%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU745^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 03:29:47 EDT 2024
% Result : Theorem 2.99s 0.92s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 628
% Syntax : Number of formulae : 690 ( 7 unt; 366 typ; 0 def)
% Number of atoms : 3272 ( 457 equ; 0 cnn)
% Maximal formula atoms : 1026 ( 10 avg)
% Number of connectives : 12577 ( 805 ~; 808 |; 501 &;8485 @)
% ( 348 <=>;1630 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1131 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 370 ( 366 usr; 271 con; 0-4 aty)
% Number of variables : 2724 ( 156 ^2488 !; 80 ?;2724 :)
% 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,
epred1_0: $o ).
thf(decl_322,type,
esk1_2: $i > $i > $i ).
thf(decl_323,type,
esk2_2: $i > $i > $i ).
thf(decl_324,type,
esk3_2: $i > $i > $i ).
thf(decl_325,type,
esk4_1: $i > $i ).
thf(decl_326,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_327,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_328,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_329,type,
esk8_1: $i > $i ).
thf(decl_330,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_331,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_332,type,
esk11_2: $i > $i > $i ).
thf(decl_333,type,
esk12_2: $i > $i > $i ).
thf(decl_334,type,
esk13_1: $i > $i ).
thf(decl_335,type,
esk14_1: $i > $i ).
thf(decl_336,type,
esk15_1: $i > $i ).
thf(decl_337,type,
esk16_2: $i > $i > $i ).
thf(decl_338,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_339,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_340,type,
esk19_1: $i > $i ).
thf(decl_341,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_342,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_346,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_347,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_348,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_349,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_350,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_351,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_352,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_353,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_354,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_355,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_356,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_357,type,
esk36_2: $i > $i > $i ).
thf(decl_358,type,
esk37_2: $i > $i > $i ).
thf(decl_359,type,
esk38_2: $i > $i > $i ).
thf(decl_360,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_361,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_362,type,
esk41_2: $i > $i > $i ).
thf(decl_363,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_364,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_366,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_367,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_368,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_369,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_370,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_371,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_372,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_373,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_374,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_375,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_376,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_377,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_378,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_379,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_380,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_381,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_382,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_383,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_384,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_385,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_386,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_387,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_388,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_389,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_390,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_391,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_392,type,
esk71_0: $i ).
thf(decl_393,type,
esk72_0: $i ).
thf(decl_394,type,
esk73_0: $i ).
thf(decl_395,type,
esk74_0: $i ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(inComplementUnionImpInComplement1,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
=> ! [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/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
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/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
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/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
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/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setminusT_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/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
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/sandbox/benchmark/theBenchmark.p',setextT) ).
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/sandbox/benchmark/theBenchmark.p',subsetTI) ).
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/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',complementTI1) ).
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/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(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/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
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/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_261,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_262,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_263,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_264,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_265,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_266,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_303,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_304,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_305,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_306,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_307,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_308,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_309,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_310,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_311,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_312,plain,
( epred1_0
<=> ! [X898: $i] :
? [X899: $i] :
( ! [X900: $i] :
( ( in @ X900 @ X899 )
=> ! [X901: $i] :
( ( in @ X901 @ X900 )
=> ( in @ X901 @ X898 ) ) )
& ! [X902: $i,X903: $i] :
( ( ( in @ X902 @ X898 )
& ( in @ X903 @ X898 ) )
=> ( ! [X904: $i] :
( ( in @ X904 @ X899 )
=> ( ( in @ X902 @ X904 )
<=> ( in @ X903 @ X904 ) ) )
=> ( X902 = X903 ) ) )
& ! [X905: $i,X906: $i] :
( ( ( in @ X905 @ X899 )
& ( in @ X906 @ X899 ) )
=> ( ! [X907: $i] :
( ( in @ X907 @ X905 )
=> ( in @ X907 @ X906 ) )
| ! [X908: $i] :
( ( in @ X908 @ X906 )
=> ( in @ X908 @ X905 ) ) ) )
& ! [X909: $i] :
( ( ! [X910: $i] :
( ( in @ X910 @ X909 )
=> ( in @ X910 @ X898 ) )
& ? [X911: $i] : ( in @ X911 @ X909 ) )
=> ? [X912: $i,X913: $i] :
( ( in @ X912 @ X899 )
& ( in @ X913 @ X909 )
& ~ ? [X914: $i] :
( ( in @ X914 @ X912 )
& ( in @ X914 @ X909 ) )
& ! [X915: $i] :
( ( in @ X915 @ X899 )
=> ( ! [X916: $i] :
( ( in @ X916 @ X915 )
=> ( in @ X916 @ X912 ) )
| ( in @ X913 @ X915 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_313,negated_conjecture,
~ ( ! [X871: $i,X872: $i] :
( ! [X873: $i] :
( ( in @ X873 @ X871 )
<=> ( in @ X873 @ X872 ) )
=> ( X871 = X872 ) )
=> ( ! [X874: $i] :
~ ( in @ X874 @ emptyset )
=> ( ! [X875: $i,X876: $i,X877: $i] :
( ( in @ X877 @ ( setadjoin @ X875 @ X876 ) )
<=> ( ( X877 = X875 )
| ( in @ X877 @ X876 ) ) )
=> ( ! [X878: $i,X879: $i] :
( ( in @ X879 @ ( powerset @ X878 ) )
<=> ! [X880: $i] :
( ( in @ X880 @ X879 )
=> ( in @ X880 @ X878 ) ) )
=> ( ! [X881: $i,X882: $i] :
( ( in @ X882 @ ( setunion @ X881 ) )
<=> ? [X883: $i] :
( ( in @ X882 @ X883 )
& ( in @ X883 @ X881 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X884: $i] :
( ( in @ X884 @ omega )
=> ( in @ ( setadjoin @ X884 @ X884 ) @ omega ) )
=> ( ! [X885: $i] :
( ( ( in @ emptyset @ X885 )
& ! [X886: $i] :
( ( ( in @ X886 @ omega )
& ( in @ X886 @ X885 ) )
=> ( in @ ( setadjoin @ X886 @ X886 ) @ X885 ) ) )
=> ! [X887: $i] :
( ( in @ X887 @ omega )
=> ( in @ X887 @ X885 ) ) )
=> ( ! [X888: $i > $i > $o,X889: $i] :
( ! [X890: $i] :
( ( in @ X890 @ X889 )
=> ( exu @ ( X888 @ X890 ) ) )
=> ? [X891: $i] :
! [X892: $i] :
( ( in @ X892 @ X891 )
<=> ? [X893: $i] :
( ( in @ X893 @ X889 )
& ( X888 @ X893 @ X892 ) ) ) )
=> ( ! [X894: $i] :
( ? [X895: $i] : ( in @ X895 @ X894 )
=> ? [X896: $i] :
( ( in @ X896 @ X894 )
& ~ ? [X897: $i] :
( ( in @ X897 @ X896 )
& ( in @ X897 @ X894 ) ) ) )
=> ( epred1_0
=> ( ! [X917: $i > $o] :
( ( exu @ X917 )
=> ( X917
@ ( descr
@ ^ [Z0: $i] : ( X917 @ Z0 ) ) ) )
=> ( ! [X918: $i,X919: $i > $o,X920: $i] :
( ( in @ X920 @ X918 )
=> ( ( X919 @ X920 )
=> ( in @ X920 @ ( dsetconstr @ X918 @ X919 ) ) ) )
=> ( ! [X921: $i,X922: $i > $o,X923: $i] :
( ( in @ X923 @ ( dsetconstr @ X921 @ X922 ) )
=> ( in @ X923 @ X921 ) )
=> ( ! [X924: $i,X925: $i > $o,X926: $i] :
( ( in @ X926 @ ( dsetconstr @ X924 @ X925 ) )
=> ( X925 @ X926 ) )
=> ( ! [X927: $i > $o] :
( ( exu @ X927 )
=> ? [X928: $i] :
( ( X927 @ X928 )
& ! [X929: $i] :
( ( X927 @ X929 )
=> ( X928 = X929 ) ) ) )
=> ( ! [X930: $o,X931: $i] :
( ( in @ X931 @ ( prop2set @ X930 ) )
=> X930 )
=> ( ! [X932: $i] :
( ( in @ X932 @ emptyset )
=> ! [X933: $o] : X933 )
=> ( ! [X934: $i] :
( ( in @ X934 @ emptyset )
=> ~ $true )
=> ( ! [X935: $i] :
~ ( in @ X935 @ emptyset )
=> ( ! [X936: $i > $o] :
( ( exu @ X936 )
=> ? [X937: $i] : ( X936 @ X937 ) )
=> ( ! [X938: $i,X939: $i] :
( ! [X940: $i] :
( ( in @ X940 @ X938 )
=> ( in @ X940 @ X939 ) )
=> ( ! [X941: $i] :
( ( in @ X941 @ X939 )
=> ( in @ X941 @ X938 ) )
=> ( X938 = X939 ) ) )
=> ( ! [X942: $i] :
( ! [X943: $i] :
~ ( in @ X943 @ X942 )
=> ( X942 = emptyset ) )
=> ( ! [X944: $i] :
( ! [X945: $i] :
~ ( in @ X945 @ X944 )
=> ( X944 = emptyset ) )
=> ( ! [X946: $i,X947: $i > $o,X948: $i] :
( ( in @ X948 @ X946 )
=> ( ( in @ X948 @ ( dsetconstr @ X946 @ X947 ) )
<=> ( X947 @ X948 ) ) )
=> ( ! [X949: $i] :
( ( nonempty @ X949 )
=> ? [X950: $i] : ( in @ X950 @ X949 ) )
=> ( ! [X951: $i,X952: $i > $o,X953: $i] :
( ( in @ X953 @ X951 )
=> ( ( X952 @ X953 )
=> ( nonempty @ ( dsetconstr @ X951 @ X952 ) ) ) )
=> ( ! [X954: $i] :
( ? [X955: $i] : ( in @ X955 @ X954 )
=> ( nonempty @ X954 ) )
=> ( ! [X956: $i,X957: $i] : ( in @ X956 @ ( setadjoin @ X956 @ X957 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X958: $i,X959: $i,X960: $i] :
( ( in @ X960 @ X959 )
=> ( in @ X960 @ ( setadjoin @ X958 @ X959 ) ) )
=> ( ! [X961: $i,X962: $i,X963: $i] :
( ( in @ X963 @ ( setadjoin @ X961 @ X962 ) )
=> ! [X964: $o] :
( ( ( X963 = X961 )
=> X964 )
=> ( ( ( in @ X963 @ X962 )
=> X964 )
=> X964 ) ) )
=> ( ! [X965: $i,X966: $i,X967: $i] :
( ( in @ X967 @ ( setadjoin @ X965 @ X966 ) )
=> ( ( X967 = X965 )
| ( in @ X967 @ X966 ) ) )
=> ( ! [X968: $i] :
( ( dsetconstr @ X968
@ ^ [Z0: $i] : $true )
= X968 )
=> ( ! [X969: $i,X970: $i] :
( ! [X971: $i] :
( ( in @ X971 @ X970 )
=> ( in @ X971 @ X969 ) )
=> ( in @ X970 @ ( powerset @ X969 ) ) )
=> ( ! [X972: $i] : ( in @ emptyset @ ( powerset @ X972 ) )
=> ( ! [X973: $i] : ( in @ emptyset @ ( powerset @ X973 ) )
=> ( ! [X974: $i,X975: $i,X976: $i] :
( ( in @ X975 @ ( powerset @ X974 ) )
=> ( ( in @ X976 @ X975 )
=> ( in @ X976 @ X974 ) ) )
=> ( ! [X977: $i,X978: $i,X979: $i] :
( ( in @ X978 @ X979 )
=> ( ( in @ X979 @ X977 )
=> ( in @ X978 @ ( setunion @ X977 ) ) ) )
=> ( ! [X980: $i,X981: $i] :
( ( in @ X981 @ ( setunion @ X980 ) )
=> ! [X982: $o] :
( ! [X983: $i] :
( ( in @ X981 @ X983 )
=> ( ( in @ X983 @ X980 )
=> X982 ) )
=> X982 ) )
=> ( ! [X984: $i,X985: $i] :
( ( in @ X985 @ X984 )
=> ( in @ X985 @ ( powerset @ ( setunion @ X984 ) ) ) )
=> ( ! [X986: $i > $o] :
( ( exu @ X986 )
=> ? [X987: $i] :
! [X988: $i] :
( ( X986 @ X988 )
<=> ( X988 = X987 ) ) )
=> ( ! [X989: $i] :
( ( nonempty @ X989 )
=> ? [X990: $i] :
( ( in @ X990 @ X989 )
& $true ) )
=> ( ! [X991: $i,X992: $i] :
( ( in @ X991 @ ( setadjoin @ X992 @ emptyset ) )
=> ( X991 = X992 ) )
=> ( ! [X993: $i,X994: $i] :
( ( X993 != X994 )
=> ~ ( in @ X994 @ ( setadjoin @ X993 @ emptyset ) ) )
=> ( ! [X995: $i,X996: $i] :
( ( X995 = X996 )
=> ( in @ X995 @ ( setadjoin @ X996 @ emptyset ) ) )
=> ( ! [X997: $i,X998: $i] :
( ( in @ X997 @ ( setadjoin @ X998 @ emptyset ) )
=> ( in @ X998 @ ( setadjoin @ X997 @ emptyset ) ) )
=> ( ! [X999: $i,X1000: $i,X1001: $i] :
( ( in @ X1001 @ ( setadjoin @ X999 @ ( setadjoin @ X1000 @ emptyset ) ) )
=> ( ( X1001 = X999 )
| ( X1001 = X1000 ) ) )
=> ( ! [X1002: $i,X1003: $i] : ( in @ X1002 @ ( setadjoin @ X1002 @ ( setadjoin @ X1003 @ emptyset ) ) )
=> ( ! [X1004: $i,X1005: $i] : ( in @ X1005 @ ( setadjoin @ X1004 @ ( setadjoin @ X1005 @ emptyset ) ) )
=> ( ! [X1006: $i,X1007: $i > $o] :
( ? [X1008: $i] :
( ( in @ X1008 @ X1006 )
& ( X1007 @ X1008 ) )
=> ( ( ( dsetconstr @ X1006 @ X1007 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1009: $i > $o,X1010: $i] :
( ( in @ X1010 @ emptyset )
=> ( X1009 @ X1010 ) )
=> ( ! [X1011: $i,X1012: $i > $o] :
( ~ ! [X1013: $i] :
( ( in @ X1013 @ X1011 )
=> ( X1012 @ X1013 ) )
=> ? [X1014: $i] :
( ( in @ X1014 @ X1011 )
& ~ ( X1012 @ X1014 ) ) )
=> ( ! [X1015: $i,X1016: $i > $o] :
( ! [X1017: $i] :
( ( in @ X1017 @ X1015 )
=> ~ ( X1016 @ X1017 ) )
=> ~ ? [X1018: $i] :
( ( in @ X1018 @ X1015 )
& ( X1016 @ X1018 ) ) )
=> ( ! [X1019: $i,X1020: $i > $o] :
( ~ ? [X1021: $i] :
( ( in @ X1021 @ X1019 )
& ( X1020 @ X1021 ) )
=> ! [X1022: $i] :
( ( in @ X1022 @ X1019 )
=> ~ ( X1020 @ X1022 ) ) )
=> ( ! [X1023: $i,X1024: $i > $o] :
( ? [X1025: $i] :
( ( in @ X1025 @ X1023 )
& ~ ( X1024 @ X1025 ) )
=> ~ ! [X1026: $i] :
( ( in @ X1026 @ X1023 )
=> ( X1024 @ X1026 ) ) )
=> ( ! [X1027: $o] :
( X1027
=> ( in @ emptyset @ ( prop2set @ X1027 ) ) )
=> ( prop2set2propI
=> ( ! [X1028: $i,X1029: $i > $o] :
( ~ ? [X1030: $i] :
( ( in @ X1030 @ X1028 )
& ( X1029 @ X1030 ) )
=> ! [X1031: $i] :
( ( in @ X1031 @ X1028 )
=> ~ ( X1029 @ X1031 ) ) )
=> ( ! [X1032: $i,X1033: $i > $o] :
( ~ ! [X1034: $i] :
( ( in @ X1034 @ X1032 )
=> ( X1033 @ X1034 ) )
=> ? [X1035: $i] :
( ( in @ X1035 @ X1032 )
& ~ ( X1033 @ X1035 ) ) )
=> ( ! [X1036: $i > $o] :
( ? [X1037: $i] :
( ( X1036 @ X1037 )
& ! [X1038: $i] :
( ( X1036 @ X1038 )
=> ( X1037 = X1038 ) ) )
=> ( exu @ X1036 ) )
=> ( ! [X1039: $i > $o] :
( ? [X1040: $i] : ( X1039 @ X1040 )
=> ( ! [X1041: $i,X1042: $i] :
( ( X1039 @ X1041 )
=> ( ( X1039 @ X1042 )
=> ( X1041 = X1042 ) ) )
=> ( exu @ X1039 ) ) )
=> ( ! [X1043: $i > $o] :
( ? [X1044: $i] :
! [X1045: $i] :
( ( X1043 @ X1045 )
<=> ( X1045 = X1044 ) )
=> ( exu @ X1043 ) )
=> ( ! [X1046: $i,X1047: $i] :
( ( X1046 = X1047 )
=> ! [X1048: $i,X1049: $i] :
( ( X1048 = X1049 )
=> ( ( in @ X1048 @ X1046 )
=> ( in @ X1049 @ X1047 ) ) ) )
=> ( ! [X1050: $i,X1051: $i] :
( ( X1050 = X1051 )
=> ! [X1052: $i,X1053: $i] :
( ( X1052 = X1053 )
=> ( ( in @ X1052 @ X1050 )
<=> ( in @ X1053 @ X1051 ) ) ) )
=> ( ! [X1054: $i > $o] :
( ( exu @ X1054 )
=> ! [X1055: $i,X1056: $i] :
( ( X1054 @ X1055 )
=> ( ( X1054 @ X1056 )
=> ( X1055 = X1056 ) ) ) )
=> ( ! [X1057: $i > $o,X1058: $i > $o] :
( ! [X1059: $i,X1060: $i] :
( ( X1059 = X1060 )
=> ( ( X1057 @ X1059 )
<=> ( X1058 @ X1060 ) ) )
=> ( ( exu @ X1057 )
<=> ( exu @ X1058 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1061: $i,X1062: $i] :
( ( X1061 = X1062 )
=> ! [X1063: $i,X1064: $i] :
( ( X1063 = X1064 )
=> ( ( setadjoin @ X1061 @ X1063 )
= ( setadjoin @ X1062 @ X1064 ) ) ) )
=> ( ! [X1065: $i,X1066: $i] :
( ( X1065 = X1066 )
=> ( ( powerset @ X1065 )
= ( powerset @ X1066 ) ) )
=> ( ! [X1067: $i,X1068: $i] :
( ( X1067 = X1068 )
=> ( ( setunion @ X1067 )
= ( setunion @ X1068 ) ) )
=> ( ( omega = omega )
=> ( ! [X1069: $i > $o] :
( ( exu @ X1069 )
=> ! [X1070: $i,X1071: $i] :
( ( X1069 @ X1070 )
=> ( ( X1069 @ X1071 )
=> ( X1070 = X1071 ) ) ) )
=> ( ! [X1072: $i > $o,X1073: $i > $o] :
( ! [X1074: $i,X1075: $i] :
( ( X1074 = X1075 )
=> ( ( X1072 @ X1074 )
<=> ( X1073 @ X1075 ) ) )
=> ( ( exu @ X1072 )
=> ( ( exu @ X1073 )
=> ( ( descr @ X1072 )
= ( descr @ X1073 ) ) ) ) )
=> ( ! [X1076: $i,X1077: $i] :
( ( X1076 = X1077 )
=> ! [X1078: $i > $o,X1079: $i > $o] :
( ! [X1080: $i] :
( ( in @ X1080 @ X1076 )
=> ! [X1081: $i] :
( ( in @ X1081 @ X1077 )
=> ( ( X1080 = X1081 )
=> ( ( X1078 @ X1080 )
<=> ( X1079 @ X1081 ) ) ) ) )
=> ( ( dsetconstr @ X1076 @ X1078 )
= ( dsetconstr @ X1077 @ X1079 ) ) ) )
=> ( ! [X1082: $i,X1083: $i] :
( ! [X1084: $i] :
( ( in @ X1084 @ X1082 )
=> ( in @ X1084 @ X1083 ) )
=> ( subset @ X1082 @ X1083 ) )
=> ( ! [X1085: $i,X1086: $i] :
( ( X1085 = X1086 )
=> ( subset @ X1086 @ X1085 ) )
=> ( ! [X1087: $i,X1088: $i] :
( ( X1087 = X1088 )
=> ( subset @ X1087 @ X1088 ) )
=> ( ! [X1089: $i,X1090: $i] :
( ! [X1091: $i] :
( ( in @ X1091 @ X1089 )
=> ( in @ X1091 @ X1090 ) )
=> ( subset @ X1089 @ X1090 ) )
=> ( ! [X1092: $i] : ( subset @ emptyset @ X1092 )
=> ( ! [X1093: $i,X1094: $i,X1095: $i] :
( ( subset @ X1093 @ X1094 )
=> ( ( in @ X1095 @ X1093 )
=> ( in @ X1095 @ X1094 ) ) )
=> ( ! [X1096: $i,X1097: $i,X1098: $i] :
( ( subset @ X1096 @ X1097 )
=> ( ~ ( in @ X1098 @ X1097 )
=> ~ ( in @ X1098 @ X1096 ) ) )
=> ( ! [X1099: $i,X1100: $i,X1101: $i] :
( ( in @ X1101 @ X1099 )
=> ( ~ ( in @ X1101 @ X1100 )
=> ~ ( subset @ X1099 @ X1100 ) ) )
=> ( ! [X1102: $i,X1103: $i] :
( ~ ( subset @ X1102 @ X1103 )
=> ( X1102 != X1103 ) )
=> ( ! [X1104: $i,X1105: $i,X1106: $i] :
( ( in @ X1106 @ X1104 )
=> ( ~ ( in @ X1106 @ X1105 )
=> ( X1104 != X1105 ) ) )
=> ( ! [X1107: $i] : ( subset @ X1107 @ X1107 )
=> ( ! [X1108: $i,X1109: $i,X1110: $i] :
( ( subset @ X1108 @ X1109 )
=> ( ( subset @ X1109 @ X1110 )
=> ( subset @ X1108 @ X1110 ) ) )
=> ( ! [X1111: $i,X1112: $i] : ( subset @ X1112 @ ( setadjoin @ X1111 @ X1112 ) )
=> ( ! [X1113: $i,X1114: $i,X1115: $i] :
( ( subset @ X1113 @ X1115 )
=> ( subset @ X1113 @ ( setadjoin @ X1114 @ X1115 ) ) )
=> ( ! [X1116: $i,X1117: $i] :
( ( subset @ X1116 @ X1117 )
=> ( in @ X1116 @ ( powerset @ X1117 ) ) )
=> ( ! [X1118: $i,X1119: $i] :
( ( subset @ X1118 @ X1119 )
=> ( ( subset @ X1119 @ X1118 )
=> ( X1118 = X1119 ) ) )
=> ( ! [X1120: $i] :
( ( subset @ X1120 @ emptyset )
=> ( X1120 = emptyset ) )
=> ( ! [X1121: $i,X1122: $i] :
( ( subset @ X1122 @ X1121 )
=> ( in @ X1122 @ ( powerset @ X1121 ) ) )
=> ( ! [X1123: $i,X1124: $i] :
( ( in @ X1124 @ ( powerset @ X1123 ) )
=> ( subset @ X1124 @ X1123 ) )
=> ( ! [X1125: $i] : ( in @ X1125 @ ( powerset @ X1125 ) )
=> ( ! [X1126: $i,X1127: $i] :
( ( subset @ X1126 @ X1127 )
=> ( subset @ ( powerset @ X1126 ) @ ( powerset @ X1127 ) ) )
=> ( ! [X1128: $i,X1129: $i > $o] : ( in @ ( dsetconstr @ X1128 @ X1129 ) @ ( powerset @ X1128 ) )
=> ( ! [X1130: $i,X1131: $i > $o] : ( subset @ ( dsetconstr @ X1130 @ X1131 ) @ X1130 )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ( in @ X1134 @ X1132 )
=> ( in @ X1134 @ ( binunion @ X1132 @ X1133 ) ) )
=> ( ! [X1135: $i,X1136: $i] : ( in @ X1136 @ ( setadjoin @ X1135 @ ( setadjoin @ X1136 @ emptyset ) ) )
=> ( ! [X1137: $i,X1138: $i,X1139: $i] :
( ( in @ X1139 @ X1138 )
=> ( in @ X1139 @ ( binunion @ X1137 @ X1138 ) ) )
=> ( ! [X1140: $i,X1141: $i,X1142: $i,X1143: $o] :
( ( in @ X1142 @ ( binunion @ X1140 @ X1141 ) )
=> ( ( ( in @ X1142 @ X1140 )
=> X1143 )
=> ( ( ( in @ X1142 @ X1141 )
=> X1143 )
=> X1143 ) ) )
=> ( ! [X1144: $i,X1145: $i,X1146: $i] :
( ( in @ X1146 @ ( binunion @ X1144 @ X1145 ) )
=> ( ( in @ X1146 @ X1144 )
| ( in @ X1146 @ X1145 ) ) )
=> ( ! [X1147: $i,X1148: $i] : ( subset @ X1147 @ ( binunion @ X1147 @ X1148 ) )
=> ( ! [X1149: $i,X1150: $i] : ( subset @ X1150 @ ( binunion @ X1149 @ X1150 ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i] :
( ( in @ X1153 @ X1151 )
=> ( ( in @ X1153 @ X1152 )
=> ( in @ X1153 @ ( binintersect @ X1151 @ X1152 ) ) ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( subset @ X1156 @ X1154 )
=> ( ( subset @ X1156 @ X1155 )
=> ( subset @ X1156 @ ( binintersect @ X1154 @ X1155 ) ) ) )
=> ( ! [X1157: $i,X1158: $i,X1159: $i] :
( ( in @ X1159 @ ( binintersect @ X1157 @ X1158 ) )
=> ( in @ X1159 @ X1157 ) )
=> ( ! [X1160: $i,X1161: $i] : ( subset @ ( binintersect @ X1160 @ X1161 ) @ X1160 )
=> ( ! [X1162: $i,X1163: $i] :
( ( subset @ X1162 @ X1163 )
=> ( ( binintersect @ X1162 @ X1163 )
= X1162 ) )
=> ( ! [X1164: $i,X1165: $i] :
( ( ( binintersect @ X1164 @ X1165 )
= X1165 )
=> ( subset @ X1165 @ X1164 ) )
=> ( ! [X1166: $i,X1167: $i,X1168: $i] :
( ( in @ X1168 @ ( binintersect @ X1166 @ X1167 ) )
=> ( in @ X1168 @ X1167 ) )
=> ( ! [X1169: $i,X1170: $i] :
( ~ ? [X1171: $i] :
( ( in @ X1171 @ X1169 )
& ( in @ X1171 @ X1170 ) )
=> ( ( binintersect @ X1169 @ X1170 )
= emptyset ) )
=> ( ! [X1172: $i,X1173: $i] : ( subset @ ( binintersect @ X1172 @ X1173 ) @ X1173 )
=> ( ! [X1174: $i,X1175: $i] :
( ( subset @ X1175 @ X1174 )
=> ( ( binintersect @ X1174 @ X1175 )
= X1175 ) )
=> ( ! [X1176: $i,X1177: $i] :
( ( ( binintersect @ X1176 @ X1177 )
= X1176 )
=> ( subset @ X1176 @ X1177 ) )
=> ( ! [X1178: $i,X1179: $i,X1180: $i] :
( ( binintersect @ X1178 @ ( binunion @ X1179 @ X1180 ) )
= ( binunion @ ( binintersect @ X1178 @ X1179 ) @ ( binintersect @ X1178 @ X1180 ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ X1181 )
=> ( ~ ( in @ X1183 @ X1182 )
=> ( in @ X1183 @ ( setminus @ X1181 @ X1182 ) ) ) )
=> ( ! [X1184: $i,X1185: $i,X1186: $i] :
( ( in @ X1186 @ ( setminus @ X1184 @ X1185 ) )
=> ( in @ X1186 @ X1184 ) )
=> ( ! [X1187: $i,X1188: $i,X1189: $i] :
( ( in @ X1189 @ ( setminus @ X1187 @ X1188 ) )
=> ~ ( in @ X1189 @ X1188 ) )
=> ( ! [X1190: $i,X1191: $i] :
( ( subset @ X1190 @ X1191 )
=> ( ( setminus @ X1190 @ X1191 )
= emptyset ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i] :
( ~ ( in @ X1194 @ ( setminus @ X1192 @ X1193 ) )
=> ( ( in @ X1194 @ X1192 )
=> ( in @ X1194 @ X1193 ) ) )
=> ( ! [X1195: $i,X1196: $i,X1197: $i] :
( ~ ( in @ X1197 @ ( setminus @ X1195 @ X1196 ) )
=> ( ~ ( in @ X1197 @ X1196 )
=> ~ ( in @ X1197 @ X1195 ) ) )
=> ( ! [X1198: $i,X1199: $i,X1200: $i] :
( ~ ( in @ X1200 @ X1198 )
=> ~ ( in @ X1200 @ ( setminus @ X1198 @ X1199 ) ) )
=> ( ! [X1201: $i,X1202: $i,X1203: $i] :
( ( in @ X1203 @ X1202 )
=> ~ ( in @ X1203 @ ( setminus @ X1201 @ X1202 ) ) )
=> ( ! [X1204: $i,X1205: $i] : ( subset @ ( setminus @ X1204 @ X1205 ) @ X1204 )
=> ( ! [X1206: $i,X1207: $i] :
( ( ( setminus @ X1206 @ X1207 )
= emptyset )
=> ( subset @ X1206 @ X1207 ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ( in @ X1210 @ ( symdiff @ X1208 @ X1209 ) )
=> ! [X1211: $o] :
( ( ( in @ X1210 @ X1208 )
=> ( ~ ( in @ X1210 @ X1209 )
=> X1211 ) )
=> ( ( ~ ( in @ X1210 @ X1208 )
=> ( ( in @ X1210 @ X1209 )
=> X1211 ) )
=> X1211 ) ) )
=> ( ! [X1212: $i,X1213: $i,X1214: $i] :
( ( in @ X1214 @ X1212 )
=> ( ~ ( in @ X1214 @ X1213 )
=> ( in @ X1214 @ ( symdiff @ X1212 @ X1213 ) ) ) )
=> ( ! [X1215: $i,X1216: $i,X1217: $i] :
( ~ ( in @ X1217 @ X1215 )
=> ( ( in @ X1217 @ X1216 )
=> ( in @ X1217 @ ( symdiff @ X1215 @ X1216 ) ) ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( in @ X1220 @ X1218 )
=> ( ( in @ X1220 @ X1219 )
=> ~ ( in @ X1220 @ ( symdiff @ X1218 @ X1219 ) ) ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i] :
( ~ ( in @ X1223 @ X1221 )
=> ( ~ ( in @ X1223 @ X1222 )
=> ~ ( in @ X1223 @ ( symdiff @ X1221 @ X1222 ) ) ) )
=> ( ! [X1224: $i,X1225: $i] : ( in @ X1225 @ ( setadjoin @ X1224 @ ( setadjoin @ X1225 @ emptyset ) ) )
=> ( ! [X1226: $i,X1227: $i] : ( in @ X1226 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1226 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1226 @ ( setadjoin @ X1227 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1228: $i,X1229: $i] : ( in @ X1229 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1228 @ ( setadjoin @ X1229 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1230: $i,X1231: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1230 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1230 @ ( setadjoin @ X1231 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1232: $i,X1233: $i] : ( iskpair @ ( kpair @ X1232 @ X1233 ) )
=> ( ! [X1234: $i,X1235: $i] :
( ( in @ X1235 @ X1234 )
=> ( subset @ ( setadjoin @ X1235 @ emptyset ) @ X1234 ) )
=> ( ! [X1236: $i,X1237: $i] :
( ( in @ X1237 @ X1236 )
=> ( in @ ( setadjoin @ X1237 @ emptyset ) @ ( powerset @ X1236 ) ) )
=> ( ! [X1238: $i,X1239: $i,X1240: $i] :
( ( in @ X1240 @ X1238 )
=> ( in @ ( setadjoin @ X1240 @ emptyset ) @ ( powerset @ ( binunion @ X1238 @ X1239 ) ) ) )
=> ( ! [X1241: $i,X1242: $i,X1243: $i] :
( ( in @ X1243 @ ( setadjoin @ X1241 @ ( setadjoin @ X1242 @ emptyset ) ) )
=> ( ( X1243 = X1241 )
| ( X1243 = X1242 ) ) )
=> ( ! [X1244: $i,X1245: $i,X1246: $i] :
( ( in @ X1246 @ X1244 )
=> ! [X1247: $i] :
( ( in @ X1247 @ X1245 )
=> ( subset @ ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) ) @ ( binunion @ X1244 @ X1245 ) ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ! [X1251: $i] :
( ( in @ X1251 @ X1249 )
=> ( in @ ( setadjoin @ X1250 @ ( setadjoin @ X1251 @ emptyset ) ) @ ( powerset @ ( binunion @ X1248 @ X1249 ) ) ) ) )
=> ( ! [X1252: $i,X1253: $i,X1254: $i] :
( ( in @ X1254 @ X1252 )
=> ! [X1255: $i] :
( ( in @ X1255 @ X1253 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1254 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1254 @ ( setadjoin @ X1255 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1252 @ X1253 ) ) ) ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i] :
( ( in @ X1258 @ X1256 )
=> ! [X1259: $i] :
( ( in @ X1259 @ X1257 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1258 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1258 @ ( setadjoin @ X1259 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1256 @ X1257 ) ) ) ) ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i] :
( ( in @ X1262 @ X1260 )
=> ! [X1263: $i] :
( ( in @ X1263 @ X1261 )
=> ( in @ ( kpair @ X1262 @ X1263 ) @ ( powerset @ ( powerset @ ( binunion @ X1260 @ X1261 ) ) ) ) ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i] :
( ( in @ X1266 @ X1264 )
=> ! [X1267: $i] :
( ( in @ X1267 @ X1265 )
=> ( in @ ( kpair @ X1266 @ X1267 ) @ ( cartprod @ X1264 @ X1265 ) ) ) )
=> ( ! [X1268: $i,X1269: $i,X1270: $i] :
( ( in @ X1270 @ ( cartprod @ X1268 @ X1269 ) )
=> ? [X1271: $i] :
( ( in @ X1271 @ X1268 )
& ? [X1272: $i] :
( ( in @ X1272 @ X1269 )
& ( X1270
= ( kpair @ X1271 @ X1272 ) ) ) ) )
=> ( ! [X1273: $i,X1274: $i,X1275: $i] :
( ( in @ X1275 @ ( cartprod @ X1273 @ X1274 ) )
=> ( iskpair @ X1275 ) )
=> ( ! [X1276: $i,X1277: $i] :
( ( in @ X1277 @ ( setunion @ X1276 ) )
=> ? [X1278: $i] :
( ( in @ X1278 @ X1276 )
& ( in @ X1277 @ X1278 ) ) )
=> ( ! [X1279: $i] : ( subset @ ( setunion @ ( setadjoin @ X1279 @ emptyset ) ) @ X1279 )
=> ( ! [X1280: $i] : ( subset @ X1280 @ ( setunion @ ( setadjoin @ X1280 @ emptyset ) ) )
=> ( ! [X1281: $i] :
( ( setunion @ ( setadjoin @ X1281 @ emptyset ) )
= X1281 )
=> ( ! [X1282: $i,X1283: $i > $o] :
( ! [X1284: $i] :
( ( in @ X1284 @ X1282 )
=> ! [X1285: $i] :
( ( in @ X1285 @ X1282 )
=> ( ( X1283 @ X1284 )
=> ( ( X1283 @ X1285 )
=> ( X1284 = X1285 ) ) ) ) )
=> ( ? [X1286: $i] :
( ( in @ X1286 @ X1282 )
& ( X1283 @ X1286 ) )
=> ( singleton @ ( dsetconstr @ X1282 @ X1283 ) ) ) )
=> ( ! [X1287: $i,X1288: $i > $o] :
( ( ex1 @ X1287 @ X1288 )
=> ? [X1289: $i] :
( ( in @ X1289 @ X1287 )
& ( X1288 @ X1289 ) ) )
=> ( ! [X1290: $i,X1291: $i > $o,X1292: $i] :
( ( in @ X1292 @ X1290 )
=> ( ( X1291 @ X1292 )
=> ( ! [X1293: $i] :
( ( in @ X1293 @ X1290 )
=> ( ( X1291 @ X1293 )
=> ( X1293 = X1292 ) ) )
=> ( ex1 @ X1290 @ X1291 ) ) ) )
=> ( ! [X1294: $i,X1295: $i > $o] :
( ! [X1296: $i] :
( ( in @ X1296 @ X1294 )
=> ! [X1297: $i] :
( ( in @ X1297 @ X1294 )
=> ( ( X1295 @ X1296 )
=> ( ( X1295 @ X1297 )
=> ( X1296 = X1297 ) ) ) ) )
=> ( ? [X1298: $i] :
( ( in @ X1298 @ X1294 )
& ( X1295 @ X1298 ) )
=> ( ex1 @ X1294 @ X1295 ) ) )
=> ( ! [X1299: $i,X1300: $i] :
( ( ( setadjoin @ X1299 @ emptyset )
= ( setadjoin @ X1300 @ emptyset ) )
=> ( X1299 = X1300 ) )
=> ( ! [X1301: $i,X1302: $i,X1303: $i] :
( ( in @ ( setadjoin @ X1303 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1301 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1301 @ ( setadjoin @ X1302 @ emptyset ) ) @ emptyset ) ) )
=> ( X1301 = X1303 ) )
=> ( ! [X1304: $i] :
( ( iskpair @ X1304 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1304 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1304 ) ) ) )
=> ( ! [X1305: $i] :
( ( singleton @ X1305 )
=> ( in @ ( setunion @ X1305 ) @ X1305 ) )
=> ( ! [X1306: $i,X1307: $i] :
( ( kfst @ ( kpair @ X1306 @ X1307 ) )
= X1306 )
=> ( ! [X1308: $i,X1309: $i,X1310: $i] :
( ( in @ X1310 @ ( cartprod @ X1308 @ X1309 ) )
=> ( in @ ( kfst @ X1310 ) @ X1308 ) )
=> ( ! [X1311: $i,X1312: $i,X1313: $i,X1314: $i] :
( ( ( setadjoin @ ( setadjoin @ X1311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1311 @ ( setadjoin @ X1312 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1313 @ ( setadjoin @ X1314 @ emptyset ) ) @ emptyset ) ) )
=> ( X1311 = X1313 ) )
=> ( ! [X1315: $i,X1316: $i,X1317: $i,X1318: $i] :
( ( ( kpair @ X1315 @ X1316 )
= ( kpair @ X1317 @ X1318 ) )
=> ( X1315 = X1317 ) )
=> ( ! [X1319: $i,X1320: $i] :
( ( X1319 = X1320 )
=> ( ( setadjoin @ X1319 @ ( setadjoin @ X1320 @ emptyset ) )
= ( setadjoin @ X1319 @ emptyset ) ) )
=> ( ! [X1321: $i,X1322: $i] :
( ( X1321 = X1322 )
=> ( ( setadjoin @ ( setadjoin @ X1321 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1321 @ ( setadjoin @ X1322 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1321 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1323: $i,X1324: $i,X1325: $i,X1326: $i] :
( ( ( setadjoin @ ( setadjoin @ X1323 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1323 @ ( setadjoin @ X1324 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1325 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1325 @ ( setadjoin @ X1326 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1325 = X1326 )
=> ( X1324 = X1326 ) ) )
=> ( ! [X1327: $i,X1328: $i,X1329: $i] :
( ( ( setadjoin @ X1327 @ ( setadjoin @ X1328 @ emptyset ) )
= ( setadjoin @ X1329 @ emptyset ) )
=> ( X1327 = X1328 ) )
=> ( ! [X1330: $i,X1331: $i,X1332: $i,X1333: $i] :
( ( ( setadjoin @ ( setadjoin @ X1330 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1330 @ ( setadjoin @ X1331 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1332 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1332 @ ( setadjoin @ X1333 @ emptyset ) ) @ emptyset ) ) )
=> ( X1331 = X1333 ) )
=> ( ! [X1334: $i,X1335: $i,X1336: $i,X1337: $i] :
( ( ( kpair @ X1334 @ X1335 )
= ( kpair @ X1336 @ X1337 ) )
=> ( X1335 = X1337 ) )
=> ( ! [X1338: $i] :
( ( iskpair @ X1338 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1338 )
@ ^ [Z0: $i] :
( X1338
= ( kpair @ ( kfst @ X1338 ) @ Z0 ) ) ) ) )
=> ( ! [X1339: $i,X1340: $i] :
( ( ksnd @ ( kpair @ X1339 @ X1340 ) )
= X1340 )
=> ( ! [X1341: $i] :
( ( iskpair @ X1341 )
=> ( ( kpair @ ( kfst @ X1341 ) @ ( ksnd @ X1341 ) )
= X1341 ) )
=> ( ! [X1342: $i,X1343: $i,X1344: $i] :
( ( in @ X1344 @ ( cartprod @ X1342 @ X1343 ) )
=> ( in @ ( ksnd @ X1344 ) @ X1343 ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i,X1348: $i] :
( ( in @ ( kpair @ X1347 @ X1348 ) @ ( cartprod @ X1345 @ X1346 ) )
=> ( in @ X1347 @ X1345 ) )
=> ( ! [X1349: $i,X1350: $i,X1351: $i,X1352: $i] :
( ( in @ ( kpair @ X1351 @ X1352 ) @ ( cartprod @ X1349 @ X1350 ) )
=> ( in @ X1352 @ X1350 ) )
=> ( ! [X1353: $i,X1354: $i,X1355: $i] :
( ( in @ X1355 @ X1353 )
=> ! [X1356: $i] :
( ( in @ X1356 @ X1354 )
=> ( ( kpair @ X1355 @ X1356 )
= ( kpair @ X1355 @ X1356 ) ) ) )
=> ( ! [X1357: $i,X1358: $i,X1359: $i] :
( ( in @ X1359 @ X1357 )
=> ! [X1360: $i] :
( ( in @ X1360 @ X1358 )
=> ( ( kfst @ ( kpair @ X1359 @ X1360 ) )
= X1359 ) ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i] :
( ( in @ X1363 @ X1361 )
=> ! [X1364: $i] :
( ( in @ X1364 @ X1362 )
=> ( ( ksnd @ ( kpair @ X1363 @ X1364 ) )
= X1364 ) ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i] :
( ( in @ X1367 @ ( cartprod @ X1365 @ X1366 ) )
=> ( ( kpair @ ( kfst @ X1367 ) @ ( ksnd @ X1367 ) )
= X1367 ) )
=> ( ! [X1368: $i,X1369: $i,X1370: $i > $i > $o,X1371: $i] :
( ( in @ X1371 @ X1368 )
=> ! [X1372: $i] :
( ( in @ X1372 @ X1369 )
=> ( ( X1370 @ X1371 @ X1372 )
=> ( in @ ( kpair @ X1371 @ X1372 ) @ ( dpsetconstr @ X1368 @ X1369 @ X1370 ) ) ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1373 @ X1374 @ X1375 ) @ ( cartprod @ X1373 @ X1374 ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i > $i > $o] : ( breln @ X1376 @ X1377 @ ( dpsetconstr @ X1376 @ X1377 @ X1378 ) )
=> ( ! [X1379: $i,X1380: $i,X1381: $i > $i > $o,X1382: $i] :
( ( in @ X1382 @ X1379 )
=> ! [X1383: $i] :
( ( in @ X1383 @ X1380 )
=> ( ( in @ ( kpair @ X1382 @ X1383 ) @ ( dpsetconstr @ X1379 @ X1380 @ X1381 ) )
=> ( X1381 @ X1382 @ X1383 ) ) ) )
=> ( ! [X1384: $i,X1385: $i,X1386: $i > $i > $o,X1387: $i,X1388: $i] :
( ( in @ ( kpair @ X1387 @ X1388 ) @ ( dpsetconstr @ X1384 @ X1385 @ X1386 ) )
=> ( in @ X1387 @ X1384 ) )
=> ( ! [X1389: $i,X1390: $i,X1391: $i > $i > $o,X1392: $i,X1393: $i] :
( ( in @ ( kpair @ X1392 @ X1393 ) @ ( dpsetconstr @ X1389 @ X1390 @ X1391 ) )
=> ( in @ X1393 @ X1390 ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i > $i > $o,X1397: $i,X1398: $i] :
( ( in @ ( kpair @ X1397 @ X1398 ) @ ( dpsetconstr @ X1394 @ X1395 @ X1396 ) )
=> ( X1396 @ X1397 @ X1398 ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( func @ X1399 @ X1400 @ X1401 )
=> ! [X1402: $i] :
( ( in @ X1402 @ X1399 )
=> ( singleton
@ ( dsetconstr @ X1400
@ ^ [Z0: $i] : ( in @ ( kpair @ X1402 @ Z0 ) @ X1401 ) ) ) ) )
=> ( ! [X1403: $i,X1404: $i,X1405: $i] :
( ( func @ X1403 @ X1404 @ X1405 )
=> ! [X1406: $i] :
( ( in @ X1406 @ X1403 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1404
@ ^ [Z0: $i] : ( in @ ( kpair @ X1406 @ Z0 ) @ X1405 ) ) )
@ X1404 ) ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i] :
( ( func @ X1407 @ X1408 @ X1409 )
=> ! [X1410: $i] :
( ( in @ X1410 @ X1407 )
=> ( in @ ( ap @ X1407 @ X1408 @ X1409 @ X1410 ) @ X1408 ) ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i] :
( ( in @ X1413 @ ( funcSet @ X1411 @ X1412 ) )
=> ( func @ X1411 @ X1412 @ X1413 ) )
=> ( ! [X1414: $i,X1415: $i,X1416: $i] :
( ( in @ X1416 @ ( funcSet @ X1414 @ X1415 ) )
=> ! [X1417: $i] :
( ( in @ X1417 @ X1414 )
=> ( in @ ( ap @ X1414 @ X1415 @ X1416 @ X1417 ) @ X1415 ) ) )
=> ( ! [X1418: $i,X1419: $i,X1420: $i] :
( ( func @ X1418 @ X1419 @ X1420 )
=> ( in @ X1420 @ ( funcSet @ X1418 @ X1419 ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i > $i] :
( ! [X1424: $i] :
( ( in @ X1424 @ X1421 )
=> ( in @ ( X1423 @ X1424 ) @ X1422 ) )
=> ( func @ X1421 @ X1422
@ ( dpsetconstr @ X1421 @ X1422
@ ^ [Z0: $i] : ( $eq @ ( X1423 @ Z0 ) ) ) ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i > $i] :
( ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ( in @ ( X1427 @ X1428 ) @ X1426 ) )
=> ( func @ X1425 @ X1426 @ ( lam @ X1425 @ X1426 @ X1427 ) ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i > $i] :
( ! [X1432: $i] :
( ( in @ X1432 @ X1429 )
=> ( in @ ( X1431 @ X1432 ) @ X1430 ) )
=> ( in @ ( lam @ X1429 @ X1430 @ X1431 ) @ ( funcSet @ X1429 @ X1430 ) ) )
=> ( ! [X1433: $i,X1434: $i,X1435: $i] :
( ( breln @ X1433 @ X1434 @ X1435 )
=> ! [X1436: $i > $o] :
( ! [X1437: $i] :
( ( in @ X1437 @ X1433 )
=> ! [X1438: $i] :
( ( in @ X1438 @ X1434 )
=> ( ( in @ ( kpair @ X1437 @ X1438 ) @ X1435 )
=> ( X1436 @ ( kpair @ X1437 @ X1438 ) ) ) ) )
=> ! [X1439: $i] :
( ( in @ X1439 @ X1435 )
=> ( X1436 @ X1439 ) ) ) )
=> ( ! [X1440: $i,X1441: $i,X1442: $i] :
( ( breln @ X1440 @ X1441 @ X1442 )
=> ! [X1443: $i > $o] :
( ! [X1444: $i] :
( ( in @ X1444 @ X1440 )
=> ! [X1445: $i] :
( ( in @ X1445 @ X1441 )
=> ( ( in @ ( kpair @ X1444 @ X1445 ) @ X1442 )
=> ( X1443 @ ( kpair @ X1444 @ X1445 ) ) ) ) )
=> ! [X1446: $i] :
( ( in @ X1446 @ X1442 )
=> ( X1443 @ X1446 ) ) ) )
=> ( ! [X1447: $i,X1448: $i > $o] :
( ( ex1 @ X1447 @ X1448 )
=> ! [X1449: $i] :
( ( in @ X1449 @ X1447 )
=> ! [X1450: $i] :
( ( in @ X1450 @ X1447 )
=> ( ( X1448 @ X1449 )
=> ( ( X1448 @ X1450 )
=> ( X1449 = X1450 ) ) ) ) ) )
=> ( ! [X1451: $i,X1452: $i,X1453: $i] :
( ( func @ X1451 @ X1452 @ X1453 )
=> ! [X1454: $i] :
( ( in @ X1454 @ X1451 )
=> ( in @ ( kpair @ X1454 @ ( ap @ X1451 @ X1452 @ X1453 @ X1454 ) ) @ X1453 ) ) )
=> ( ! [X1455: $i,X1456: $i,X1457: $i] :
( ( in @ X1457 @ ( funcSet @ X1455 @ X1456 ) )
=> ! [X1458: $i] :
( ( in @ X1458 @ X1455 )
=> ( in @ ( kpair @ X1458 @ ( ap @ X1455 @ X1456 @ X1457 @ X1458 ) ) @ X1457 ) ) )
=> ( ! [X1459: $i,X1460: $i,X1461: $i] :
( ( func @ X1459 @ X1460 @ X1461 )
=> ! [X1462: $i] :
( ( in @ X1462 @ X1459 )
=> ! [X1463: $i] :
( ( in @ X1463 @ X1460 )
=> ( ( in @ ( kpair @ X1462 @ X1463 ) @ X1461 )
=> ( ( ap @ X1459 @ X1460 @ X1461 @ X1462 )
= X1463 ) ) ) ) )
=> ( ! [X1464: $i,X1465: $i,X1466: $i] :
( ( func @ X1464 @ X1465 @ X1466 )
=> ! [X1467: $i] :
( ( func @ X1464 @ X1465 @ X1467 )
=> ( ! [X1468: $i] :
( ( in @ X1468 @ X1464 )
=> ( ( ap @ X1464 @ X1465 @ X1466 @ X1468 )
= ( ap @ X1464 @ X1465 @ X1467 @ X1468 ) ) )
=> ! [X1469: $i] :
( ( in @ X1469 @ X1464 )
=> ! [X1470: $i] :
( ( in @ X1470 @ X1465 )
=> ( ( in @ ( kpair @ X1469 @ X1470 ) @ X1467 )
=> ( in @ ( kpair @ X1469 @ X1470 ) @ X1466 ) ) ) ) ) ) )
=> ( ! [X1471: $i,X1472: $i,X1473: $i] :
( ( in @ X1473 @ ( funcSet @ X1471 @ X1472 ) )
=> ! [X1474: $i] :
( ( in @ X1474 @ X1471 )
=> ! [X1475: $i] :
( ( in @ X1475 @ X1472 )
=> ( ( in @ ( kpair @ X1474 @ X1475 ) @ X1473 )
=> ( ( ap @ X1471 @ X1472 @ X1473 @ X1474 )
= X1475 ) ) ) ) )
=> ( ! [X1476: $i,X1477: $i,X1478: $i] :
( ( breln @ X1476 @ X1477 @ X1478 )
=> ! [X1479: $i] :
( ( breln @ X1476 @ X1477 @ X1479 )
=> ( ! [X1480: $i] :
( ( in @ X1480 @ X1476 )
=> ! [X1481: $i] :
( ( in @ X1481 @ X1477 )
=> ( ( in @ ( kpair @ X1480 @ X1481 ) @ X1478 )
=> ( in @ ( kpair @ X1480 @ X1481 ) @ X1479 ) ) ) )
=> ( subset @ X1478 @ X1479 ) ) ) )
=> ( ! [X1482: $i,X1483: $i,X1484: $i] :
( ( breln @ X1482 @ X1483 @ X1484 )
=> ! [X1485: $i] :
( ( breln @ X1482 @ X1483 @ X1485 )
=> ( ! [X1486: $i] :
( ( in @ X1486 @ X1482 )
=> ! [X1487: $i] :
( ( in @ X1487 @ X1483 )
=> ( ( in @ ( kpair @ X1486 @ X1487 ) @ X1484 )
=> ( in @ ( kpair @ X1486 @ X1487 ) @ X1485 ) ) ) )
=> ( ! [X1488: $i] :
( ( in @ X1488 @ X1482 )
=> ! [X1489: $i] :
( ( in @ X1489 @ X1483 )
=> ( ( in @ ( kpair @ X1488 @ X1489 ) @ X1485 )
=> ( in @ ( kpair @ X1488 @ X1489 ) @ X1484 ) ) ) )
=> ( X1484 = X1485 ) ) ) ) )
=> ( ! [X1490: $i,X1491: $i,X1492: $i] :
( ( func @ X1490 @ X1491 @ X1492 )
=> ! [X1493: $i] :
( ( func @ X1490 @ X1491 @ X1493 )
=> ( ! [X1494: $i] :
( ( in @ X1494 @ X1490 )
=> ( ( ap @ X1490 @ X1491 @ X1492 @ X1494 )
= ( ap @ X1490 @ X1491 @ X1493 @ X1494 ) ) )
=> ( X1492 = X1493 ) ) ) )
=> ( ! [X1495: $i,X1496: $i,X1497: $i] :
( ( in @ X1497 @ ( funcSet @ X1495 @ X1496 ) )
=> ! [X1498: $i] :
( ( in @ X1498 @ ( funcSet @ X1495 @ X1496 ) )
=> ( ! [X1499: $i] :
( ( in @ X1499 @ X1495 )
=> ( ( ap @ X1495 @ X1496 @ X1497 @ X1499 )
= ( ap @ X1495 @ X1496 @ X1498 @ X1499 ) ) )
=> ( X1497 = X1498 ) ) ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i] :
( ( in @ X1502 @ ( funcSet @ X1500 @ X1501 ) )
=> ! [X1503: $i] :
( ( in @ X1503 @ X1500 )
=> ( ( ap @ X1500 @ X1501 @ X1502 @ X1503 )
= ( ap @ X1500 @ X1501 @ X1502 @ X1503 ) ) ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i] :
( ( func @ X1504 @ X1505 @ X1506 )
=> ! [X1507: $i] :
( ( in @ X1507 @ X1504 )
=> ( ( ap @ X1504 @ X1505 @ X1506 @ X1507 )
= ( ap @ X1504 @ X1505 @ X1506 @ X1507 ) ) ) )
=> ( ! [X1508: $i,X1509: $i,X1510: $i > $i] :
( ! [X1511: $i] :
( ( in @ X1511 @ X1508 )
=> ( in @ ( X1510 @ X1511 ) @ X1509 ) )
=> ! [X1512: $i] :
( ( in @ X1512 @ X1508 )
=> ( ( ap @ X1508 @ X1509 @ ( lam @ X1508 @ X1509 @ X1510 ) @ X1512 )
= ( X1510 @ X1512 ) ) ) )
=> ( ! [X1513: $i,X1514: $i,X1515: $i] :
( ( func @ X1513 @ X1514 @ X1515 )
=> ( ( lam @ X1513 @ X1514 @ ( ap @ X1513 @ X1514 @ X1515 ) )
= X1515 ) )
=> ( ! [X1516: $i,X1517: $i,X1518: $i > $i] :
( ! [X1519: $i] :
( ( in @ X1519 @ X1516 )
=> ( in @ ( X1518 @ X1519 ) @ X1517 ) )
=> ( ( lam @ X1516 @ X1517 @ X1518 )
= ( lam @ X1516 @ X1517 @ X1518 ) ) )
=> ( ! [X1520: $i,X1521: $i,X1522: $i > $i] :
( ! [X1523: $i] :
( ( in @ X1523 @ X1520 )
=> ( in @ ( X1522 @ X1523 ) @ X1521 ) )
=> ! [X1524: $i] :
( ( in @ X1524 @ X1520 )
=> ( ( ap @ X1520 @ X1521 @ ( lam @ X1520 @ X1521 @ X1522 ) @ X1524 )
= ( X1522 @ X1524 ) ) ) )
=> ( ! [X1525: $i,X1526: $i,X1527: $i] :
( ( in @ X1527 @ ( funcSet @ X1525 @ X1526 ) )
=> ( ( lam @ X1525 @ X1526 @ ( ap @ X1525 @ X1526 @ X1527 ) )
= X1527 ) )
=> ( ! [X1528: $i,X1529: $o,X1530: $i] :
( ( in @ X1530 @ X1528 )
=> ! [X1531: $i] :
( ( in @ X1531 @ X1528 )
=> ( ~ X1529
=> ( in @ X1531
@ ( dsetconstr @ X1528
@ ^ [Z0: $i] :
( ( X1529
& ( Z0 = X1530 ) )
| ( ~ X1529
& ( Z0 = X1531 ) ) ) ) ) ) ) )
=> ( ! [X1532: $i,X1533: $o,X1534: $i] :
( ( in @ X1534 @ X1532 )
=> ! [X1535: $i] :
( ( in @ X1535 @ X1532 )
=> ( ~ X1533
=> ( ( dsetconstr @ X1532
@ ^ [Z0: $i] :
( ( X1533
& ( Z0 = X1534 ) )
| ( ~ X1533
& ( Z0 = X1535 ) ) ) )
= ( setadjoin @ X1535 @ emptyset ) ) ) ) )
=> ( ! [X1536: $i,X1537: $o,X1538: $i] :
( ( in @ X1538 @ X1536 )
=> ! [X1539: $i] :
( ( in @ X1539 @ X1536 )
=> ( X1537
=> ( in @ X1538
@ ( dsetconstr @ X1536
@ ^ [Z0: $i] :
( ( X1537
& ( Z0 = X1538 ) )
| ( ~ X1537
& ( Z0 = X1539 ) ) ) ) ) ) ) )
=> ( ! [X1540: $i,X1541: $o,X1542: $i] :
( ( in @ X1542 @ X1540 )
=> ! [X1543: $i] :
( ( in @ X1543 @ X1540 )
=> ( X1541
=> ( ( dsetconstr @ X1540
@ ^ [Z0: $i] :
( ( X1541
& ( Z0 = X1542 ) )
| ( ~ X1541
& ( Z0 = X1543 ) ) ) )
= ( setadjoin @ X1542 @ emptyset ) ) ) ) )
=> ( ! [X1544: $i,X1545: $o,X1546: $i] :
( ( in @ X1546 @ X1544 )
=> ! [X1547: $i] :
( ( in @ X1547 @ X1544 )
=> ( singleton
@ ( dsetconstr @ X1544
@ ^ [Z0: $i] :
( ( X1545
& ( Z0 = X1546 ) )
| ( ~ X1545
& ( Z0 = X1547 ) ) ) ) ) ) )
=> ( ! [X1548: $i,X1549: $o,X1550: $i] :
( ( in @ X1550 @ X1548 )
=> ! [X1551: $i] :
( ( in @ X1551 @ X1548 )
=> ( in @ ( if @ X1548 @ X1549 @ X1550 @ X1551 ) @ X1548 ) ) )
=> ( ! [X1552: $i] :
( ( singleton @ X1552 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1552 )
=> ( ( setunion @ X1552 )
= X1553 ) ) )
=> ( ! [X1554: $i,X1555: $o,X1556: $i] :
( ( in @ X1556 @ X1554 )
=> ! [X1557: $i] :
( ( in @ X1557 @ X1554 )
=> ( X1555
=> ( ( if @ X1554 @ X1555 @ X1556 @ X1557 )
= X1556 ) ) ) )
=> ( ! [X1558: $i,X1559: $o,X1560: $i] :
( ( in @ X1560 @ X1558 )
=> ! [X1561: $i] :
( ( in @ X1561 @ X1558 )
=> ( ~ X1559
=> ( ( if @ X1558 @ X1559 @ X1560 @ X1561 )
= X1561 ) ) ) )
=> ( ! [X1562: $i,X1563: $o,X1564: $i] :
( ( in @ X1564 @ X1562 )
=> ! [X1565: $i] :
( ( in @ X1565 @ X1562 )
=> ( in @ ( if @ X1562 @ X1563 @ X1564 @ X1565 ) @ ( setadjoin @ X1564 @ ( setadjoin @ X1565 @ emptyset ) ) ) ) )
=> ( ! [X1566: $i,X1567: $i] :
( ( in @ X1567 @ ( powerset @ X1566 ) )
=> ! [X1568: $i] :
( ( in @ X1568 @ ( powerset @ X1566 ) )
=> ( in @ ( binintersect @ X1567 @ X1568 ) @ ( powerset @ X1566 ) ) ) )
=> ( ! [X1569: $i,X1570: $i] :
( ( in @ X1570 @ ( powerset @ X1569 ) )
=> ! [X1571: $i] :
( ( in @ X1571 @ ( powerset @ X1569 ) )
=> ( in @ ( binunion @ X1570 @ X1571 ) @ ( powerset @ X1569 ) ) ) )
=> ( ! [X1572: $i,X1573: $i] :
( ( in @ X1573 @ ( powerset @ X1572 ) )
=> ( in @ ( powerset @ X1573 ) @ ( powerset @ ( powerset @ X1572 ) ) ) )
=> ( ! [X1574: $i,X1575: $i] :
( ( in @ X1575 @ ( powerset @ X1574 ) )
=> ! [X1576: $i] :
( ( in @ X1576 @ ( powerset @ X1574 ) )
=> ( in @ ( setminus @ X1575 @ X1576 ) @ ( powerset @ X1574 ) ) ) )
=> ( ! [X1577: $i,X1578: $i] :
( ( in @ X1578 @ ( powerset @ X1577 ) )
=> ( in @ ( setminus @ X1577 @ X1578 ) @ ( powerset @ X1577 ) ) )
=> ( ! [X1579: $i,X1580: $i] :
( ( in @ X1580 @ ( powerset @ X1579 ) )
=> ! [X1581: $i] :
( ( in @ X1581 @ ( powerset @ X1579 ) )
=> ( ! [X1582: $i] :
( ( in @ X1582 @ X1579 )
=> ( ( in @ X1582 @ X1580 )
=> ( in @ X1582 @ X1581 ) ) )
=> ( ! [X1583: $i] :
( ( in @ X1583 @ X1579 )
=> ( ( in @ X1583 @ X1581 )
=> ( in @ X1583 @ X1580 ) ) )
=> ( X1580 = X1581 ) ) ) ) )
=> ( ! [X1584: $i,X1585: $i] :
( ( in @ X1585 @ ( powerset @ X1584 ) )
=> ! [X1586: $i] :
( ( in @ X1586 @ ( powerset @ X1584 ) )
=> ( ! [X1587: $i] :
( ( in @ X1587 @ X1584 )
=> ( ( in @ X1587 @ X1585 )
=> ( in @ X1587 @ X1586 ) ) )
=> ( subset @ X1585 @ X1586 ) ) ) )
=> ( ! [X1588: $i,X1589: $i] :
( ( in @ X1589 @ ( powerset @ X1588 ) )
=> ! [X1590: $i] :
( ( in @ X1590 @ ( powerset @ X1588 ) )
=> ( ! [X1591: $i] :
( ( in @ X1591 @ X1588 )
=> ( ( in @ X1591 @ X1589 )
=> ( in @ X1591 @ X1590 ) ) )
=> ( in @ X1589 @ ( powerset @ X1590 ) ) ) ) )
=> ( ! [X1592: $i,X1593: $i] :
( ( in @ X1593 @ ( powerset @ X1592 ) )
=> ! [X1594: $i] :
( ( in @ X1594 @ ( powerset @ X1592 ) )
=> ! [X1595: $i] :
( ( in @ X1595 @ X1592 )
=> ( ( in @ X1593 @ ( powerset @ X1594 ) )
=> ( ( in @ X1595 @ X1593 )
=> ( in @ X1595 @ X1594 ) ) ) ) ) )
=> ( ! [X1596: $i,X1597: $i] :
( ( in @ X1597 @ ( powerset @ X1596 ) )
=> ! [X1598: $i] :
( ( in @ X1598 @ X1596 )
=> ( ( in @ X1598 @ X1597 )
=> ~ ( in @ X1598 @ ( setminus @ X1596 @ X1597 ) ) ) ) )
=> ( ! [X1599: $i,X1600: $i] :
( ( in @ X1600 @ ( powerset @ X1599 ) )
=> ! [X1601: $i] :
( ( in @ X1601 @ X1599 )
=> ( ~ ( in @ X1601 @ ( setminus @ X1599 @ X1600 ) )
=> ( in @ X1601 @ X1600 ) ) ) )
=> ( ! [X1602: $i,X1603: $i] :
( ( in @ X1603 @ ( powerset @ X1602 ) )
=> ! [X1604: $i] :
( ( in @ X1604 @ ( powerset @ X1602 ) )
=> ! [X1605: $i] :
( ( in @ X1605 @ X1602 )
=> ( ~ ( in @ X1605 @ X1603 )
=> ~ ( in @ X1605 @ ( binintersect @ X1603 @ X1604 ) ) ) ) ) )
=> ( ! [X1606: $i,X1607: $i] :
( ( in @ X1607 @ ( powerset @ X1606 ) )
=> ! [X1608: $i] :
( ( in @ X1608 @ ( powerset @ X1606 ) )
=> ! [X1609: $i] :
( ( in @ X1609 @ X1606 )
=> ( ~ ( in @ X1609 @ X1608 )
=> ~ ( in @ X1609 @ ( binintersect @ X1607 @ X1608 ) ) ) ) ) )
=> ( ! [X1610: $i,X1611: $i] :
( ( in @ X1611 @ ( powerset @ X1610 ) )
=> ! [X1612: $i] :
( ( in @ X1612 @ ( powerset @ X1610 ) )
=> ! [X1613: $i] :
( ( in @ X1613 @ X1610 )
=> ( ( subset @ X1611 @ ( setminus @ X1610 @ X1612 ) )
=> ( ( in @ X1613 @ X1612 )
=> ~ ( in @ X1613 @ X1611 ) ) ) ) ) )
=> ( ! [X1614: $i,X1615: $i] :
( ( in @ X1615 @ ( powerset @ X1614 ) )
=> ! [X1616: $i] :
( ( in @ X1616 @ ( powerset @ X1614 ) )
=> ! [X1617: $i] :
( ( in @ X1617 @ X1614 )
=> ( ( subset @ X1615 @ X1616 )
=> ( ~ ( in @ X1617 @ X1616 )
=> ~ ( in @ X1617 @ X1615 ) ) ) ) ) )
=> ( ! [X1618: $i,X1619: $i] :
( ( in @ X1619 @ ( powerset @ X1618 ) )
=> ! [X1620: $i] :
( ( in @ X1620 @ ( powerset @ X1618 ) )
=> ( ( subset @ X1619 @ X1620 )
=> ( subset @ ( setminus @ X1618 @ X1620 ) @ ( setminus @ X1618 @ X1619 ) ) ) ) )
=> ( ! [X1621: $i,X1622: $i] :
( ( in @ X1622 @ ( powerset @ X1621 ) )
=> ! [X1623: $i] :
( ( in @ X1623 @ ( powerset @ X1621 ) )
=> ( ( subset @ ( setminus @ X1621 @ X1623 ) @ ( setminus @ X1621 @ X1622 ) )
=> ( subset @ X1622 @ X1623 ) ) ) )
=> ( ! [X1624: $i,X1625: $i] :
( ( in @ X1625 @ ( powerset @ X1624 ) )
=> ! [X1626: $i] :
( ( in @ X1626 @ X1624 )
=> ( ( in @ X1626 @ X1625 )
=> ( in @ X1626 @ ( setminus @ X1624 @ ( setminus @ X1624 @ X1625 ) ) ) ) ) )
=> ( ! [X1627: $i,X1628: $i] :
( ( in @ X1628 @ ( powerset @ X1627 ) )
=> ! [X1629: $i] :
( ( in @ X1629 @ X1627 )
=> ( ( in @ X1629 @ ( setminus @ X1627 @ ( setminus @ X1627 @ X1628 ) ) )
=> ( in @ X1629 @ X1628 ) ) ) )
=> ( ! [X1630: $i,X1631: $i] :
( ( in @ X1631 @ ( powerset @ X1630 ) )
=> ( subset @ X1631 @ ( setminus @ X1630 @ ( setminus @ X1630 @ X1631 ) ) ) )
=> ( ! [X1632: $i,X1633: $i] :
( ( in @ X1633 @ ( powerset @ X1632 ) )
=> ( subset @ ( setminus @ X1632 @ ( setminus @ X1632 @ X1633 ) ) @ X1633 ) )
=> ( ! [X1634: $i,X1635: $i] :
( ( in @ X1635 @ ( powerset @ X1634 ) )
=> ( X1635
= ( setminus @ X1634 @ ( setminus @ X1634 @ X1635 ) ) ) )
=> ( ! [X1636: $i,X1637: $i] :
( ( in @ X1637 @ ( powerset @ X1636 ) )
=> ! [X1638: $i] :
( ( in @ X1638 @ ( powerset @ X1636 ) )
=> ! [X1639: $i] :
( ( in @ X1639 @ X1636 )
=> ( ( in @ X1639 @ ( setminus @ X1636 @ X1637 ) )
=> ~ ( in @ X1639 @ ( binintersect @ X1637 @ X1638 ) ) ) ) ) )
=> ( ! [X1640: $i,X1641: $i] :
( ( in @ X1641 @ ( powerset @ X1640 ) )
=> ! [X1642: $i] :
( ( in @ X1642 @ ( powerset @ X1640 ) )
=> ! [X1643: $i] :
( ( in @ X1643 @ X1640 )
=> ( ( in @ X1643 @ ( setminus @ X1640 @ X1641 ) )
=> ( in @ X1643 @ ( setminus @ X1640 @ ( binintersect @ X1641 @ X1642 ) ) ) ) ) ) )
=> ( ! [X1644: $i,X1645: $i] :
( ( in @ X1645 @ ( powerset @ X1644 ) )
=> ! [X1646: $i] :
( ( in @ X1646 @ ( powerset @ X1644 ) )
=> ( subset @ ( setminus @ X1644 @ X1645 ) @ ( setminus @ X1644 @ ( binintersect @ X1645 @ X1646 ) ) ) ) )
=> ( ! [X1647: $i,X1648: $i] :
( ( in @ X1648 @ ( powerset @ X1647 ) )
=> ! [X1649: $i] :
( ( in @ X1649 @ ( powerset @ X1647 ) )
=> ( in @ ( setminus @ X1647 @ X1648 ) @ ( powerset @ ( setminus @ X1647 @ ( binintersect @ X1648 @ X1649 ) ) ) ) ) )
=> ( ! [X1650: $i,X1651: $i] :
( ( in @ X1651 @ ( powerset @ X1650 ) )
=> ! [X1652: $i] :
( ( in @ X1652 @ ( powerset @ X1650 ) )
=> ( ( subset @ X1651 @ ( setminus @ X1650 @ X1652 ) )
=> ! [X1653: $i] :
( ( in @ X1653 @ X1650 )
=> ( ( in @ X1653 @ X1652 )
=> ( in @ X1653 @ ( setminus @ X1650 @ X1651 ) ) ) ) ) ) )
=> ( ! [X1654: $i,X1655: $i] :
( ( in @ X1655 @ ( powerset @ X1654 ) )
=> ! [X1656: $i] :
( ( in @ X1656 @ ( powerset @ X1654 ) )
=> ( ( subset @ X1655 @ ( setminus @ X1654 @ X1656 ) )
=> ( subset @ X1656 @ ( setminus @ X1654 @ X1655 ) ) ) ) )
=> ( ! [X1657: $i,X1658: $i] :
( ( in @ X1658 @ ( powerset @ X1657 ) )
=> ! [X1659: $i] :
( ( in @ X1659 @ ( powerset @ X1657 ) )
=> ! [X1660: $i] :
( ( in @ X1660 @ X1657 )
=> ( ~ ( in @ X1660 @ ( binunion @ X1658 @ X1659 ) )
=> ~ ( in @ X1660 @ X1658 ) ) ) ) )
=> ( ! [X1661: $i,X1662: $i] :
( ( in @ X1662 @ ( powerset @ X1661 ) )
=> ! [X1663: $i] :
( ( in @ X1663 @ ( powerset @ X1661 ) )
=> ! [X1664: $i] :
( ( in @ X1664 @ X1661 )
=> ( ~ ( in @ X1664 @ ( binunion @ X1662 @ X1663 ) )
=> ~ ( in @ X1664 @ X1663 ) ) ) ) )
=> ( ! [X1665: $i,X1666: $i] :
( ( in @ X1666 @ ( powerset @ X1665 ) )
=> ! [X1667: $i] :
( ( in @ X1667 @ ( powerset @ X1665 ) )
=> ! [X1668: $i] :
( ( in @ X1668 @ ( powerset @ X1665 ) )
=> ! [X1669: $i] :
( ( in @ X1669 @ X1665 )
=> ( ( in @ X1669 @ ( binintersect @ X1666 @ X1667 ) )
=> ( in @ X1669 @ ( binunion @ X1666 @ X1668 ) ) ) ) ) ) )
=> ( ! [X1670: $i,X1671: $i] :
( ( in @ X1671 @ ( powerset @ X1670 ) )
=> ! [X1672: $i] :
( ( in @ X1672 @ ( powerset @ X1670 ) )
=> ! [X1673: $i] :
( ( in @ X1673 @ ( powerset @ X1670 ) )
=> ! [X1674: $i] :
( ( in @ X1674 @ X1670 )
=> ( ( in @ X1674 @ ( binintersect @ X1671 @ X1672 ) )
=> ( in @ X1674 @ ( binunion @ X1672 @ 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 @ ( binintersect @ ( binunion @ X1676 @ X1678 ) @ ( binunion @ X1677 @ X1678 ) ) ) ) ) ) ) )
=> ( ! [X1680: $i,X1681: $i] :
( ( in @ X1681 @ ( powerset @ X1680 ) )
=> ! [X1682: $i] :
( ( in @ X1682 @ ( powerset @ X1680 ) )
=> ! [X1683: $i] :
( ( in @ X1683 @ ( powerset @ X1680 ) )
=> ( in @ ( binintersect @ X1681 @ X1682 ) @ ( powerset @ ( binintersect @ ( binunion @ X1681 @ X1683 ) @ ( binunion @ X1682 @ X1683 ) ) ) ) ) ) )
=> ( ! [X1684: $i,X1685: $i] :
( ( in @ X1685 @ ( powerset @ X1684 ) )
=> ! [X1686: $i] :
( ( in @ X1686 @ ( powerset @ X1684 ) )
=> ! [X1687: $i] :
( ( in @ X1687 @ X1684 )
=> ( ( in @ X1687 @ ( setminus @ X1684 @ ( binunion @ X1685 @ X1686 ) ) )
=> ~ ( in @ X1687 @ X1685 ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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doubleComplementEq]),binintersectSubset2]),complementTnotintersectT]),complementImpComplementIntersect]),binintersectSubset3]),complementSubsetComplementIntersect]),complementInPowersetComplementIntersect]),binintersectER]),contraSubsetComplement]),complementTcontraSubset]),disjointsetsI1]),binunionTILcontra]),binunionTIRcontra]),binintersectRsub]),inIntersectImpInUnion]),inIntersectImpInUnion2]),binintersectSubset4]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),theprop]),kfstpairEq]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),subsetRefl]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_268]),c_0_269]),subsetTrans]),setadjoinSub]),c_0_270]),c_0_271]),setadjoinSub2]),singletonsuniq]),setukpairinjL1]),c_0_272]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),subset2powerset]),setukpairinjR]),c_0_273]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_274]),c_0_275]),c_0_276]),c_0_277]),c_0_278]),c_0_279]),c_0_280]),c_0_281]),c_0_282]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_283]),c_0_284]),c_0_285]),brelnall1]),brelnall2]),c_0_286]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),setextsub]),c_0_291]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_292]),c_0_293]),c_0_294]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_295]),c_0_296]),in__Cong]),inCongP]),c_0_297]),c_0_298]),c_0_299]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_300]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_301]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_302]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_303]),nonemptyE1]),c_0_304]),noeltsimpempty]),emptyI]),setext]),c_0_305]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),c_0_310]),wellorderingAx]),foundationAx]),c_0_311]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_312]) ).
thf(c_0_314,negated_conjecture,
! 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$i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,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 > $i > $o,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i > $i > $o,X2183: $i,X2184: $i,X2185: $i > $i > $o,X2186: $i,X2187: $i,X2188: $i > $i > $o,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i > $i > $o,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i > $i > $o,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i > $i > $o,X2204: $i,X2205: $i,X2206: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i > $i,X2232: $i,X2233: $i,X2234: $i > $i,X2236: $i,X2237: $i,X2238: $i > $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i > $o,X2246: $i,X2247: $i,X2248: $i,X2249: $i,X2250: $i > $o,X2253: $i,X2254: $i,X2255: $i > $o,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i,X2272: $i,X2273: $i,X2274: $i,X2276: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i,X2297: $i,X2298: $i,X2299: $i,X2300: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i,X2311: $i,X2312: $i,X2313: $i,X2314: $i,X2315: $i,X2316: $i,X2317: $i > $i,X2319: $i,X2320: $i,X2321: $i,X2322: $i,X2323: $i,X2324: $i,X2325: $i > $i,X2327: $i,X2328: $i,X2329: $i > $i,X2331: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $o,X2337: $i,X2338: $i,X2339: $i,X2340: $o,X2341: $i,X2342: $i,X2343: $i,X2344: $o,X2345: $i,X2346: $i,X2347: $i,X2348: $o,X2349: $i,X2350: $i,X2351: $i,X2352: $o,X2353: $i,X2354: $i,X2355: $i,X2356: $o,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $o,X2363: $i,X2364: $i,X2365: $i,X2366: $o,X2367: $i,X2368: $i,X2369: $i,X2370: $o,X2371: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2376: $i,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2381: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2388: $i,X2391: $i,X2392: $i,X2393: $i,X2395: $i,X2396: $i,X2397: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $i,X2412: $i,X2413: $i,X2414: $i,X2415: $i,X2416: $i,X2417: $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] :
( ( ~ ( in @ ( esk1_2 @ X1688 @ X1689 ) @ X1688 )
| ~ ( in @ ( esk1_2 @ X1688 @ X1689 ) @ X1689 )
| ( X1688 = X1689 ) )
& ( ( in @ ( esk1_2 @ X1688 @ X1689 ) @ X1688 )
| ( in @ ( esk1_2 @ X1688 @ X1689 ) @ X1689 )
| ( X1688 = X1689 ) )
& ~ ( in @ X1691 @ emptyset )
& ( ~ ( in @ X1694 @ ( setadjoin @ X1692 @ X1693 ) )
| ( X1694 = X1692 )
| ( in @ X1694 @ X1693 ) )
& ( ( X1694 != X1692 )
| ( in @ X1694 @ ( setadjoin @ X1692 @ X1693 ) ) )
& ( ~ ( in @ X1694 @ X1693 )
| ( in @ X1694 @ ( setadjoin @ X1692 @ X1693 ) ) )
& ( ~ ( in @ X1696 @ ( powerset @ X1695 ) )
| ~ ( in @ X1697 @ X1696 )
| ( in @ X1697 @ X1695 ) )
& ( ( in @ ( esk2_2 @ X1698 @ X1699 ) @ X1699 )
| ( in @ X1699 @ ( powerset @ X1698 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1698 @ X1699 ) @ X1698 )
| ( in @ X1699 @ ( powerset @ X1698 ) ) )
& ( ( in @ X1702 @ ( esk3_2 @ X1701 @ X1702 ) )
| ~ ( in @ X1702 @ ( setunion @ X1701 ) ) )
& ( ( in @ ( esk3_2 @ X1701 @ X1702 ) @ X1701 )
| ~ ( in @ X1702 @ ( setunion @ X1701 ) ) )
& ( ~ ( in @ X1705 @ X1706 )
| ~ ( in @ X1706 @ X1704 )
| ( in @ X1705 @ ( setunion @ X1704 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1707 @ omega )
| ( in @ ( setadjoin @ X1707 @ X1707 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1708 ) @ omega )
| ~ ( in @ emptyset @ X1708 )
| ~ ( in @ X1710 @ omega )
| ( in @ X1710 @ X1708 ) )
& ( ( in @ ( esk4_1 @ X1708 ) @ X1708 )
| ~ ( in @ emptyset @ X1708 )
| ~ ( in @ X1710 @ omega )
| ( in @ X1710 @ X1708 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1708 ) @ ( esk4_1 @ X1708 ) ) @ X1708 )
| ~ ( in @ emptyset @ X1708 )
| ~ ( in @ X1710 @ omega )
| ( in @ X1710 @ X1708 ) )
& ( ( in @ ( esk7_3 @ X1711 @ X1712 @ X1715 ) @ X1712 )
| ~ ( in @ X1715 @ ( esk6_2 @ X1711 @ X1712 ) )
| ( in @ ( esk5_2 @ X1711 @ X1712 ) @ X1712 ) )
& ( ( X1711 @ ( esk7_3 @ X1711 @ X1712 @ X1715 ) @ X1715 )
| ~ ( in @ X1715 @ ( esk6_2 @ X1711 @ X1712 ) )
| ( in @ ( esk5_2 @ X1711 @ X1712 ) @ X1712 ) )
& ( ~ ( in @ X1718 @ X1712 )
| ~ ( X1711 @ X1718 @ X1717 )
| ( in @ X1717 @ ( esk6_2 @ X1711 @ X1712 ) )
| ( in @ ( esk5_2 @ X1711 @ X1712 ) @ X1712 ) )
& ( ( in @ ( esk7_3 @ X1711 @ X1712 @ X1715 ) @ X1712 )
| ~ ( in @ X1715 @ ( esk6_2 @ X1711 @ X1712 ) )
| ~ ( exu @ ( X1711 @ ( esk5_2 @ X1711 @ X1712 ) ) ) )
& ( ( X1711 @ ( esk7_3 @ X1711 @ X1712 @ X1715 ) @ X1715 )
| ~ ( in @ X1715 @ ( esk6_2 @ X1711 @ X1712 ) )
| ~ ( exu @ ( X1711 @ ( esk5_2 @ X1711 @ X1712 ) ) ) )
& ( ~ ( in @ X1718 @ X1712 )
| ~ ( X1711 @ X1718 @ X1717 )
| ( in @ X1717 @ ( esk6_2 @ X1711 @ X1712 ) )
| ~ ( exu @ ( X1711 @ ( esk5_2 @ X1711 @ X1712 ) ) ) )
& ( ( in @ ( esk8_1 @ X1719 ) @ X1719 )
| ~ ( in @ X1720 @ X1719 ) )
& ( ~ ( in @ X1722 @ ( esk8_1 @ X1719 ) )
| ~ ( in @ X1722 @ X1719 )
| ~ ( in @ X1720 @ X1719 ) )
& epred1_0
& ( ~ ( exu @ X1723 )
| ( X1723 @ ( descr @ X1723 ) ) )
& ( ~ ( in @ X1726 @ X1724 )
| ~ ( X1725 @ X1726 )
| ( in @ X1726 @ ( dsetconstr @ X1724 @ X1725 ) ) )
& ( ~ ( in @ X1729 @ ( dsetconstr @ X1727 @ X1728 ) )
| ( in @ X1729 @ X1727 ) )
& ( ~ ( in @ X1732 @ ( dsetconstr @ X1730 @ X1731 ) )
| ( X1731 @ X1732 ) )
& ( ( X1733 @ ( esk9_1 @ X1733 ) )
| ~ ( exu @ X1733 ) )
& ( ~ ( X1733 @ X1735 )
| ( ( esk9_1 @ X1733 )
= X1735 )
| ~ ( exu @ X1733 ) )
& ( ~ ( in @ X1737 @ ( prop2set @ X1736 ) )
| X1736 )
& ( ~ ( in @ X1738 @ emptyset )
| X1739 )
& ( ~ ( in @ X1740 @ emptyset )
| ~ $true )
& ~ ( in @ X1741 @ emptyset )
& ( ~ ( exu @ X1742 )
| ( X1742 @ ( esk10_1 @ X1742 ) ) )
& ( ( in @ ( esk12_2 @ X1744 @ X1745 ) @ X1745 )
| ( X1744 = X1745 )
| ( in @ ( esk11_2 @ X1744 @ X1745 ) @ X1744 ) )
& ( ~ ( in @ ( esk12_2 @ X1744 @ X1745 ) @ X1744 )
| ( X1744 = X1745 )
| ( in @ ( esk11_2 @ X1744 @ X1745 ) @ X1744 ) )
& ( ( in @ ( esk12_2 @ X1744 @ X1745 ) @ X1745 )
| ( X1744 = X1745 )
| ~ ( in @ ( esk11_2 @ X1744 @ X1745 ) @ X1745 ) )
& ( ~ ( in @ ( esk12_2 @ X1744 @ X1745 ) @ X1744 )
| ( X1744 = X1745 )
| ~ ( in @ ( esk11_2 @ X1744 @ X1745 ) @ X1745 ) )
& ( ( in @ ( esk13_1 @ X1748 ) @ X1748 )
| ( X1748 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1750 ) @ X1750 )
| ( X1750 = emptyset ) )
& ( ~ ( in @ X1754 @ ( dsetconstr @ X1752 @ X1753 ) )
| ( X1753 @ X1754 )
| ~ ( in @ X1754 @ X1752 ) )
& ( ~ ( X1753 @ X1754 )
| ( in @ X1754 @ ( dsetconstr @ X1752 @ X1753 ) )
| ~ ( in @ X1754 @ X1752 ) )
& ( ~ ( nonempty @ X1755 )
| ( in @ ( esk15_1 @ X1755 ) @ X1755 ) )
& ( ~ ( in @ X1759 @ X1757 )
| ~ ( X1758 @ X1759 )
| ( nonempty @ ( dsetconstr @ X1757 @ X1758 ) ) )
& ( ~ ( in @ X1761 @ X1760 )
| ( nonempty @ X1760 ) )
& ( in @ X1762 @ ( setadjoin @ X1762 @ X1763 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1766 @ X1765 )
| ( in @ X1766 @ ( setadjoin @ X1764 @ X1765 ) ) )
& ( ( in @ X1769 @ X1768 )
| X1770
| ( X1769 = X1767 )
| ~ ( in @ X1769 @ ( setadjoin @ X1767 @ X1768 ) ) )
& ( ~ X1770
| X1770
| ( X1769 = X1767 )
| ~ ( in @ X1769 @ ( setadjoin @ X1767 @ X1768 ) ) )
& ( ( in @ X1769 @ X1768 )
| X1770
| ~ X1770
| ~ ( in @ X1769 @ ( setadjoin @ X1767 @ X1768 ) ) )
& ( ~ X1770
| X1770
| ~ X1770
| ~ ( in @ X1769 @ ( setadjoin @ X1767 @ X1768 ) ) )
& ( ~ ( in @ X1773 @ ( setadjoin @ X1771 @ X1772 ) )
| ( X1773 = X1771 )
| ( in @ X1773 @ X1772 ) )
& ( ( dsetconstr @ X1774
@ ^ [Z0: $i] : $true )
= X1774 )
& ( ( in @ ( esk16_2 @ X1775 @ X1776 ) @ X1776 )
| ( in @ X1776 @ ( powerset @ X1775 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1775 @ X1776 ) @ X1775 )
| ( in @ X1776 @ ( powerset @ X1775 ) ) )
& ( in @ emptyset @ ( powerset @ X1778 ) )
& ( in @ emptyset @ ( powerset @ X1779 ) )
& ( ~ ( in @ X1781 @ ( powerset @ X1780 ) )
| ~ ( in @ X1782 @ X1781 )
| ( in @ X1782 @ X1780 ) )
& ( ~ ( in @ X1784 @ X1785 )
| ~ ( in @ X1785 @ X1783 )
| ( in @ X1784 @ ( setunion @ X1783 ) ) )
& ( ( in @ X1787 @ ( esk17_3 @ X1786 @ X1787 @ X1788 ) )
| X1788
| ~ ( in @ X1787 @ ( setunion @ X1786 ) ) )
& ( ( in @ ( esk17_3 @ X1786 @ X1787 @ X1788 ) @ X1786 )
| X1788
| ~ ( in @ X1787 @ ( setunion @ X1786 ) ) )
& ( ~ X1788
| X1788
| ~ ( in @ X1787 @ ( setunion @ X1786 ) ) )
& ( ~ ( in @ X1791 @ X1790 )
| ( in @ X1791 @ ( powerset @ ( setunion @ X1790 ) ) ) )
& ( ~ ( X1792 @ X1794 )
| ( X1794
= ( esk18_1 @ X1792 ) )
| ~ ( exu @ X1792 ) )
& ( ( X1795
!= ( esk18_1 @ X1792 ) )
| ( X1792 @ X1795 )
| ~ ( exu @ X1792 ) )
& ( ( in @ ( esk19_1 @ X1796 ) @ X1796 )
| ~ ( nonempty @ X1796 ) )
& ( $true
| ~ ( nonempty @ X1796 ) )
& ( ~ ( in @ X1798 @ ( setadjoin @ X1799 @ emptyset ) )
| ( X1798 = X1799 ) )
& ( ( X1800 = X1801 )
| ~ ( in @ X1801 @ ( setadjoin @ X1800 @ emptyset ) ) )
& ( ( X1802 != X1803 )
| ( in @ X1802 @ ( setadjoin @ X1803 @ emptyset ) ) )
& ( ~ ( in @ X1804 @ ( setadjoin @ X1805 @ emptyset ) )
| ( in @ X1805 @ ( setadjoin @ X1804 @ emptyset ) ) )
& ( ~ ( in @ X1808 @ ( setadjoin @ X1806 @ ( setadjoin @ X1807 @ emptyset ) ) )
| ( X1808 = X1806 )
| ( X1808 = X1807 ) )
& ( in @ X1809 @ ( setadjoin @ X1809 @ ( setadjoin @ X1810 @ emptyset ) ) )
& ( in @ X1812 @ ( setadjoin @ X1811 @ ( setadjoin @ X1812 @ emptyset ) ) )
& ( ~ ( in @ X1815 @ X1813 )
| ~ ( X1814 @ X1815 )
| ( ( dsetconstr @ X1813 @ X1814 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1817 @ emptyset )
| ( X1816 @ X1817 ) )
& ( ( in @ ( esk20_2 @ X1818 @ X1819 ) @ X1818 )
| ~ ( in @ X1820 @ X1818 )
| ( X1819 @ X1820 ) )
& ( ~ ( X1819 @ ( esk20_2 @ X1818 @ X1819 ) )
| ~ ( in @ X1820 @ X1818 )
| ( X1819 @ X1820 ) )
& ( ( in @ ( esk21_2 @ X1822 @ X1823 ) @ X1822 )
| ~ ( in @ X1825 @ X1822 )
| ~ ( X1823 @ X1825 ) )
& ( ( X1823 @ ( esk21_2 @ X1822 @ X1823 ) )
| ~ ( in @ X1825 @ X1822 )
| ~ ( X1823 @ X1825 ) )
& ( ( in @ ( esk22_2 @ X1826 @ X1827 ) @ X1826 )
| ~ ( in @ X1829 @ X1826 )
| ~ ( X1827 @ X1829 ) )
& ( ( X1827 @ ( esk22_2 @ X1826 @ X1827 ) )
| ~ ( in @ X1829 @ X1826 )
| ~ ( X1827 @ X1829 ) )
& ( ( in @ ( esk23_2 @ X1830 @ X1831 ) @ X1830 )
| ~ ( in @ X1832 @ X1830 )
| ( X1831 @ X1832 ) )
& ( ~ ( X1831 @ ( esk23_2 @ X1830 @ X1831 ) )
| ~ ( in @ X1832 @ X1830 )
| ( X1831 @ X1832 ) )
& ( ~ X1834
| ( in @ emptyset @ ( prop2set @ X1834 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1835 @ X1836 ) @ X1835 )
| ~ ( in @ X1838 @ X1835 )
| ~ ( X1836 @ X1838 ) )
& ( ( X1836 @ ( esk24_2 @ X1835 @ X1836 ) )
| ~ ( in @ X1838 @ X1835 )
| ~ ( X1836 @ X1838 ) )
& ( ( in @ ( esk25_2 @ X1839 @ X1840 ) @ X1839 )
| ~ ( in @ X1841 @ X1839 )
| ( X1840 @ X1841 ) )
& ( ~ ( X1840 @ ( esk25_2 @ X1839 @ X1840 ) )
| ~ ( in @ X1841 @ X1839 )
| ( X1840 @ X1841 ) )
& ( ( X1843 @ ( esk26_2 @ X1843 @ X1844 ) )
| ~ ( X1843 @ X1844 )
| ( exu @ X1843 ) )
& ( ( X1844
!= ( esk26_2 @ X1843 @ X1844 ) )
| ~ ( X1843 @ X1844 )
| ( exu @ X1843 ) )
& ( ( X1846 @ ( esk27_1 @ X1846 ) )
| ( exu @ X1846 )
| ~ ( X1846 @ X1847 ) )
& ( ( X1846 @ ( esk28_1 @ X1846 ) )
| ( exu @ X1846 )
| ~ ( X1846 @ X1847 ) )
& ( ( ( esk27_1 @ X1846 )
!= ( esk28_1 @ X1846 ) )
| ( exu @ X1846 )
| ~ ( X1846 @ X1847 ) )
& ( ~ ( X1850 @ ( esk29_2 @ X1850 @ X1851 ) )
| ( ( esk29_2 @ X1850 @ X1851 )
!= X1851 )
| ( exu @ X1850 ) )
& ( ( X1850 @ ( esk29_2 @ X1850 @ X1851 ) )
| ( ( esk29_2 @ X1850 @ X1851 )
= X1851 )
| ( exu @ X1850 ) )
& ( ( X1853 != X1854 )
| ( X1855 != X1856 )
| ~ ( in @ X1855 @ X1853 )
| ( in @ X1856 @ X1854 ) )
& ( ~ ( in @ X1859 @ X1857 )
| ( in @ X1860 @ X1858 )
| ( X1859 != X1860 )
| ( X1857 != X1858 ) )
& ( ~ ( in @ X1860 @ X1858 )
| ( in @ X1859 @ X1857 )
| ( X1859 != X1860 )
| ( X1857 != X1858 ) )
& ( ~ ( exu @ X1861 )
| ~ ( X1861 @ X1862 )
| ~ ( X1861 @ X1863 )
| ( X1862 = X1863 ) )
& ( ~ ( exu @ X1864 )
| ( exu @ X1865 )
| ( ( esk30_2 @ X1864 @ X1865 )
= ( esk31_2 @ X1864 @ X1865 ) ) )
& ( ~ ( exu @ X1865 )
| ( exu @ X1864 )
| ( ( esk30_2 @ X1864 @ X1865 )
= ( esk31_2 @ X1864 @ X1865 ) ) )
& ( ~ ( exu @ X1864 )
| ( exu @ X1865 )
| ~ ( X1864 @ ( esk30_2 @ X1864 @ X1865 ) )
| ~ ( X1865 @ ( esk31_2 @ X1864 @ X1865 ) ) )
& ( ~ ( exu @ X1865 )
| ( exu @ X1864 )
| ~ ( X1864 @ ( esk30_2 @ X1864 @ X1865 ) )
| ~ ( X1865 @ ( esk31_2 @ X1864 @ X1865 ) ) )
& ( ~ ( exu @ X1864 )
| ( exu @ X1865 )
| ( X1864 @ ( esk30_2 @ X1864 @ X1865 ) )
| ( X1865 @ ( esk31_2 @ X1864 @ X1865 ) ) )
& ( ~ ( exu @ X1865 )
| ( exu @ X1864 )
| ( X1864 @ ( esk30_2 @ X1864 @ X1865 ) )
| ( X1865 @ ( esk31_2 @ X1864 @ X1865 ) ) )
& ( emptyset = emptyset )
& ( ( X1868 != X1869 )
| ( X1870 != X1871 )
| ( ( setadjoin @ X1868 @ X1870 )
= ( setadjoin @ X1869 @ X1871 ) ) )
& ( ( X1872 != X1873 )
| ( ( powerset @ X1872 )
= ( powerset @ X1873 ) ) )
& ( ( X1874 != X1875 )
| ( ( setunion @ X1874 )
= ( setunion @ X1875 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1876 )
| ~ ( X1876 @ X1877 )
| ~ ( X1876 @ X1878 )
| ( X1877 = X1878 ) )
& ( ( ( esk32_2 @ X1879 @ X1880 )
= ( esk33_2 @ X1879 @ X1880 ) )
| ~ ( exu @ X1879 )
| ~ ( exu @ X1880 )
| ( ( descr @ X1879 )
= ( descr @ X1880 ) ) )
& ( ~ ( X1879 @ ( esk32_2 @ X1879 @ X1880 ) )
| ~ ( X1880 @ ( esk33_2 @ X1879 @ X1880 ) )
| ~ ( exu @ X1879 )
| ~ ( exu @ X1880 )
| ( ( descr @ X1879 )
= ( descr @ X1880 ) ) )
& ( ( X1879 @ ( esk32_2 @ X1879 @ X1880 ) )
| ( X1880 @ ( esk33_2 @ X1879 @ X1880 ) )
| ~ ( exu @ X1879 )
| ~ ( exu @ X1880 )
| ( ( descr @ X1879 )
= ( descr @ X1880 ) ) )
& ( ( in @ ( esk34_4 @ X1883 @ X1884 @ X1885 @ X1886 ) @ X1883 )
| ( ( dsetconstr @ X1883 @ X1885 )
= ( dsetconstr @ X1884 @ X1886 ) )
| ( X1883 != X1884 ) )
& ( ( in @ ( esk35_4 @ X1883 @ X1884 @ X1885 @ X1886 ) @ X1884 )
| ( ( dsetconstr @ X1883 @ X1885 )
= ( dsetconstr @ X1884 @ X1886 ) )
| ( X1883 != X1884 ) )
& ( ( ( esk34_4 @ X1883 @ X1884 @ X1885 @ X1886 )
= ( esk35_4 @ X1883 @ X1884 @ X1885 @ X1886 ) )
| ( ( dsetconstr @ X1883 @ X1885 )
= ( dsetconstr @ X1884 @ X1886 ) )
| ( X1883 != X1884 ) )
& ( ~ ( X1885 @ ( esk34_4 @ X1883 @ X1884 @ X1885 @ X1886 ) )
| ~ ( X1886 @ ( esk35_4 @ X1883 @ X1884 @ X1885 @ X1886 ) )
| ( ( dsetconstr @ X1883 @ X1885 )
= ( dsetconstr @ X1884 @ X1886 ) )
| ( X1883 != X1884 ) )
& ( ( X1885 @ ( esk34_4 @ X1883 @ X1884 @ X1885 @ X1886 ) )
| ( X1886 @ ( esk35_4 @ X1883 @ X1884 @ X1885 @ X1886 ) )
| ( ( dsetconstr @ X1883 @ X1885 )
= ( dsetconstr @ X1884 @ X1886 ) )
| ( X1883 != X1884 ) )
& ( ( in @ ( esk36_2 @ X1889 @ X1890 ) @ X1889 )
| ( subset @ X1889 @ X1890 ) )
& ( ~ ( in @ ( esk36_2 @ X1889 @ X1890 ) @ X1890 )
| ( subset @ X1889 @ X1890 ) )
& ( ( X1892 != X1893 )
| ( subset @ X1893 @ X1892 ) )
& ( ( X1894 != X1895 )
| ( subset @ X1894 @ X1895 ) )
& ( ( in @ ( esk37_2 @ X1896 @ X1897 ) @ X1896 )
| ( subset @ X1896 @ X1897 ) )
& ( ~ ( in @ ( esk37_2 @ X1896 @ X1897 ) @ X1897 )
| ( subset @ X1896 @ X1897 ) )
& ( subset @ emptyset @ X1899 )
& ( ~ ( subset @ X1900 @ X1901 )
| ~ ( in @ X1902 @ X1900 )
| ( in @ X1902 @ X1901 ) )
& ( ~ ( subset @ X1903 @ X1904 )
| ( in @ X1905 @ X1904 )
| ~ ( in @ X1905 @ X1903 ) )
& ( ~ ( in @ X1908 @ X1906 )
| ( in @ X1908 @ X1907 )
| ~ ( subset @ X1906 @ X1907 ) )
& ( ( subset @ X1909 @ X1910 )
| ( X1909 != X1910 ) )
& ( ~ ( in @ X1913 @ X1911 )
| ( in @ X1913 @ X1912 )
| ( X1911 != X1912 ) )
& ( subset @ X1914 @ X1914 )
& ( ~ ( subset @ X1915 @ X1916 )
| ~ ( subset @ X1916 @ X1917 )
| ( subset @ X1915 @ X1917 ) )
& ( subset @ X1919 @ ( setadjoin @ X1918 @ X1919 ) )
& ( ~ ( subset @ X1920 @ X1922 )
| ( subset @ X1920 @ ( setadjoin @ X1921 @ X1922 ) ) )
& ( ~ ( subset @ X1923 @ X1924 )
| ( in @ X1923 @ ( powerset @ X1924 ) ) )
& ( ~ ( subset @ X1925 @ X1926 )
| ~ ( subset @ X1926 @ X1925 )
| ( X1925 = X1926 ) )
& ( ~ ( subset @ X1927 @ emptyset )
| ( X1927 = emptyset ) )
& ( ~ ( subset @ X1929 @ X1928 )
| ( in @ X1929 @ ( powerset @ X1928 ) ) )
& ( ~ ( in @ X1931 @ ( powerset @ X1930 ) )
| ( subset @ X1931 @ X1930 ) )
& ( in @ X1932 @ ( powerset @ X1932 ) )
& ( ~ ( subset @ X1933 @ X1934 )
| ( subset @ ( powerset @ X1933 ) @ ( powerset @ X1934 ) ) )
& ( in @ ( dsetconstr @ X1935 @ X1936 ) @ ( powerset @ X1935 ) )
& ( subset @ ( dsetconstr @ X1937 @ X1938 ) @ X1937 )
& ( ~ ( in @ X1941 @ X1939 )
| ( in @ X1941 @ ( binunion @ X1939 @ X1940 ) ) )
& ( in @ X1943 @ ( setadjoin @ X1942 @ ( setadjoin @ X1943 @ emptyset ) ) )
& ( ~ ( in @ X1946 @ X1945 )
| ( in @ X1946 @ ( binunion @ X1944 @ X1945 ) ) )
& ( ( in @ X1949 @ X1948 )
| X1950
| ( in @ X1949 @ X1947 )
| ~ ( in @ X1949 @ ( binunion @ X1947 @ X1948 ) ) )
& ( ~ X1950
| X1950
| ( in @ X1949 @ X1947 )
| ~ ( in @ X1949 @ ( binunion @ X1947 @ X1948 ) ) )
& ( ( in @ X1949 @ X1948 )
| X1950
| ~ X1950
| ~ ( in @ X1949 @ ( binunion @ X1947 @ X1948 ) ) )
& ( ~ X1950
| X1950
| ~ X1950
| ~ ( in @ X1949 @ ( binunion @ X1947 @ X1948 ) ) )
& ( ~ ( in @ X1953 @ ( binunion @ X1951 @ X1952 ) )
| ( in @ X1953 @ X1951 )
| ( in @ X1953 @ X1952 ) )
& ( subset @ X1954 @ ( binunion @ X1954 @ X1955 ) )
& ( subset @ X1957 @ ( binunion @ X1956 @ X1957 ) )
& ( ~ ( in @ X1960 @ X1958 )
| ~ ( in @ X1960 @ X1959 )
| ( in @ X1960 @ ( binintersect @ X1958 @ X1959 ) ) )
& ( ~ ( subset @ X1963 @ X1961 )
| ~ ( subset @ X1963 @ X1962 )
| ( subset @ X1963 @ ( binintersect @ X1961 @ X1962 ) ) )
& ( ~ ( in @ X1966 @ ( binintersect @ X1964 @ X1965 ) )
| ( in @ X1966 @ X1964 ) )
& ( subset @ ( binintersect @ X1967 @ X1968 ) @ X1967 )
& ( ~ ( subset @ X1969 @ X1970 )
| ( ( binintersect @ X1969 @ X1970 )
= X1969 ) )
& ( ( ( binintersect @ X1971 @ X1972 )
!= X1972 )
| ( subset @ X1972 @ X1971 ) )
& ( ~ ( in @ X1975 @ ( binintersect @ X1973 @ X1974 ) )
| ( in @ X1975 @ X1974 ) )
& ( ( in @ ( esk38_2 @ X1976 @ X1977 ) @ X1976 )
| ( ( binintersect @ X1976 @ X1977 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1976 @ X1977 ) @ X1977 )
| ( ( binintersect @ X1976 @ X1977 )
= emptyset ) )
& ( subset @ ( binintersect @ X1979 @ X1980 ) @ X1980 )
& ( ~ ( subset @ X1982 @ X1981 )
| ( ( binintersect @ X1981 @ X1982 )
= X1982 ) )
& ( ( ( binintersect @ X1983 @ X1984 )
!= X1983 )
| ( subset @ X1983 @ X1984 ) )
& ( ( binintersect @ X1985 @ ( binunion @ X1986 @ X1987 ) )
= ( binunion @ ( binintersect @ X1985 @ X1986 ) @ ( binintersect @ X1985 @ X1987 ) ) )
& ( ~ ( in @ X1990 @ X1988 )
| ( in @ X1990 @ X1989 )
| ( in @ X1990 @ ( setminus @ X1988 @ X1989 ) ) )
& ( ~ ( in @ X1993 @ ( setminus @ X1991 @ X1992 ) )
| ( in @ X1993 @ X1991 ) )
& ( ~ ( in @ X1996 @ ( setminus @ X1994 @ X1995 ) )
| ~ ( in @ X1996 @ X1995 ) )
& ( ~ ( subset @ X1997 @ X1998 )
| ( ( setminus @ X1997 @ X1998 )
= emptyset ) )
& ( ( in @ X2001 @ ( setminus @ X1999 @ X2000 ) )
| ~ ( in @ X2001 @ X1999 )
| ( in @ X2001 @ X2000 ) )
& ( ( in @ X2004 @ ( setminus @ X2002 @ X2003 ) )
| ( in @ X2004 @ X2003 )
| ~ ( in @ X2004 @ X2002 ) )
& ( ( in @ X2007 @ X2005 )
| ~ ( in @ X2007 @ ( setminus @ X2005 @ X2006 ) ) )
& ( ~ ( in @ X2010 @ X2009 )
| ~ ( in @ X2010 @ ( setminus @ X2008 @ X2009 ) ) )
& ( subset @ ( setminus @ X2011 @ X2012 ) @ X2011 )
& ( ( ( setminus @ X2013 @ X2014 )
!= emptyset )
| ( subset @ X2013 @ X2014 ) )
& ( ~ ( in @ X2017 @ X2015 )
| X2018
| ( in @ X2017 @ X2015 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ( in @ X2017 @ X2016 )
| X2018
| ( in @ X2017 @ X2015 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ X2018
| X2018
| ( in @ X2017 @ X2015 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ ( in @ X2017 @ X2015 )
| X2018
| ~ ( in @ X2017 @ X2016 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ( in @ X2017 @ X2016 )
| X2018
| ~ ( in @ X2017 @ X2016 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ X2018
| X2018
| ~ ( in @ X2017 @ X2016 )
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ ( in @ X2017 @ X2015 )
| X2018
| ~ X2018
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ( in @ X2017 @ X2016 )
| X2018
| ~ X2018
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ X2018
| X2018
| ~ X2018
| ~ ( in @ X2017 @ ( symdiff @ X2015 @ X2016 ) ) )
& ( ~ ( in @ X2021 @ X2019 )
| ( in @ X2021 @ X2020 )
| ( in @ X2021 @ ( symdiff @ X2019 @ X2020 ) ) )
& ( ( in @ X2024 @ X2022 )
| ~ ( in @ X2024 @ X2023 )
| ( in @ X2024 @ ( symdiff @ X2022 @ X2023 ) ) )
& ( ~ ( in @ X2027 @ X2025 )
| ~ ( in @ X2027 @ X2026 )
| ~ ( in @ X2027 @ ( symdiff @ X2025 @ X2026 ) ) )
& ( ( in @ X2030 @ X2028 )
| ( in @ X2030 @ X2029 )
| ~ ( in @ X2030 @ ( symdiff @ X2028 @ X2029 ) ) )
& ( in @ X2032 @ ( setadjoin @ X2031 @ ( setadjoin @ X2032 @ emptyset ) ) )
& ( in @ X2033 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2033 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2033 @ ( setadjoin @ X2034 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2036 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2035 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2035 @ ( setadjoin @ X2036 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2037 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2037 @ ( setadjoin @ X2038 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2039 @ X2040 ) )
& ( ~ ( in @ X2042 @ X2041 )
| ( subset @ ( setadjoin @ X2042 @ emptyset ) @ X2041 ) )
& ( ~ ( in @ X2044 @ X2043 )
| ( in @ ( setadjoin @ X2044 @ emptyset ) @ ( powerset @ X2043 ) ) )
& ( ~ ( in @ X2047 @ X2045 )
| ( in @ ( setadjoin @ X2047 @ emptyset ) @ ( powerset @ ( binunion @ X2045 @ X2046 ) ) ) )
& ( ~ ( in @ X2050 @ ( setadjoin @ X2048 @ ( setadjoin @ X2049 @ emptyset ) ) )
| ( X2050 = X2048 )
| ( X2050 = X2049 ) )
& ( ~ ( in @ X2053 @ X2051 )
| ~ ( in @ X2054 @ X2052 )
| ( subset @ ( setadjoin @ X2053 @ ( setadjoin @ X2054 @ emptyset ) ) @ ( binunion @ X2051 @ X2052 ) ) )
& ( ~ ( in @ X2057 @ X2055 )
| ~ ( in @ X2058 @ X2056 )
| ( in @ ( setadjoin @ X2057 @ ( setadjoin @ X2058 @ emptyset ) ) @ ( powerset @ ( binunion @ X2055 @ X2056 ) ) ) )
& ( ~ ( in @ X2061 @ X2059 )
| ~ ( in @ X2062 @ X2060 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2061 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2061 @ ( setadjoin @ X2062 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2059 @ X2060 ) ) ) )
& ( ~ ( in @ X2065 @ X2063 )
| ~ ( in @ X2066 @ X2064 )
| ( in @ ( setadjoin @ ( setadjoin @ X2065 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2065 @ ( setadjoin @ X2066 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2063 @ X2064 ) ) ) ) )
& ( ~ ( in @ X2069 @ X2067 )
| ~ ( in @ X2070 @ X2068 )
| ( in @ ( kpair @ X2069 @ X2070 ) @ ( powerset @ ( powerset @ ( binunion @ X2067 @ X2068 ) ) ) ) )
& ( ~ ( in @ X2073 @ X2071 )
| ~ ( in @ X2074 @ X2072 )
| ( in @ ( kpair @ X2073 @ X2074 ) @ ( cartprod @ X2071 @ X2072 ) ) )
& ( ( in @ ( esk39_3 @ X2075 @ X2076 @ X2077 ) @ X2075 )
| ~ ( in @ X2077 @ ( cartprod @ X2075 @ X2076 ) ) )
& ( ( in @ ( esk40_3 @ X2075 @ X2076 @ X2077 ) @ X2076 )
| ~ ( in @ X2077 @ ( cartprod @ X2075 @ X2076 ) ) )
& ( ( X2077
= ( kpair @ ( esk39_3 @ X2075 @ X2076 @ X2077 ) @ ( esk40_3 @ X2075 @ X2076 @ X2077 ) ) )
| ~ ( in @ X2077 @ ( cartprod @ X2075 @ X2076 ) ) )
& ( ~ ( in @ X2082 @ ( cartprod @ X2080 @ X2081 ) )
| ( iskpair @ X2082 ) )
& ( ( in @ ( esk41_2 @ X2083 @ X2084 ) @ X2083 )
| ~ ( in @ X2084 @ ( setunion @ X2083 ) ) )
& ( ( in @ X2084 @ ( esk41_2 @ X2083 @ X2084 ) )
| ~ ( in @ X2084 @ ( setunion @ X2083 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2086 @ emptyset ) ) @ X2086 )
& ( subset @ X2087 @ ( setunion @ ( setadjoin @ X2087 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2088 @ emptyset ) )
= X2088 )
& ( ( in @ ( esk42_2 @ X2089 @ X2090 ) @ X2089 )
| ~ ( in @ X2093 @ X2089 )
| ~ ( X2090 @ X2093 )
| ( singleton @ ( dsetconstr @ X2089 @ X2090 ) ) )
& ( ( in @ ( esk43_2 @ X2089 @ X2090 ) @ X2089 )
| ~ ( in @ X2093 @ X2089 )
| ~ ( X2090 @ X2093 )
| ( singleton @ ( dsetconstr @ X2089 @ X2090 ) ) )
& ( ( X2090 @ ( esk42_2 @ X2089 @ X2090 ) )
| ~ ( in @ X2093 @ X2089 )
| ~ ( X2090 @ X2093 )
| ( singleton @ ( dsetconstr @ X2089 @ X2090 ) ) )
& ( ( X2090 @ ( esk43_2 @ X2089 @ X2090 ) )
| ~ ( in @ X2093 @ X2089 )
| ~ ( X2090 @ X2093 )
| ( singleton @ ( dsetconstr @ X2089 @ X2090 ) ) )
& ( ( ( esk42_2 @ X2089 @ X2090 )
!= ( esk43_2 @ X2089 @ X2090 ) )
| ~ ( in @ X2093 @ X2089 )
| ~ ( X2090 @ X2093 )
| ( singleton @ ( dsetconstr @ X2089 @ X2090 ) ) )
& ( ( in @ ( esk44_2 @ X2094 @ X2095 ) @ X2094 )
| ~ ( ex1 @ X2094 @ X2095 ) )
& ( ( X2095 @ ( esk44_2 @ X2094 @ X2095 ) )
| ~ ( ex1 @ X2094 @ X2095 ) )
& ( ( in @ ( esk45_3 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ( ex1 @ X2097 @ X2098 )
| ~ ( X2098 @ X2099 )
| ~ ( in @ X2099 @ X2097 ) )
& ( ( X2098 @ ( esk45_3 @ X2097 @ X2098 @ X2099 ) )
| ( ex1 @ X2097 @ X2098 )
| ~ ( X2098 @ X2099 )
| ~ ( in @ X2099 @ X2097 ) )
& ( ( ( esk45_3 @ X2097 @ X2098 @ X2099 )
!= X2099 )
| ( ex1 @ X2097 @ X2098 )
| ~ ( X2098 @ X2099 )
| ~ ( in @ X2099 @ X2097 ) )
& ( ( in @ ( esk46_2 @ X2101 @ X2102 ) @ X2101 )
| ~ ( in @ X2105 @ X2101 )
| ~ ( X2102 @ X2105 )
| ( ex1 @ X2101 @ X2102 ) )
& ( ( in @ ( esk47_2 @ X2101 @ X2102 ) @ X2101 )
| ~ ( in @ X2105 @ X2101 )
| ~ ( X2102 @ X2105 )
| ( ex1 @ X2101 @ X2102 ) )
& ( ( X2102 @ ( esk46_2 @ X2101 @ X2102 ) )
| ~ ( in @ X2105 @ X2101 )
| ~ ( X2102 @ X2105 )
| ( ex1 @ X2101 @ X2102 ) )
& ( ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) )
| ~ ( in @ X2105 @ X2101 )
| ~ ( X2102 @ X2105 )
| ( ex1 @ X2101 @ X2102 ) )
& ( ( ( esk46_2 @ X2101 @ X2102 )
!= ( esk47_2 @ X2101 @ X2102 ) )
| ~ ( in @ X2105 @ X2101 )
| ~ ( X2102 @ X2105 )
| ( ex1 @ X2101 @ X2102 ) )
& ( ( ( setadjoin @ X2106 @ emptyset )
!= ( setadjoin @ X2107 @ emptyset ) )
| ( X2106 = X2107 ) )
& ( ~ ( in @ ( setadjoin @ X2110 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2108 @ ( setadjoin @ X2109 @ emptyset ) ) @ emptyset ) ) )
| ( X2108 = X2110 ) )
& ( ~ ( iskpair @ X2111 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2111 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2111 ) ) ) )
& ( ~ ( singleton @ X2112 )
| ( in @ ( setunion @ X2112 ) @ X2112 ) )
& ( ( kfst @ ( kpair @ X2113 @ X2114 ) )
= X2113 )
& ( ~ ( in @ X2117 @ ( cartprod @ X2115 @ X2116 ) )
| ( in @ ( kfst @ X2117 ) @ X2115 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2118 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2118 @ ( setadjoin @ X2119 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2120 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2120 @ ( setadjoin @ X2121 @ emptyset ) ) @ emptyset ) ) )
| ( X2118 = X2120 ) )
& ( ( ( kpair @ X2122 @ X2123 )
!= ( kpair @ X2124 @ X2125 ) )
| ( X2122 = X2124 ) )
& ( ( X2126 != X2127 )
| ( ( setadjoin @ X2126 @ ( setadjoin @ X2127 @ emptyset ) )
= ( setadjoin @ X2126 @ emptyset ) ) )
& ( ( X2128 != X2129 )
| ( ( setadjoin @ ( setadjoin @ X2128 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2128 @ ( setadjoin @ X2129 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2128 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2130 @ ( setadjoin @ X2131 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2132 @ ( setadjoin @ X2133 @ emptyset ) ) @ emptyset ) ) )
| ( X2132 != X2133 )
| ( X2131 = X2133 ) )
& ( ( ( setadjoin @ X2134 @ ( setadjoin @ X2135 @ emptyset ) )
!= ( setadjoin @ X2136 @ emptyset ) )
| ( X2134 = X2135 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2137 @ ( setadjoin @ X2138 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2139 @ ( setadjoin @ X2140 @ emptyset ) ) @ emptyset ) ) )
| ( X2138 = X2140 ) )
& ( ( ( kpair @ X2141 @ X2142 )
!= ( kpair @ X2143 @ X2144 ) )
| ( X2142 = X2144 ) )
& ( ~ ( iskpair @ X2145 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2145 )
@ ^ [Z0: $i] :
( X2145
= ( kpair @ ( kfst @ X2145 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2146 @ X2147 ) )
= X2147 )
& ( ~ ( iskpair @ X2148 )
| ( ( kpair @ ( kfst @ X2148 ) @ ( ksnd @ X2148 ) )
= X2148 ) )
& ( ~ ( in @ X2151 @ ( cartprod @ X2149 @ X2150 ) )
| ( in @ ( ksnd @ X2151 ) @ X2150 ) )
& ( ~ ( in @ ( kpair @ X2154 @ X2155 ) @ ( cartprod @ X2152 @ X2153 ) )
| ( in @ X2154 @ X2152 ) )
& ( ~ ( in @ ( kpair @ X2158 @ X2159 ) @ ( cartprod @ X2156 @ X2157 ) )
| ( in @ X2159 @ X2157 ) )
& ( ~ ( in @ X2162 @ X2160 )
| ~ ( in @ X2163 @ X2161 )
| ( ( kpair @ X2162 @ X2163 )
= ( kpair @ X2162 @ X2163 ) ) )
& ( ~ ( in @ X2166 @ X2164 )
| ~ ( in @ X2167 @ X2165 )
| ( ( kfst @ ( kpair @ X2166 @ X2167 ) )
= X2166 ) )
& ( ~ ( in @ X2170 @ X2168 )
| ~ ( in @ X2171 @ X2169 )
| ( ( ksnd @ ( kpair @ X2170 @ X2171 ) )
= X2171 ) )
& ( ~ ( in @ X2174 @ ( cartprod @ X2172 @ X2173 ) )
| ( ( kpair @ ( kfst @ X2174 ) @ ( ksnd @ X2174 ) )
= X2174 ) )
& ( ~ ( in @ X2178 @ X2175 )
| ~ ( in @ X2179 @ X2176 )
| ~ ( X2177 @ X2178 @ X2179 )
| ( in @ ( kpair @ X2178 @ X2179 ) @ ( dpsetconstr @ X2175 @ X2176 @ X2177 ) ) )
& ( subset @ ( dpsetconstr @ X2180 @ X2181 @ X2182 ) @ ( cartprod @ X2180 @ X2181 ) )
& ( breln @ X2183 @ X2184 @ ( dpsetconstr @ X2183 @ X2184 @ X2185 ) )
& ( ~ ( in @ X2189 @ X2186 )
| ~ ( in @ X2190 @ X2187 )
| ~ ( in @ ( kpair @ X2189 @ X2190 ) @ ( dpsetconstr @ X2186 @ X2187 @ X2188 ) )
| ( X2188 @ X2189 @ X2190 ) )
& ( ~ ( in @ ( kpair @ X2194 @ X2195 ) @ ( dpsetconstr @ X2191 @ X2192 @ X2193 ) )
| ( in @ X2194 @ X2191 ) )
& ( ~ ( in @ ( kpair @ X2199 @ X2200 ) @ ( dpsetconstr @ X2196 @ X2197 @ X2198 ) )
| ( in @ X2200 @ X2197 ) )
& ( ~ ( in @ ( kpair @ X2204 @ X2205 ) @ ( dpsetconstr @ X2201 @ X2202 @ X2203 ) )
| ( X2203 @ X2204 @ X2205 ) )
& ( ~ ( func @ X2206 @ X2207 @ X2208 )
| ~ ( in @ X2209 @ X2206 )
| ( singleton
@ ( dsetconstr @ X2207
@ ^ [Z0: $i] : ( in @ ( kpair @ X2209 @ Z0 ) @ X2208 ) ) ) )
& ( ~ ( func @ X2210 @ X2211 @ X2212 )
| ~ ( in @ X2213 @ X2210 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2211
@ ^ [Z0: $i] : ( in @ ( kpair @ X2213 @ Z0 ) @ X2212 ) ) )
@ X2211 ) )
& ( ~ ( func @ X2214 @ X2215 @ X2216 )
| ~ ( in @ X2217 @ X2214 )
| ( in @ ( ap @ X2214 @ X2215 @ X2216 @ X2217 ) @ X2215 ) )
& ( ~ ( in @ X2220 @ ( funcSet @ X2218 @ X2219 ) )
| ( func @ X2218 @ X2219 @ X2220 ) )
& ( ~ ( in @ X2223 @ ( funcSet @ X2221 @ X2222 ) )
| ~ ( in @ X2224 @ X2221 )
| ( in @ ( ap @ X2221 @ X2222 @ X2223 @ X2224 ) @ X2222 ) )
& ( ~ ( func @ X2225 @ X2226 @ X2227 )
| ( in @ X2227 @ ( funcSet @ X2225 @ X2226 ) ) )
& ( ( in @ ( esk48_3 @ X2228 @ X2229 @ X2230 ) @ X2228 )
| ( func @ X2228 @ X2229
@ ( dpsetconstr @ X2228 @ X2229
@ ^ [Z0: $i] : ( $eq @ ( X2230 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2230 @ ( esk48_3 @ X2228 @ X2229 @ X2230 ) ) @ X2229 )
| ( func @ X2228 @ X2229
@ ( dpsetconstr @ X2228 @ X2229
@ ^ [Z0: $i] : ( $eq @ ( X2230 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2232 @ X2233 @ X2234 ) @ X2232 )
| ( func @ X2232 @ X2233 @ ( lam @ X2232 @ X2233 @ X2234 ) ) )
& ( ~ ( in @ ( X2234 @ ( esk49_3 @ X2232 @ X2233 @ X2234 ) ) @ X2233 )
| ( func @ X2232 @ X2233 @ ( lam @ X2232 @ X2233 @ X2234 ) ) )
& ( ( in @ ( esk50_3 @ X2236 @ X2237 @ X2238 ) @ X2236 )
| ( in @ ( lam @ X2236 @ X2237 @ X2238 ) @ ( funcSet @ X2236 @ X2237 ) ) )
& ( ~ ( in @ ( X2238 @ ( esk50_3 @ X2236 @ X2237 @ X2238 ) ) @ X2237 )
| ( in @ ( lam @ X2236 @ X2237 @ X2238 ) @ ( funcSet @ X2236 @ X2237 ) ) )
& ( ( in @ ( esk51_4 @ X2240 @ X2241 @ X2242 @ X2243 ) @ X2240 )
| ~ ( in @ X2246 @ X2242 )
| ( X2243 @ X2246 )
| ~ ( breln @ X2240 @ X2241 @ X2242 ) )
& ( ( in @ ( esk52_4 @ X2240 @ X2241 @ X2242 @ X2243 ) @ X2241 )
| ~ ( in @ X2246 @ X2242 )
| ( X2243 @ X2246 )
| ~ ( breln @ X2240 @ X2241 @ X2242 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2240 @ X2241 @ X2242 @ X2243 ) @ ( esk52_4 @ X2240 @ X2241 @ X2242 @ X2243 ) ) @ X2242 )
| ~ ( in @ X2246 @ X2242 )
| ( X2243 @ X2246 )
| ~ ( breln @ X2240 @ X2241 @ X2242 ) )
& ( ~ ( X2243 @ ( kpair @ ( esk51_4 @ X2240 @ X2241 @ X2242 @ X2243 ) @ ( esk52_4 @ X2240 @ X2241 @ X2242 @ X2243 ) ) )
| ~ ( in @ X2246 @ X2242 )
| ( X2243 @ X2246 )
| ~ ( breln @ X2240 @ X2241 @ X2242 ) )
& ( ( in @ ( esk53_4 @ X2247 @ X2248 @ X2249 @ X2250 ) @ X2247 )
| ~ ( in @ X2253 @ X2249 )
| ( X2250 @ X2253 )
| ~ ( breln @ X2247 @ X2248 @ X2249 ) )
& ( ( in @ ( esk54_4 @ X2247 @ X2248 @ X2249 @ X2250 ) @ X2248 )
| ~ ( in @ X2253 @ X2249 )
| ( X2250 @ X2253 )
| ~ ( breln @ X2247 @ X2248 @ X2249 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2247 @ X2248 @ X2249 @ X2250 ) @ ( esk54_4 @ X2247 @ X2248 @ X2249 @ X2250 ) ) @ X2249 )
| ~ ( in @ X2253 @ X2249 )
| ( X2250 @ X2253 )
| ~ ( breln @ X2247 @ X2248 @ X2249 ) )
& ( ~ ( X2250 @ ( kpair @ ( esk53_4 @ X2247 @ X2248 @ X2249 @ X2250 ) @ ( esk54_4 @ X2247 @ X2248 @ X2249 @ X2250 ) ) )
| ~ ( in @ X2253 @ X2249 )
| ( X2250 @ X2253 )
| ~ ( breln @ X2247 @ X2248 @ X2249 ) )
& ( ~ ( ex1 @ X2254 @ X2255 )
| ~ ( in @ X2256 @ X2254 )
| ~ ( in @ X2257 @ X2254 )
| ~ ( X2255 @ X2256 )
| ~ ( X2255 @ X2257 )
| ( X2256 = X2257 ) )
& ( ~ ( func @ X2258 @ X2259 @ X2260 )
| ~ ( in @ X2261 @ X2258 )
| ( in @ ( kpair @ X2261 @ ( ap @ X2258 @ X2259 @ X2260 @ X2261 ) ) @ X2260 ) )
& ( ~ ( in @ X2264 @ ( funcSet @ X2262 @ X2263 ) )
| ~ ( in @ X2265 @ X2262 )
| ( in @ ( kpair @ X2265 @ ( ap @ X2262 @ X2263 @ X2264 @ X2265 ) ) @ X2264 ) )
& ( ~ ( func @ X2266 @ X2267 @ X2268 )
| ~ ( in @ X2269 @ X2266 )
| ~ ( in @ X2270 @ X2267 )
| ~ ( in @ ( kpair @ X2269 @ X2270 ) @ X2268 )
| ( ( ap @ X2266 @ X2267 @ X2268 @ X2269 )
= X2270 ) )
& ( ( in @ ( esk55_4 @ X2271 @ X2272 @ X2273 @ X2274 ) @ X2271 )
| ~ ( in @ X2276 @ X2271 )
| ~ ( in @ X2277 @ X2272 )
| ~ ( in @ ( kpair @ X2276 @ X2277 ) @ X2274 )
| ( in @ ( kpair @ X2276 @ X2277 ) @ X2273 )
| ~ ( func @ X2271 @ X2272 @ X2274 )
| ~ ( func @ X2271 @ X2272 @ X2273 ) )
& ( ( ( ap @ X2271 @ X2272 @ X2273 @ ( esk55_4 @ X2271 @ X2272 @ X2273 @ X2274 ) )
!= ( ap @ X2271 @ X2272 @ X2274 @ ( esk55_4 @ X2271 @ X2272 @ X2273 @ X2274 ) ) )
| ~ ( in @ X2276 @ X2271 )
| ~ ( in @ X2277 @ X2272 )
| ~ ( in @ ( kpair @ X2276 @ X2277 ) @ X2274 )
| ( in @ ( kpair @ X2276 @ X2277 ) @ X2273 )
| ~ ( func @ X2271 @ X2272 @ X2274 )
| ~ ( func @ X2271 @ X2272 @ X2273 ) )
& ( ~ ( in @ X2280 @ ( funcSet @ X2278 @ X2279 ) )
| ~ ( in @ X2281 @ X2278 )
| ~ ( in @ X2282 @ X2279 )
| ~ ( in @ ( kpair @ X2281 @ X2282 ) @ X2280 )
| ( ( ap @ X2278 @ X2279 @ X2280 @ X2281 )
= X2282 ) )
& ( ( in @ ( esk56_4 @ X2283 @ X2284 @ X2285 @ X2286 ) @ X2283 )
| ( subset @ X2285 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2285 ) )
& ( ( in @ ( esk57_4 @ X2283 @ X2284 @ X2285 @ X2286 ) @ X2284 )
| ( subset @ X2285 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2285 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2283 @ X2284 @ X2285 @ X2286 ) @ ( esk57_4 @ X2283 @ X2284 @ X2285 @ X2286 ) ) @ X2285 )
| ( subset @ X2285 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2285 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2283 @ X2284 @ X2285 @ X2286 ) @ ( esk57_4 @ X2283 @ X2284 @ X2285 @ X2286 ) ) @ X2286 )
| ( subset @ X2285 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2286 )
| ~ ( breln @ X2283 @ X2284 @ X2285 ) )
& ( ( in @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ( X2291 = X2292 )
| ( in @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ( X2291 = X2292 )
| ( in @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ( X2291 = X2292 )
| ( in @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ( X2291 = X2292 )
| ( in @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ( X2291 = X2292 )
| ( in @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ( X2291 = X2292 )
| ( in @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ( X2291 = X2292 )
| ( in @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ( X2291 = X2292 )
| ( in @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ( X2291 = X2292 )
| ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ( X2291 = X2292 )
| ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ( X2291 = X2292 )
| ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ( X2291 = X2292 )
| ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
| ( X2291 = X2292 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ( X2291 = X2292 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ( X2291 = X2292 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk61_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ( X2291 = X2292 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ ( esk59_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2292 )
| ~ ( breln @ X2289 @ X2290 @ X2291 ) )
& ( ( in @ ( esk62_4 @ X2297 @ X2298 @ X2299 @ X2300 ) @ X2297 )
| ( X2299 = X2300 )
| ~ ( func @ X2297 @ X2298 @ X2300 )
| ~ ( func @ X2297 @ X2298 @ X2299 ) )
& ( ( ( ap @ X2297 @ X2298 @ X2299 @ ( esk62_4 @ X2297 @ X2298 @ X2299 @ X2300 ) )
!= ( ap @ X2297 @ X2298 @ X2300 @ ( esk62_4 @ X2297 @ X2298 @ X2299 @ X2300 ) ) )
| ( X2299 = X2300 )
| ~ ( func @ X2297 @ X2298 @ X2300 )
| ~ ( func @ X2297 @ X2298 @ X2299 ) )
& ( ( in @ ( esk63_4 @ X2302 @ X2303 @ X2304 @ X2305 ) @ X2302 )
| ( X2304 = X2305 )
| ~ ( in @ X2305 @ ( funcSet @ X2302 @ X2303 ) )
| ~ ( in @ X2304 @ ( funcSet @ X2302 @ X2303 ) ) )
& ( ( ( ap @ X2302 @ X2303 @ X2304 @ ( esk63_4 @ X2302 @ X2303 @ X2304 @ X2305 ) )
!= ( ap @ X2302 @ X2303 @ X2305 @ ( esk63_4 @ X2302 @ X2303 @ X2304 @ X2305 ) ) )
| ( X2304 = X2305 )
| ~ ( in @ X2305 @ ( funcSet @ X2302 @ X2303 ) )
| ~ ( in @ X2304 @ ( funcSet @ X2302 @ X2303 ) ) )
& ( ~ ( in @ X2309 @ ( funcSet @ X2307 @ X2308 ) )
| ~ ( in @ X2310 @ X2307 )
| ( ( ap @ X2307 @ X2308 @ X2309 @ X2310 )
= ( ap @ X2307 @ X2308 @ X2309 @ X2310 ) ) )
& ( ~ ( func @ X2311 @ X2312 @ X2313 )
| ~ ( in @ X2314 @ X2311 )
| ( ( ap @ X2311 @ X2312 @ X2313 @ X2314 )
= ( ap @ X2311 @ X2312 @ X2313 @ X2314 ) ) )
& ( ( in @ ( esk64_3 @ X2315 @ X2316 @ X2317 ) @ X2315 )
| ~ ( in @ X2319 @ X2315 )
| ( ( ap @ X2315 @ X2316 @ ( lam @ X2315 @ X2316 @ X2317 ) @ X2319 )
= ( X2317 @ X2319 ) ) )
& ( ~ ( in @ ( X2317 @ ( esk64_3 @ X2315 @ X2316 @ X2317 ) ) @ X2316 )
| ~ ( in @ X2319 @ X2315 )
| ( ( ap @ X2315 @ X2316 @ ( lam @ X2315 @ X2316 @ X2317 ) @ X2319 )
= ( X2317 @ X2319 ) ) )
& ( ~ ( func @ X2320 @ X2321 @ X2322 )
| ( ( lam @ X2320 @ X2321 @ ( ap @ X2320 @ X2321 @ X2322 ) )
= X2322 ) )
& ( ( in @ ( esk65_3 @ X2323 @ X2324 @ X2325 ) @ X2323 )
| ( ( lam @ X2323 @ X2324 @ X2325 )
= ( lam @ X2323 @ X2324 @ X2325 ) ) )
& ( ~ ( in @ ( X2325 @ ( esk65_3 @ X2323 @ X2324 @ X2325 ) ) @ X2324 )
| ( ( lam @ X2323 @ X2324 @ X2325 )
= ( lam @ X2323 @ X2324 @ X2325 ) ) )
& ( ( in @ ( esk66_3 @ X2327 @ X2328 @ X2329 ) @ X2327 )
| ~ ( in @ X2331 @ X2327 )
| ( ( ap @ X2327 @ X2328 @ ( lam @ X2327 @ X2328 @ X2329 ) @ X2331 )
= ( X2329 @ X2331 ) ) )
& ( ~ ( in @ ( X2329 @ ( esk66_3 @ X2327 @ X2328 @ X2329 ) ) @ X2328 )
| ~ ( in @ X2331 @ X2327 )
| ( ( ap @ X2327 @ X2328 @ ( lam @ X2327 @ X2328 @ X2329 ) @ X2331 )
= ( X2329 @ X2331 ) ) )
& ( ~ ( in @ X2334 @ ( funcSet @ X2332 @ X2333 ) )
| ( ( lam @ X2332 @ X2333 @ ( ap @ X2332 @ X2333 @ X2334 ) )
= X2334 ) )
& ( ~ ( in @ X2337 @ X2335 )
| ~ ( in @ X2338 @ X2335 )
| X2336
| ( in @ X2338
@ ( dsetconstr @ X2335
@ ^ [Z0: $i] :
( ( X2336
& ( Z0 = X2337 ) )
| ( ~ X2336
& ( Z0 = X2338 ) ) ) ) ) )
& ( ~ ( in @ X2341 @ X2339 )
| ~ ( in @ X2342 @ X2339 )
| X2340
| ( ( dsetconstr @ X2339
@ ^ [Z0: $i] :
( ( X2340
& ( Z0 = X2341 ) )
| ( ~ X2340
& ( Z0 = X2342 ) ) ) )
= ( setadjoin @ X2342 @ emptyset ) ) )
& ( ~ ( in @ X2345 @ X2343 )
| ~ ( in @ X2346 @ X2343 )
| ~ X2344
| ( in @ X2345
@ ( dsetconstr @ X2343
@ ^ [Z0: $i] :
( ( X2344
& ( Z0 = X2345 ) )
| ( ~ X2344
& ( Z0 = X2346 ) ) ) ) ) )
& ( ~ ( in @ X2349 @ X2347 )
| ~ ( in @ X2350 @ X2347 )
| ~ X2348
| ( ( dsetconstr @ X2347
@ ^ [Z0: $i] :
( ( X2348
& ( Z0 = X2349 ) )
| ( ~ X2348
& ( Z0 = X2350 ) ) ) )
= ( setadjoin @ X2349 @ emptyset ) ) )
& ( ~ ( in @ X2353 @ X2351 )
| ~ ( in @ X2354 @ X2351 )
| ( singleton
@ ( dsetconstr @ X2351
@ ^ [Z0: $i] :
( ( X2352
& ( Z0 = X2353 ) )
| ( ~ X2352
& ( Z0 = X2354 ) ) ) ) ) )
& ( ~ ( in @ X2357 @ X2355 )
| ~ ( in @ X2358 @ X2355 )
| ( in @ ( if @ X2355 @ X2356 @ X2357 @ X2358 ) @ X2355 ) )
& ( ~ ( singleton @ X2359 )
| ~ ( in @ X2360 @ X2359 )
| ( ( setunion @ X2359 )
= X2360 ) )
& ( ~ ( in @ X2363 @ X2361 )
| ~ ( in @ X2364 @ X2361 )
| ~ X2362
| ( ( if @ X2361 @ X2362 @ X2363 @ X2364 )
= X2363 ) )
& ( ~ ( in @ X2367 @ X2365 )
| ~ ( in @ X2368 @ X2365 )
| X2366
| ( ( if @ X2365 @ X2366 @ X2367 @ X2368 )
= X2368 ) )
& ( ~ ( in @ X2371 @ X2369 )
| ~ ( in @ X2372 @ X2369 )
| ( in @ ( if @ X2369 @ X2370 @ X2371 @ X2372 ) @ ( setadjoin @ X2371 @ ( setadjoin @ X2372 @ emptyset ) ) ) )
& ( ~ ( in @ X2374 @ ( powerset @ X2373 ) )
| ~ ( in @ X2375 @ ( powerset @ X2373 ) )
| ( in @ ( binintersect @ X2374 @ X2375 ) @ ( powerset @ X2373 ) ) )
& ( ~ ( in @ X2377 @ ( powerset @ X2376 ) )
| ~ ( in @ X2378 @ ( powerset @ X2376 ) )
| ( in @ ( binunion @ X2377 @ X2378 ) @ ( powerset @ X2376 ) ) )
& ( ~ ( in @ X2380 @ ( powerset @ X2379 ) )
| ( in @ ( powerset @ X2380 ) @ ( powerset @ ( powerset @ X2379 ) ) ) )
& ( ~ ( in @ X2382 @ ( powerset @ X2381 ) )
| ~ ( in @ X2383 @ ( powerset @ X2381 ) )
| ( in @ ( setminus @ X2382 @ X2383 ) @ ( powerset @ X2381 ) ) )
& ( ~ ( in @ X2385 @ ( powerset @ X2384 ) )
| ( in @ ( setminus @ X2384 @ X2385 ) @ ( powerset @ X2384 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ( X2387 = X2388 )
| ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2386 )
| ( X2387 = X2388 )
| ~ ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ( X2387 = X2388 )
| ~ ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2386 @ X2387 @ X2388 ) @ X2387 )
| ( X2387 = X2388 )
| ~ ( in @ ( esk67_3 @ X2386 @ X2387 @ X2388 ) @ X2388 )
| ~ ( in @ X2388 @ ( powerset @ X2386 ) )
| ~ ( in @ X2387 @ ( powerset @ X2386 ) ) )
& ( ( in @ ( esk69_3 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ( subset @ X2392 @ X2393 )
| ~ ( in @ X2393 @ ( powerset @ X2391 ) )
| ~ ( in @ X2392 @ ( powerset @ X2391 ) ) )
& ( ( in @ ( esk69_3 @ X2391 @ X2392 @ X2393 ) @ X2392 )
| ( subset @ X2392 @ X2393 )
| ~ ( in @ X2393 @ ( powerset @ X2391 ) )
| ~ ( in @ X2392 @ ( powerset @ X2391 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2391 @ X2392 @ X2393 ) @ X2393 )
| ( subset @ X2392 @ X2393 )
| ~ ( in @ X2393 @ ( powerset @ X2391 ) )
| ~ ( in @ X2392 @ ( powerset @ X2391 ) ) )
& ( ( in @ ( esk70_3 @ X2395 @ X2396 @ X2397 ) @ X2395 )
| ( in @ X2396 @ ( powerset @ X2397 ) )
| ~ ( in @ X2397 @ ( powerset @ X2395 ) )
| ~ ( in @ X2396 @ ( powerset @ X2395 ) ) )
& ( ( in @ ( esk70_3 @ X2395 @ X2396 @ X2397 ) @ X2396 )
| ( in @ X2396 @ ( powerset @ X2397 ) )
| ~ ( in @ X2397 @ ( powerset @ X2395 ) )
| ~ ( in @ X2396 @ ( powerset @ X2395 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2395 @ X2396 @ X2397 ) @ X2397 )
| ( in @ X2396 @ ( powerset @ X2397 ) )
| ~ ( in @ X2397 @ ( powerset @ X2395 ) )
| ~ ( in @ X2396 @ ( powerset @ X2395 ) ) )
& ( ~ ( in @ X2400 @ ( powerset @ X2399 ) )
| ~ ( in @ X2401 @ ( powerset @ X2399 ) )
| ~ ( in @ X2402 @ X2399 )
| ~ ( in @ X2400 @ ( powerset @ X2401 ) )
| ~ ( in @ X2402 @ X2400 )
| ( in @ X2402 @ X2401 ) )
& ( ~ ( in @ X2404 @ ( powerset @ X2403 ) )
| ~ ( in @ X2405 @ X2403 )
| ~ ( in @ X2405 @ X2404 )
| ~ ( in @ X2405 @ ( setminus @ X2403 @ X2404 ) ) )
& ( ~ ( in @ X2407 @ ( powerset @ X2406 ) )
| ~ ( in @ X2408 @ X2406 )
| ( in @ X2408 @ ( setminus @ X2406 @ X2407 ) )
| ( in @ X2408 @ X2407 ) )
& ( ~ ( in @ X2410 @ ( powerset @ X2409 ) )
| ~ ( in @ X2411 @ ( powerset @ X2409 ) )
| ~ ( in @ X2412 @ X2409 )
| ( in @ X2412 @ X2410 )
| ~ ( in @ X2412 @ ( binintersect @ X2410 @ X2411 ) ) )
& ( ~ ( in @ X2414 @ ( powerset @ X2413 ) )
| ~ ( in @ X2415 @ ( powerset @ X2413 ) )
| ~ ( in @ X2416 @ X2413 )
| ( in @ X2416 @ X2415 )
| ~ ( in @ X2416 @ ( binintersect @ X2414 @ X2415 ) ) )
& ( ~ ( in @ X2418 @ ( powerset @ X2417 ) )
| ~ ( in @ X2419 @ ( powerset @ X2417 ) )
| ~ ( in @ X2420 @ X2417 )
| ~ ( subset @ X2418 @ ( setminus @ X2417 @ X2419 ) )
| ~ ( in @ X2420 @ X2419 )
| ~ ( in @ X2420 @ X2418 ) )
& ( ~ ( in @ X2422 @ ( powerset @ X2421 ) )
| ~ ( in @ X2423 @ ( powerset @ X2421 ) )
| ~ ( in @ X2424 @ X2421 )
| ~ ( subset @ X2422 @ X2423 )
| ( in @ X2424 @ X2423 )
| ~ ( in @ X2424 @ X2422 ) )
& ( ~ ( in @ X2426 @ ( powerset @ X2425 ) )
| ~ ( in @ X2427 @ ( powerset @ X2425 ) )
| ~ ( subset @ X2426 @ X2427 )
| ( subset @ ( setminus @ X2425 @ X2427 ) @ ( setminus @ X2425 @ X2426 ) ) )
& ( ~ ( in @ X2429 @ ( powerset @ X2428 ) )
| ~ ( in @ X2430 @ ( powerset @ X2428 ) )
| ~ ( subset @ ( setminus @ X2428 @ X2430 ) @ ( setminus @ X2428 @ X2429 ) )
| ( subset @ X2429 @ X2430 ) )
& ( ~ ( in @ X2432 @ ( powerset @ X2431 ) )
| ~ ( in @ X2433 @ X2431 )
| ~ ( in @ X2433 @ X2432 )
| ( in @ X2433 @ ( setminus @ X2431 @ ( setminus @ X2431 @ X2432 ) ) ) )
& ( ~ ( in @ X2435 @ ( powerset @ X2434 ) )
| ~ ( in @ X2436 @ X2434 )
| ~ ( in @ X2436 @ ( setminus @ X2434 @ ( setminus @ X2434 @ X2435 ) ) )
| ( in @ X2436 @ X2435 ) )
& ( ~ ( in @ X2438 @ ( powerset @ X2437 ) )
| ( subset @ X2438 @ ( setminus @ X2437 @ ( setminus @ X2437 @ X2438 ) ) ) )
& ( ~ ( in @ X2440 @ ( powerset @ X2439 ) )
| ( subset @ ( setminus @ X2439 @ ( setminus @ X2439 @ X2440 ) ) @ X2440 ) )
& ( ~ ( in @ X2442 @ ( powerset @ X2441 ) )
| ( X2442
= ( setminus @ X2441 @ ( setminus @ X2441 @ X2442 ) ) ) )
& ( ~ ( in @ X2444 @ ( powerset @ X2443 ) )
| ~ ( in @ X2445 @ ( powerset @ X2443 ) )
| ~ ( in @ X2446 @ X2443 )
| ~ ( in @ X2446 @ ( setminus @ X2443 @ X2444 ) )
| ~ ( in @ X2446 @ ( binintersect @ X2444 @ X2445 ) ) )
& ( ~ ( in @ X2448 @ ( powerset @ X2447 ) )
| ~ ( in @ X2449 @ ( powerset @ X2447 ) )
| ~ ( in @ X2450 @ X2447 )
| ~ ( in @ X2450 @ ( setminus @ X2447 @ X2448 ) )
| ( in @ X2450 @ ( setminus @ X2447 @ ( binintersect @ X2448 @ X2449 ) ) ) )
& ( ~ ( in @ X2452 @ ( powerset @ X2451 ) )
| ~ ( in @ X2453 @ ( powerset @ X2451 ) )
| ( subset @ ( setminus @ X2451 @ X2452 ) @ ( setminus @ X2451 @ ( binintersect @ X2452 @ X2453 ) ) ) )
& ( ~ ( in @ X2455 @ ( powerset @ X2454 ) )
| ~ ( in @ X2456 @ ( powerset @ X2454 ) )
| ( in @ ( setminus @ X2454 @ X2455 ) @ ( powerset @ ( setminus @ X2454 @ ( binintersect @ X2455 @ X2456 ) ) ) ) )
& ( ~ ( in @ X2458 @ ( powerset @ X2457 ) )
| ~ ( in @ X2459 @ ( powerset @ X2457 ) )
| ~ ( subset @ X2458 @ ( setminus @ X2457 @ X2459 ) )
| ~ ( in @ X2460 @ X2457 )
| ~ ( in @ X2460 @ X2459 )
| ( in @ X2460 @ ( setminus @ X2457 @ X2458 ) ) )
& ( ~ ( in @ X2462 @ ( powerset @ X2461 ) )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( subset @ X2462 @ ( setminus @ X2461 @ X2463 ) )
| ( subset @ X2463 @ ( setminus @ X2461 @ X2462 ) ) )
& ( ~ ( in @ X2465 @ ( powerset @ X2464 ) )
| ~ ( in @ X2466 @ ( powerset @ X2464 ) )
| ~ ( in @ X2467 @ X2464 )
| ( in @ X2467 @ ( binunion @ X2465 @ X2466 ) )
| ~ ( in @ X2467 @ X2465 ) )
& ( ~ ( in @ X2469 @ ( powerset @ X2468 ) )
| ~ ( in @ X2470 @ ( powerset @ X2468 ) )
| ~ ( in @ X2471 @ X2468 )
| ( in @ X2471 @ ( binunion @ X2469 @ X2470 ) )
| ~ ( in @ X2471 @ X2470 ) )
& ( ~ ( in @ X2473 @ ( powerset @ X2472 ) )
| ~ ( in @ X2474 @ ( powerset @ X2472 ) )
| ~ ( in @ X2475 @ ( powerset @ X2472 ) )
| ~ ( in @ X2476 @ X2472 )
| ~ ( in @ X2476 @ ( binintersect @ X2473 @ X2474 ) )
| ( in @ X2476 @ ( binunion @ X2473 @ X2475 ) ) )
& ( ~ ( in @ X2478 @ ( powerset @ X2477 ) )
| ~ ( in @ X2479 @ ( powerset @ X2477 ) )
| ~ ( in @ X2480 @ ( powerset @ X2477 ) )
| ~ ( in @ X2481 @ X2477 )
| ~ ( in @ X2481 @ ( binintersect @ X2478 @ X2479 ) )
| ( in @ X2481 @ ( binunion @ X2479 @ X2480 ) ) )
& ( ~ ( in @ X2483 @ ( powerset @ X2482 ) )
| ~ ( in @ X2484 @ ( powerset @ X2482 ) )
| ~ ( in @ X2485 @ ( powerset @ X2482 ) )
| ~ ( in @ X2486 @ X2482 )
| ~ ( in @ X2486 @ ( binintersect @ X2483 @ X2484 ) )
| ( in @ X2486 @ ( binintersect @ ( binunion @ X2483 @ X2485 ) @ ( binunion @ X2484 @ X2485 ) ) ) )
& ( ~ ( in @ X2488 @ ( powerset @ X2487 ) )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2490 @ ( powerset @ X2487 ) )
| ( in @ ( binintersect @ X2488 @ X2489 ) @ ( powerset @ ( binintersect @ ( binunion @ X2488 @ X2490 ) @ ( binunion @ X2489 @ X2490 ) ) ) ) )
& ( ~ ( in @ X2492 @ ( powerset @ X2491 ) )
| ~ ( in @ X2493 @ ( powerset @ X2491 ) )
| ~ ( in @ X2494 @ X2491 )
| ~ ( in @ X2494 @ ( setminus @ X2491 @ ( binunion @ X2492 @ X2493 ) ) )
| ~ ( in @ X2494 @ X2492 ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk74_0 @ esk71_0 )
& ( in @ esk74_0 @ ( setminus @ esk71_0 @ ( binunion @ esk72_0 @ esk73_0 ) ) )
& ~ ( in @ esk74_0 @ ( setminus @ esk71_0 @ esk72_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_313])])])])])])]) ).
thf(c_0_315,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) )
| ~ ( in @ X5 @ X3 )
| ~ ( in @ X5 @ ( setminus @ X3 @ ( binunion @ X2 @ X4 ) ) )
| ~ ( in @ X5 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_316,negated_conjecture,
in @ esk74_0 @ ( setminus @ esk71_0 @ ( binunion @ esk72_0 @ esk73_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_317,negated_conjecture,
in @ esk73_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_318,negated_conjecture,
in @ esk72_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_319,negated_conjecture,
in @ esk74_0 @ esk71_0,
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_320,negated_conjecture,
~ ( in @ esk74_0 @ ( setminus @ esk71_0 @ esk72_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_321,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( setminus @ X3 @ X4 ) )
| ( in @ X2 @ X4 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
thf(c_0_322,negated_conjecture,
~ ( in @ esk74_0 @ esk72_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_316]),c_0_317]),c_0_318]),c_0_319])]) ).
thf(c_0_323,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_321]),c_0_319])]),c_0_322]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SEU745^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 17:36:52 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.16/0.43 Running higher-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.99/0.92 # Version: 3.1.0-ho
% 2.99/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.99/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.99/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.99/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.99/0.92 # Starting pre_casc_3 with 300s (1) cores
% 2.99/0.92 # Starting ho_unfolding_8 with 300s (1) cores
% 2.99/0.92 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.99/0.92 # Starting new_bool_3 with 300s (1) cores
% 2.99/0.92 # Starting new_ho_5 with 300s (1) cores
% 2.99/0.92 # new_ho_5 with pid 19800 completed with status 8
% 2.99/0.92 # pre_casc_3 with pid 19796 completed with status 8
% 2.99/0.92 # new_bool_5 with pid 19795 completed with status 0
% 2.99/0.92 # Result found by new_bool_5
% 2.99/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.99/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.99/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.99/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.99/0.92 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.99/0.92 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.99/0.92 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.99/0.92 # Starting ho_unfolding_8 with 55s (1) cores
% 2.99/0.92 # ho_unfolding_8 with pid 19822 completed with status 0
% 2.99/0.92 # Result found by ho_unfolding_8
% 2.99/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.99/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.99/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.99/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.99/0.92 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.99/0.92 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.99/0.92 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.99/0.92 # Starting ho_unfolding_8 with 55s (1) cores
% 2.99/0.92 # Preprocessing time : 0.066 s
% 2.99/0.92 # Presaturation interreduction done
% 2.99/0.92
% 2.99/0.92 # Proof found!
% 2.99/0.92 # SZS status Theorem
% 2.99/0.92 # SZS output start CNFRefutation
% See solution above
% 2.99/0.93 # Parsed axioms : 565
% 2.99/0.93 # Removed by relevancy pruning/SinE : 304
% 2.99/0.93 # Initial clauses : 423
% 2.99/0.93 # Removed in clause preprocessing : 34
% 2.99/0.93 # Initial clauses in saturation : 389
% 2.99/0.93 # Processed clauses : 762
% 2.99/0.93 # ...of these trivial : 10
% 2.99/0.93 # ...subsumed : 41
% 2.99/0.93 # ...remaining for further processing : 710
% 2.99/0.93 # Other redundant clauses eliminated : 54
% 2.99/0.93 # Clauses deleted for lack of memory : 0
% 2.99/0.93 # Backward-subsumed : 0
% 2.99/0.93 # Backward-rewritten : 2
% 2.99/0.93 # Generated clauses : 7879
% 2.99/0.93 # ...of the previous two non-redundant : 7640
% 2.99/0.93 # ...aggressively subsumed : 0
% 2.99/0.93 # Contextual simplify-reflections : 6
% 2.99/0.93 # Paramodulations : 7790
% 2.99/0.93 # Factorizations : 2
% 2.99/0.93 # NegExts : 0
% 2.99/0.93 # Equation resolutions : 61
% 2.99/0.93 # Disequality decompositions : 0
% 2.99/0.93 # Total rewrite steps : 204
% 2.99/0.93 # ...of those cached : 135
% 2.99/0.93 # Propositional unsat checks : 0
% 2.99/0.93 # Propositional check models : 0
% 2.99/0.93 # Propositional check unsatisfiable : 0
% 2.99/0.93 # Propositional clauses : 0
% 2.99/0.93 # Propositional clauses after purity: 0
% 2.99/0.93 # Propositional unsat core size : 0
% 2.99/0.93 # Propositional preprocessing time : 0.000
% 2.99/0.93 # Propositional encoding time : 0.000
% 2.99/0.93 # Propositional solver time : 0.000
% 2.99/0.93 # Success case prop preproc time : 0.000
% 2.99/0.93 # Success case prop encoding time : 0.000
% 2.99/0.93 # Success case prop solver time : 0.000
% 2.99/0.93 # Current number of processed clauses : 352
% 2.99/0.93 # Positive orientable unit clauses : 45
% 2.99/0.93 # Positive unorientable unit clauses: 0
% 2.99/0.93 # Negative unit clauses : 7
% 2.99/0.93 # Non-unit-clauses : 300
% 2.99/0.93 # Current number of unprocessed clauses: 7603
% 2.99/0.93 # ...number of literals in the above : 32379
% 2.99/0.93 # Current number of archived formulas : 0
% 2.99/0.93 # Current number of archived clauses : 342
% 2.99/0.93 # Clause-clause subsumption calls (NU) : 49594
% 2.99/0.93 # Rec. Clause-clause subsumption calls : 20011
% 2.99/0.93 # Non-unit clause-clause subsumptions : 39
% 2.99/0.93 # Unit Clause-clause subsumption calls : 1632
% 2.99/0.93 # Rewrite failures with RHS unbound : 0
% 2.99/0.93 # BW rewrite match attempts : 33
% 2.99/0.93 # BW rewrite match successes : 2
% 2.99/0.93 # Condensation attempts : 0
% 2.99/0.93 # Condensation successes : 0
% 2.99/0.93 # Termbank termtop insertions : 199132
% 2.99/0.93 # Search garbage collected termcells : 26170
% 2.99/0.93
% 2.99/0.93 # -------------------------------------------------
% 2.99/0.93 # User time : 0.428 s
% 2.99/0.93 # System time : 0.028 s
% 2.99/0.93 # Total time : 0.456 s
% 2.99/0.93 # Maximum resident set size: 8364 pages
% 2.99/0.93
% 2.99/0.93 # -------------------------------------------------
% 2.99/0.93 # User time : 0.649 s
% 2.99/0.93 # System time : 0.101 s
% 2.99/0.93 # Total time : 0.750 s
% 2.99/0.93 # Maximum resident set size: 2484 pages
% 2.99/0.93 % E---3.1 exiting
% 2.99/0.93 % E exiting
%------------------------------------------------------------------------------