%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU742^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 03:29:44 EDT 2024
% Result : Theorem 1.14s 0.86s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 623
% Syntax : Number of formulae : 687 ( 6 unt; 364 typ; 0 def)
% Number of atoms : 3226 ( 457 equ; 0 cnn)
% Maximal formula atoms : 1012 ( 9 avg)
% Number of connectives : 12366 ( 791 ~; 796 |; 499 &;8333 @)
% ( 345 <=>;1602 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1117 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 368 ( 364 usr; 269 con; 0-4 aty)
% Number of variables : 2692 ( 156 ^2456 !; 80 ?;2692 :)
% 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,
epred1_0: $o ).
thf(decl_319,type,
esk1_2: $i > $i > $i ).
thf(decl_320,type,
esk2_2: $i > $i > $i ).
thf(decl_321,type,
esk3_2: $i > $i > $i ).
thf(decl_322,type,
esk4_1: $i > $i ).
thf(decl_323,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_324,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_325,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_326,type,
esk8_1: $i > $i ).
thf(decl_327,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_328,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_329,type,
esk11_2: $i > $i > $i ).
thf(decl_330,type,
esk12_2: $i > $i > $i ).
thf(decl_331,type,
esk13_1: $i > $i ).
thf(decl_332,type,
esk14_1: $i > $i ).
thf(decl_333,type,
esk15_1: $i > $i ).
thf(decl_334,type,
esk16_2: $i > $i > $i ).
thf(decl_335,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_336,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_337,type,
esk19_1: $i > $i ).
thf(decl_338,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_339,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_340,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_341,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_342,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_345,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_346,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_347,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_348,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_349,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_350,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_351,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_352,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_353,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_354,type,
esk36_2: $i > $i > $i ).
thf(decl_355,type,
esk37_2: $i > $i > $i ).
thf(decl_356,type,
esk38_2: $i > $i > $i ).
thf(decl_357,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_358,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_359,type,
esk41_2: $i > $i > $i ).
thf(decl_360,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_361,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_364,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_366,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_367,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_368,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_369,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_370,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_371,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_372,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_373,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_374,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_375,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_376,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_377,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_378,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_379,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_380,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_381,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_382,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_383,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_384,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_385,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_386,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_387,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_388,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_389,type,
esk71_0: $i ).
thf(decl_390,type,
esk72_0: $i ).
thf(decl_391,type,
esk73_0: $i ).
thf(decl_392,type,
esk74_0: $i ).
thf(decl_393,type,
esk75_0: $i ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,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(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(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(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(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(inIntersectImpInIntersectUnions,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
=> ! [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(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(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(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(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(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(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(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(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(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(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
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(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(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(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(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(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(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(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(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(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
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(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(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
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(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(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(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(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(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(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(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(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(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(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(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
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(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(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
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(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(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
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(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(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(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(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(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(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(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(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(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
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(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
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(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(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(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(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_258,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_259,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_260,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_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,
( 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_263,plain,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X41
& ( Z0 = X2 ) )
| ( ~ X41
& ( Z0 = X3 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp1]) ).
thf(c_0_264,plain,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X42
& ( Z0 = X2 ) )
| ( ~ X42
& ( Z0 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iftrueProp2]) ).
thf(c_0_265,plain,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] :
( ( X43
& ( Z0 = X2 ) )
| ( ~ X43
& ( Z0 = X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifSingleton]) ).
thf(c_0_266,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_267,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
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,
( 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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_300,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_301,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_302,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_303,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_304,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_305,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_306,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_307,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_308,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_309,plain,
( epred1_0
<=> ! [X886: $i] :
? [X887: $i] :
( ! [X888: $i] :
( ( in @ X888 @ X887 )
=> ! [X889: $i] :
( ( in @ X889 @ X888 )
=> ( in @ X889 @ X886 ) ) )
& ! [X890: $i,X891: $i] :
( ( ( in @ X890 @ X886 )
& ( in @ X891 @ X886 ) )
=> ( ! [X892: $i] :
( ( in @ X892 @ X887 )
=> ( ( in @ X890 @ X892 )
<=> ( in @ X891 @ X892 ) ) )
=> ( X890 = X891 ) ) )
& ! [X893: $i,X894: $i] :
( ( ( in @ X893 @ X887 )
& ( in @ X894 @ X887 ) )
=> ( ! [X895: $i] :
( ( in @ X895 @ X893 )
=> ( in @ X895 @ X894 ) )
| ! [X896: $i] :
( ( in @ X896 @ X894 )
=> ( in @ X896 @ X893 ) ) ) )
& ! [X897: $i] :
( ( ! [X898: $i] :
( ( in @ X898 @ X897 )
=> ( in @ X898 @ X886 ) )
& ? [X899: $i] : ( in @ X899 @ X897 ) )
=> ? [X900: $i,X901: $i] :
( ( in @ X900 @ X887 )
& ( in @ X901 @ X897 )
& ~ ? [X902: $i] :
( ( in @ X902 @ X900 )
& ( in @ X902 @ X897 ) )
& ! [X903: $i] :
( ( in @ X903 @ X887 )
=> ( ! [X904: $i] :
( ( in @ X904 @ X903 )
=> ( in @ X904 @ X900 ) )
| ( in @ X901 @ X903 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_310,negated_conjecture,
~ ( ! [X859: $i,X860: $i] :
( ! [X861: $i] :
( ( in @ X861 @ X859 )
<=> ( in @ X861 @ X860 ) )
=> ( X859 = X860 ) )
=> ( ! [X862: $i] :
~ ( in @ X862 @ emptyset )
=> ( ! [X863: $i,X864: $i,X865: $i] :
( ( in @ X865 @ ( setadjoin @ X863 @ X864 ) )
<=> ( ( X865 = X863 )
| ( in @ X865 @ X864 ) ) )
=> ( ! [X866: $i,X867: $i] :
( ( in @ X867 @ ( powerset @ X866 ) )
<=> ! [X868: $i] :
( ( in @ X868 @ X867 )
=> ( in @ X868 @ X866 ) ) )
=> ( ! [X869: $i,X870: $i] :
( ( in @ X870 @ ( setunion @ X869 ) )
<=> ? [X871: $i] :
( ( in @ X870 @ X871 )
& ( in @ X871 @ X869 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X872: $i] :
( ( in @ X872 @ omega )
=> ( in @ ( setadjoin @ X872 @ X872 ) @ omega ) )
=> ( ! [X873: $i] :
( ( ( in @ emptyset @ X873 )
& ! [X874: $i] :
( ( ( in @ X874 @ omega )
& ( in @ X874 @ X873 ) )
=> ( in @ ( setadjoin @ X874 @ X874 ) @ X873 ) ) )
=> ! [X875: $i] :
( ( in @ X875 @ omega )
=> ( in @ X875 @ X873 ) ) )
=> ( ! [X876: $i > $i > $o,X877: $i] :
( ! [X878: $i] :
( ( in @ X878 @ X877 )
=> ( exu @ ( X876 @ X878 ) ) )
=> ? [X879: $i] :
! [X880: $i] :
( ( in @ X880 @ X879 )
<=> ? [X881: $i] :
( ( in @ X881 @ X877 )
& ( X876 @ X881 @ X880 ) ) ) )
=> ( ! [X882: $i] :
( ? [X883: $i] : ( in @ X883 @ X882 )
=> ? [X884: $i] :
( ( in @ X884 @ X882 )
& ~ ? [X885: $i] :
( ( in @ X885 @ X884 )
& ( in @ X885 @ X882 ) ) ) )
=> ( epred1_0
=> ( ! [X905: $i > $o] :
( ( exu @ X905 )
=> ( X905
@ ( descr
@ ^ [Z0: $i] : ( X905 @ Z0 ) ) ) )
=> ( ! [X906: $i,X907: $i > $o,X908: $i] :
( ( in @ X908 @ X906 )
=> ( ( X907 @ X908 )
=> ( in @ X908 @ ( dsetconstr @ X906 @ X907 ) ) ) )
=> ( ! [X909: $i,X910: $i > $o,X911: $i] :
( ( in @ X911 @ ( dsetconstr @ X909 @ X910 ) )
=> ( in @ X911 @ X909 ) )
=> ( ! [X912: $i,X913: $i > $o,X914: $i] :
( ( in @ X914 @ ( dsetconstr @ X912 @ X913 ) )
=> ( X913 @ X914 ) )
=> ( ! [X915: $i > $o] :
( ( exu @ X915 )
=> ? [X916: $i] :
( ( X915 @ X916 )
& ! [X917: $i] :
( ( X915 @ X917 )
=> ( X916 = X917 ) ) ) )
=> ( ! [X918: $o,X919: $i] :
( ( in @ X919 @ ( prop2set @ X918 ) )
=> X918 )
=> ( ! [X920: $i] :
( ( in @ X920 @ emptyset )
=> ! [X921: $o] : X921 )
=> ( ! [X922: $i] :
( ( in @ X922 @ emptyset )
=> ~ $true )
=> ( ! [X923: $i] :
~ ( in @ X923 @ emptyset )
=> ( ! [X924: $i > $o] :
( ( exu @ X924 )
=> ? [X925: $i] : ( X924 @ X925 ) )
=> ( ! [X926: $i,X927: $i] :
( ! [X928: $i] :
( ( in @ X928 @ X926 )
=> ( in @ X928 @ X927 ) )
=> ( ! [X929: $i] :
( ( in @ X929 @ X927 )
=> ( in @ X929 @ X926 ) )
=> ( X926 = X927 ) ) )
=> ( ! [X930: $i] :
( ! [X931: $i] :
~ ( in @ X931 @ X930 )
=> ( X930 = emptyset ) )
=> ( ! [X932: $i] :
( ! [X933: $i] :
~ ( in @ X933 @ X932 )
=> ( X932 = emptyset ) )
=> ( ! [X934: $i,X935: $i > $o,X936: $i] :
( ( in @ X936 @ X934 )
=> ( ( in @ X936 @ ( dsetconstr @ X934 @ X935 ) )
<=> ( X935 @ X936 ) ) )
=> ( ! [X937: $i] :
( ( nonempty @ X937 )
=> ? [X938: $i] : ( in @ X938 @ X937 ) )
=> ( ! [X939: $i,X940: $i > $o,X941: $i] :
( ( in @ X941 @ X939 )
=> ( ( X940 @ X941 )
=> ( nonempty @ ( dsetconstr @ X939 @ X940 ) ) ) )
=> ( ! [X942: $i] :
( ? [X943: $i] : ( in @ X943 @ X942 )
=> ( nonempty @ X942 ) )
=> ( ! [X944: $i,X945: $i] : ( in @ X944 @ ( setadjoin @ X944 @ X945 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X946: $i,X947: $i,X948: $i] :
( ( in @ X948 @ X947 )
=> ( in @ X948 @ ( setadjoin @ X946 @ X947 ) ) )
=> ( ! [X949: $i,X950: $i,X951: $i] :
( ( in @ X951 @ ( setadjoin @ X949 @ X950 ) )
=> ! [X952: $o] :
( ( ( X951 = X949 )
=> X952 )
=> ( ( ( in @ X951 @ X950 )
=> X952 )
=> X952 ) ) )
=> ( ! [X953: $i,X954: $i,X955: $i] :
( ( in @ X955 @ ( setadjoin @ X953 @ X954 ) )
=> ( ( X955 = X953 )
| ( in @ X955 @ X954 ) ) )
=> ( ! [X956: $i] :
( ( dsetconstr @ X956
@ ^ [Z0: $i] : $true )
= X956 )
=> ( ! [X957: $i,X958: $i] :
( ! [X959: $i] :
( ( in @ X959 @ X958 )
=> ( in @ X959 @ X957 ) )
=> ( in @ X958 @ ( powerset @ X957 ) ) )
=> ( ! [X960: $i] : ( in @ emptyset @ ( powerset @ X960 ) )
=> ( ! [X961: $i] : ( in @ emptyset @ ( powerset @ X961 ) )
=> ( ! [X962: $i,X963: $i,X964: $i] :
( ( in @ X963 @ ( powerset @ X962 ) )
=> ( ( in @ X964 @ X963 )
=> ( in @ X964 @ X962 ) ) )
=> ( ! [X965: $i,X966: $i,X967: $i] :
( ( in @ X966 @ X967 )
=> ( ( in @ X967 @ X965 )
=> ( in @ X966 @ ( setunion @ X965 ) ) ) )
=> ( ! [X968: $i,X969: $i] :
( ( in @ X969 @ ( setunion @ X968 ) )
=> ! [X970: $o] :
( ! [X971: $i] :
( ( in @ X969 @ X971 )
=> ( ( in @ X971 @ X968 )
=> X970 ) )
=> X970 ) )
=> ( ! [X972: $i,X973: $i] :
( ( in @ X973 @ X972 )
=> ( in @ X973 @ ( powerset @ ( setunion @ X972 ) ) ) )
=> ( ! [X974: $i > $o] :
( ( exu @ X974 )
=> ? [X975: $i] :
! [X976: $i] :
( ( X974 @ X976 )
<=> ( X976 = X975 ) ) )
=> ( ! [X977: $i] :
( ( nonempty @ X977 )
=> ? [X978: $i] :
( ( in @ X978 @ X977 )
& $true ) )
=> ( ! [X979: $i,X980: $i] :
( ( in @ X979 @ ( setadjoin @ X980 @ emptyset ) )
=> ( X979 = X980 ) )
=> ( ! [X981: $i,X982: $i] :
( ( X981 != X982 )
=> ~ ( in @ X982 @ ( setadjoin @ X981 @ emptyset ) ) )
=> ( ! [X983: $i,X984: $i] :
( ( X983 = X984 )
=> ( in @ X983 @ ( setadjoin @ X984 @ emptyset ) ) )
=> ( ! [X985: $i,X986: $i] :
( ( in @ X985 @ ( setadjoin @ X986 @ emptyset ) )
=> ( in @ X986 @ ( setadjoin @ X985 @ emptyset ) ) )
=> ( ! [X987: $i,X988: $i,X989: $i] :
( ( in @ X989 @ ( setadjoin @ X987 @ ( setadjoin @ X988 @ emptyset ) ) )
=> ( ( X989 = X987 )
| ( X989 = X988 ) ) )
=> ( ! [X990: $i,X991: $i] : ( in @ X990 @ ( setadjoin @ X990 @ ( setadjoin @ X991 @ emptyset ) ) )
=> ( ! [X992: $i,X993: $i] : ( in @ X993 @ ( setadjoin @ X992 @ ( setadjoin @ X993 @ emptyset ) ) )
=> ( ! [X994: $i,X995: $i > $o] :
( ? [X996: $i] :
( ( in @ X996 @ X994 )
& ( X995 @ X996 ) )
=> ( ( ( dsetconstr @ X994 @ X995 )
= emptyset )
=> ~ $true ) )
=> ( ! [X997: $i > $o,X998: $i] :
( ( in @ X998 @ emptyset )
=> ( X997 @ X998 ) )
=> ( ! [X999: $i,X1000: $i > $o] :
( ~ ! [X1001: $i] :
( ( in @ X1001 @ X999 )
=> ( X1000 @ X1001 ) )
=> ? [X1002: $i] :
( ( in @ X1002 @ X999 )
& ~ ( X1000 @ X1002 ) ) )
=> ( ! [X1003: $i,X1004: $i > $o] :
( ! [X1005: $i] :
( ( in @ X1005 @ X1003 )
=> ~ ( X1004 @ X1005 ) )
=> ~ ? [X1006: $i] :
( ( in @ X1006 @ X1003 )
& ( X1004 @ X1006 ) ) )
=> ( ! [X1007: $i,X1008: $i > $o] :
( ~ ? [X1009: $i] :
( ( in @ X1009 @ X1007 )
& ( X1008 @ X1009 ) )
=> ! [X1010: $i] :
( ( in @ X1010 @ X1007 )
=> ~ ( X1008 @ X1010 ) ) )
=> ( ! [X1011: $i,X1012: $i > $o] :
( ? [X1013: $i] :
( ( in @ X1013 @ X1011 )
& ~ ( X1012 @ X1013 ) )
=> ~ ! [X1014: $i] :
( ( in @ X1014 @ X1011 )
=> ( X1012 @ X1014 ) ) )
=> ( ! [X1015: $o] :
( X1015
=> ( in @ emptyset @ ( prop2set @ X1015 ) ) )
=> ( prop2set2propI
=> ( ! [X1016: $i,X1017: $i > $o] :
( ~ ? [X1018: $i] :
( ( in @ X1018 @ X1016 )
& ( X1017 @ X1018 ) )
=> ! [X1019: $i] :
( ( in @ X1019 @ X1016 )
=> ~ ( X1017 @ X1019 ) ) )
=> ( ! [X1020: $i,X1021: $i > $o] :
( ~ ! [X1022: $i] :
( ( in @ X1022 @ X1020 )
=> ( X1021 @ X1022 ) )
=> ? [X1023: $i] :
( ( in @ X1023 @ X1020 )
& ~ ( X1021 @ X1023 ) ) )
=> ( ! [X1024: $i > $o] :
( ? [X1025: $i] :
( ( X1024 @ X1025 )
& ! [X1026: $i] :
( ( X1024 @ X1026 )
=> ( X1025 = X1026 ) ) )
=> ( exu @ X1024 ) )
=> ( ! [X1027: $i > $o] :
( ? [X1028: $i] : ( X1027 @ X1028 )
=> ( ! [X1029: $i,X1030: $i] :
( ( X1027 @ X1029 )
=> ( ( X1027 @ X1030 )
=> ( X1029 = X1030 ) ) )
=> ( exu @ X1027 ) ) )
=> ( ! [X1031: $i > $o] :
( ? [X1032: $i] :
! [X1033: $i] :
( ( X1031 @ X1033 )
<=> ( X1033 = X1032 ) )
=> ( exu @ X1031 ) )
=> ( ! [X1034: $i,X1035: $i] :
( ( X1034 = X1035 )
=> ! [X1036: $i,X1037: $i] :
( ( X1036 = X1037 )
=> ( ( in @ X1036 @ X1034 )
=> ( in @ X1037 @ X1035 ) ) ) )
=> ( ! [X1038: $i,X1039: $i] :
( ( X1038 = X1039 )
=> ! [X1040: $i,X1041: $i] :
( ( X1040 = X1041 )
=> ( ( in @ X1040 @ X1038 )
<=> ( in @ X1041 @ X1039 ) ) ) )
=> ( ! [X1042: $i > $o] :
( ( exu @ X1042 )
=> ! [X1043: $i,X1044: $i] :
( ( X1042 @ X1043 )
=> ( ( X1042 @ X1044 )
=> ( X1043 = X1044 ) ) ) )
=> ( ! [X1045: $i > $o,X1046: $i > $o] :
( ! [X1047: $i,X1048: $i] :
( ( X1047 = X1048 )
=> ( ( X1045 @ X1047 )
<=> ( X1046 @ X1048 ) ) )
=> ( ( exu @ X1045 )
<=> ( exu @ X1046 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1049: $i,X1050: $i] :
( ( X1049 = X1050 )
=> ! [X1051: $i,X1052: $i] :
( ( X1051 = X1052 )
=> ( ( setadjoin @ X1049 @ X1051 )
= ( setadjoin @ X1050 @ X1052 ) ) ) )
=> ( ! [X1053: $i,X1054: $i] :
( ( X1053 = X1054 )
=> ( ( powerset @ X1053 )
= ( powerset @ X1054 ) ) )
=> ( ! [X1055: $i,X1056: $i] :
( ( X1055 = X1056 )
=> ( ( setunion @ X1055 )
= ( setunion @ X1056 ) ) )
=> ( ( omega = omega )
=> ( ! [X1057: $i > $o] :
( ( exu @ X1057 )
=> ! [X1058: $i,X1059: $i] :
( ( X1057 @ X1058 )
=> ( ( X1057 @ X1059 )
=> ( X1058 = X1059 ) ) ) )
=> ( ! [X1060: $i > $o,X1061: $i > $o] :
( ! [X1062: $i,X1063: $i] :
( ( X1062 = X1063 )
=> ( ( X1060 @ X1062 )
<=> ( X1061 @ X1063 ) ) )
=> ( ( exu @ X1060 )
=> ( ( exu @ X1061 )
=> ( ( descr @ X1060 )
= ( descr @ X1061 ) ) ) ) )
=> ( ! [X1064: $i,X1065: $i] :
( ( X1064 = X1065 )
=> ! [X1066: $i > $o,X1067: $i > $o] :
( ! [X1068: $i] :
( ( in @ X1068 @ X1064 )
=> ! [X1069: $i] :
( ( in @ X1069 @ X1065 )
=> ( ( X1068 = X1069 )
=> ( ( X1066 @ X1068 )
<=> ( X1067 @ X1069 ) ) ) ) )
=> ( ( dsetconstr @ X1064 @ X1066 )
= ( dsetconstr @ X1065 @ X1067 ) ) ) )
=> ( ! [X1070: $i,X1071: $i] :
( ! [X1072: $i] :
( ( in @ X1072 @ X1070 )
=> ( in @ X1072 @ X1071 ) )
=> ( subset @ X1070 @ X1071 ) )
=> ( ! [X1073: $i,X1074: $i] :
( ( X1073 = X1074 )
=> ( subset @ X1074 @ X1073 ) )
=> ( ! [X1075: $i,X1076: $i] :
( ( X1075 = X1076 )
=> ( subset @ X1075 @ X1076 ) )
=> ( ! [X1077: $i,X1078: $i] :
( ! [X1079: $i] :
( ( in @ X1079 @ X1077 )
=> ( in @ X1079 @ X1078 ) )
=> ( subset @ X1077 @ X1078 ) )
=> ( ! [X1080: $i] : ( subset @ emptyset @ X1080 )
=> ( ! [X1081: $i,X1082: $i,X1083: $i] :
( ( subset @ X1081 @ X1082 )
=> ( ( in @ X1083 @ X1081 )
=> ( in @ X1083 @ X1082 ) ) )
=> ( ! [X1084: $i,X1085: $i,X1086: $i] :
( ( subset @ X1084 @ X1085 )
=> ( ~ ( in @ X1086 @ X1085 )
=> ~ ( in @ X1086 @ X1084 ) ) )
=> ( ! [X1087: $i,X1088: $i,X1089: $i] :
( ( in @ X1089 @ X1087 )
=> ( ~ ( in @ X1089 @ X1088 )
=> ~ ( subset @ X1087 @ X1088 ) ) )
=> ( ! [X1090: $i,X1091: $i] :
( ~ ( subset @ X1090 @ X1091 )
=> ( X1090 != X1091 ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i] :
( ( in @ X1094 @ X1092 )
=> ( ~ ( in @ X1094 @ X1093 )
=> ( X1092 != X1093 ) ) )
=> ( ! [X1095: $i] : ( subset @ X1095 @ X1095 )
=> ( ! [X1096: $i,X1097: $i,X1098: $i] :
( ( subset @ X1096 @ X1097 )
=> ( ( subset @ X1097 @ X1098 )
=> ( subset @ X1096 @ X1098 ) ) )
=> ( ! [X1099: $i,X1100: $i] : ( subset @ X1100 @ ( setadjoin @ X1099 @ X1100 ) )
=> ( ! [X1101: $i,X1102: $i,X1103: $i] :
( ( subset @ X1101 @ X1103 )
=> ( subset @ X1101 @ ( setadjoin @ X1102 @ X1103 ) ) )
=> ( ! [X1104: $i,X1105: $i] :
( ( subset @ X1104 @ X1105 )
=> ( in @ X1104 @ ( powerset @ X1105 ) ) )
=> ( ! [X1106: $i,X1107: $i] :
( ( subset @ X1106 @ X1107 )
=> ( ( subset @ X1107 @ X1106 )
=> ( X1106 = X1107 ) ) )
=> ( ! [X1108: $i] :
( ( subset @ X1108 @ emptyset )
=> ( X1108 = emptyset ) )
=> ( ! [X1109: $i,X1110: $i] :
( ( subset @ X1110 @ X1109 )
=> ( in @ X1110 @ ( powerset @ X1109 ) ) )
=> ( ! [X1111: $i,X1112: $i] :
( ( in @ X1112 @ ( powerset @ X1111 ) )
=> ( subset @ X1112 @ X1111 ) )
=> ( ! [X1113: $i] : ( in @ X1113 @ ( powerset @ X1113 ) )
=> ( ! [X1114: $i,X1115: $i] :
( ( subset @ X1114 @ X1115 )
=> ( subset @ ( powerset @ X1114 ) @ ( powerset @ X1115 ) ) )
=> ( ! [X1116: $i,X1117: $i > $o] : ( in @ ( dsetconstr @ X1116 @ X1117 ) @ ( powerset @ X1116 ) )
=> ( ! [X1118: $i,X1119: $i > $o] : ( subset @ ( dsetconstr @ X1118 @ X1119 ) @ X1118 )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ( in @ X1122 @ X1120 )
=> ( in @ X1122 @ ( binunion @ X1120 @ X1121 ) ) )
=> ( ! [X1123: $i,X1124: $i] : ( in @ X1124 @ ( setadjoin @ X1123 @ ( setadjoin @ X1124 @ emptyset ) ) )
=> ( ! [X1125: $i,X1126: $i,X1127: $i] :
( ( in @ X1127 @ X1126 )
=> ( in @ X1127 @ ( binunion @ X1125 @ X1126 ) ) )
=> ( ! [X1128: $i,X1129: $i,X1130: $i,X1131: $o] :
( ( in @ X1130 @ ( binunion @ X1128 @ X1129 ) )
=> ( ( ( in @ X1130 @ X1128 )
=> X1131 )
=> ( ( ( in @ X1130 @ X1129 )
=> X1131 )
=> X1131 ) ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ( in @ X1134 @ ( binunion @ X1132 @ X1133 ) )
=> ( ( in @ X1134 @ X1132 )
| ( in @ X1134 @ X1133 ) ) )
=> ( ! [X1135: $i,X1136: $i] : ( subset @ X1135 @ ( binunion @ X1135 @ X1136 ) )
=> ( ! [X1137: $i,X1138: $i] : ( subset @ X1138 @ ( binunion @ X1137 @ X1138 ) )
=> ( ! [X1139: $i,X1140: $i,X1141: $i] :
( ( in @ X1141 @ X1139 )
=> ( ( in @ X1141 @ X1140 )
=> ( in @ X1141 @ ( binintersect @ X1139 @ X1140 ) ) ) )
=> ( ! [X1142: $i,X1143: $i,X1144: $i] :
( ( subset @ X1144 @ X1142 )
=> ( ( subset @ X1144 @ X1143 )
=> ( subset @ X1144 @ ( binintersect @ X1142 @ X1143 ) ) ) )
=> ( ! [X1145: $i,X1146: $i,X1147: $i] :
( ( in @ X1147 @ ( binintersect @ X1145 @ X1146 ) )
=> ( in @ X1147 @ X1145 ) )
=> ( ! [X1148: $i,X1149: $i] : ( subset @ ( binintersect @ X1148 @ X1149 ) @ X1148 )
=> ( ! [X1150: $i,X1151: $i] :
( ( subset @ X1150 @ X1151 )
=> ( ( binintersect @ X1150 @ X1151 )
= X1150 ) )
=> ( ! [X1152: $i,X1153: $i] :
( ( ( binintersect @ X1152 @ X1153 )
= X1153 )
=> ( subset @ X1153 @ X1152 ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ ( binintersect @ X1154 @ X1155 ) )
=> ( in @ X1156 @ X1155 ) )
=> ( ! [X1157: $i,X1158: $i] :
( ~ ? [X1159: $i] :
( ( in @ X1159 @ X1157 )
& ( in @ X1159 @ X1158 ) )
=> ( ( binintersect @ X1157 @ X1158 )
= emptyset ) )
=> ( ! [X1160: $i,X1161: $i] : ( subset @ ( binintersect @ X1160 @ X1161 ) @ X1161 )
=> ( ! [X1162: $i,X1163: $i] :
( ( subset @ X1163 @ X1162 )
=> ( ( binintersect @ X1162 @ X1163 )
= X1163 ) )
=> ( ! [X1164: $i,X1165: $i] :
( ( ( binintersect @ X1164 @ X1165 )
= X1164 )
=> ( subset @ X1164 @ X1165 ) )
=> ( ! [X1166: $i,X1167: $i,X1168: $i] :
( ( binintersect @ X1166 @ ( binunion @ X1167 @ X1168 ) )
= ( binunion @ ( binintersect @ X1166 @ X1167 ) @ ( binintersect @ X1166 @ X1168 ) ) )
=> ( ! [X1169: $i,X1170: $i,X1171: $i] :
( ( in @ X1171 @ X1169 )
=> ( ~ ( in @ X1171 @ X1170 )
=> ( in @ X1171 @ ( setminus @ X1169 @ X1170 ) ) ) )
=> ( ! [X1172: $i,X1173: $i,X1174: $i] :
( ( in @ X1174 @ ( setminus @ X1172 @ X1173 ) )
=> ( in @ X1174 @ X1172 ) )
=> ( ! [X1175: $i,X1176: $i,X1177: $i] :
( ( in @ X1177 @ ( setminus @ X1175 @ X1176 ) )
=> ~ ( in @ X1177 @ X1176 ) )
=> ( ! [X1178: $i,X1179: $i] :
( ( subset @ X1178 @ X1179 )
=> ( ( setminus @ X1178 @ X1179 )
= emptyset ) )
=> ( ! [X1180: $i,X1181: $i,X1182: $i] :
( ~ ( in @ X1182 @ ( setminus @ X1180 @ X1181 ) )
=> ( ( in @ X1182 @ X1180 )
=> ( in @ X1182 @ X1181 ) ) )
=> ( ! [X1183: $i,X1184: $i,X1185: $i] :
( ~ ( in @ X1185 @ ( setminus @ X1183 @ X1184 ) )
=> ( ~ ( in @ X1185 @ X1184 )
=> ~ ( in @ X1185 @ X1183 ) ) )
=> ( ! [X1186: $i,X1187: $i,X1188: $i] :
( ~ ( in @ X1188 @ X1186 )
=> ~ ( in @ X1188 @ ( setminus @ X1186 @ X1187 ) ) )
=> ( ! [X1189: $i,X1190: $i,X1191: $i] :
( ( in @ X1191 @ X1190 )
=> ~ ( in @ X1191 @ ( setminus @ X1189 @ X1190 ) ) )
=> ( ! [X1192: $i,X1193: $i] : ( subset @ ( setminus @ X1192 @ X1193 ) @ X1192 )
=> ( ! [X1194: $i,X1195: $i] :
( ( ( setminus @ X1194 @ X1195 )
= emptyset )
=> ( subset @ X1194 @ X1195 ) )
=> ( ! [X1196: $i,X1197: $i,X1198: $i] :
( ( in @ X1198 @ ( symdiff @ X1196 @ X1197 ) )
=> ! [X1199: $o] :
( ( ( in @ X1198 @ X1196 )
=> ( ~ ( in @ X1198 @ X1197 )
=> X1199 ) )
=> ( ( ~ ( in @ X1198 @ X1196 )
=> ( ( in @ X1198 @ X1197 )
=> X1199 ) )
=> X1199 ) ) )
=> ( ! [X1200: $i,X1201: $i,X1202: $i] :
( ( in @ X1202 @ X1200 )
=> ( ~ ( in @ X1202 @ X1201 )
=> ( in @ X1202 @ ( symdiff @ X1200 @ X1201 ) ) ) )
=> ( ! [X1203: $i,X1204: $i,X1205: $i] :
( ~ ( in @ X1205 @ X1203 )
=> ( ( in @ X1205 @ X1204 )
=> ( in @ X1205 @ ( symdiff @ X1203 @ X1204 ) ) ) )
=> ( ! [X1206: $i,X1207: $i,X1208: $i] :
( ( in @ X1208 @ X1206 )
=> ( ( in @ X1208 @ X1207 )
=> ~ ( in @ X1208 @ ( symdiff @ X1206 @ X1207 ) ) ) )
=> ( ! [X1209: $i,X1210: $i,X1211: $i] :
( ~ ( in @ X1211 @ X1209 )
=> ( ~ ( in @ X1211 @ X1210 )
=> ~ ( in @ X1211 @ ( symdiff @ X1209 @ X1210 ) ) ) )
=> ( ! [X1212: $i,X1213: $i] : ( in @ X1213 @ ( setadjoin @ X1212 @ ( setadjoin @ X1213 @ emptyset ) ) )
=> ( ! [X1214: $i,X1215: $i] : ( in @ X1214 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1214 @ ( setadjoin @ X1215 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1216: $i,X1217: $i] : ( in @ X1217 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1216 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1216 @ ( setadjoin @ X1217 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1218: $i,X1219: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1218 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1218 @ ( setadjoin @ X1219 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1220: $i,X1221: $i] : ( iskpair @ ( kpair @ X1220 @ X1221 ) )
=> ( ! [X1222: $i,X1223: $i] :
( ( in @ X1223 @ X1222 )
=> ( subset @ ( setadjoin @ X1223 @ emptyset ) @ X1222 ) )
=> ( ! [X1224: $i,X1225: $i] :
( ( in @ X1225 @ X1224 )
=> ( in @ ( setadjoin @ X1225 @ emptyset ) @ ( powerset @ X1224 ) ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i] :
( ( in @ X1228 @ X1226 )
=> ( in @ ( setadjoin @ X1228 @ emptyset ) @ ( powerset @ ( binunion @ X1226 @ X1227 ) ) ) )
=> ( ! [X1229: $i,X1230: $i,X1231: $i] :
( ( in @ X1231 @ ( setadjoin @ X1229 @ ( setadjoin @ X1230 @ emptyset ) ) )
=> ( ( X1231 = X1229 )
| ( X1231 = X1230 ) ) )
=> ( ! [X1232: $i,X1233: $i,X1234: $i] :
( ( in @ X1234 @ X1232 )
=> ! [X1235: $i] :
( ( in @ X1235 @ X1233 )
=> ( subset @ ( setadjoin @ X1234 @ ( setadjoin @ X1235 @ emptyset ) ) @ ( binunion @ X1232 @ X1233 ) ) ) )
=> ( ! [X1236: $i,X1237: $i,X1238: $i] :
( ( in @ X1238 @ X1236 )
=> ! [X1239: $i] :
( ( in @ X1239 @ X1237 )
=> ( in @ ( setadjoin @ X1238 @ ( setadjoin @ X1239 @ emptyset ) ) @ ( powerset @ ( binunion @ X1236 @ X1237 ) ) ) ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i] :
( ( in @ X1242 @ X1240 )
=> ! [X1243: $i] :
( ( in @ X1243 @ X1241 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1242 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1242 @ ( setadjoin @ X1243 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1240 @ X1241 ) ) ) ) )
=> ( ! [X1244: $i,X1245: $i,X1246: $i] :
( ( in @ X1246 @ X1244 )
=> ! [X1247: $i] :
( ( in @ X1247 @ X1245 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1244 @ X1245 ) ) ) ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ! [X1251: $i] :
( ( in @ X1251 @ X1249 )
=> ( in @ ( kpair @ X1250 @ X1251 ) @ ( powerset @ ( powerset @ ( binunion @ X1248 @ X1249 ) ) ) ) ) )
=> ( ! [X1252: $i,X1253: $i,X1254: $i] :
( ( in @ X1254 @ X1252 )
=> ! [X1255: $i] :
( ( in @ X1255 @ X1253 )
=> ( in @ ( kpair @ X1254 @ X1255 ) @ ( cartprod @ X1252 @ X1253 ) ) ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i] :
( ( in @ X1258 @ ( cartprod @ X1256 @ X1257 ) )
=> ? [X1259: $i] :
( ( in @ X1259 @ X1256 )
& ? [X1260: $i] :
( ( in @ X1260 @ X1257 )
& ( X1258
= ( kpair @ X1259 @ X1260 ) ) ) ) )
=> ( ! [X1261: $i,X1262: $i,X1263: $i] :
( ( in @ X1263 @ ( cartprod @ X1261 @ X1262 ) )
=> ( iskpair @ X1263 ) )
=> ( ! [X1264: $i,X1265: $i] :
( ( in @ X1265 @ ( setunion @ X1264 ) )
=> ? [X1266: $i] :
( ( in @ X1266 @ X1264 )
& ( in @ X1265 @ X1266 ) ) )
=> ( ! [X1267: $i] : ( subset @ ( setunion @ ( setadjoin @ X1267 @ emptyset ) ) @ X1267 )
=> ( ! [X1268: $i] : ( subset @ X1268 @ ( setunion @ ( setadjoin @ X1268 @ emptyset ) ) )
=> ( ! [X1269: $i] :
( ( setunion @ ( setadjoin @ X1269 @ emptyset ) )
= X1269 )
=> ( ! [X1270: $i,X1271: $i > $o] :
( ! [X1272: $i] :
( ( in @ X1272 @ X1270 )
=> ! [X1273: $i] :
( ( in @ X1273 @ X1270 )
=> ( ( X1271 @ X1272 )
=> ( ( X1271 @ X1273 )
=> ( X1272 = X1273 ) ) ) ) )
=> ( ? [X1274: $i] :
( ( in @ X1274 @ X1270 )
& ( X1271 @ X1274 ) )
=> ( singleton @ ( dsetconstr @ X1270 @ X1271 ) ) ) )
=> ( ! [X1275: $i,X1276: $i > $o] :
( ( ex1 @ X1275 @ X1276 )
=> ? [X1277: $i] :
( ( in @ X1277 @ X1275 )
& ( X1276 @ X1277 ) ) )
=> ( ! [X1278: $i,X1279: $i > $o,X1280: $i] :
( ( in @ X1280 @ X1278 )
=> ( ( X1279 @ X1280 )
=> ( ! [X1281: $i] :
( ( in @ X1281 @ X1278 )
=> ( ( X1279 @ X1281 )
=> ( X1281 = X1280 ) ) )
=> ( ex1 @ X1278 @ X1279 ) ) ) )
=> ( ! [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 ) )
=> ( ex1 @ X1282 @ X1283 ) ) )
=> ( ! [X1287: $i,X1288: $i] :
( ( ( setadjoin @ X1287 @ emptyset )
= ( setadjoin @ X1288 @ emptyset ) )
=> ( X1287 = X1288 ) )
=> ( ! [X1289: $i,X1290: $i,X1291: $i] :
( ( in @ ( setadjoin @ X1291 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1289 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1289 @ ( setadjoin @ X1290 @ emptyset ) ) @ emptyset ) ) )
=> ( X1289 = X1291 ) )
=> ( ! [X1292: $i] :
( ( iskpair @ X1292 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1292 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1292 ) ) ) )
=> ( ! [X1293: $i] :
( ( singleton @ X1293 )
=> ( in @ ( setunion @ X1293 ) @ X1293 ) )
=> ( ! [X1294: $i,X1295: $i] :
( ( kfst @ ( kpair @ X1294 @ X1295 ) )
= X1294 )
=> ( ! [X1296: $i,X1297: $i,X1298: $i] :
( ( in @ X1298 @ ( cartprod @ X1296 @ X1297 ) )
=> ( in @ ( kfst @ X1298 ) @ X1296 ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i,X1302: $i] :
( ( ( setadjoin @ ( setadjoin @ X1299 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1299 @ ( setadjoin @ X1300 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1301 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1301 @ ( setadjoin @ X1302 @ emptyset ) ) @ emptyset ) ) )
=> ( X1299 = X1301 ) )
=> ( ! [X1303: $i,X1304: $i,X1305: $i,X1306: $i] :
( ( ( kpair @ X1303 @ X1304 )
= ( kpair @ X1305 @ X1306 ) )
=> ( X1303 = X1305 ) )
=> ( ! [X1307: $i,X1308: $i] :
( ( X1307 = X1308 )
=> ( ( setadjoin @ X1307 @ ( setadjoin @ X1308 @ emptyset ) )
= ( setadjoin @ X1307 @ emptyset ) ) )
=> ( ! [X1309: $i,X1310: $i] :
( ( X1309 = X1310 )
=> ( ( setadjoin @ ( setadjoin @ X1309 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1309 @ ( setadjoin @ X1310 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1309 @ emptyset ) @ emptyset ) ) )
=> ( ! [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 ) ) )
=> ( ( X1313 = X1314 )
=> ( X1312 = X1314 ) ) )
=> ( ! [X1315: $i,X1316: $i,X1317: $i] :
( ( ( setadjoin @ X1315 @ ( setadjoin @ X1316 @ emptyset ) )
= ( setadjoin @ X1317 @ emptyset ) )
=> ( X1315 = X1316 ) )
=> ( ! [X1318: $i,X1319: $i,X1320: $i,X1321: $i] :
( ( ( setadjoin @ ( setadjoin @ X1318 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1318 @ ( setadjoin @ X1319 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1320 @ ( setadjoin @ X1321 @ emptyset ) ) @ emptyset ) ) )
=> ( X1319 = X1321 ) )
=> ( ! [X1322: $i,X1323: $i,X1324: $i,X1325: $i] :
( ( ( kpair @ X1322 @ X1323 )
= ( kpair @ X1324 @ X1325 ) )
=> ( X1323 = X1325 ) )
=> ( ! [X1326: $i] :
( ( iskpair @ X1326 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1326 )
@ ^ [Z0: $i] :
( X1326
= ( kpair @ ( kfst @ X1326 ) @ Z0 ) ) ) ) )
=> ( ! [X1327: $i,X1328: $i] :
( ( ksnd @ ( kpair @ X1327 @ X1328 ) )
= X1328 )
=> ( ! [X1329: $i] :
( ( iskpair @ X1329 )
=> ( ( kpair @ ( kfst @ X1329 ) @ ( ksnd @ X1329 ) )
= X1329 ) )
=> ( ! [X1330: $i,X1331: $i,X1332: $i] :
( ( in @ X1332 @ ( cartprod @ X1330 @ X1331 ) )
=> ( in @ ( ksnd @ X1332 ) @ X1331 ) )
=> ( ! [X1333: $i,X1334: $i,X1335: $i,X1336: $i] :
( ( in @ ( kpair @ X1335 @ X1336 ) @ ( cartprod @ X1333 @ X1334 ) )
=> ( in @ X1335 @ X1333 ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i,X1340: $i] :
( ( in @ ( kpair @ X1339 @ X1340 ) @ ( cartprod @ X1337 @ X1338 ) )
=> ( in @ X1340 @ X1338 ) )
=> ( ! [X1341: $i,X1342: $i,X1343: $i] :
( ( in @ X1343 @ X1341 )
=> ! [X1344: $i] :
( ( in @ X1344 @ X1342 )
=> ( ( kpair @ X1343 @ X1344 )
= ( kpair @ X1343 @ X1344 ) ) ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i] :
( ( in @ X1347 @ X1345 )
=> ! [X1348: $i] :
( ( in @ X1348 @ X1346 )
=> ( ( kfst @ ( kpair @ X1347 @ X1348 ) )
= X1347 ) ) )
=> ( ! [X1349: $i,X1350: $i,X1351: $i] :
( ( in @ X1351 @ X1349 )
=> ! [X1352: $i] :
( ( in @ X1352 @ X1350 )
=> ( ( ksnd @ ( kpair @ X1351 @ X1352 ) )
= X1352 ) ) )
=> ( ! [X1353: $i,X1354: $i,X1355: $i] :
( ( in @ X1355 @ ( cartprod @ X1353 @ X1354 ) )
=> ( ( kpair @ ( kfst @ X1355 ) @ ( ksnd @ X1355 ) )
= X1355 ) )
=> ( ! [X1356: $i,X1357: $i,X1358: $i > $i > $o,X1359: $i] :
( ( in @ X1359 @ X1356 )
=> ! [X1360: $i] :
( ( in @ X1360 @ X1357 )
=> ( ( X1358 @ X1359 @ X1360 )
=> ( in @ ( kpair @ X1359 @ X1360 ) @ ( dpsetconstr @ X1356 @ X1357 @ X1358 ) ) ) ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1361 @ X1362 @ X1363 ) @ ( cartprod @ X1361 @ X1362 ) )
=> ( ! [X1364: $i,X1365: $i,X1366: $i > $i > $o] : ( breln @ X1364 @ X1365 @ ( dpsetconstr @ X1364 @ X1365 @ X1366 ) )
=> ( ! [X1367: $i,X1368: $i,X1369: $i > $i > $o,X1370: $i] :
( ( in @ X1370 @ X1367 )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1368 )
=> ( ( in @ ( kpair @ X1370 @ X1371 ) @ ( dpsetconstr @ X1367 @ X1368 @ X1369 ) )
=> ( X1369 @ X1370 @ X1371 ) ) ) )
=> ( ! [X1372: $i,X1373: $i,X1374: $i > $i > $o,X1375: $i,X1376: $i] :
( ( in @ ( kpair @ X1375 @ X1376 ) @ ( dpsetconstr @ X1372 @ X1373 @ X1374 ) )
=> ( in @ X1375 @ X1372 ) )
=> ( ! [X1377: $i,X1378: $i,X1379: $i > $i > $o,X1380: $i,X1381: $i] :
( ( in @ ( kpair @ X1380 @ X1381 ) @ ( dpsetconstr @ X1377 @ X1378 @ X1379 ) )
=> ( in @ X1381 @ X1378 ) )
=> ( ! [X1382: $i,X1383: $i,X1384: $i > $i > $o,X1385: $i,X1386: $i] :
( ( in @ ( kpair @ X1385 @ X1386 ) @ ( dpsetconstr @ X1382 @ X1383 @ X1384 ) )
=> ( X1384 @ X1385 @ X1386 ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i] :
( ( func @ X1387 @ X1388 @ X1389 )
=> ! [X1390: $i] :
( ( in @ X1390 @ X1387 )
=> ( singleton
@ ( dsetconstr @ X1388
@ ^ [Z0: $i] : ( in @ ( kpair @ X1390 @ Z0 ) @ X1389 ) ) ) ) )
=> ( ! [X1391: $i,X1392: $i,X1393: $i] :
( ( func @ X1391 @ X1392 @ X1393 )
=> ! [X1394: $i] :
( ( in @ X1394 @ X1391 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1392
@ ^ [Z0: $i] : ( in @ ( kpair @ X1394 @ Z0 ) @ X1393 ) ) )
@ X1392 ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i] :
( ( func @ X1395 @ X1396 @ X1397 )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1395 )
=> ( in @ ( ap @ X1395 @ X1396 @ X1397 @ X1398 ) @ X1396 ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( in @ X1401 @ ( funcSet @ X1399 @ X1400 ) )
=> ( func @ X1399 @ X1400 @ X1401 ) )
=> ( ! [X1402: $i,X1403: $i,X1404: $i] :
( ( in @ X1404 @ ( funcSet @ X1402 @ X1403 ) )
=> ! [X1405: $i] :
( ( in @ X1405 @ X1402 )
=> ( in @ ( ap @ X1402 @ X1403 @ X1404 @ X1405 ) @ X1403 ) ) )
=> ( ! [X1406: $i,X1407: $i,X1408: $i] :
( ( func @ X1406 @ X1407 @ X1408 )
=> ( in @ X1408 @ ( funcSet @ X1406 @ X1407 ) ) )
=> ( ! [X1409: $i,X1410: $i,X1411: $i > $i] :
( ! [X1412: $i] :
( ( in @ X1412 @ X1409 )
=> ( in @ ( X1411 @ X1412 ) @ X1410 ) )
=> ( func @ X1409 @ X1410
@ ( dpsetconstr @ X1409 @ X1410
@ ^ [Z0: $i] : ( $eq @ ( X1411 @ Z0 ) ) ) ) )
=> ( ! [X1413: $i,X1414: $i,X1415: $i > $i] :
( ! [X1416: $i] :
( ( in @ X1416 @ X1413 )
=> ( in @ ( X1415 @ X1416 ) @ X1414 ) )
=> ( func @ X1413 @ X1414 @ ( lam @ X1413 @ X1414 @ X1415 ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i > $i] :
( ! [X1420: $i] :
( ( in @ X1420 @ X1417 )
=> ( in @ ( X1419 @ X1420 ) @ X1418 ) )
=> ( in @ ( lam @ X1417 @ X1418 @ X1419 ) @ ( funcSet @ X1417 @ X1418 ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i] :
( ( breln @ X1421 @ X1422 @ X1423 )
=> ! [X1424: $i > $o] :
( ! [X1425: $i] :
( ( in @ X1425 @ X1421 )
=> ! [X1426: $i] :
( ( in @ X1426 @ X1422 )
=> ( ( in @ ( kpair @ X1425 @ X1426 ) @ X1423 )
=> ( X1424 @ ( kpair @ X1425 @ X1426 ) ) ) ) )
=> ! [X1427: $i] :
( ( in @ X1427 @ X1423 )
=> ( X1424 @ X1427 ) ) ) )
=> ( ! [X1428: $i,X1429: $i,X1430: $i] :
( ( breln @ X1428 @ X1429 @ X1430 )
=> ! [X1431: $i > $o] :
( ! [X1432: $i] :
( ( in @ X1432 @ X1428 )
=> ! [X1433: $i] :
( ( in @ X1433 @ X1429 )
=> ( ( in @ ( kpair @ X1432 @ X1433 ) @ X1430 )
=> ( X1431 @ ( kpair @ X1432 @ X1433 ) ) ) ) )
=> ! [X1434: $i] :
( ( in @ X1434 @ X1430 )
=> ( X1431 @ X1434 ) ) ) )
=> ( ! [X1435: $i,X1436: $i > $o] :
( ( ex1 @ X1435 @ X1436 )
=> ! [X1437: $i] :
( ( in @ X1437 @ X1435 )
=> ! [X1438: $i] :
( ( in @ X1438 @ X1435 )
=> ( ( X1436 @ X1437 )
=> ( ( X1436 @ X1438 )
=> ( X1437 = X1438 ) ) ) ) ) )
=> ( ! [X1439: $i,X1440: $i,X1441: $i] :
( ( func @ X1439 @ X1440 @ X1441 )
=> ! [X1442: $i] :
( ( in @ X1442 @ X1439 )
=> ( in @ ( kpair @ X1442 @ ( ap @ X1439 @ X1440 @ X1441 @ X1442 ) ) @ X1441 ) ) )
=> ( ! [X1443: $i,X1444: $i,X1445: $i] :
( ( in @ X1445 @ ( funcSet @ X1443 @ X1444 ) )
=> ! [X1446: $i] :
( ( in @ X1446 @ X1443 )
=> ( in @ ( kpair @ X1446 @ ( ap @ X1443 @ X1444 @ X1445 @ X1446 ) ) @ X1445 ) ) )
=> ( ! [X1447: $i,X1448: $i,X1449: $i] :
( ( func @ X1447 @ X1448 @ X1449 )
=> ! [X1450: $i] :
( ( in @ X1450 @ X1447 )
=> ! [X1451: $i] :
( ( in @ X1451 @ X1448 )
=> ( ( in @ ( kpair @ X1450 @ X1451 ) @ X1449 )
=> ( ( ap @ X1447 @ X1448 @ X1449 @ X1450 )
= X1451 ) ) ) ) )
=> ( ! [X1452: $i,X1453: $i,X1454: $i] :
( ( func @ X1452 @ X1453 @ X1454 )
=> ! [X1455: $i] :
( ( func @ X1452 @ X1453 @ X1455 )
=> ( ! [X1456: $i] :
( ( in @ X1456 @ X1452 )
=> ( ( ap @ X1452 @ X1453 @ X1454 @ X1456 )
= ( ap @ X1452 @ X1453 @ X1455 @ X1456 ) ) )
=> ! [X1457: $i] :
( ( in @ X1457 @ X1452 )
=> ! [X1458: $i] :
( ( in @ X1458 @ X1453 )
=> ( ( in @ ( kpair @ X1457 @ X1458 ) @ X1455 )
=> ( in @ ( kpair @ X1457 @ X1458 ) @ X1454 ) ) ) ) ) ) )
=> ( ! [X1459: $i,X1460: $i,X1461: $i] :
( ( in @ X1461 @ ( funcSet @ X1459 @ X1460 ) )
=> ! [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] :
( ( breln @ X1464 @ X1465 @ X1466 )
=> ! [X1467: $i] :
( ( breln @ X1464 @ X1465 @ X1467 )
=> ( ! [X1468: $i] :
( ( in @ X1468 @ X1464 )
=> ! [X1469: $i] :
( ( in @ X1469 @ X1465 )
=> ( ( in @ ( kpair @ X1468 @ X1469 ) @ X1466 )
=> ( in @ ( kpair @ X1468 @ X1469 ) @ X1467 ) ) ) )
=> ( subset @ X1466 @ X1467 ) ) ) )
=> ( ! [X1470: $i,X1471: $i,X1472: $i] :
( ( breln @ X1470 @ X1471 @ X1472 )
=> ! [X1473: $i] :
( ( breln @ X1470 @ X1471 @ X1473 )
=> ( ! [X1474: $i] :
( ( in @ X1474 @ X1470 )
=> ! [X1475: $i] :
( ( in @ X1475 @ X1471 )
=> ( ( in @ ( kpair @ X1474 @ X1475 ) @ X1472 )
=> ( in @ ( kpair @ X1474 @ X1475 ) @ X1473 ) ) ) )
=> ( ! [X1476: $i] :
( ( in @ X1476 @ X1470 )
=> ! [X1477: $i] :
( ( in @ X1477 @ X1471 )
=> ( ( in @ ( kpair @ X1476 @ X1477 ) @ X1473 )
=> ( in @ ( kpair @ X1476 @ X1477 ) @ X1472 ) ) ) )
=> ( X1472 = X1473 ) ) ) ) )
=> ( ! [X1478: $i,X1479: $i,X1480: $i] :
( ( func @ X1478 @ X1479 @ X1480 )
=> ! [X1481: $i] :
( ( func @ X1478 @ X1479 @ X1481 )
=> ( ! [X1482: $i] :
( ( in @ X1482 @ X1478 )
=> ( ( ap @ X1478 @ X1479 @ X1480 @ X1482 )
= ( ap @ X1478 @ X1479 @ X1481 @ X1482 ) ) )
=> ( X1480 = X1481 ) ) ) )
=> ( ! [X1483: $i,X1484: $i,X1485: $i] :
( ( in @ X1485 @ ( funcSet @ X1483 @ X1484 ) )
=> ! [X1486: $i] :
( ( in @ X1486 @ ( funcSet @ X1483 @ X1484 ) )
=> ( ! [X1487: $i] :
( ( in @ X1487 @ X1483 )
=> ( ( ap @ X1483 @ X1484 @ X1485 @ X1487 )
= ( ap @ X1483 @ X1484 @ X1486 @ X1487 ) ) )
=> ( X1485 = X1486 ) ) ) )
=> ( ! [X1488: $i,X1489: $i,X1490: $i] :
( ( in @ X1490 @ ( funcSet @ X1488 @ X1489 ) )
=> ! [X1491: $i] :
( ( in @ X1491 @ X1488 )
=> ( ( ap @ X1488 @ X1489 @ X1490 @ X1491 )
= ( ap @ X1488 @ X1489 @ X1490 @ X1491 ) ) ) )
=> ( ! [X1492: $i,X1493: $i,X1494: $i] :
( ( func @ X1492 @ X1493 @ X1494 )
=> ! [X1495: $i] :
( ( in @ X1495 @ X1492 )
=> ( ( ap @ X1492 @ X1493 @ X1494 @ X1495 )
= ( ap @ X1492 @ X1493 @ X1494 @ X1495 ) ) ) )
=> ( ! [X1496: $i,X1497: $i,X1498: $i > $i] :
( ! [X1499: $i] :
( ( in @ X1499 @ X1496 )
=> ( in @ ( X1498 @ X1499 ) @ X1497 ) )
=> ! [X1500: $i] :
( ( in @ X1500 @ X1496 )
=> ( ( ap @ X1496 @ X1497 @ ( lam @ X1496 @ X1497 @ X1498 ) @ X1500 )
= ( X1498 @ X1500 ) ) ) )
=> ( ! [X1501: $i,X1502: $i,X1503: $i] :
( ( func @ X1501 @ X1502 @ X1503 )
=> ( ( lam @ X1501 @ X1502 @ ( ap @ X1501 @ X1502 @ X1503 ) )
= X1503 ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i > $i] :
( ! [X1507: $i] :
( ( in @ X1507 @ X1504 )
=> ( in @ ( X1506 @ X1507 ) @ X1505 ) )
=> ( ( lam @ X1504 @ X1505 @ X1506 )
= ( lam @ X1504 @ X1505 @ X1506 ) ) )
=> ( ! [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] :
( ( in @ X1515 @ ( funcSet @ X1513 @ X1514 ) )
=> ( ( lam @ X1513 @ X1514 @ ( ap @ X1513 @ X1514 @ X1515 ) )
= X1515 ) )
=> ( ! [X1516: $i,X1517: $o,X1518: $i] :
( ( in @ X1518 @ X1516 )
=> ! [X1519: $i] :
( ( in @ X1519 @ X1516 )
=> ( ~ X1517
=> ( in @ X1519
@ ( dsetconstr @ X1516
@ ^ [Z0: $i] :
( ( X1517
& ( Z0 = X1518 ) )
| ( ~ X1517
& ( Z0 = X1519 ) ) ) ) ) ) ) )
=> ( ! [X1520: $i,X1521: $o,X1522: $i] :
( ( in @ X1522 @ X1520 )
=> ! [X1523: $i] :
( ( in @ X1523 @ X1520 )
=> ( ~ X1521
=> ( ( dsetconstr @ X1520
@ ^ [Z0: $i] :
( ( X1521
& ( Z0 = X1522 ) )
| ( ~ X1521
& ( Z0 = X1523 ) ) ) )
= ( setadjoin @ X1523 @ emptyset ) ) ) ) )
=> ( ! [X1524: $i,X1525: $o,X1526: $i] :
( ( in @ X1526 @ X1524 )
=> ! [X1527: $i] :
( ( in @ X1527 @ X1524 )
=> ( X1525
=> ( in @ X1526
@ ( dsetconstr @ X1524
@ ^ [Z0: $i] :
( ( X1525
& ( Z0 = X1526 ) )
| ( ~ X1525
& ( Z0 = X1527 ) ) ) ) ) ) ) )
=> ( ! [X1528: $i,X1529: $o,X1530: $i] :
( ( in @ X1530 @ X1528 )
=> ! [X1531: $i] :
( ( in @ X1531 @ X1528 )
=> ( X1529
=> ( ( dsetconstr @ X1528
@ ^ [Z0: $i] :
( ( X1529
& ( Z0 = X1530 ) )
| ( ~ X1529
& ( Z0 = X1531 ) ) ) )
= ( setadjoin @ X1530 @ emptyset ) ) ) ) )
=> ( ! [X1532: $i,X1533: $o,X1534: $i] :
( ( in @ X1534 @ X1532 )
=> ! [X1535: $i] :
( ( in @ X1535 @ X1532 )
=> ( singleton
@ ( dsetconstr @ X1532
@ ^ [Z0: $i] :
( ( X1533
& ( Z0 = X1534 ) )
| ( ~ X1533
& ( Z0 = X1535 ) ) ) ) ) ) )
=> ( ! [X1536: $i,X1537: $o,X1538: $i] :
( ( in @ X1538 @ X1536 )
=> ! [X1539: $i] :
( ( in @ X1539 @ X1536 )
=> ( in @ ( if @ X1536 @ X1537 @ X1538 @ X1539 ) @ X1536 ) ) )
=> ( ! [X1540: $i] :
( ( singleton @ X1540 )
=> ! [X1541: $i] :
( ( in @ X1541 @ X1540 )
=> ( ( setunion @ X1540 )
= X1541 ) ) )
=> ( ! [X1542: $i,X1543: $o,X1544: $i] :
( ( in @ X1544 @ X1542 )
=> ! [X1545: $i] :
( ( in @ X1545 @ X1542 )
=> ( X1543
=> ( ( if @ X1542 @ X1543 @ X1544 @ X1545 )
= X1544 ) ) ) )
=> ( ! [X1546: $i,X1547: $o,X1548: $i] :
( ( in @ X1548 @ X1546 )
=> ! [X1549: $i] :
( ( in @ X1549 @ X1546 )
=> ( ~ X1547
=> ( ( if @ X1546 @ X1547 @ X1548 @ X1549 )
= X1549 ) ) ) )
=> ( ! [X1550: $i,X1551: $o,X1552: $i] :
( ( in @ X1552 @ X1550 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1550 )
=> ( in @ ( if @ X1550 @ X1551 @ X1552 @ X1553 ) @ ( setadjoin @ X1552 @ ( setadjoin @ X1553 @ emptyset ) ) ) ) )
=> ( ! [X1554: $i,X1555: $i] :
( ( in @ X1555 @ ( powerset @ X1554 ) )
=> ! [X1556: $i] :
( ( in @ X1556 @ ( powerset @ X1554 ) )
=> ( in @ ( binintersect @ X1555 @ X1556 ) @ ( powerset @ X1554 ) ) ) )
=> ( ! [X1557: $i,X1558: $i] :
( ( in @ X1558 @ ( powerset @ X1557 ) )
=> ! [X1559: $i] :
( ( in @ X1559 @ ( powerset @ X1557 ) )
=> ( in @ ( binunion @ X1558 @ X1559 ) @ ( powerset @ X1557 ) ) ) )
=> ( ! [X1560: $i,X1561: $i] :
( ( in @ X1561 @ ( powerset @ X1560 ) )
=> ( in @ ( powerset @ X1561 ) @ ( powerset @ ( powerset @ X1560 ) ) ) )
=> ( ! [X1562: $i,X1563: $i] :
( ( in @ X1563 @ ( powerset @ X1562 ) )
=> ! [X1564: $i] :
( ( in @ X1564 @ ( powerset @ X1562 ) )
=> ( in @ ( setminus @ X1563 @ X1564 ) @ ( powerset @ X1562 ) ) ) )
=> ( ! [X1565: $i,X1566: $i] :
( ( in @ X1566 @ ( powerset @ X1565 ) )
=> ( in @ ( setminus @ X1565 @ X1566 ) @ ( powerset @ X1565 ) ) )
=> ( ! [X1567: $i,X1568: $i] :
( ( in @ X1568 @ ( powerset @ X1567 ) )
=> ! [X1569: $i] :
( ( in @ X1569 @ ( powerset @ X1567 ) )
=> ( ! [X1570: $i] :
( ( in @ X1570 @ X1567 )
=> ( ( in @ X1570 @ X1568 )
=> ( in @ X1570 @ X1569 ) ) )
=> ( ! [X1571: $i] :
( ( in @ X1571 @ X1567 )
=> ( ( in @ X1571 @ X1569 )
=> ( in @ X1571 @ X1568 ) ) )
=> ( X1568 = X1569 ) ) ) ) )
=> ( ! [X1572: $i,X1573: $i] :
( ( in @ X1573 @ ( powerset @ X1572 ) )
=> ! [X1574: $i] :
( ( in @ X1574 @ ( powerset @ X1572 ) )
=> ( ! [X1575: $i] :
( ( in @ X1575 @ X1572 )
=> ( ( in @ X1575 @ X1573 )
=> ( in @ X1575 @ X1574 ) ) )
=> ( subset @ X1573 @ X1574 ) ) ) )
=> ( ! [X1576: $i,X1577: $i] :
( ( in @ X1577 @ ( powerset @ X1576 ) )
=> ! [X1578: $i] :
( ( in @ X1578 @ ( powerset @ X1576 ) )
=> ( ! [X1579: $i] :
( ( in @ X1579 @ X1576 )
=> ( ( in @ X1579 @ X1577 )
=> ( in @ X1579 @ X1578 ) ) )
=> ( in @ X1577 @ ( powerset @ X1578 ) ) ) ) )
=> ( ! [X1580: $i,X1581: $i] :
( ( in @ X1581 @ ( powerset @ X1580 ) )
=> ! [X1582: $i] :
( ( in @ X1582 @ ( powerset @ X1580 ) )
=> ! [X1583: $i] :
( ( in @ X1583 @ X1580 )
=> ( ( in @ X1581 @ ( powerset @ X1582 ) )
=> ( ( in @ X1583 @ X1581 )
=> ( in @ X1583 @ X1582 ) ) ) ) ) )
=> ( ! [X1584: $i,X1585: $i] :
( ( in @ X1585 @ ( powerset @ X1584 ) )
=> ! [X1586: $i] :
( ( in @ X1586 @ X1584 )
=> ( ( in @ X1586 @ X1585 )
=> ~ ( in @ X1586 @ ( setminus @ X1584 @ X1585 ) ) ) ) )
=> ( ! [X1587: $i,X1588: $i] :
( ( in @ X1588 @ ( powerset @ X1587 ) )
=> ! [X1589: $i] :
( ( in @ X1589 @ X1587 )
=> ( ~ ( in @ X1589 @ ( setminus @ X1587 @ X1588 ) )
=> ( in @ X1589 @ X1588 ) ) ) )
=> ( ! [X1590: $i,X1591: $i] :
( ( in @ X1591 @ ( powerset @ X1590 ) )
=> ! [X1592: $i] :
( ( in @ X1592 @ ( powerset @ X1590 ) )
=> ! [X1593: $i] :
( ( in @ X1593 @ X1590 )
=> ( ~ ( in @ X1593 @ X1591 )
=> ~ ( in @ X1593 @ ( binintersect @ X1591 @ X1592 ) ) ) ) ) )
=> ( ! [X1594: $i,X1595: $i] :
( ( in @ X1595 @ ( powerset @ X1594 ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ ( powerset @ X1594 ) )
=> ! [X1597: $i] :
( ( in @ X1597 @ X1594 )
=> ( ~ ( in @ X1597 @ X1596 )
=> ~ ( in @ X1597 @ ( binintersect @ X1595 @ X1596 ) ) ) ) ) )
=> ( ! [X1598: $i,X1599: $i] :
( ( in @ X1599 @ ( powerset @ X1598 ) )
=> ! [X1600: $i] :
( ( in @ X1600 @ ( powerset @ X1598 ) )
=> ! [X1601: $i] :
( ( in @ X1601 @ X1598 )
=> ( ( subset @ X1599 @ ( setminus @ X1598 @ X1600 ) )
=> ( ( in @ X1601 @ X1600 )
=> ~ ( in @ X1601 @ X1599 ) ) ) ) ) )
=> ( ! [X1602: $i,X1603: $i] :
( ( in @ X1603 @ ( powerset @ X1602 ) )
=> ! [X1604: $i] :
( ( in @ X1604 @ ( powerset @ X1602 ) )
=> ! [X1605: $i] :
( ( in @ X1605 @ X1602 )
=> ( ( subset @ X1603 @ X1604 )
=> ( ~ ( in @ X1605 @ X1604 )
=> ~ ( in @ X1605 @ X1603 ) ) ) ) ) )
=> ( ! [X1606: $i,X1607: $i] :
( ( in @ X1607 @ ( powerset @ X1606 ) )
=> ! [X1608: $i] :
( ( in @ X1608 @ ( powerset @ X1606 ) )
=> ( ( subset @ X1607 @ X1608 )
=> ( subset @ ( setminus @ X1606 @ X1608 ) @ ( setminus @ X1606 @ X1607 ) ) ) ) )
=> ( ! [X1609: $i,X1610: $i] :
( ( in @ X1610 @ ( powerset @ X1609 ) )
=> ! [X1611: $i] :
( ( in @ X1611 @ ( powerset @ X1609 ) )
=> ( ( subset @ ( setminus @ X1609 @ X1611 ) @ ( setminus @ X1609 @ X1610 ) )
=> ( subset @ X1610 @ X1611 ) ) ) )
=> ( ! [X1612: $i,X1613: $i] :
( ( in @ X1613 @ ( powerset @ X1612 ) )
=> ! [X1614: $i] :
( ( in @ X1614 @ X1612 )
=> ( ( in @ X1614 @ X1613 )
=> ( in @ X1614 @ ( setminus @ X1612 @ ( setminus @ X1612 @ X1613 ) ) ) ) ) )
=> ( ! [X1615: $i,X1616: $i] :
( ( in @ X1616 @ ( powerset @ X1615 ) )
=> ! [X1617: $i] :
( ( in @ X1617 @ X1615 )
=> ( ( in @ X1617 @ ( setminus @ X1615 @ ( setminus @ X1615 @ X1616 ) ) )
=> ( in @ X1617 @ X1616 ) ) ) )
=> ( ! [X1618: $i,X1619: $i] :
( ( in @ X1619 @ ( powerset @ X1618 ) )
=> ( subset @ X1619 @ ( setminus @ X1618 @ ( setminus @ X1618 @ X1619 ) ) ) )
=> ( ! [X1620: $i,X1621: $i] :
( ( in @ X1621 @ ( powerset @ X1620 ) )
=> ( subset @ ( setminus @ X1620 @ ( setminus @ X1620 @ X1621 ) ) @ X1621 ) )
=> ( ! [X1622: $i,X1623: $i] :
( ( in @ X1623 @ ( powerset @ X1622 ) )
=> ( X1623
= ( setminus @ X1622 @ ( setminus @ X1622 @ X1623 ) ) ) )
=> ( ! [X1624: $i,X1625: $i] :
( ( in @ X1625 @ ( powerset @ X1624 ) )
=> ! [X1626: $i] :
( ( in @ X1626 @ ( powerset @ X1624 ) )
=> ! [X1627: $i] :
( ( in @ X1627 @ X1624 )
=> ( ( in @ X1627 @ ( setminus @ X1624 @ X1625 ) )
=> ~ ( in @ X1627 @ ( binintersect @ X1625 @ X1626 ) ) ) ) ) )
=> ( ! [X1628: $i,X1629: $i] :
( ( in @ X1629 @ ( powerset @ X1628 ) )
=> ! [X1630: $i] :
( ( in @ X1630 @ ( powerset @ X1628 ) )
=> ! [X1631: $i] :
( ( in @ X1631 @ X1628 )
=> ( ( in @ X1631 @ ( setminus @ X1628 @ X1629 ) )
=> ( in @ X1631 @ ( setminus @ X1628 @ ( binintersect @ X1629 @ X1630 ) ) ) ) ) ) )
=> ( ! [X1632: $i,X1633: $i] :
( ( in @ X1633 @ ( powerset @ X1632 ) )
=> ! [X1634: $i] :
( ( in @ X1634 @ ( powerset @ X1632 ) )
=> ( subset @ ( setminus @ X1632 @ X1633 ) @ ( setminus @ X1632 @ ( binintersect @ X1633 @ X1634 ) ) ) ) )
=> ( ! [X1635: $i,X1636: $i] :
( ( in @ X1636 @ ( powerset @ X1635 ) )
=> ! [X1637: $i] :
( ( in @ X1637 @ ( powerset @ X1635 ) )
=> ( in @ ( setminus @ X1635 @ X1636 ) @ ( powerset @ ( setminus @ X1635 @ ( binintersect @ X1636 @ X1637 ) ) ) ) ) )
=> ( ! [X1638: $i,X1639: $i] :
( ( in @ X1639 @ ( powerset @ X1638 ) )
=> ! [X1640: $i] :
( ( in @ X1640 @ ( powerset @ X1638 ) )
=> ( ( subset @ X1639 @ ( setminus @ X1638 @ X1640 ) )
=> ! [X1641: $i] :
( ( in @ X1641 @ X1638 )
=> ( ( in @ X1641 @ X1640 )
=> ( in @ X1641 @ ( setminus @ X1638 @ X1639 ) ) ) ) ) ) )
=> ( ! [X1642: $i,X1643: $i] :
( ( in @ X1643 @ ( powerset @ X1642 ) )
=> ! [X1644: $i] :
( ( in @ X1644 @ ( powerset @ X1642 ) )
=> ( ( subset @ X1643 @ ( setminus @ X1642 @ X1644 ) )
=> ( subset @ X1644 @ ( setminus @ X1642 @ X1643 ) ) ) ) )
=> ( ! [X1645: $i,X1646: $i] :
( ( in @ X1646 @ ( powerset @ X1645 ) )
=> ! [X1647: $i] :
( ( in @ X1647 @ ( powerset @ X1645 ) )
=> ! [X1648: $i] :
( ( in @ X1648 @ X1645 )
=> ( ~ ( in @ X1648 @ ( binunion @ X1646 @ X1647 ) )
=> ~ ( in @ X1648 @ X1646 ) ) ) ) )
=> ( ! [X1649: $i,X1650: $i] :
( ( in @ X1650 @ ( powerset @ X1649 ) )
=> ! [X1651: $i] :
( ( in @ X1651 @ ( powerset @ X1649 ) )
=> ! [X1652: $i] :
( ( in @ X1652 @ X1649 )
=> ( ~ ( in @ X1652 @ ( binunion @ X1650 @ X1651 ) )
=> ~ ( in @ X1652 @ X1651 ) ) ) ) )
=> ( ! [X1653: $i,X1654: $i] :
( ( in @ X1654 @ ( powerset @ X1653 ) )
=> ! [X1655: $i] :
( ( in @ X1655 @ ( powerset @ X1653 ) )
=> ! [X1656: $i] :
( ( in @ X1656 @ ( powerset @ X1653 ) )
=> ! [X1657: $i] :
( ( in @ X1657 @ X1653 )
=> ( ( in @ X1657 @ ( binintersect @ X1654 @ X1655 ) )
=> ( in @ X1657 @ ( binunion @ X1654 @ X1656 ) ) ) ) ) ) )
=> ( ! [X1658: $i,X1659: $i] :
( ( in @ X1659 @ ( powerset @ X1658 ) )
=> ! [X1660: $i] :
( ( in @ X1660 @ ( powerset @ X1658 ) )
=> ! [X1661: $i] :
( ( in @ X1661 @ ( powerset @ X1658 ) )
=> ! [X1662: $i] :
( ( in @ X1662 @ X1658 )
=> ( ( in @ X1662 @ ( binintersect @ X1659 @ X1660 ) )
=> ( in @ X1662 @ ( binunion @ X1660 @ X1661 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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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ectLsub]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),binintersectSubset2]),complementInPowersetComplementIntersect]),contraSubsetComplement]),binintersectSubset3]),complementTcontraSubset]),binunionTILcontra]),binintersectER]),binunionTIRcontra]),inIntersectImpInUnion]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),singletonsuniq]),setukpairinjL1]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),notequalI2]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),subsetRefl]),setunionsingleton2]),subsetTrans]),setunionsingleton]),c_0_268]),setadjoinSub]),c_0_269]),c_0_270]),c_0_271]),c_0_272]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setadjoinSub2]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),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]),subset2powerset]),c_0_288]),setextsub]),subsetemptysetimpeq]),powersetI1]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_289]),c_0_290]),c_0_291]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_292]),c_0_293]),in__Cong]),inCongP]),c_0_294]),c_0_295]),c_0_296]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_297]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_298]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_299]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_300]),nonemptyE1]),c_0_301]),noeltsimpempty]),emptyI]),setext]),c_0_302]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_303]),c_0_304]),c_0_305]),c_0_306]),c_0_307]),wellorderingAx]),foundationAx]),c_0_308]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_309]) ).
thf(c_0_311,negated_conjecture,
! 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$i,X2091: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $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 > $i > $o,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i > $i > $o,X2158: $i,X2159: $i,X2160: $i > $i > $o,X2161: $i,X2162: $i,X2163: $i > $i > $o,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i > $i > $o,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i > $i > $o,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $i > $i > $o,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i,X2204: $i,X2205: $i > $i,X2207: $i,X2208: $i,X2209: $i > $i,X2211: $i,X2212: $i,X2213: $i > $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i > $o,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i > $o,X2228: $i,X2229: $i,X2230: $i > $o,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2245: $i,X2246: $i,X2247: $i,X2248: $i,X2249: $i,X2251: $i,X2252: $i,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2272: $i,X2273: $i,X2274: $i,X2275: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2287: $i,X2288: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i > $i,X2294: $i,X2295: $i,X2296: $i,X2297: $i,X2298: $i,X2299: $i,X2300: $i > $i,X2302: $i,X2303: $i,X2304: $i > $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i,X2311: $o,X2312: $i,X2313: $i,X2314: $i,X2315: $o,X2316: $i,X2317: $i,X2318: $i,X2319: $o,X2320: $i,X2321: $i,X2322: $i,X2323: $o,X2324: $i,X2325: $i,X2326: $i,X2327: $o,X2328: $i,X2329: $i,X2330: $i,X2331: $o,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $o,X2338: $i,X2339: $i,X2340: $i,X2341: $o,X2342: $i,X2343: $i,X2344: $i,X2345: $o,X2346: $i,X2347: $i,X2348: $i,X2349: $i,X2350: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,X2363: $i,X2366: $i,X2367: $i,X2368: $i,X2370: $i,X2371: $i,X2372: $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,X2389: $i,X2390: $i,X2391: $i,X2392: $i,X2393: $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,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] :
( ( ~ ( in @ ( esk1_2 @ X1663 @ X1664 ) @ X1663 )
| ~ ( in @ ( esk1_2 @ X1663 @ X1664 ) @ X1664 )
| ( X1663 = X1664 ) )
& ( ( in @ ( esk1_2 @ X1663 @ X1664 ) @ X1663 )
| ( in @ ( esk1_2 @ X1663 @ X1664 ) @ X1664 )
| ( X1663 = X1664 ) )
& ~ ( in @ X1666 @ emptyset )
& ( ~ ( in @ X1669 @ ( setadjoin @ X1667 @ X1668 ) )
| ( X1669 = X1667 )
| ( in @ X1669 @ X1668 ) )
& ( ( X1669 != X1667 )
| ( in @ X1669 @ ( setadjoin @ X1667 @ X1668 ) ) )
& ( ~ ( in @ X1669 @ X1668 )
| ( in @ X1669 @ ( setadjoin @ X1667 @ X1668 ) ) )
& ( ~ ( in @ X1671 @ ( powerset @ X1670 ) )
| ~ ( in @ X1672 @ X1671 )
| ( in @ X1672 @ X1670 ) )
& ( ( in @ ( esk2_2 @ X1673 @ X1674 ) @ X1674 )
| ( in @ X1674 @ ( powerset @ X1673 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1673 @ X1674 ) @ X1673 )
| ( in @ X1674 @ ( powerset @ X1673 ) ) )
& ( ( in @ X1677 @ ( esk3_2 @ X1676 @ X1677 ) )
| ~ ( in @ X1677 @ ( setunion @ X1676 ) ) )
& ( ( in @ ( esk3_2 @ X1676 @ X1677 ) @ X1676 )
| ~ ( in @ X1677 @ ( setunion @ X1676 ) ) )
& ( ~ ( in @ X1680 @ X1681 )
| ~ ( in @ X1681 @ X1679 )
| ( in @ X1680 @ ( setunion @ X1679 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1682 @ omega )
| ( in @ ( setadjoin @ X1682 @ X1682 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1683 ) @ omega )
| ~ ( in @ emptyset @ X1683 )
| ~ ( in @ X1685 @ omega )
| ( in @ X1685 @ X1683 ) )
& ( ( in @ ( esk4_1 @ X1683 ) @ X1683 )
| ~ ( in @ emptyset @ X1683 )
| ~ ( in @ X1685 @ omega )
| ( in @ X1685 @ X1683 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1683 ) @ ( esk4_1 @ X1683 ) ) @ X1683 )
| ~ ( in @ emptyset @ X1683 )
| ~ ( in @ X1685 @ omega )
| ( in @ X1685 @ X1683 ) )
& ( ( in @ ( esk7_3 @ X1686 @ X1687 @ X1690 ) @ X1687 )
| ~ ( in @ X1690 @ ( esk6_2 @ X1686 @ X1687 ) )
| ( in @ ( esk5_2 @ X1686 @ X1687 ) @ X1687 ) )
& ( ( X1686 @ ( esk7_3 @ X1686 @ X1687 @ X1690 ) @ X1690 )
| ~ ( in @ X1690 @ ( esk6_2 @ X1686 @ X1687 ) )
| ( in @ ( esk5_2 @ X1686 @ X1687 ) @ X1687 ) )
& ( ~ ( in @ X1693 @ X1687 )
| ~ ( X1686 @ X1693 @ X1692 )
| ( in @ X1692 @ ( esk6_2 @ X1686 @ X1687 ) )
| ( in @ ( esk5_2 @ X1686 @ X1687 ) @ X1687 ) )
& ( ( in @ ( esk7_3 @ X1686 @ X1687 @ X1690 ) @ X1687 )
| ~ ( in @ X1690 @ ( esk6_2 @ X1686 @ X1687 ) )
| ~ ( exu @ ( X1686 @ ( esk5_2 @ X1686 @ X1687 ) ) ) )
& ( ( X1686 @ ( esk7_3 @ X1686 @ X1687 @ X1690 ) @ X1690 )
| ~ ( in @ X1690 @ ( esk6_2 @ X1686 @ X1687 ) )
| ~ ( exu @ ( X1686 @ ( esk5_2 @ X1686 @ X1687 ) ) ) )
& ( ~ ( in @ X1693 @ X1687 )
| ~ ( X1686 @ X1693 @ X1692 )
| ( in @ X1692 @ ( esk6_2 @ X1686 @ X1687 ) )
| ~ ( exu @ ( X1686 @ ( esk5_2 @ X1686 @ X1687 ) ) ) )
& ( ( in @ ( esk8_1 @ X1694 ) @ X1694 )
| ~ ( in @ X1695 @ X1694 ) )
& ( ~ ( in @ X1697 @ ( esk8_1 @ X1694 ) )
| ~ ( in @ X1697 @ X1694 )
| ~ ( in @ X1695 @ X1694 ) )
& epred1_0
& ( ~ ( exu @ X1698 )
| ( X1698 @ ( descr @ X1698 ) ) )
& ( ~ ( in @ X1701 @ X1699 )
| ~ ( X1700 @ X1701 )
| ( in @ X1701 @ ( dsetconstr @ X1699 @ X1700 ) ) )
& ( ~ ( in @ X1704 @ ( dsetconstr @ X1702 @ X1703 ) )
| ( in @ X1704 @ X1702 ) )
& ( ~ ( in @ X1707 @ ( dsetconstr @ X1705 @ X1706 ) )
| ( X1706 @ X1707 ) )
& ( ( X1708 @ ( esk9_1 @ X1708 ) )
| ~ ( exu @ X1708 ) )
& ( ~ ( X1708 @ X1710 )
| ( ( esk9_1 @ X1708 )
= X1710 )
| ~ ( exu @ X1708 ) )
& ( ~ ( in @ X1712 @ ( prop2set @ X1711 ) )
| X1711 )
& ( ~ ( in @ X1713 @ emptyset )
| X1714 )
& ( ~ ( in @ X1715 @ emptyset )
| ~ $true )
& ~ ( in @ X1716 @ emptyset )
& ( ~ ( exu @ X1717 )
| ( X1717 @ ( esk10_1 @ X1717 ) ) )
& ( ( in @ ( esk12_2 @ X1719 @ X1720 ) @ X1720 )
| ( X1719 = X1720 )
| ( in @ ( esk11_2 @ X1719 @ X1720 ) @ X1719 ) )
& ( ~ ( in @ ( esk12_2 @ X1719 @ X1720 ) @ X1719 )
| ( X1719 = X1720 )
| ( in @ ( esk11_2 @ X1719 @ X1720 ) @ X1719 ) )
& ( ( in @ ( esk12_2 @ X1719 @ X1720 ) @ X1720 )
| ( X1719 = X1720 )
| ~ ( in @ ( esk11_2 @ X1719 @ X1720 ) @ X1720 ) )
& ( ~ ( in @ ( esk12_2 @ X1719 @ X1720 ) @ X1719 )
| ( X1719 = X1720 )
| ~ ( in @ ( esk11_2 @ X1719 @ X1720 ) @ X1720 ) )
& ( ( in @ ( esk13_1 @ X1723 ) @ X1723 )
| ( X1723 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1725 ) @ X1725 )
| ( X1725 = emptyset ) )
& ( ~ ( in @ X1729 @ ( dsetconstr @ X1727 @ X1728 ) )
| ( X1728 @ X1729 )
| ~ ( in @ X1729 @ X1727 ) )
& ( ~ ( X1728 @ X1729 )
| ( in @ X1729 @ ( dsetconstr @ X1727 @ X1728 ) )
| ~ ( in @ X1729 @ X1727 ) )
& ( ~ ( nonempty @ X1730 )
| ( in @ ( esk15_1 @ X1730 ) @ X1730 ) )
& ( ~ ( in @ X1734 @ X1732 )
| ~ ( X1733 @ X1734 )
| ( nonempty @ ( dsetconstr @ X1732 @ X1733 ) ) )
& ( ~ ( in @ X1736 @ X1735 )
| ( nonempty @ X1735 ) )
& ( in @ X1737 @ ( setadjoin @ X1737 @ X1738 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1741 @ X1740 )
| ( in @ X1741 @ ( setadjoin @ X1739 @ X1740 ) ) )
& ( ( in @ X1744 @ X1743 )
| X1745
| ( X1744 = X1742 )
| ~ ( in @ X1744 @ ( setadjoin @ X1742 @ X1743 ) ) )
& ( ~ X1745
| X1745
| ( X1744 = X1742 )
| ~ ( in @ X1744 @ ( setadjoin @ X1742 @ X1743 ) ) )
& ( ( in @ X1744 @ X1743 )
| X1745
| ~ X1745
| ~ ( in @ X1744 @ ( setadjoin @ X1742 @ X1743 ) ) )
& ( ~ X1745
| X1745
| ~ X1745
| ~ ( in @ X1744 @ ( setadjoin @ X1742 @ X1743 ) ) )
& ( ~ ( in @ X1748 @ ( setadjoin @ X1746 @ X1747 ) )
| ( X1748 = X1746 )
| ( in @ X1748 @ X1747 ) )
& ( ( dsetconstr @ X1749
@ ^ [Z0: $i] : $true )
= X1749 )
& ( ( in @ ( esk16_2 @ X1750 @ X1751 ) @ X1751 )
| ( in @ X1751 @ ( powerset @ X1750 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1750 @ X1751 ) @ X1750 )
| ( in @ X1751 @ ( powerset @ X1750 ) ) )
& ( in @ emptyset @ ( powerset @ X1753 ) )
& ( in @ emptyset @ ( powerset @ X1754 ) )
& ( ~ ( in @ X1756 @ ( powerset @ X1755 ) )
| ~ ( in @ X1757 @ X1756 )
| ( in @ X1757 @ X1755 ) )
& ( ~ ( in @ X1759 @ X1760 )
| ~ ( in @ X1760 @ X1758 )
| ( in @ X1759 @ ( setunion @ X1758 ) ) )
& ( ( in @ X1762 @ ( esk17_3 @ X1761 @ X1762 @ X1763 ) )
| X1763
| ~ ( in @ X1762 @ ( setunion @ X1761 ) ) )
& ( ( in @ ( esk17_3 @ X1761 @ X1762 @ X1763 ) @ X1761 )
| X1763
| ~ ( in @ X1762 @ ( setunion @ X1761 ) ) )
& ( ~ X1763
| X1763
| ~ ( in @ X1762 @ ( setunion @ X1761 ) ) )
& ( ~ ( in @ X1766 @ X1765 )
| ( in @ X1766 @ ( powerset @ ( setunion @ X1765 ) ) ) )
& ( ~ ( X1767 @ X1769 )
| ( X1769
= ( esk18_1 @ X1767 ) )
| ~ ( exu @ X1767 ) )
& ( ( X1770
!= ( esk18_1 @ X1767 ) )
| ( X1767 @ X1770 )
| ~ ( exu @ X1767 ) )
& ( ( in @ ( esk19_1 @ X1771 ) @ X1771 )
| ~ ( nonempty @ X1771 ) )
& ( $true
| ~ ( nonempty @ X1771 ) )
& ( ~ ( in @ X1773 @ ( setadjoin @ X1774 @ emptyset ) )
| ( X1773 = X1774 ) )
& ( ( X1775 = X1776 )
| ~ ( in @ X1776 @ ( setadjoin @ X1775 @ emptyset ) ) )
& ( ( X1777 != X1778 )
| ( in @ X1777 @ ( setadjoin @ X1778 @ emptyset ) ) )
& ( ~ ( in @ X1779 @ ( setadjoin @ X1780 @ emptyset ) )
| ( in @ X1780 @ ( setadjoin @ X1779 @ emptyset ) ) )
& ( ~ ( in @ X1783 @ ( setadjoin @ X1781 @ ( setadjoin @ X1782 @ emptyset ) ) )
| ( X1783 = X1781 )
| ( X1783 = X1782 ) )
& ( in @ X1784 @ ( setadjoin @ X1784 @ ( setadjoin @ X1785 @ emptyset ) ) )
& ( in @ X1787 @ ( setadjoin @ X1786 @ ( setadjoin @ X1787 @ emptyset ) ) )
& ( ~ ( in @ X1790 @ X1788 )
| ~ ( X1789 @ X1790 )
| ( ( dsetconstr @ X1788 @ X1789 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1792 @ emptyset )
| ( X1791 @ X1792 ) )
& ( ( in @ ( esk20_2 @ X1793 @ X1794 ) @ X1793 )
| ~ ( in @ X1795 @ X1793 )
| ( X1794 @ X1795 ) )
& ( ~ ( X1794 @ ( esk20_2 @ X1793 @ X1794 ) )
| ~ ( in @ X1795 @ X1793 )
| ( X1794 @ X1795 ) )
& ( ( in @ ( esk21_2 @ X1797 @ X1798 ) @ X1797 )
| ~ ( in @ X1800 @ X1797 )
| ~ ( X1798 @ X1800 ) )
& ( ( X1798 @ ( esk21_2 @ X1797 @ X1798 ) )
| ~ ( in @ X1800 @ X1797 )
| ~ ( X1798 @ X1800 ) )
& ( ( in @ ( esk22_2 @ X1801 @ X1802 ) @ X1801 )
| ~ ( in @ X1804 @ X1801 )
| ~ ( X1802 @ X1804 ) )
& ( ( X1802 @ ( esk22_2 @ X1801 @ X1802 ) )
| ~ ( in @ X1804 @ X1801 )
| ~ ( X1802 @ X1804 ) )
& ( ( in @ ( esk23_2 @ X1805 @ X1806 ) @ X1805 )
| ~ ( in @ X1807 @ X1805 )
| ( X1806 @ X1807 ) )
& ( ~ ( X1806 @ ( esk23_2 @ X1805 @ X1806 ) )
| ~ ( in @ X1807 @ X1805 )
| ( X1806 @ X1807 ) )
& ( ~ X1809
| ( in @ emptyset @ ( prop2set @ X1809 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1810 @ X1811 ) @ X1810 )
| ~ ( in @ X1813 @ X1810 )
| ~ ( X1811 @ X1813 ) )
& ( ( X1811 @ ( esk24_2 @ X1810 @ X1811 ) )
| ~ ( in @ X1813 @ X1810 )
| ~ ( X1811 @ X1813 ) )
& ( ( in @ ( esk25_2 @ X1814 @ X1815 ) @ X1814 )
| ~ ( in @ X1816 @ X1814 )
| ( X1815 @ X1816 ) )
& ( ~ ( X1815 @ ( esk25_2 @ X1814 @ X1815 ) )
| ~ ( in @ X1816 @ X1814 )
| ( X1815 @ X1816 ) )
& ( ( X1818 @ ( esk26_2 @ X1818 @ X1819 ) )
| ~ ( X1818 @ X1819 )
| ( exu @ X1818 ) )
& ( ( X1819
!= ( esk26_2 @ X1818 @ X1819 ) )
| ~ ( X1818 @ X1819 )
| ( exu @ X1818 ) )
& ( ( X1821 @ ( esk27_1 @ X1821 ) )
| ( exu @ X1821 )
| ~ ( X1821 @ X1822 ) )
& ( ( X1821 @ ( esk28_1 @ X1821 ) )
| ( exu @ X1821 )
| ~ ( X1821 @ X1822 ) )
& ( ( ( esk27_1 @ X1821 )
!= ( esk28_1 @ X1821 ) )
| ( exu @ X1821 )
| ~ ( X1821 @ X1822 ) )
& ( ~ ( X1825 @ ( esk29_2 @ X1825 @ X1826 ) )
| ( ( esk29_2 @ X1825 @ X1826 )
!= X1826 )
| ( exu @ X1825 ) )
& ( ( X1825 @ ( esk29_2 @ X1825 @ X1826 ) )
| ( ( esk29_2 @ X1825 @ X1826 )
= X1826 )
| ( exu @ X1825 ) )
& ( ( X1828 != X1829 )
| ( X1830 != X1831 )
| ~ ( in @ X1830 @ X1828 )
| ( in @ X1831 @ X1829 ) )
& ( ~ ( in @ X1834 @ X1832 )
| ( in @ X1835 @ X1833 )
| ( X1834 != X1835 )
| ( X1832 != X1833 ) )
& ( ~ ( in @ X1835 @ X1833 )
| ( in @ X1834 @ X1832 )
| ( X1834 != X1835 )
| ( X1832 != X1833 ) )
& ( ~ ( exu @ X1836 )
| ~ ( X1836 @ X1837 )
| ~ ( X1836 @ X1838 )
| ( X1837 = X1838 ) )
& ( ~ ( exu @ X1839 )
| ( exu @ X1840 )
| ( ( esk30_2 @ X1839 @ X1840 )
= ( esk31_2 @ X1839 @ X1840 ) ) )
& ( ~ ( exu @ X1840 )
| ( exu @ X1839 )
| ( ( esk30_2 @ X1839 @ X1840 )
= ( esk31_2 @ X1839 @ X1840 ) ) )
& ( ~ ( exu @ X1839 )
| ( exu @ X1840 )
| ~ ( X1839 @ ( esk30_2 @ X1839 @ X1840 ) )
| ~ ( X1840 @ ( esk31_2 @ X1839 @ X1840 ) ) )
& ( ~ ( exu @ X1840 )
| ( exu @ X1839 )
| ~ ( X1839 @ ( esk30_2 @ X1839 @ X1840 ) )
| ~ ( X1840 @ ( esk31_2 @ X1839 @ X1840 ) ) )
& ( ~ ( exu @ X1839 )
| ( exu @ X1840 )
| ( X1839 @ ( esk30_2 @ X1839 @ X1840 ) )
| ( X1840 @ ( esk31_2 @ X1839 @ X1840 ) ) )
& ( ~ ( exu @ X1840 )
| ( exu @ X1839 )
| ( X1839 @ ( esk30_2 @ X1839 @ X1840 ) )
| ( X1840 @ ( esk31_2 @ X1839 @ X1840 ) ) )
& ( emptyset = emptyset )
& ( ( X1843 != X1844 )
| ( X1845 != X1846 )
| ( ( setadjoin @ X1843 @ X1845 )
= ( setadjoin @ X1844 @ X1846 ) ) )
& ( ( X1847 != X1848 )
| ( ( powerset @ X1847 )
= ( powerset @ X1848 ) ) )
& ( ( X1849 != X1850 )
| ( ( setunion @ X1849 )
= ( setunion @ X1850 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1851 )
| ~ ( X1851 @ X1852 )
| ~ ( X1851 @ X1853 )
| ( X1852 = X1853 ) )
& ( ( ( esk32_2 @ X1854 @ X1855 )
= ( esk33_2 @ X1854 @ X1855 ) )
| ~ ( exu @ X1854 )
| ~ ( exu @ X1855 )
| ( ( descr @ X1854 )
= ( descr @ X1855 ) ) )
& ( ~ ( X1854 @ ( esk32_2 @ X1854 @ X1855 ) )
| ~ ( X1855 @ ( esk33_2 @ X1854 @ X1855 ) )
| ~ ( exu @ X1854 )
| ~ ( exu @ X1855 )
| ( ( descr @ X1854 )
= ( descr @ X1855 ) ) )
& ( ( X1854 @ ( esk32_2 @ X1854 @ X1855 ) )
| ( X1855 @ ( esk33_2 @ X1854 @ X1855 ) )
| ~ ( exu @ X1854 )
| ~ ( exu @ X1855 )
| ( ( descr @ X1854 )
= ( descr @ X1855 ) ) )
& ( ( in @ ( esk34_4 @ X1858 @ X1859 @ X1860 @ X1861 ) @ X1858 )
| ( ( dsetconstr @ X1858 @ X1860 )
= ( dsetconstr @ X1859 @ X1861 ) )
| ( X1858 != X1859 ) )
& ( ( in @ ( esk35_4 @ X1858 @ X1859 @ X1860 @ X1861 ) @ X1859 )
| ( ( dsetconstr @ X1858 @ X1860 )
= ( dsetconstr @ X1859 @ X1861 ) )
| ( X1858 != X1859 ) )
& ( ( ( esk34_4 @ X1858 @ X1859 @ X1860 @ X1861 )
= ( esk35_4 @ X1858 @ X1859 @ X1860 @ X1861 ) )
| ( ( dsetconstr @ X1858 @ X1860 )
= ( dsetconstr @ X1859 @ X1861 ) )
| ( X1858 != X1859 ) )
& ( ~ ( X1860 @ ( esk34_4 @ X1858 @ X1859 @ X1860 @ X1861 ) )
| ~ ( X1861 @ ( esk35_4 @ X1858 @ X1859 @ X1860 @ X1861 ) )
| ( ( dsetconstr @ X1858 @ X1860 )
= ( dsetconstr @ X1859 @ X1861 ) )
| ( X1858 != X1859 ) )
& ( ( X1860 @ ( esk34_4 @ X1858 @ X1859 @ X1860 @ X1861 ) )
| ( X1861 @ ( esk35_4 @ X1858 @ X1859 @ X1860 @ X1861 ) )
| ( ( dsetconstr @ X1858 @ X1860 )
= ( dsetconstr @ X1859 @ X1861 ) )
| ( X1858 != X1859 ) )
& ( ( in @ ( esk36_2 @ X1864 @ X1865 ) @ X1864 )
| ( subset @ X1864 @ X1865 ) )
& ( ~ ( in @ ( esk36_2 @ X1864 @ X1865 ) @ X1865 )
| ( subset @ X1864 @ X1865 ) )
& ( ( X1867 != X1868 )
| ( subset @ X1868 @ X1867 ) )
& ( ( X1869 != X1870 )
| ( subset @ X1869 @ X1870 ) )
& ( ( in @ ( esk37_2 @ X1871 @ X1872 ) @ X1871 )
| ( subset @ X1871 @ X1872 ) )
& ( ~ ( in @ ( esk37_2 @ X1871 @ X1872 ) @ X1872 )
| ( subset @ X1871 @ X1872 ) )
& ( subset @ emptyset @ X1874 )
& ( ~ ( subset @ X1875 @ X1876 )
| ~ ( in @ X1877 @ X1875 )
| ( in @ X1877 @ X1876 ) )
& ( ~ ( subset @ X1878 @ X1879 )
| ( in @ X1880 @ X1879 )
| ~ ( in @ X1880 @ X1878 ) )
& ( ~ ( in @ X1883 @ X1881 )
| ( in @ X1883 @ X1882 )
| ~ ( subset @ X1881 @ X1882 ) )
& ( ( subset @ X1884 @ X1885 )
| ( X1884 != X1885 ) )
& ( ~ ( in @ X1888 @ X1886 )
| ( in @ X1888 @ X1887 )
| ( X1886 != X1887 ) )
& ( subset @ X1889 @ X1889 )
& ( ~ ( subset @ X1890 @ X1891 )
| ~ ( subset @ X1891 @ X1892 )
| ( subset @ X1890 @ X1892 ) )
& ( subset @ X1894 @ ( setadjoin @ X1893 @ X1894 ) )
& ( ~ ( subset @ X1895 @ X1897 )
| ( subset @ X1895 @ ( setadjoin @ X1896 @ X1897 ) ) )
& ( ~ ( subset @ X1898 @ X1899 )
| ( in @ X1898 @ ( powerset @ X1899 ) ) )
& ( ~ ( subset @ X1900 @ X1901 )
| ~ ( subset @ X1901 @ X1900 )
| ( X1900 = X1901 ) )
& ( ~ ( subset @ X1902 @ emptyset )
| ( X1902 = emptyset ) )
& ( ~ ( subset @ X1904 @ X1903 )
| ( in @ X1904 @ ( powerset @ X1903 ) ) )
& ( ~ ( in @ X1906 @ ( powerset @ X1905 ) )
| ( subset @ X1906 @ X1905 ) )
& ( in @ X1907 @ ( powerset @ X1907 ) )
& ( ~ ( subset @ X1908 @ X1909 )
| ( subset @ ( powerset @ X1908 ) @ ( powerset @ X1909 ) ) )
& ( in @ ( dsetconstr @ X1910 @ X1911 ) @ ( powerset @ X1910 ) )
& ( subset @ ( dsetconstr @ X1912 @ X1913 ) @ X1912 )
& ( ~ ( in @ X1916 @ X1914 )
| ( in @ X1916 @ ( binunion @ X1914 @ X1915 ) ) )
& ( in @ X1918 @ ( setadjoin @ X1917 @ ( setadjoin @ X1918 @ emptyset ) ) )
& ( ~ ( in @ X1921 @ X1920 )
| ( in @ X1921 @ ( binunion @ X1919 @ X1920 ) ) )
& ( ( in @ X1924 @ X1923 )
| X1925
| ( in @ X1924 @ X1922 )
| ~ ( in @ X1924 @ ( binunion @ X1922 @ X1923 ) ) )
& ( ~ X1925
| X1925
| ( in @ X1924 @ X1922 )
| ~ ( in @ X1924 @ ( binunion @ X1922 @ X1923 ) ) )
& ( ( in @ X1924 @ X1923 )
| X1925
| ~ X1925
| ~ ( in @ X1924 @ ( binunion @ X1922 @ X1923 ) ) )
& ( ~ X1925
| X1925
| ~ X1925
| ~ ( in @ X1924 @ ( binunion @ X1922 @ X1923 ) ) )
& ( ~ ( in @ X1928 @ ( binunion @ X1926 @ X1927 ) )
| ( in @ X1928 @ X1926 )
| ( in @ X1928 @ X1927 ) )
& ( subset @ X1929 @ ( binunion @ X1929 @ X1930 ) )
& ( subset @ X1932 @ ( binunion @ X1931 @ X1932 ) )
& ( ~ ( in @ X1935 @ X1933 )
| ~ ( in @ X1935 @ X1934 )
| ( in @ X1935 @ ( binintersect @ X1933 @ X1934 ) ) )
& ( ~ ( subset @ X1938 @ X1936 )
| ~ ( subset @ X1938 @ X1937 )
| ( subset @ X1938 @ ( binintersect @ X1936 @ X1937 ) ) )
& ( ~ ( in @ X1941 @ ( binintersect @ X1939 @ X1940 ) )
| ( in @ X1941 @ X1939 ) )
& ( subset @ ( binintersect @ X1942 @ X1943 ) @ X1942 )
& ( ~ ( subset @ X1944 @ X1945 )
| ( ( binintersect @ X1944 @ X1945 )
= X1944 ) )
& ( ( ( binintersect @ X1946 @ X1947 )
!= X1947 )
| ( subset @ X1947 @ X1946 ) )
& ( ~ ( in @ X1950 @ ( binintersect @ X1948 @ X1949 ) )
| ( in @ X1950 @ X1949 ) )
& ( ( in @ ( esk38_2 @ X1951 @ X1952 ) @ X1951 )
| ( ( binintersect @ X1951 @ X1952 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1951 @ X1952 ) @ X1952 )
| ( ( binintersect @ X1951 @ X1952 )
= emptyset ) )
& ( subset @ ( binintersect @ X1954 @ X1955 ) @ X1955 )
& ( ~ ( subset @ X1957 @ X1956 )
| ( ( binintersect @ X1956 @ X1957 )
= X1957 ) )
& ( ( ( binintersect @ X1958 @ X1959 )
!= X1958 )
| ( subset @ X1958 @ X1959 ) )
& ( ( binintersect @ X1960 @ ( binunion @ X1961 @ X1962 ) )
= ( binunion @ ( binintersect @ X1960 @ X1961 ) @ ( binintersect @ X1960 @ X1962 ) ) )
& ( ~ ( in @ X1965 @ X1963 )
| ( in @ X1965 @ X1964 )
| ( in @ X1965 @ ( setminus @ X1963 @ X1964 ) ) )
& ( ~ ( in @ X1968 @ ( setminus @ X1966 @ X1967 ) )
| ( in @ X1968 @ X1966 ) )
& ( ~ ( in @ X1971 @ ( setminus @ X1969 @ X1970 ) )
| ~ ( in @ X1971 @ X1970 ) )
& ( ~ ( subset @ X1972 @ X1973 )
| ( ( setminus @ X1972 @ X1973 )
= emptyset ) )
& ( ( in @ X1976 @ ( setminus @ X1974 @ X1975 ) )
| ~ ( in @ X1976 @ X1974 )
| ( in @ X1976 @ X1975 ) )
& ( ( in @ X1979 @ ( setminus @ X1977 @ X1978 ) )
| ( in @ X1979 @ X1978 )
| ~ ( in @ X1979 @ X1977 ) )
& ( ( in @ X1982 @ X1980 )
| ~ ( in @ X1982 @ ( setminus @ X1980 @ X1981 ) ) )
& ( ~ ( in @ X1985 @ X1984 )
| ~ ( in @ X1985 @ ( setminus @ X1983 @ X1984 ) ) )
& ( subset @ ( setminus @ X1986 @ X1987 ) @ X1986 )
& ( ( ( setminus @ X1988 @ X1989 )
!= emptyset )
| ( subset @ X1988 @ X1989 ) )
& ( ~ ( in @ X1992 @ X1990 )
| X1993
| ( in @ X1992 @ X1990 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ( in @ X1992 @ X1991 )
| X1993
| ( in @ X1992 @ X1990 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ X1993
| X1993
| ( in @ X1992 @ X1990 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ ( in @ X1992 @ X1990 )
| X1993
| ~ ( in @ X1992 @ X1991 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ( in @ X1992 @ X1991 )
| X1993
| ~ ( in @ X1992 @ X1991 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ X1993
| X1993
| ~ ( in @ X1992 @ X1991 )
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ ( in @ X1992 @ X1990 )
| X1993
| ~ X1993
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ( in @ X1992 @ X1991 )
| X1993
| ~ X1993
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ X1993
| X1993
| ~ X1993
| ~ ( in @ X1992 @ ( symdiff @ X1990 @ X1991 ) ) )
& ( ~ ( in @ X1996 @ X1994 )
| ( in @ X1996 @ X1995 )
| ( in @ X1996 @ ( symdiff @ X1994 @ X1995 ) ) )
& ( ( in @ X1999 @ X1997 )
| ~ ( in @ X1999 @ X1998 )
| ( in @ X1999 @ ( symdiff @ X1997 @ X1998 ) ) )
& ( ~ ( in @ X2002 @ X2000 )
| ~ ( in @ X2002 @ X2001 )
| ~ ( in @ X2002 @ ( symdiff @ X2000 @ X2001 ) ) )
& ( ( in @ X2005 @ X2003 )
| ( in @ X2005 @ X2004 )
| ~ ( in @ X2005 @ ( symdiff @ X2003 @ X2004 ) ) )
& ( in @ X2007 @ ( setadjoin @ X2006 @ ( setadjoin @ X2007 @ emptyset ) ) )
& ( in @ X2008 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2008 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2008 @ ( setadjoin @ X2009 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2011 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2010 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2010 @ ( setadjoin @ X2011 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2012 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2012 @ ( setadjoin @ X2013 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2014 @ X2015 ) )
& ( ~ ( in @ X2017 @ X2016 )
| ( subset @ ( setadjoin @ X2017 @ emptyset ) @ X2016 ) )
& ( ~ ( in @ X2019 @ X2018 )
| ( in @ ( setadjoin @ X2019 @ emptyset ) @ ( powerset @ X2018 ) ) )
& ( ~ ( in @ X2022 @ X2020 )
| ( in @ ( setadjoin @ X2022 @ emptyset ) @ ( powerset @ ( binunion @ X2020 @ X2021 ) ) ) )
& ( ~ ( in @ X2025 @ ( setadjoin @ X2023 @ ( setadjoin @ X2024 @ emptyset ) ) )
| ( X2025 = X2023 )
| ( X2025 = X2024 ) )
& ( ~ ( in @ X2028 @ X2026 )
| ~ ( in @ X2029 @ X2027 )
| ( subset @ ( setadjoin @ X2028 @ ( setadjoin @ X2029 @ emptyset ) ) @ ( binunion @ X2026 @ X2027 ) ) )
& ( ~ ( in @ X2032 @ X2030 )
| ~ ( in @ X2033 @ X2031 )
| ( in @ ( setadjoin @ X2032 @ ( setadjoin @ X2033 @ emptyset ) ) @ ( powerset @ ( binunion @ X2030 @ X2031 ) ) ) )
& ( ~ ( in @ X2036 @ X2034 )
| ~ ( in @ X2037 @ X2035 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2036 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2036 @ ( setadjoin @ X2037 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2034 @ X2035 ) ) ) )
& ( ~ ( in @ X2040 @ X2038 )
| ~ ( in @ X2041 @ X2039 )
| ( in @ ( setadjoin @ ( setadjoin @ X2040 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2040 @ ( setadjoin @ X2041 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2038 @ X2039 ) ) ) ) )
& ( ~ ( in @ X2044 @ X2042 )
| ~ ( in @ X2045 @ X2043 )
| ( in @ ( kpair @ X2044 @ X2045 ) @ ( powerset @ ( powerset @ ( binunion @ X2042 @ X2043 ) ) ) ) )
& ( ~ ( in @ X2048 @ X2046 )
| ~ ( in @ X2049 @ X2047 )
| ( in @ ( kpair @ X2048 @ X2049 ) @ ( cartprod @ X2046 @ X2047 ) ) )
& ( ( in @ ( esk39_3 @ X2050 @ X2051 @ X2052 ) @ X2050 )
| ~ ( in @ X2052 @ ( cartprod @ X2050 @ X2051 ) ) )
& ( ( in @ ( esk40_3 @ X2050 @ X2051 @ X2052 ) @ X2051 )
| ~ ( in @ X2052 @ ( cartprod @ X2050 @ X2051 ) ) )
& ( ( X2052
= ( kpair @ ( esk39_3 @ X2050 @ X2051 @ X2052 ) @ ( esk40_3 @ X2050 @ X2051 @ X2052 ) ) )
| ~ ( in @ X2052 @ ( cartprod @ X2050 @ X2051 ) ) )
& ( ~ ( in @ X2057 @ ( cartprod @ X2055 @ X2056 ) )
| ( iskpair @ X2057 ) )
& ( ( in @ ( esk41_2 @ X2058 @ X2059 ) @ X2058 )
| ~ ( in @ X2059 @ ( setunion @ X2058 ) ) )
& ( ( in @ X2059 @ ( esk41_2 @ X2058 @ X2059 ) )
| ~ ( in @ X2059 @ ( setunion @ X2058 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2061 @ emptyset ) ) @ X2061 )
& ( subset @ X2062 @ ( setunion @ ( setadjoin @ X2062 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2063 @ emptyset ) )
= X2063 )
& ( ( in @ ( esk42_2 @ X2064 @ X2065 ) @ X2064 )
| ~ ( in @ X2068 @ X2064 )
| ~ ( X2065 @ X2068 )
| ( singleton @ ( dsetconstr @ X2064 @ X2065 ) ) )
& ( ( in @ ( esk43_2 @ X2064 @ X2065 ) @ X2064 )
| ~ ( in @ X2068 @ X2064 )
| ~ ( X2065 @ X2068 )
| ( singleton @ ( dsetconstr @ X2064 @ X2065 ) ) )
& ( ( X2065 @ ( esk42_2 @ X2064 @ X2065 ) )
| ~ ( in @ X2068 @ X2064 )
| ~ ( X2065 @ X2068 )
| ( singleton @ ( dsetconstr @ X2064 @ X2065 ) ) )
& ( ( X2065 @ ( esk43_2 @ X2064 @ X2065 ) )
| ~ ( in @ X2068 @ X2064 )
| ~ ( X2065 @ X2068 )
| ( singleton @ ( dsetconstr @ X2064 @ X2065 ) ) )
& ( ( ( esk42_2 @ X2064 @ X2065 )
!= ( esk43_2 @ X2064 @ X2065 ) )
| ~ ( in @ X2068 @ X2064 )
| ~ ( X2065 @ X2068 )
| ( singleton @ ( dsetconstr @ X2064 @ X2065 ) ) )
& ( ( in @ ( esk44_2 @ X2069 @ X2070 ) @ X2069 )
| ~ ( ex1 @ X2069 @ X2070 ) )
& ( ( X2070 @ ( esk44_2 @ X2069 @ X2070 ) )
| ~ ( ex1 @ X2069 @ X2070 ) )
& ( ( in @ ( esk45_3 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ( ex1 @ X2072 @ X2073 )
| ~ ( X2073 @ X2074 )
| ~ ( in @ X2074 @ X2072 ) )
& ( ( X2073 @ ( esk45_3 @ X2072 @ X2073 @ X2074 ) )
| ( ex1 @ X2072 @ X2073 )
| ~ ( X2073 @ X2074 )
| ~ ( in @ X2074 @ X2072 ) )
& ( ( ( esk45_3 @ X2072 @ X2073 @ X2074 )
!= X2074 )
| ( ex1 @ X2072 @ X2073 )
| ~ ( X2073 @ X2074 )
| ~ ( in @ X2074 @ X2072 ) )
& ( ( in @ ( esk46_2 @ X2076 @ X2077 ) @ X2076 )
| ~ ( in @ X2080 @ X2076 )
| ~ ( X2077 @ X2080 )
| ( ex1 @ X2076 @ X2077 ) )
& ( ( in @ ( esk47_2 @ X2076 @ X2077 ) @ X2076 )
| ~ ( in @ X2080 @ X2076 )
| ~ ( X2077 @ X2080 )
| ( ex1 @ X2076 @ X2077 ) )
& ( ( X2077 @ ( esk46_2 @ X2076 @ X2077 ) )
| ~ ( in @ X2080 @ X2076 )
| ~ ( X2077 @ X2080 )
| ( ex1 @ X2076 @ X2077 ) )
& ( ( X2077 @ ( esk47_2 @ X2076 @ X2077 ) )
| ~ ( in @ X2080 @ X2076 )
| ~ ( X2077 @ X2080 )
| ( ex1 @ X2076 @ X2077 ) )
& ( ( ( esk46_2 @ X2076 @ X2077 )
!= ( esk47_2 @ X2076 @ X2077 ) )
| ~ ( in @ X2080 @ X2076 )
| ~ ( X2077 @ X2080 )
| ( ex1 @ X2076 @ X2077 ) )
& ( ( ( setadjoin @ X2081 @ emptyset )
!= ( setadjoin @ X2082 @ emptyset ) )
| ( X2081 = X2082 ) )
& ( ~ ( in @ ( setadjoin @ X2085 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2083 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2083 @ ( setadjoin @ X2084 @ emptyset ) ) @ emptyset ) ) )
| ( X2083 = X2085 ) )
& ( ~ ( iskpair @ X2086 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2086 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2086 ) ) ) )
& ( ~ ( singleton @ X2087 )
| ( in @ ( setunion @ X2087 ) @ X2087 ) )
& ( ( kfst @ ( kpair @ X2088 @ X2089 ) )
= X2088 )
& ( ~ ( in @ X2092 @ ( cartprod @ X2090 @ X2091 ) )
| ( in @ ( kfst @ X2092 ) @ X2090 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2093 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2093 @ ( setadjoin @ X2094 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2095 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2095 @ ( setadjoin @ X2096 @ emptyset ) ) @ emptyset ) ) )
| ( X2093 = X2095 ) )
& ( ( ( kpair @ X2097 @ X2098 )
!= ( kpair @ X2099 @ X2100 ) )
| ( X2097 = X2099 ) )
& ( ( X2101 != X2102 )
| ( ( setadjoin @ X2101 @ ( setadjoin @ X2102 @ emptyset ) )
= ( setadjoin @ X2101 @ emptyset ) ) )
& ( ( X2103 != X2104 )
| ( ( setadjoin @ ( setadjoin @ X2103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2103 @ ( setadjoin @ X2104 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2103 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2105 @ ( setadjoin @ X2106 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2107 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2107 @ ( setadjoin @ X2108 @ emptyset ) ) @ emptyset ) ) )
| ( X2107 != X2108 )
| ( X2106 = X2108 ) )
& ( ( ( setadjoin @ X2109 @ ( setadjoin @ X2110 @ emptyset ) )
!= ( setadjoin @ X2111 @ emptyset ) )
| ( X2109 = X2110 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2112 @ ( setadjoin @ X2113 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2114 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2114 @ ( setadjoin @ X2115 @ emptyset ) ) @ emptyset ) ) )
| ( X2113 = X2115 ) )
& ( ( ( kpair @ X2116 @ X2117 )
!= ( kpair @ X2118 @ X2119 ) )
| ( X2117 = X2119 ) )
& ( ~ ( iskpair @ X2120 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2120 )
@ ^ [Z0: $i] :
( X2120
= ( kpair @ ( kfst @ X2120 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2121 @ X2122 ) )
= X2122 )
& ( ~ ( iskpair @ X2123 )
| ( ( kpair @ ( kfst @ X2123 ) @ ( ksnd @ X2123 ) )
= X2123 ) )
& ( ~ ( in @ X2126 @ ( cartprod @ X2124 @ X2125 ) )
| ( in @ ( ksnd @ X2126 ) @ X2125 ) )
& ( ~ ( in @ ( kpair @ X2129 @ X2130 ) @ ( cartprod @ X2127 @ X2128 ) )
| ( in @ X2129 @ X2127 ) )
& ( ~ ( in @ ( kpair @ X2133 @ X2134 ) @ ( cartprod @ X2131 @ X2132 ) )
| ( in @ X2134 @ X2132 ) )
& ( ~ ( in @ X2137 @ X2135 )
| ~ ( in @ X2138 @ X2136 )
| ( ( kpair @ X2137 @ X2138 )
= ( kpair @ X2137 @ X2138 ) ) )
& ( ~ ( in @ X2141 @ X2139 )
| ~ ( in @ X2142 @ X2140 )
| ( ( kfst @ ( kpair @ X2141 @ X2142 ) )
= X2141 ) )
& ( ~ ( in @ X2145 @ X2143 )
| ~ ( in @ X2146 @ X2144 )
| ( ( ksnd @ ( kpair @ X2145 @ X2146 ) )
= X2146 ) )
& ( ~ ( in @ X2149 @ ( cartprod @ X2147 @ X2148 ) )
| ( ( kpair @ ( kfst @ X2149 ) @ ( ksnd @ X2149 ) )
= X2149 ) )
& ( ~ ( in @ X2153 @ X2150 )
| ~ ( in @ X2154 @ X2151 )
| ~ ( X2152 @ X2153 @ X2154 )
| ( in @ ( kpair @ X2153 @ X2154 ) @ ( dpsetconstr @ X2150 @ X2151 @ X2152 ) ) )
& ( subset @ ( dpsetconstr @ X2155 @ X2156 @ X2157 ) @ ( cartprod @ X2155 @ X2156 ) )
& ( breln @ X2158 @ X2159 @ ( dpsetconstr @ X2158 @ X2159 @ X2160 ) )
& ( ~ ( in @ X2164 @ X2161 )
| ~ ( in @ X2165 @ X2162 )
| ~ ( in @ ( kpair @ X2164 @ X2165 ) @ ( dpsetconstr @ X2161 @ X2162 @ X2163 ) )
| ( X2163 @ X2164 @ X2165 ) )
& ( ~ ( in @ ( kpair @ X2169 @ X2170 ) @ ( dpsetconstr @ X2166 @ X2167 @ X2168 ) )
| ( in @ X2169 @ X2166 ) )
& ( ~ ( in @ ( kpair @ X2174 @ X2175 ) @ ( dpsetconstr @ X2171 @ X2172 @ X2173 ) )
| ( in @ X2175 @ X2172 ) )
& ( ~ ( in @ ( kpair @ X2179 @ X2180 ) @ ( dpsetconstr @ X2176 @ X2177 @ X2178 ) )
| ( X2178 @ X2179 @ X2180 ) )
& ( ~ ( func @ X2181 @ X2182 @ X2183 )
| ~ ( in @ X2184 @ X2181 )
| ( singleton
@ ( dsetconstr @ X2182
@ ^ [Z0: $i] : ( in @ ( kpair @ X2184 @ Z0 ) @ X2183 ) ) ) )
& ( ~ ( func @ X2185 @ X2186 @ X2187 )
| ~ ( in @ X2188 @ X2185 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2186
@ ^ [Z0: $i] : ( in @ ( kpair @ X2188 @ Z0 ) @ X2187 ) ) )
@ X2186 ) )
& ( ~ ( func @ X2189 @ X2190 @ X2191 )
| ~ ( in @ X2192 @ X2189 )
| ( in @ ( ap @ X2189 @ X2190 @ X2191 @ X2192 ) @ X2190 ) )
& ( ~ ( in @ X2195 @ ( funcSet @ X2193 @ X2194 ) )
| ( func @ X2193 @ X2194 @ X2195 ) )
& ( ~ ( in @ X2198 @ ( funcSet @ X2196 @ X2197 ) )
| ~ ( in @ X2199 @ X2196 )
| ( in @ ( ap @ X2196 @ X2197 @ X2198 @ X2199 ) @ X2197 ) )
& ( ~ ( func @ X2200 @ X2201 @ X2202 )
| ( in @ X2202 @ ( funcSet @ X2200 @ X2201 ) ) )
& ( ( in @ ( esk48_3 @ X2203 @ X2204 @ X2205 ) @ X2203 )
| ( func @ X2203 @ X2204
@ ( dpsetconstr @ X2203 @ X2204
@ ^ [Z0: $i] : ( $eq @ ( X2205 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2205 @ ( esk48_3 @ X2203 @ X2204 @ X2205 ) ) @ X2204 )
| ( func @ X2203 @ X2204
@ ( dpsetconstr @ X2203 @ X2204
@ ^ [Z0: $i] : ( $eq @ ( X2205 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2207 @ X2208 @ X2209 ) @ X2207 )
| ( func @ X2207 @ X2208 @ ( lam @ X2207 @ X2208 @ X2209 ) ) )
& ( ~ ( in @ ( X2209 @ ( esk49_3 @ X2207 @ X2208 @ X2209 ) ) @ X2208 )
| ( func @ X2207 @ X2208 @ ( lam @ X2207 @ X2208 @ X2209 ) ) )
& ( ( in @ ( esk50_3 @ X2211 @ X2212 @ X2213 ) @ X2211 )
| ( in @ ( lam @ X2211 @ X2212 @ X2213 ) @ ( funcSet @ X2211 @ X2212 ) ) )
& ( ~ ( in @ ( X2213 @ ( esk50_3 @ X2211 @ X2212 @ X2213 ) ) @ X2212 )
| ( in @ ( lam @ X2211 @ X2212 @ X2213 ) @ ( funcSet @ X2211 @ X2212 ) ) )
& ( ( in @ ( esk51_4 @ X2215 @ X2216 @ X2217 @ X2218 ) @ X2215 )
| ~ ( in @ X2221 @ X2217 )
| ( X2218 @ X2221 )
| ~ ( breln @ X2215 @ X2216 @ X2217 ) )
& ( ( in @ ( esk52_4 @ X2215 @ X2216 @ X2217 @ X2218 ) @ X2216 )
| ~ ( in @ X2221 @ X2217 )
| ( X2218 @ X2221 )
| ~ ( breln @ X2215 @ X2216 @ X2217 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2215 @ X2216 @ X2217 @ X2218 ) @ ( esk52_4 @ X2215 @ X2216 @ X2217 @ X2218 ) ) @ X2217 )
| ~ ( in @ X2221 @ X2217 )
| ( X2218 @ X2221 )
| ~ ( breln @ X2215 @ X2216 @ X2217 ) )
& ( ~ ( X2218 @ ( kpair @ ( esk51_4 @ X2215 @ X2216 @ X2217 @ X2218 ) @ ( esk52_4 @ X2215 @ X2216 @ X2217 @ X2218 ) ) )
| ~ ( in @ X2221 @ X2217 )
| ( X2218 @ X2221 )
| ~ ( breln @ X2215 @ X2216 @ X2217 ) )
& ( ( in @ ( esk53_4 @ X2222 @ X2223 @ X2224 @ X2225 ) @ X2222 )
| ~ ( in @ X2228 @ X2224 )
| ( X2225 @ X2228 )
| ~ ( breln @ X2222 @ X2223 @ X2224 ) )
& ( ( in @ ( esk54_4 @ X2222 @ X2223 @ X2224 @ X2225 ) @ X2223 )
| ~ ( in @ X2228 @ X2224 )
| ( X2225 @ X2228 )
| ~ ( breln @ X2222 @ X2223 @ X2224 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2222 @ X2223 @ X2224 @ X2225 ) @ ( esk54_4 @ X2222 @ X2223 @ X2224 @ X2225 ) ) @ X2224 )
| ~ ( in @ X2228 @ X2224 )
| ( X2225 @ X2228 )
| ~ ( breln @ X2222 @ X2223 @ X2224 ) )
& ( ~ ( X2225 @ ( kpair @ ( esk53_4 @ X2222 @ X2223 @ X2224 @ X2225 ) @ ( esk54_4 @ X2222 @ X2223 @ X2224 @ X2225 ) ) )
| ~ ( in @ X2228 @ X2224 )
| ( X2225 @ X2228 )
| ~ ( breln @ X2222 @ X2223 @ X2224 ) )
& ( ~ ( ex1 @ X2229 @ X2230 )
| ~ ( in @ X2231 @ X2229 )
| ~ ( in @ X2232 @ X2229 )
| ~ ( X2230 @ X2231 )
| ~ ( X2230 @ X2232 )
| ( X2231 = X2232 ) )
& ( ~ ( func @ X2233 @ X2234 @ X2235 )
| ~ ( in @ X2236 @ X2233 )
| ( in @ ( kpair @ X2236 @ ( ap @ X2233 @ X2234 @ X2235 @ X2236 ) ) @ X2235 ) )
& ( ~ ( in @ X2239 @ ( funcSet @ X2237 @ X2238 ) )
| ~ ( in @ X2240 @ X2237 )
| ( in @ ( kpair @ X2240 @ ( ap @ X2237 @ X2238 @ X2239 @ X2240 ) ) @ X2239 ) )
& ( ~ ( func @ X2241 @ X2242 @ X2243 )
| ~ ( in @ X2244 @ X2241 )
| ~ ( in @ X2245 @ X2242 )
| ~ ( in @ ( kpair @ X2244 @ X2245 ) @ X2243 )
| ( ( ap @ X2241 @ X2242 @ X2243 @ X2244 )
= X2245 ) )
& ( ( in @ ( esk55_4 @ X2246 @ X2247 @ X2248 @ X2249 ) @ X2246 )
| ~ ( in @ X2251 @ X2246 )
| ~ ( in @ X2252 @ X2247 )
| ~ ( in @ ( kpair @ X2251 @ X2252 ) @ X2249 )
| ( in @ ( kpair @ X2251 @ X2252 ) @ X2248 )
| ~ ( func @ X2246 @ X2247 @ X2249 )
| ~ ( func @ X2246 @ X2247 @ X2248 ) )
& ( ( ( ap @ X2246 @ X2247 @ X2248 @ ( esk55_4 @ X2246 @ X2247 @ X2248 @ X2249 ) )
!= ( ap @ X2246 @ X2247 @ X2249 @ ( esk55_4 @ X2246 @ X2247 @ X2248 @ X2249 ) ) )
| ~ ( in @ X2251 @ X2246 )
| ~ ( in @ X2252 @ X2247 )
| ~ ( in @ ( kpair @ X2251 @ X2252 ) @ X2249 )
| ( in @ ( kpair @ X2251 @ X2252 ) @ X2248 )
| ~ ( func @ X2246 @ X2247 @ X2249 )
| ~ ( func @ X2246 @ X2247 @ X2248 ) )
& ( ~ ( in @ X2255 @ ( funcSet @ X2253 @ X2254 ) )
| ~ ( in @ X2256 @ X2253 )
| ~ ( in @ X2257 @ X2254 )
| ~ ( in @ ( kpair @ X2256 @ X2257 ) @ X2255 )
| ( ( ap @ X2253 @ X2254 @ X2255 @ X2256 )
= X2257 ) )
& ( ( in @ ( esk56_4 @ X2258 @ X2259 @ X2260 @ X2261 ) @ X2258 )
| ( subset @ X2260 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2260 ) )
& ( ( in @ ( esk57_4 @ X2258 @ X2259 @ X2260 @ X2261 ) @ X2259 )
| ( subset @ X2260 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2260 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2258 @ X2259 @ X2260 @ X2261 ) @ ( esk57_4 @ X2258 @ X2259 @ X2260 @ X2261 ) ) @ X2260 )
| ( subset @ X2260 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2260 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2258 @ X2259 @ X2260 @ X2261 ) @ ( esk57_4 @ X2258 @ X2259 @ X2260 @ X2261 ) ) @ X2261 )
| ( subset @ X2260 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2261 )
| ~ ( breln @ X2258 @ X2259 @ X2260 ) )
& ( ( in @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ( X2266 = X2267 )
| ( in @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ( X2266 = X2267 )
| ( in @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ( X2266 = X2267 )
| ( in @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ( X2266 = X2267 )
| ( in @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ( X2266 = X2267 )
| ( in @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ( X2266 = X2267 )
| ( in @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ( X2266 = X2267 )
| ( in @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ( X2266 = X2267 )
| ( in @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ( X2266 = X2267 )
| ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ( X2266 = X2267 )
| ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ( X2266 = X2267 )
| ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ( X2266 = X2267 )
| ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2264 )
| ( X2266 = X2267 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ X2265 )
| ( X2266 = X2267 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ( X2266 = X2267 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk61_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2266 )
| ( X2266 = X2267 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2264 @ X2265 @ X2266 @ X2267 ) @ ( esk59_4 @ X2264 @ X2265 @ X2266 @ X2267 ) ) @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2267 )
| ~ ( breln @ X2264 @ X2265 @ X2266 ) )
& ( ( in @ ( esk62_4 @ X2272 @ X2273 @ X2274 @ X2275 ) @ X2272 )
| ( X2274 = X2275 )
| ~ ( func @ X2272 @ X2273 @ X2275 )
| ~ ( func @ X2272 @ X2273 @ X2274 ) )
& ( ( ( ap @ X2272 @ X2273 @ X2274 @ ( esk62_4 @ X2272 @ X2273 @ X2274 @ X2275 ) )
!= ( ap @ X2272 @ X2273 @ X2275 @ ( esk62_4 @ X2272 @ X2273 @ X2274 @ X2275 ) ) )
| ( X2274 = X2275 )
| ~ ( func @ X2272 @ X2273 @ X2275 )
| ~ ( func @ X2272 @ X2273 @ X2274 ) )
& ( ( in @ ( esk63_4 @ X2277 @ X2278 @ X2279 @ X2280 ) @ X2277 )
| ( X2279 = X2280 )
| ~ ( in @ X2280 @ ( funcSet @ X2277 @ X2278 ) )
| ~ ( in @ X2279 @ ( funcSet @ X2277 @ X2278 ) ) )
& ( ( ( ap @ X2277 @ X2278 @ X2279 @ ( esk63_4 @ X2277 @ X2278 @ X2279 @ X2280 ) )
!= ( ap @ X2277 @ X2278 @ X2280 @ ( esk63_4 @ X2277 @ X2278 @ X2279 @ X2280 ) ) )
| ( X2279 = X2280 )
| ~ ( in @ X2280 @ ( funcSet @ X2277 @ X2278 ) )
| ~ ( in @ X2279 @ ( funcSet @ X2277 @ X2278 ) ) )
& ( ~ ( in @ X2284 @ ( funcSet @ X2282 @ X2283 ) )
| ~ ( in @ X2285 @ X2282 )
| ( ( ap @ X2282 @ X2283 @ X2284 @ X2285 )
= ( ap @ X2282 @ X2283 @ X2284 @ X2285 ) ) )
& ( ~ ( func @ X2286 @ X2287 @ X2288 )
| ~ ( in @ X2289 @ X2286 )
| ( ( ap @ X2286 @ X2287 @ X2288 @ X2289 )
= ( ap @ X2286 @ X2287 @ X2288 @ X2289 ) ) )
& ( ( in @ ( esk64_3 @ X2290 @ X2291 @ X2292 ) @ X2290 )
| ~ ( in @ X2294 @ X2290 )
| ( ( ap @ X2290 @ X2291 @ ( lam @ X2290 @ X2291 @ X2292 ) @ X2294 )
= ( X2292 @ X2294 ) ) )
& ( ~ ( in @ ( X2292 @ ( esk64_3 @ X2290 @ X2291 @ X2292 ) ) @ X2291 )
| ~ ( in @ X2294 @ X2290 )
| ( ( ap @ X2290 @ X2291 @ ( lam @ X2290 @ X2291 @ X2292 ) @ X2294 )
= ( X2292 @ X2294 ) ) )
& ( ~ ( func @ X2295 @ X2296 @ X2297 )
| ( ( lam @ X2295 @ X2296 @ ( ap @ X2295 @ X2296 @ X2297 ) )
= X2297 ) )
& ( ( in @ ( esk65_3 @ X2298 @ X2299 @ X2300 ) @ X2298 )
| ( ( lam @ X2298 @ X2299 @ X2300 )
= ( lam @ X2298 @ X2299 @ X2300 ) ) )
& ( ~ ( in @ ( X2300 @ ( esk65_3 @ X2298 @ X2299 @ X2300 ) ) @ X2299 )
| ( ( lam @ X2298 @ X2299 @ X2300 )
= ( lam @ X2298 @ X2299 @ X2300 ) ) )
& ( ( in @ ( esk66_3 @ X2302 @ X2303 @ X2304 ) @ X2302 )
| ~ ( in @ X2306 @ X2302 )
| ( ( ap @ X2302 @ X2303 @ ( lam @ X2302 @ X2303 @ X2304 ) @ X2306 )
= ( X2304 @ X2306 ) ) )
& ( ~ ( in @ ( X2304 @ ( esk66_3 @ X2302 @ X2303 @ X2304 ) ) @ X2303 )
| ~ ( in @ X2306 @ X2302 )
| ( ( ap @ X2302 @ X2303 @ ( lam @ X2302 @ X2303 @ X2304 ) @ X2306 )
= ( X2304 @ X2306 ) ) )
& ( ~ ( in @ X2309 @ ( funcSet @ X2307 @ X2308 ) )
| ( ( lam @ X2307 @ X2308 @ ( ap @ X2307 @ X2308 @ X2309 ) )
= X2309 ) )
& ( ~ ( in @ X2312 @ X2310 )
| ~ ( in @ X2313 @ X2310 )
| X2311
| ( in @ X2313
@ ( dsetconstr @ X2310
@ ^ [Z0: $i] :
( ( X2311
& ( Z0 = X2312 ) )
| ( ~ X2311
& ( Z0 = X2313 ) ) ) ) ) )
& ( ~ ( in @ X2316 @ X2314 )
| ~ ( in @ X2317 @ X2314 )
| X2315
| ( ( dsetconstr @ X2314
@ ^ [Z0: $i] :
( ( X2315
& ( Z0 = X2316 ) )
| ( ~ X2315
& ( Z0 = X2317 ) ) ) )
= ( setadjoin @ X2317 @ emptyset ) ) )
& ( ~ ( in @ X2320 @ X2318 )
| ~ ( in @ X2321 @ X2318 )
| ~ X2319
| ( in @ X2320
@ ( dsetconstr @ X2318
@ ^ [Z0: $i] :
( ( X2319
& ( Z0 = X2320 ) )
| ( ~ X2319
& ( Z0 = X2321 ) ) ) ) ) )
& ( ~ ( in @ X2324 @ X2322 )
| ~ ( in @ X2325 @ X2322 )
| ~ X2323
| ( ( dsetconstr @ X2322
@ ^ [Z0: $i] :
( ( X2323
& ( Z0 = X2324 ) )
| ( ~ X2323
& ( Z0 = X2325 ) ) ) )
= ( setadjoin @ X2324 @ emptyset ) ) )
& ( ~ ( in @ X2328 @ X2326 )
| ~ ( in @ X2329 @ X2326 )
| ( singleton
@ ( dsetconstr @ X2326
@ ^ [Z0: $i] :
( ( X2327
& ( Z0 = X2328 ) )
| ( ~ X2327
& ( Z0 = X2329 ) ) ) ) ) )
& ( ~ ( in @ X2332 @ X2330 )
| ~ ( in @ X2333 @ X2330 )
| ( in @ ( if @ X2330 @ X2331 @ X2332 @ X2333 ) @ X2330 ) )
& ( ~ ( singleton @ X2334 )
| ~ ( in @ X2335 @ X2334 )
| ( ( setunion @ X2334 )
= X2335 ) )
& ( ~ ( in @ X2338 @ X2336 )
| ~ ( in @ X2339 @ X2336 )
| ~ X2337
| ( ( if @ X2336 @ X2337 @ X2338 @ X2339 )
= X2338 ) )
& ( ~ ( in @ X2342 @ X2340 )
| ~ ( in @ X2343 @ X2340 )
| X2341
| ( ( if @ X2340 @ X2341 @ X2342 @ X2343 )
= X2343 ) )
& ( ~ ( in @ X2346 @ X2344 )
| ~ ( in @ X2347 @ X2344 )
| ( in @ ( if @ X2344 @ X2345 @ X2346 @ X2347 ) @ ( setadjoin @ X2346 @ ( setadjoin @ X2347 @ emptyset ) ) ) )
& ( ~ ( in @ X2349 @ ( powerset @ X2348 ) )
| ~ ( in @ X2350 @ ( powerset @ X2348 ) )
| ( in @ ( binintersect @ X2349 @ X2350 ) @ ( powerset @ X2348 ) ) )
& ( ~ ( in @ X2352 @ ( powerset @ X2351 ) )
| ~ ( in @ X2353 @ ( powerset @ X2351 ) )
| ( in @ ( binunion @ X2352 @ X2353 ) @ ( powerset @ X2351 ) ) )
& ( ~ ( in @ X2355 @ ( powerset @ X2354 ) )
| ( in @ ( powerset @ X2355 ) @ ( powerset @ ( powerset @ X2354 ) ) ) )
& ( ~ ( in @ X2357 @ ( powerset @ X2356 ) )
| ~ ( in @ X2358 @ ( powerset @ X2356 ) )
| ( in @ ( setminus @ X2357 @ X2358 ) @ ( powerset @ X2356 ) ) )
& ( ~ ( in @ X2360 @ ( powerset @ X2359 ) )
| ( in @ ( setminus @ X2359 @ X2360 ) @ ( powerset @ X2359 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ( X2362 = X2363 )
| ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2361 )
| ( X2362 = X2363 )
| ~ ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ( X2362 = X2363 )
| ~ ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2361 @ X2362 @ X2363 ) @ X2362 )
| ( X2362 = X2363 )
| ~ ( in @ ( esk67_3 @ X2361 @ X2362 @ X2363 ) @ X2363 )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2362 @ ( powerset @ X2361 ) ) )
& ( ( in @ ( esk69_3 @ X2366 @ X2367 @ X2368 ) @ X2366 )
| ( subset @ X2367 @ X2368 )
| ~ ( in @ X2368 @ ( powerset @ X2366 ) )
| ~ ( in @ X2367 @ ( powerset @ X2366 ) ) )
& ( ( in @ ( esk69_3 @ X2366 @ X2367 @ X2368 ) @ X2367 )
| ( subset @ X2367 @ X2368 )
| ~ ( in @ X2368 @ ( powerset @ X2366 ) )
| ~ ( in @ X2367 @ ( powerset @ X2366 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2366 @ X2367 @ X2368 ) @ X2368 )
| ( subset @ X2367 @ X2368 )
| ~ ( in @ X2368 @ ( powerset @ X2366 ) )
| ~ ( in @ X2367 @ ( powerset @ X2366 ) ) )
& ( ( in @ ( esk70_3 @ X2370 @ X2371 @ X2372 ) @ X2370 )
| ( in @ X2371 @ ( powerset @ X2372 ) )
| ~ ( in @ X2372 @ ( powerset @ X2370 ) )
| ~ ( in @ X2371 @ ( powerset @ X2370 ) ) )
& ( ( in @ ( esk70_3 @ X2370 @ X2371 @ X2372 ) @ X2371 )
| ( in @ X2371 @ ( powerset @ X2372 ) )
| ~ ( in @ X2372 @ ( powerset @ X2370 ) )
| ~ ( in @ X2371 @ ( powerset @ X2370 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2370 @ X2371 @ X2372 ) @ X2372 )
| ( in @ X2371 @ ( powerset @ X2372 ) )
| ~ ( in @ X2372 @ ( powerset @ X2370 ) )
| ~ ( in @ X2371 @ ( powerset @ X2370 ) ) )
& ( ~ ( in @ X2375 @ ( powerset @ X2374 ) )
| ~ ( in @ X2376 @ ( powerset @ X2374 ) )
| ~ ( in @ X2377 @ X2374 )
| ~ ( in @ X2375 @ ( powerset @ X2376 ) )
| ~ ( in @ X2377 @ X2375 )
| ( in @ X2377 @ X2376 ) )
& ( ~ ( in @ X2379 @ ( powerset @ X2378 ) )
| ~ ( in @ X2380 @ X2378 )
| ~ ( in @ X2380 @ X2379 )
| ~ ( in @ X2380 @ ( setminus @ X2378 @ X2379 ) ) )
& ( ~ ( in @ X2382 @ ( powerset @ X2381 ) )
| ~ ( in @ X2383 @ X2381 )
| ( in @ X2383 @ ( setminus @ X2381 @ X2382 ) )
| ( in @ X2383 @ X2382 ) )
& ( ~ ( in @ X2385 @ ( powerset @ X2384 ) )
| ~ ( in @ X2386 @ ( powerset @ X2384 ) )
| ~ ( in @ X2387 @ X2384 )
| ( in @ X2387 @ X2385 )
| ~ ( in @ X2387 @ ( binintersect @ X2385 @ X2386 ) ) )
& ( ~ ( in @ X2389 @ ( powerset @ X2388 ) )
| ~ ( in @ X2390 @ ( powerset @ X2388 ) )
| ~ ( in @ X2391 @ X2388 )
| ( in @ X2391 @ X2390 )
| ~ ( in @ X2391 @ ( binintersect @ X2389 @ X2390 ) ) )
& ( ~ ( in @ X2393 @ ( powerset @ X2392 ) )
| ~ ( in @ X2394 @ ( powerset @ X2392 ) )
| ~ ( in @ X2395 @ X2392 )
| ~ ( subset @ X2393 @ ( setminus @ X2392 @ X2394 ) )
| ~ ( in @ X2395 @ X2394 )
| ~ ( in @ X2395 @ X2393 ) )
& ( ~ ( in @ X2397 @ ( powerset @ X2396 ) )
| ~ ( in @ X2398 @ ( powerset @ X2396 ) )
| ~ ( in @ X2399 @ X2396 )
| ~ ( subset @ X2397 @ X2398 )
| ( in @ X2399 @ X2398 )
| ~ ( in @ X2399 @ X2397 ) )
& ( ~ ( in @ X2401 @ ( powerset @ X2400 ) )
| ~ ( in @ X2402 @ ( powerset @ X2400 ) )
| ~ ( subset @ X2401 @ X2402 )
| ( subset @ ( setminus @ X2400 @ X2402 ) @ ( setminus @ X2400 @ X2401 ) ) )
& ( ~ ( in @ X2404 @ ( powerset @ X2403 ) )
| ~ ( in @ X2405 @ ( powerset @ X2403 ) )
| ~ ( subset @ ( setminus @ X2403 @ X2405 ) @ ( setminus @ X2403 @ X2404 ) )
| ( subset @ X2404 @ X2405 ) )
& ( ~ ( in @ X2407 @ ( powerset @ X2406 ) )
| ~ ( in @ X2408 @ X2406 )
| ~ ( in @ X2408 @ X2407 )
| ( in @ X2408 @ ( setminus @ X2406 @ ( setminus @ X2406 @ X2407 ) ) ) )
& ( ~ ( in @ X2410 @ ( powerset @ X2409 ) )
| ~ ( in @ X2411 @ X2409 )
| ~ ( in @ X2411 @ ( setminus @ X2409 @ ( setminus @ X2409 @ X2410 ) ) )
| ( in @ X2411 @ X2410 ) )
& ( ~ ( in @ X2413 @ ( powerset @ X2412 ) )
| ( subset @ X2413 @ ( setminus @ X2412 @ ( setminus @ X2412 @ X2413 ) ) ) )
& ( ~ ( in @ X2415 @ ( powerset @ X2414 ) )
| ( subset @ ( setminus @ X2414 @ ( setminus @ X2414 @ X2415 ) ) @ X2415 ) )
& ( ~ ( in @ X2417 @ ( powerset @ X2416 ) )
| ( X2417
= ( setminus @ X2416 @ ( setminus @ X2416 @ X2417 ) ) ) )
& ( ~ ( in @ X2419 @ ( powerset @ X2418 ) )
| ~ ( in @ X2420 @ ( powerset @ X2418 ) )
| ~ ( in @ X2421 @ X2418 )
| ~ ( in @ X2421 @ ( setminus @ X2418 @ X2419 ) )
| ~ ( in @ X2421 @ ( binintersect @ X2419 @ X2420 ) ) )
& ( ~ ( in @ X2423 @ ( powerset @ X2422 ) )
| ~ ( in @ X2424 @ ( powerset @ X2422 ) )
| ~ ( in @ X2425 @ X2422 )
| ~ ( in @ X2425 @ ( setminus @ X2422 @ X2423 ) )
| ( in @ X2425 @ ( setminus @ X2422 @ ( binintersect @ X2423 @ X2424 ) ) ) )
& ( ~ ( in @ X2427 @ ( powerset @ X2426 ) )
| ~ ( in @ X2428 @ ( powerset @ X2426 ) )
| ( subset @ ( setminus @ X2426 @ X2427 ) @ ( setminus @ X2426 @ ( binintersect @ X2427 @ X2428 ) ) ) )
& ( ~ ( in @ X2430 @ ( powerset @ X2429 ) )
| ~ ( in @ X2431 @ ( powerset @ X2429 ) )
| ( in @ ( setminus @ X2429 @ X2430 ) @ ( powerset @ ( setminus @ X2429 @ ( binintersect @ X2430 @ X2431 ) ) ) ) )
& ( ~ ( in @ X2433 @ ( powerset @ X2432 ) )
| ~ ( in @ X2434 @ ( powerset @ X2432 ) )
| ~ ( subset @ X2433 @ ( setminus @ X2432 @ X2434 ) )
| ~ ( in @ X2435 @ X2432 )
| ~ ( in @ X2435 @ X2434 )
| ( in @ X2435 @ ( setminus @ X2432 @ X2433 ) ) )
& ( ~ ( in @ X2437 @ ( powerset @ X2436 ) )
| ~ ( in @ X2438 @ ( powerset @ X2436 ) )
| ~ ( subset @ X2437 @ ( setminus @ X2436 @ X2438 ) )
| ( subset @ X2438 @ ( setminus @ X2436 @ X2437 ) ) )
& ( ~ ( in @ X2440 @ ( powerset @ X2439 ) )
| ~ ( in @ X2441 @ ( powerset @ X2439 ) )
| ~ ( in @ X2442 @ X2439 )
| ( in @ X2442 @ ( binunion @ X2440 @ X2441 ) )
| ~ ( in @ X2442 @ X2440 ) )
& ( ~ ( in @ X2444 @ ( powerset @ X2443 ) )
| ~ ( in @ X2445 @ ( powerset @ X2443 ) )
| ~ ( in @ X2446 @ X2443 )
| ( in @ X2446 @ ( binunion @ X2444 @ X2445 ) )
| ~ ( in @ X2446 @ X2445 ) )
& ( ~ ( in @ X2448 @ ( powerset @ X2447 ) )
| ~ ( in @ X2449 @ ( powerset @ X2447 ) )
| ~ ( in @ X2450 @ ( powerset @ X2447 ) )
| ~ ( in @ X2451 @ X2447 )
| ~ ( in @ X2451 @ ( binintersect @ X2448 @ X2449 ) )
| ( in @ X2451 @ ( binunion @ X2448 @ X2450 ) ) )
& ( ~ ( in @ X2453 @ ( powerset @ X2452 ) )
| ~ ( in @ X2454 @ ( powerset @ X2452 ) )
| ~ ( in @ X2455 @ ( powerset @ X2452 ) )
| ~ ( in @ X2456 @ X2452 )
| ~ ( in @ X2456 @ ( binintersect @ X2453 @ X2454 ) )
| ( in @ X2456 @ ( binunion @ X2454 @ X2455 ) ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk74_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk75_0 @ esk71_0 )
& ( in @ esk75_0 @ ( binintersect @ esk72_0 @ esk73_0 ) )
& ~ ( in @ esk75_0 @ ( binintersect @ ( binunion @ esk72_0 @ esk74_0 ) @ ( binunion @ esk73_0 @ esk74_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_310])])])])])])]) ).
thf(c_0_312,negated_conjecture,
~ ( in @ esk75_0 @ ( binintersect @ ( binunion @ esk72_0 @ esk74_0 ) @ ( binunion @ esk73_0 @ esk74_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_313,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ ( binintersect @ X3 @ X4 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_314,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X4 )
| ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_315,negated_conjecture,
in @ esk75_0 @ ( binintersect @ esk72_0 @ esk73_0 ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_316,negated_conjecture,
( ~ ( in @ esk75_0 @ ( binunion @ esk73_0 @ esk74_0 ) )
| ~ ( in @ esk75_0 @ ( binunion @ esk72_0 @ esk74_0 ) ) ),
inference(spm,[status(thm)],[c_0_312,c_0_313]) ).
thf(c_0_317,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_318,negated_conjecture,
in @ esk75_0 @ esk73_0,
inference(spm,[status(thm)],[c_0_314,c_0_315]) ).
thf(c_0_319,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X3 )
| ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
thf(c_0_320,negated_conjecture,
~ ( in @ esk75_0 @ ( binunion @ esk72_0 @ esk74_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_318])]) ).
thf(c_0_321,negated_conjecture,
in @ esk75_0 @ esk72_0,
inference(spm,[status(thm)],[c_0_319,c_0_315]) ).
thf(c_0_322,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_317]),c_0_321])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU742^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 17:09:53 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running higher-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.14/0.86 # Version: 3.1.0-ho
% 1.14/0.86 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.14/0.86 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.86 # Starting ehoh_best5 with 300s (1) cores
% 1.14/0.86 # Starting almost_fo_3_lam with 300s (1) cores
% 1.14/0.86 # Starting new_bool_5 with 300s (1) cores
% 1.14/0.86 # Starting pre_casc_3 with 300s (1) cores
% 1.14/0.86 # Starting ho_unfolding_8 with 300s (1) cores
% 1.14/0.86 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.14/0.86 # Starting new_bool_3 with 300s (1) cores
% 1.14/0.86 # Starting new_ho_5 with 300s (1) cores
% 1.14/0.86 # new_ho_5 with pid 10119 completed with status 8
% 1.14/0.86 # pre_casc_3 with pid 10115 completed with status 8
% 1.14/0.86 # new_bool_5 with pid 10114 completed with status 0
% 1.14/0.86 # Result found by new_bool_5
% 1.14/0.86 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.14/0.86 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.86 # Starting ehoh_best5 with 300s (1) cores
% 1.14/0.86 # Starting almost_fo_3_lam with 300s (1) cores
% 1.14/0.86 # Starting new_bool_5 with 300s (1) cores
% 1.14/0.86 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.14/0.86 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.14/0.86 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.14/0.86 # Starting ho_unfolding_8 with 55s (1) cores
% 1.14/0.86 # ho_unfolding_8 with pid 10138 completed with status 0
% 1.14/0.86 # Result found by ho_unfolding_8
% 1.14/0.86 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.14/0.86 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.86 # Starting ehoh_best5 with 300s (1) cores
% 1.14/0.86 # Starting almost_fo_3_lam with 300s (1) cores
% 1.14/0.86 # Starting new_bool_5 with 300s (1) cores
% 1.14/0.86 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.14/0.86 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.14/0.86 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.14/0.86 # Starting ho_unfolding_8 with 55s (1) cores
% 1.14/0.86 # Preprocessing time : 0.046 s
% 1.14/0.86 # Presaturation interreduction done
% 1.14/0.86
% 1.14/0.86 # Proof found!
% 1.14/0.86 # SZS status Theorem
% 1.14/0.86 # SZS output start CNFRefutation
% See solution above
% 1.14/0.86 # Parsed axioms : 559
% 1.14/0.86 # Removed by relevancy pruning/SinE : 301
% 1.14/0.86 # Initial clauses : 421
% 1.14/0.86 # Removed in clause preprocessing : 34
% 1.14/0.86 # Initial clauses in saturation : 387
% 1.14/0.86 # Processed clauses : 764
% 1.14/0.86 # ...of these trivial : 12
% 1.14/0.86 # ...subsumed : 41
% 1.14/0.86 # ...remaining for further processing : 711
% 1.14/0.86 # Other redundant clauses eliminated : 54
% 1.14/0.86 # Clauses deleted for lack of memory : 0
% 1.14/0.86 # Backward-subsumed : 1
% 1.14/0.86 # Backward-rewritten : 3
% 1.14/0.86 # Generated clauses : 7837
% 1.14/0.86 # ...of the previous two non-redundant : 7598
% 1.14/0.86 # ...aggressively subsumed : 0
% 1.14/0.86 # Contextual simplify-reflections : 6
% 1.14/0.86 # Paramodulations : 7748
% 1.14/0.86 # Factorizations : 2
% 1.14/0.86 # NegExts : 0
% 1.14/0.86 # Equation resolutions : 61
% 1.14/0.86 # Disequality decompositions : 0
% 1.14/0.86 # Total rewrite steps : 204
% 1.14/0.86 # ...of those cached : 136
% 1.14/0.86 # Propositional unsat checks : 0
% 1.14/0.86 # Propositional check models : 0
% 1.14/0.86 # Propositional check unsatisfiable : 0
% 1.14/0.86 # Propositional clauses : 0
% 1.14/0.86 # Propositional clauses after purity: 0
% 1.14/0.86 # Propositional unsat core size : 0
% 1.14/0.86 # Propositional preprocessing time : 0.000
% 1.14/0.86 # Propositional encoding time : 0.000
% 1.14/0.86 # Propositional solver time : 0.000
% 1.14/0.86 # Success case prop preproc time : 0.000
% 1.14/0.86 # Success case prop encoding time : 0.000
% 1.14/0.86 # Success case prop solver time : 0.000
% 1.14/0.86 # Current number of processed clauses : 353
% 1.14/0.86 # Positive orientable unit clauses : 50
% 1.14/0.86 # Positive unorientable unit clauses: 0
% 1.14/0.86 # Negative unit clauses : 5
% 1.14/0.86 # Non-unit-clauses : 298
% 1.14/0.86 # Current number of unprocessed clauses: 7556
% 1.14/0.86 # ...number of literals in the above : 31642
% 1.14/0.86 # Current number of archived formulas : 0
% 1.14/0.86 # Current number of archived clauses : 342
% 1.14/0.86 # Clause-clause subsumption calls (NU) : 60378
% 1.14/0.86 # Rec. Clause-clause subsumption calls : 25185
% 1.14/0.86 # Non-unit clause-clause subsumptions : 39
% 1.14/0.86 # Unit Clause-clause subsumption calls : 1832
% 1.14/0.86 # Rewrite failures with RHS unbound : 0
% 1.14/0.86 # BW rewrite match attempts : 34
% 1.14/0.86 # BW rewrite match successes : 2
% 1.14/0.86 # Condensation attempts : 0
% 1.14/0.86 # Condensation successes : 0
% 1.14/0.86 # Termbank termtop insertions : 206389
% 1.14/0.86 # Search garbage collected termcells : 25778
% 1.14/0.86
% 1.14/0.86 # -------------------------------------------------
% 1.14/0.86 # User time : 0.331 s
% 1.14/0.86 # System time : 0.020 s
% 1.14/0.86 # Total time : 0.351 s
% 1.14/0.86 # Maximum resident set size: 8268 pages
% 1.14/0.86
% 1.14/0.86 # -------------------------------------------------
% 1.14/0.86 # User time : 0.556 s
% 1.14/0.86 # System time : 0.086 s
% 1.14/0.86 # Total time : 0.642 s
% 1.14/0.86 # Maximum resident set size: 2496 pages
% 1.14/0.86 % E---3.1 exiting
% 1.14/0.86 % E exiting
%------------------------------------------------------------------------------