255 @ X2256 @ X2257 ) ) @ X2256 )
| ( in @ ( lam @ X2255 @ X2256 @ X2257 ) @ ( funcSet @ X2255 @ X2256 ) ) )
& ( ( in @ ( esk51_4 @ X2259 @ X2260 @ X2261 @ X2262 ) @ X2259 )
| ~ ( in @ X2265 @ X2261 )
| ( X2262 @ X2265 )
| ~ ( breln @ X2259 @ X2260 @ X2261 ) )
& ( ( in @ ( esk52_4 @ X2259 @ X2260 @ X2261 @ X2262 ) @ X2260 )
| ~ ( in @ X2265 @ X2261 )
| ( X2262 @ X2265 )
| ~ ( breln @ X2259 @ X2260 @ X2261 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2259 @ X2260 @ X2261 @ X2262 ) @ ( esk52_4 @ X2259 @ X2260 @ X2261 @ X2262 ) ) @ X2261 )
| ~ ( in @ X2265 @ X2261 )
| ( X2262 @ X2265 )
| ~ ( breln @ X2259 @ X2260 @ X2261 ) )
& ( ~ ( X2262 @ ( kpair @ ( esk51_4 @ X2259 @ X2260 @ X2261 @ X2262 ) @ ( esk52_4 @ X2259 @ X2260 @ X2261 @ X2262 ) ) )
| ~ ( in @ X2265 @ X2261 )
| ( X2262 @ X2265 )
| ~ ( breln @ X2259 @ X2260 @ X2261 ) )
& ( ( in @ ( esk53_4 @ X2266 @ X2267 @ X2268 @ X2269 ) @ X2266 )
| ~ ( in @ X2272 @ X2268 )
| ( X2269 @ X2272 )
| ~ ( breln @ X2266 @ X2267 @ X2268 ) )
& ( ( in @ ( esk54_4 @ X2266 @ X2267 @ X2268 @ X2269 ) @ X2267 )
| ~ ( in @ X2272 @ X2268 )
| ( X2269 @ X2272 )
| ~ ( breln @ X2266 @ X2267 @ X2268 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2266 @ X2267 @ X2268 @ X2269 ) @ ( esk54_4 @ X2266 @ X2267 @ X2268 @ X2269 ) ) @ X2268 )
| ~ ( in @ X2272 @ X2268 )
| ( X2269 @ X2272 )
| ~ ( breln @ X2266 @ X2267 @ X2268 ) )
& ( ~ ( X2269 @ ( kpair @ ( esk53_4 @ X2266 @ X2267 @ X2268 @ X2269 ) @ ( esk54_4 @ X2266 @ X2267 @ X2268 @ X2269 ) ) )
| ~ ( in @ X2272 @ X2268 )
| ( X2269 @ X2272 )
| ~ ( breln @ X2266 @ X2267 @ X2268 ) )
& ( ~ ( ex1 @ X2273 @ X2274 )
| ~ ( in @ X2275 @ X2273 )
| ~ ( in @ X2276 @ X2273 )
| ~ ( X2274 @ X2275 )
| ~ ( X2274 @ X2276 )
| ( X2275 = X2276 ) )
& ( ~ ( func @ X2277 @ X2278 @ X2279 )
| ~ ( in @ X2280 @ X2277 )
| ( in @ ( kpair @ X2280 @ ( ap @ X2277 @ X2278 @ X2279 @ X2280 ) ) @ X2279 ) )
& ( ~ ( in @ X2283 @ ( funcSet @ X2281 @ X2282 ) )
| ~ ( in @ X2284 @ X2281 )
| ( in @ ( kpair @ X2284 @ ( ap @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 ) )
& ( ~ ( func @ X2285 @ X2286 @ X2287 )
| ~ ( in @ X2288 @ X2285 )
| ~ ( in @ X2289 @ X2286 )
| ~ ( in @ ( kpair @ X2288 @ X2289 ) @ X2287 )
| ( ( ap @ X2285 @ X2286 @ X2287 @ X2288 )
= X2289 ) )
& ( ( in @ ( esk55_4 @ X2290 @ X2291 @ X2292 @ X2293 ) @ X2290 )
| ~ ( in @ X2295 @ X2290 )
| ~ ( in @ X2296 @ X2291 )
| ~ ( in @ ( kpair @ X2295 @ X2296 ) @ X2293 )
| ( in @ ( kpair @ X2295 @ X2296 ) @ X2292 )
| ~ ( func @ X2290 @ X2291 @ X2293 )
| ~ ( func @ X2290 @ X2291 @ X2292 ) )
& ( ( ( ap @ X2290 @ X2291 @ X2292 @ ( esk55_4 @ X2290 @ X2291 @ X2292 @ X2293 ) )
!= ( ap @ X2290 @ X2291 @ X2293 @ ( esk55_4 @ X2290 @ X2291 @ X2292 @ X2293 ) ) )
| ~ ( in @ X2295 @ X2290 )
| ~ ( in @ X2296 @ X2291 )
| ~ ( in @ ( kpair @ X2295 @ X2296 ) @ X2293 )
| ( in @ ( kpair @ X2295 @ X2296 ) @ X2292 )
| ~ ( func @ X2290 @ X2291 @ X2293 )
| ~ ( func @ X2290 @ X2291 @ X2292 ) )
& ( ~ ( in @ X2299 @ ( funcSet @ X2297 @ X2298 ) )
| ~ ( in @ X2300 @ X2297 )
| ~ ( in @ X2301 @ X2298 )
| ~ ( in @ ( kpair @ X2300 @ X2301 ) @ X2299 )
| ( ( ap @ X2297 @ X2298 @ X2299 @ X2300 )
= X2301 ) )
& ( ( in @ ( esk56_4 @ X2302 @ X2303 @ X2304 @ X2305 ) @ X2302 )
| ( subset @ X2304 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2304 ) )
& ( ( in @ ( esk57_4 @ X2302 @ X2303 @ X2304 @ X2305 ) @ X2303 )
| ( subset @ X2304 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2304 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2302 @ X2303 @ X2304 @ X2305 ) @ ( esk57_4 @ X2302 @ X2303 @ X2304 @ X2305 ) ) @ X2304 )
| ( subset @ X2304 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2304 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2302 @ X2303 @ X2304 @ X2305 ) @ ( esk57_4 @ X2302 @ X2303 @ X2304 @ X2305 ) ) @ X2305 )
| ( subset @ X2304 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2305 )
| ~ ( breln @ X2302 @ X2303 @ X2304 ) )
& ( ( in @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ( X2310 = X2311 )
| ( in @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ( X2310 = X2311 )
| ( in @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ( X2310 = X2311 )
| ( in @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ( X2310 = X2311 )
| ( in @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ( X2310 = X2311 )
| ( in @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ( X2310 = X2311 )
| ( in @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ( X2310 = X2311 )
| ( in @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ( X2310 = X2311 )
| ( in @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ( X2310 = X2311 )
| ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ( X2310 = X2311 )
| ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ( X2310 = X2311 )
| ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ( X2310 = X2311 )
| ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2308 )
| ( X2310 = X2311 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ X2309 )
| ( X2310 = X2311 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ( X2310 = X2311 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk61_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2310 )
| ( X2310 = X2311 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2308 @ X2309 @ X2310 @ X2311 ) @ ( esk59_4 @ X2308 @ X2309 @ X2310 @ X2311 ) ) @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2311 )
| ~ ( breln @ X2308 @ X2309 @ X2310 ) )
& ( ( in @ ( esk62_4 @ X2316 @ X2317 @ X2318 @ X2319 ) @ X2316 )
| ( X2318 = X2319 )
| ~ ( func @ X2316 @ X2317 @ X2319 )
| ~ ( func @ X2316 @ X2317 @ X2318 ) )
& ( ( ( ap @ X2316 @ X2317 @ X2318 @ ( esk62_4 @ X2316 @ X2317 @ X2318 @ X2319 ) )
!= ( ap @ X2316 @ X2317 @ X2319 @ ( esk62_4 @ X2316 @ X2317 @ X2318 @ X2319 ) ) )
| ( X2318 = X2319 )
| ~ ( func @ X2316 @ X2317 @ X2319 )
| ~ ( func @ X2316 @ X2317 @ X2318 ) )
& ( ( in @ ( esk63_4 @ X2321 @ X2322 @ X2323 @ X2324 ) @ X2321 )
| ( X2323 = X2324 )
| ~ ( in @ X2324 @ ( funcSet @ X2321 @ X2322 ) )
| ~ ( in @ X2323 @ ( funcSet @ X2321 @ X2322 ) ) )
& ( ( ( ap @ X2321 @ X2322 @ X2323 @ ( esk63_4 @ X2321 @ X2322 @ X2323 @ X2324 ) )
!= ( ap @ X2321 @ X2322 @ X2324 @ ( esk63_4 @ X2321 @ X2322 @ X2323 @ X2324 ) ) )
| ( X2323 = X2324 )
| ~ ( in @ X2324 @ ( funcSet @ X2321 @ X2322 ) )
| ~ ( in @ X2323 @ ( funcSet @ X2321 @ X2322 ) ) )
& ( ~ ( in @ X2328 @ ( funcSet @ X2326 @ X2327 ) )
| ~ ( in @ X2329 @ X2326 )
| ( ( ap @ X2326 @ X2327 @ X2328 @ X2329 )
= ( ap @ X2326 @ X2327 @ X2328 @ X2329 ) ) )
& ( ~ ( func @ X2330 @ X2331 @ X2332 )
| ~ ( in @ X2333 @ X2330 )
| ( ( ap @ X2330 @ X2331 @ X2332 @ X2333 )
= ( ap @ X2330 @ X2331 @ X2332 @ X2333 ) ) )
& ( ( in @ ( esk64_3 @ X2334 @ X2335 @ X2336 ) @ X2334 )
| ~ ( in @ X2338 @ X2334 )
| ( ( ap @ X2334 @ X2335 @ ( lam @ X2334 @ X2335 @ X2336 ) @ X2338 )
= ( X2336 @ X2338 ) ) )
& ( ~ ( in @ ( X2336 @ ( esk64_3 @ X2334 @ X2335 @ X2336 ) ) @ X2335 )
| ~ ( in @ X2338 @ X2334 )
| ( ( ap @ X2334 @ X2335 @ ( lam @ X2334 @ X2335 @ X2336 ) @ X2338 )
= ( X2336 @ X2338 ) ) )
& ( ~ ( func @ X2339 @ X2340 @ X2341 )
| ( ( lam @ X2339 @ X2340 @ ( ap @ X2339 @ X2340 @ X2341 ) )
= X2341 ) )
& ( ( in @ ( esk65_3 @ X2342 @ X2343 @ X2344 ) @ X2342 )
| ( ( lam @ X2342 @ X2343 @ X2344 )
= ( lam @ X2342 @ X2343 @ X2344 ) ) )
& ( ~ ( in @ ( X2344 @ ( esk65_3 @ X2342 @ X2343 @ X2344 ) ) @ X2343 )
| ( ( lam @ X2342 @ X2343 @ X2344 )
= ( lam @ X2342 @ X2343 @ X2344 ) ) )
& ( ( in @ ( esk66_3 @ X2346 @ X2347 @ X2348 ) @ X2346 )
| ~ ( in @ X2350 @ X2346 )
| ( ( ap @ X2346 @ X2347 @ ( lam @ X2346 @ X2347 @ X2348 ) @ X2350 )
= ( X2348 @ X2350 ) ) )
& ( ~ ( in @ ( X2348 @ ( esk66_3 @ X2346 @ X2347 @ X2348 ) ) @ X2347 )
| ~ ( in @ X2350 @ X2346 )
| ( ( ap @ X2346 @ X2347 @ ( lam @ X2346 @ X2347 @ X2348 ) @ X2350 )
= ( X2348 @ X2350 ) ) )
& ( ~ ( in @ X2353 @ ( funcSet @ X2351 @ X2352 ) )
| ( ( lam @ X2351 @ X2352 @ ( ap @ X2351 @ X2352 @ X2353 ) )
= X2353 ) )
& ( ~ ( in @ X2356 @ X2354 )
| ~ ( in @ X2357 @ X2354 )
| X2355
| ( in @ X2357
@ ( dsetconstr @ X2354
@ ^ [Z0: $i] :
( ( X2355
& ( Z0 = X2356 ) )
| ( ~ X2355
& ( Z0 = X2357 ) ) ) ) ) )
& ( ~ ( in @ X2360 @ X2358 )
| ~ ( in @ X2361 @ X2358 )
| X2359
| ( ( dsetconstr @ X2358
@ ^ [Z0: $i] :
( ( X2359
& ( Z0 = X2360 ) )
| ( ~ X2359
& ( Z0 = X2361 ) ) ) )
= ( setadjoin @ X2361 @ emptyset ) ) )
& ( ~ ( in @ X2364 @ X2362 )
| ~ ( in @ X2365 @ X2362 )
| ~ X2363
| ( in @ X2364
@ ( dsetconstr @ X2362
@ ^ [Z0: $i] :
( ( X2363
& ( Z0 = X2364 ) )
| ( ~ X2363
& ( Z0 = X2365 ) ) ) ) ) )
& ( ~ ( in @ X2368 @ X2366 )
| ~ ( in @ X2369 @ X2366 )
| ~ X2367
| ( ( dsetconstr @ X2366
@ ^ [Z0: $i] :
( ( X2367
& ( Z0 = X2368 ) )
| ( ~ X2367
& ( Z0 = X2369 ) ) ) )
= ( setadjoin @ X2368 @ emptyset ) ) )
& ( ~ ( in @ X2372 @ X2370 )
| ~ ( in @ X2373 @ X2370 )
| ( singleton
@ ( dsetconstr @ X2370
@ ^ [Z0: $i] :
( ( X2371
& ( Z0 = X2372 ) )
| ( ~ X2371
& ( Z0 = X2373 ) ) ) ) ) )
& ( ~ ( in @ X2376 @ X2374 )
| ~ ( in @ X2377 @ X2374 )
| ( in @ ( if @ X2374 @ X2375 @ X2376 @ X2377 ) @ X2374 ) )
& ( ~ ( singleton @ X2378 )
| ~ ( in @ X2379 @ X2378 )
| ( ( setunion @ X2378 )
= X2379 ) )
& ( ~ ( in @ X2382 @ X2380 )
| ~ ( in @ X2383 @ X2380 )
| ~ X2381
| ( ( if @ X2380 @ X2381 @ X2382 @ X2383 )
= X2382 ) )
& ( ~ ( in @ X2386 @ X2384 )
| ~ ( in @ X2387 @ X2384 )
| X2385
| ( ( if @ X2384 @ X2385 @ X2386 @ X2387 )
= X2387 ) )
& ( ~ ( in @ X2390 @ X2388 )
| ~ ( in @ X2391 @ X2388 )
| ( in @ ( if @ X2388 @ X2389 @ X2390 @ X2391 ) @ ( setadjoin @ X2390 @ ( setadjoin @ X2391 @ emptyset ) ) ) )
& ( ~ ( in @ X2393 @ ( powerset @ X2392 ) )
| ~ ( in @ X2394 @ ( powerset @ X2392 ) )
| ( in @ ( binintersect @ X2393 @ X2394 ) @ ( powerset @ X2392 ) ) )
& ( ~ ( in @ X2396 @ ( powerset @ X2395 ) )
| ~ ( in @ X2397 @ ( powerset @ X2395 ) )
| ( in @ ( binunion @ X2396 @ X2397 ) @ ( powerset @ X2395 ) ) )
& ( ~ ( in @ X2399 @ ( powerset @ X2398 ) )
| ( in @ ( powerset @ X2399 ) @ ( powerset @ ( powerset @ X2398 ) ) ) )
& ( ~ ( in @ X2401 @ ( powerset @ X2400 ) )
| ~ ( in @ X2402 @ ( powerset @ X2400 ) )
| ( in @ ( setminus @ X2401 @ X2402 ) @ ( powerset @ X2400 ) ) )
& ( ~ ( in @ X2404 @ ( powerset @ X2403 ) )
| ( in @ ( setminus @ X2403 @ X2404 ) @ ( powerset @ X2403 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ( X2406 = X2407 )
| ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2405 )
| ( X2406 = X2407 )
| ~ ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ( X2406 = X2407 )
| ~ ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2405 @ X2406 @ X2407 ) @ X2406 )
| ( X2406 = X2407 )
| ~ ( in @ ( esk67_3 @ X2405 @ X2406 @ X2407 ) @ X2407 )
| ~ ( in @ X2407 @ ( powerset @ X2405 ) )
| ~ ( in @ X2406 @ ( powerset @ X2405 ) ) )
& ( ( in @ ( esk69_3 @ X2410 @ X2411 @ X2412 ) @ X2410 )
| ( subset @ X2411 @ X2412 )
| ~ ( in @ X2412 @ ( powerset @ X2410 ) )
| ~ ( in @ X2411 @ ( powerset @ X2410 ) ) )
& ( ( in @ ( esk69_3 @ X2410 @ X2411 @ X2412 ) @ X2411 )
| ( subset @ X2411 @ X2412 )
| ~ ( in @ X2412 @ ( powerset @ X2410 ) )
| ~ ( in @ X2411 @ ( powerset @ X2410 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2410 @ X2411 @ X2412 ) @ X2412 )
| ( subset @ X2411 @ X2412 )
| ~ ( in @ X2412 @ ( powerset @ X2410 ) )
| ~ ( in @ X2411 @ ( powerset @ X2410 ) ) )
& ( ( in @ ( esk70_3 @ X2414 @ X2415 @ X2416 ) @ X2414 )
| ( in @ X2415 @ ( powerset @ X2416 ) )
| ~ ( in @ X2416 @ ( powerset @ X2414 ) )
| ~ ( in @ X2415 @ ( powerset @ X2414 ) ) )
& ( ( in @ ( esk70_3 @ X2414 @ X2415 @ X2416 ) @ X2415 )
| ( in @ X2415 @ ( powerset @ X2416 ) )
| ~ ( in @ X2416 @ ( powerset @ X2414 ) )
| ~ ( in @ X2415 @ ( powerset @ X2414 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2414 @ X2415 @ X2416 ) @ X2416 )
| ( in @ X2415 @ ( powerset @ X2416 ) )
| ~ ( in @ X2416 @ ( powerset @ X2414 ) )
| ~ ( in @ X2415 @ ( powerset @ X2414 ) ) )
& ( ~ ( in @ X2419 @ ( powerset @ X2418 ) )
| ~ ( in @ X2420 @ ( powerset @ X2418 ) )
| ~ ( in @ X2421 @ X2418 )
| ~ ( in @ X2419 @ ( powerset @ X2420 ) )
| ~ ( in @ X2421 @ X2419 )
| ( in @ X2421 @ X2420 ) )
& ( ~ ( in @ X2423 @ ( powerset @ X2422 ) )
| ~ ( in @ X2424 @ X2422 )
| ~ ( in @ X2424 @ X2423 )
| ~ ( in @ X2424 @ ( setminus @ X2422 @ X2423 ) ) )
& ( ~ ( in @ X2426 @ ( powerset @ X2425 ) )
| ~ ( in @ X2427 @ X2425 )
| ( in @ X2427 @ ( setminus @ X2425 @ X2426 ) )
| ( in @ X2427 @ X2426 ) )
& ( ~ ( in @ X2429 @ ( powerset @ X2428 ) )
| ~ ( in @ X2430 @ ( powerset @ X2428 ) )
| ~ ( in @ X2431 @ X2428 )
| ( in @ X2431 @ X2429 )
| ~ ( in @ X2431 @ ( binintersect @ X2429 @ X2430 ) ) )
& ( ~ ( in @ X2433 @ ( powerset @ X2432 ) )
| ~ ( in @ X2434 @ ( powerset @ X2432 ) )
| ~ ( in @ X2435 @ X2432 )
| ( in @ X2435 @ X2434 )
| ~ ( in @ X2435 @ ( binintersect @ X2433 @ X2434 ) ) )
& ( ~ ( in @ X2437 @ ( powerset @ X2436 ) )
| ~ ( in @ X2438 @ ( powerset @ X2436 ) )
| ~ ( in @ X2439 @ X2436 )
| ~ ( subset @ X2437 @ ( setminus @ X2436 @ X2438 ) )
| ~ ( in @ X2439 @ X2438 )
| ~ ( in @ X2439 @ X2437 ) )
& ( ~ ( in @ X2441 @ ( powerset @ X2440 ) )
| ~ ( in @ X2442 @ ( powerset @ X2440 ) )
| ~ ( in @ X2443 @ X2440 )
| ~ ( subset @ X2441 @ X2442 )
| ( in @ X2443 @ X2442 )
| ~ ( in @ X2443 @ X2441 ) )
& ( ~ ( in @ X2445 @ ( powerset @ X2444 ) )
| ~ ( in @ X2446 @ ( powerset @ X2444 ) )
| ~ ( subset @ X2445 @ X2446 )
| ( subset @ ( setminus @ X2444 @ X2446 ) @ ( setminus @ X2444 @ X2445 ) ) )
& ( ~ ( in @ X2448 @ ( powerset @ X2447 ) )
| ~ ( in @ X2449 @ ( powerset @ X2447 ) )
| ~ ( subset @ ( setminus @ X2447 @ X2449 ) @ ( setminus @ X2447 @ X2448 ) )
| ( subset @ X2448 @ X2449 ) )
& ( ~ ( in @ X2451 @ ( powerset @ X2450 ) )
| ~ ( in @ X2452 @ X2450 )
| ~ ( in @ X2452 @ X2451 )
| ( in @ X2452 @ ( setminus @ X2450 @ ( setminus @ X2450 @ X2451 ) ) ) )
& ( ~ ( in @ X2454 @ ( powerset @ X2453 ) )
| ~ ( in @ X2455 @ X2453 )
| ~ ( in @ X2455 @ ( setminus @ X2453 @ ( setminus @ X2453 @ X2454 ) ) )
| ( in @ X2455 @ X2454 ) )
& ( ~ ( in @ X2457 @ ( powerset @ X2456 ) )
| ( subset @ X2457 @ ( setminus @ X2456 @ ( setminus @ X2456 @ X2457 ) ) ) )
& ( ~ ( in @ X2459 @ ( powerset @ X2458 ) )
| ( subset @ ( setminus @ X2458 @ ( setminus @ X2458 @ X2459 ) ) @ X2459 ) )
& ( ~ ( in @ X2461 @ ( powerset @ X2460 ) )
| ( X2461
= ( setminus @ X2460 @ ( setminus @ X2460 @ X2461 ) ) ) )
& ( ~ ( in @ X2463 @ ( powerset @ X2462 ) )
| ~ ( in @ X2464 @ ( powerset @ X2462 ) )
| ~ ( in @ X2465 @ X2462 )
| ~ ( in @ X2465 @ ( setminus @ X2462 @ X2463 ) )
| ~ ( in @ X2465 @ ( binintersect @ X2463 @ X2464 ) ) )
& ( ~ ( in @ X2467 @ ( powerset @ X2466 ) )
| ~ ( in @ X2468 @ ( powerset @ X2466 ) )
| ~ ( in @ X2469 @ X2466 )
| ~ ( in @ X2469 @ ( setminus @ X2466 @ X2467 ) )
| ( in @ X2469 @ ( setminus @ X2466 @ ( binintersect @ X2467 @ X2468 ) ) ) )
& ( ~ ( in @ X2471 @ ( powerset @ X2470 ) )
| ~ ( in @ X2472 @ ( powerset @ X2470 ) )
| ( subset @ ( setminus @ X2470 @ X2471 ) @ ( setminus @ X2470 @ ( binintersect @ X2471 @ X2472 ) ) ) )
& ( ~ ( in @ X2474 @ ( powerset @ X2473 ) )
| ~ ( in @ X2475 @ ( powerset @ X2473 ) )
| ( in @ ( setminus @ X2473 @ X2474 ) @ ( powerset @ ( setminus @ X2473 @ ( binintersect @ X2474 @ X2475 ) ) ) ) )
& ( ~ ( in @ X2477 @ ( powerset @ X2476 ) )
| ~ ( in @ X2478 @ ( powerset @ X2476 ) )
| ~ ( subset @ X2477 @ ( setminus @ X2476 @ X2478 ) )
| ~ ( in @ X2479 @ X2476 )
| ~ ( in @ X2479 @ X2478 )
| ( in @ X2479 @ ( setminus @ X2476 @ X2477 ) ) )
& ( ~ ( in @ X2481 @ ( powerset @ X2480 ) )
| ~ ( in @ X2482 @ ( powerset @ X2480 ) )
| ~ ( subset @ X2481 @ ( setminus @ X2480 @ X2482 ) )
| ( subset @ X2482 @ ( setminus @ X2480 @ X2481 ) ) )
& ( ~ ( in @ X2484 @ ( powerset @ X2483 ) )
| ~ ( in @ X2485 @ ( powerset @ X2483 ) )
| ~ ( in @ X2486 @ X2483 )
| ( in @ X2486 @ ( binunion @ X2484 @ X2485 ) )
| ~ ( in @ X2486 @ X2484 ) )
& ( ~ ( in @ X2488 @ ( powerset @ X2487 ) )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2490 @ X2487 )
| ( in @ X2490 @ ( binunion @ X2488 @ X2489 ) )
| ~ ( in @ X2490 @ X2489 ) )
& ( ~ ( in @ X2492 @ ( powerset @ X2491 ) )
| ~ ( in @ X2493 @ ( powerset @ X2491 ) )
| ~ ( in @ X2494 @ ( powerset @ X2491 ) )
| ~ ( in @ X2495 @ X2491 )
| ~ ( in @ X2495 @ ( binintersect @ X2492 @ X2493 ) )
| ( in @ X2495 @ ( binunion @ X2492 @ X2494 ) ) )
& ( ~ ( in @ X2497 @ ( powerset @ X2496 ) )
| ~ ( in @ X2498 @ ( powerset @ X2496 ) )
| ~ ( in @ X2499 @ ( powerset @ X2496 ) )
| ~ ( in @ X2500 @ X2496 )
| ~ ( in @ X2500 @ ( binintersect @ X2497 @ X2498 ) )
| ( in @ X2500 @ ( binunion @ X2498 @ X2499 ) ) )
& ( ~ ( in @ X2502 @ ( powerset @ X2501 ) )
| ~ ( in @ X2503 @ ( powerset @ X2501 ) )
| ~ ( in @ X2504 @ ( powerset @ X2501 ) )
| ~ ( in @ X2505 @ X2501 )
| ~ ( in @ X2505 @ ( binintersect @ X2502 @ X2503 ) )
| ( in @ X2505 @ ( binintersect @ ( binunion @ X2502 @ X2504 ) @ ( binunion @ X2503 @ X2504 ) ) ) )
& ( ~ ( in @ X2507 @ ( powerset @ X2506 ) )
| ~ ( in @ X2508 @ ( powerset @ X2506 ) )
| ~ ( in @ X2509 @ ( powerset @ X2506 ) )
| ( in @ ( binintersect @ X2507 @ X2508 ) @ ( powerset @ ( binintersect @ ( binunion @ X2507 @ X2509 ) @ ( binunion @ X2508 @ X2509 ) ) ) ) )
& ( ~ ( in @ X2511 @ ( powerset @ X2510 ) )
| ~ ( in @ X2512 @ ( powerset @ X2510 ) )
| ~ ( in @ X2513 @ X2510 )
| ~ ( in @ X2513 @ ( setminus @ X2510 @ ( binunion @ X2511 @ X2512 ) ) )
| ~ ( in @ X2513 @ X2511 ) )
& ( ~ ( in @ X2515 @ ( powerset @ X2514 ) )
| ~ ( in @ X2516 @ ( powerset @ X2514 ) )
| ~ ( in @ X2517 @ X2514 )
| ~ ( in @ X2517 @ ( setminus @ X2514 @ ( binunion @ X2515 @ X2516 ) ) )
| ( in @ X2517 @ ( setminus @ X2514 @ X2515 ) ) )
& ( ( in @ X2522 @ X2520 )
| X2521
| ( in @ X2522 @ X2519 )
| ~ ( in @ X2522 @ ( binunion @ X2519 @ X2520 ) )
| ~ ( in @ X2522 @ X2518 )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2519 @ ( powerset @ X2518 ) ) )
& ( ~ X2521
| X2521
| ( in @ X2522 @ X2519 )
| ~ ( in @ X2522 @ ( binunion @ X2519 @ X2520 ) )
| ~ ( in @ X2522 @ X2518 )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2519 @ ( powerset @ X2518 ) ) )
& ( ( in @ X2522 @ X2520 )
| X2521
| ~ X2521
| ~ ( in @ X2522 @ ( binunion @ X2519 @ X2520 ) )
| ~ ( in @ X2522 @ X2518 )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2519 @ ( powerset @ X2518 ) ) )
& ( ~ X2521
| X2521
| ~ X2521
| ~ ( in @ X2522 @ ( binunion @ X2519 @ X2520 ) )
| ~ ( in @ X2522 @ X2518 )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2519 @ ( powerset @ X2518 ) ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk74_0 @ esk71_0 )
& ~ ( in @ esk74_0 @ esk72_0 )
& ~ ( in @ esk74_0 @ esk73_0 )
& ( in @ esk74_0 @ ( binunion @ esk72_0 @ esk73_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_315])])])])])])]) ).
thf(c_0_317,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ( in @ X2 @ X4 )
| ~ ( in @ X2 @ ( binunion @ X4 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_316])])]) ).
thf(c_0_318,negated_conjecture,
in @ esk74_0 @ ( binunion @ esk72_0 @ esk73_0 ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
thf(c_0_319,negated_conjecture,
~ ( in @ esk74_0 @ esk72_0 ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
thf(c_0_320,negated_conjecture,
~ ( in @ esk74_0 @ esk73_0 ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
thf(c_0_321,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_318]),c_0_319]),c_0_320]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU747^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:12:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.22/0.71 # Version: 3.1.0-ho
% 1.22/0.71 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.22/0.71 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.71 # Starting ehoh_best5 with 300s (1) cores
% 1.22/0.71 # Starting almost_fo_3_lam with 300s (1) cores
% 1.22/0.71 # Starting new_bool_5 with 300s (1) cores
% 1.22/0.71 # Starting pre_casc_3 with 300s (1) cores
% 1.22/0.71 # Starting ho_unfolding_8 with 300s (1) cores
% 1.22/0.71 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.22/0.71 # Starting new_bool_3 with 300s (1) cores
% 1.22/0.71 # Starting new_ho_5 with 300s (1) cores
% 1.22/0.71 # new_ho_5 with pid 28202 completed with status 8
% 1.22/0.71 # pre_casc_3 with pid 28198 completed with status 8
% 1.22/0.71 # new_bool_5 with pid 28197 completed with status 0
% 1.22/0.71 # Result found by new_bool_5
% 1.22/0.71 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.22/0.71 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.71 # Starting ehoh_best5 with 300s (1) cores
% 1.22/0.71 # Starting almost_fo_3_lam with 300s (1) cores
% 1.22/0.71 # Starting new_bool_5 with 300s (1) cores
% 1.22/0.71 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.22/0.71 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.22/0.71 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.22/0.71 # Starting ho_unfolding_8 with 55s (1) cores
% 1.22/0.71 # ho_unfolding_8 with pid 28273 completed with status 0
% 1.22/0.71 # Result found by ho_unfolding_8
% 1.22/0.71 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.22/0.71 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.22/0.71 # Starting ehoh_best5 with 300s (1) cores
% 1.22/0.71 # Starting almost_fo_3_lam with 300s (1) cores
% 1.22/0.71 # Starting new_bool_5 with 300s (1) cores
% 1.22/0.71 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.22/0.71 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.22/0.71 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.22/0.71 # Starting ho_unfolding_8 with 55s (1) cores
% 1.22/0.71 # Preprocessing time : 0.050 s
% 1.22/0.71 # Presaturation interreduction done
% 1.22/0.71
% 1.22/0.71 # Proof found!
% 1.22/0.71 # SZS status Theorem
% 1.22/0.71 # SZS output start CNFRefutation
% See solution above
% 1.22/0.72 # Parsed axioms : 569
% 1.22/0.72 # Removed by relevancy pruning/SinE : 306
% 1.22/0.72 # Initial clauses : 429
% 1.22/0.72 # Removed in clause preprocessing : 37
% 1.22/0.72 # Initial clauses in saturation : 392
% 1.22/0.72 # Processed clauses : 582
% 1.22/0.72 # ...of these trivial : 9
% 1.22/0.72 # ...subsumed : 36
% 1.22/0.72 # ...remaining for further processing : 537
% 1.22/0.72 # Other redundant clauses eliminated : 29
% 1.22/0.72 # Clauses deleted for lack of memory : 0
% 1.22/0.72 # Backward-subsumed : 0
% 1.22/0.72 # Backward-rewritten : 1
% 1.22/0.72 # Generated clauses : 1509
% 1.22/0.72 # ...of the previous two non-redundant : 1381
% 1.22/0.72 # ...aggressively subsumed : 0
% 1.22/0.72 # Contextual simplify-reflections : 7
% 1.22/0.72 # Paramodulations : 1471
% 1.22/0.72 # Factorizations : 0
% 1.22/0.72 # NegExts : 0
% 1.22/0.72 # Equation resolutions : 34
% 1.22/0.72 # Disequality decompositions : 0
% 1.22/0.72 # Total rewrite steps : 106
% 1.22/0.72 # ...of those cached : 75
% 1.22/0.72 # Propositional unsat checks : 0
% 1.22/0.72 # Propositional check models : 0
% 1.22/0.72 # Propositional check unsatisfiable : 0
% 1.22/0.72 # Propositional clauses : 0
% 1.22/0.72 # Propositional clauses after purity: 0
% 1.22/0.72 # Propositional unsat core size : 0
% 1.22/0.72 # Propositional preprocessing time : 0.000
% 1.22/0.72 # Propositional encoding time : 0.000
% 1.22/0.72 # Propositional solver time : 0.000
% 1.22/0.72 # Success case prop preproc time : 0.000
% 1.22/0.72 # Success case prop encoding time : 0.000
% 1.22/0.72 # Success case prop solver time : 0.000
% 1.22/0.72 # Current number of processed clauses : 179
% 1.22/0.72 # Positive orientable unit clauses : 39
% 1.22/0.72 # Positive unorientable unit clauses: 0
% 1.22/0.72 # Negative unit clauses : 4
% 1.22/0.72 # Non-unit-clauses : 136
% 1.22/0.72 # Current number of unprocessed clauses: 1531
% 1.22/0.72 # ...number of literals in the above : 4154
% 1.22/0.72 # Current number of archived formulas : 0
% 1.22/0.72 # Current number of archived clauses : 342
% 1.22/0.72 # Clause-clause subsumption calls (NU) : 29660
% 1.22/0.72 # Rec. Clause-clause subsumption calls : 12923
% 1.22/0.72 # Non-unit clause-clause subsumptions : 39
% 1.22/0.72 # Unit Clause-clause subsumption calls : 310
% 1.22/0.72 # Rewrite failures with RHS unbound : 0
% 1.22/0.72 # BW rewrite match attempts : 32
% 1.22/0.72 # BW rewrite match successes : 1
% 1.22/0.72 # Condensation attempts : 0
% 1.22/0.72 # Condensation successes : 0
% 1.22/0.72 # Termbank termtop insertions : 93065
% 1.22/0.72 # Search garbage collected termcells : 26566
% 1.22/0.72
% 1.22/0.72 # -------------------------------------------------
% 1.22/0.72 # User time : 0.195 s
% 1.22/0.72 # System time : 0.023 s
% 1.22/0.72 # Total time : 0.218 s
% 1.22/0.72 # Maximum resident set size: 8432 pages
% 1.22/0.72
% 1.22/0.72 # -------------------------------------------------
% 1.22/0.72 # User time : 0.381 s
% 1.22/0.72 # System time : 0.108 s
% 1.22/0.72 # Total time : 0.489 s
% 1.22/0.72 # Maximum resident set size: 2484 pages
% 1.22/0.72 % E---3.1 exiting
% 1.22/0.72 % E exiting
%------------------------------------------------------------------------------