%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU768^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 03:30:05 EDT 2024
% Result : Theorem 1.09s 0.69s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 698
% Syntax : Number of formulae : 796 ( 44 unt; 407 typ; 0 def)
% Number of atoms : 3881 ( 644 equ; 0 cnn)
% Maximal formula atoms : 1200 ( 9 avg)
% Number of connectives : 15886 (1064 ~;1125 |; 607 &;10748 @)
% ( 378 <=>;1964 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1311 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 600 ( 600 >; 0 *; 0 +; 0 <<)
% Number of symbols : 411 ( 407 usr; 293 con; 0-4 aty)
% Number of variables : 3211 ( 188 ^2900 !; 123 ?;3211 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
binunionTEcontra: $o ).
thf(decl_324,type,
demorgan2a1: $o ).
thf(decl_325,type,
complementUnionInPowersetComplement: $o ).
thf(decl_326,type,
demorgan2a2: $o ).
thf(decl_327,type,
demorgan1a: $o ).
thf(decl_328,type,
demorgan1b: $o ).
thf(decl_329,type,
demorgan1: $o ).
thf(decl_330,type,
demorgan2a: $o ).
thf(decl_331,type,
demorgan2b2: $o ).
thf(decl_332,type,
demorgan2b: $o ).
thf(decl_333,type,
demorgan2: $o ).
thf(decl_334,type,
woz13rule0: $o ).
thf(decl_335,type,
woz13rule1: $o ).
thf(decl_336,type,
woz13rule2: $o ).
thf(decl_337,type,
woz13rule3: $o ).
thf(decl_338,type,
woz13rule4: $o ).
thf(decl_339,type,
woz1_1: $o ).
thf(decl_340,type,
woz1_2: $o ).
thf(decl_341,type,
woz1_3: $o ).
thf(decl_342,type,
woz1_4: $o ).
thf(decl_343,type,
woz1_5: $o ).
thf(decl_344,type,
breln1: $i > $i > $o ).
thf(decl_345,type,
epred1_0: $o ).
thf(decl_346,type,
esk1_2: $i > $i > $i ).
thf(decl_347,type,
esk2_2: $i > $i > $i ).
thf(decl_348,type,
esk3_2: $i > $i > $i ).
thf(decl_349,type,
esk4_1: $i > $i ).
thf(decl_350,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_351,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_352,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_353,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_354,type,
esk9_1: $i > $i ).
thf(decl_355,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_356,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_357,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_358,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_359,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_360,type,
esk15_2: $i > $i > $i ).
thf(decl_361,type,
esk16_2: $i > $i > $i ).
thf(decl_362,type,
esk17_1: $i > $i ).
thf(decl_363,type,
esk18_1: $i > $i ).
thf(decl_364,type,
esk19_1: $i > $i ).
thf(decl_365,type,
esk20_2: $i > $i > $i ).
thf(decl_366,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_367,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_368,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_369,type,
esk24_1: $i > $i ).
thf(decl_370,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_371,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_372,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_373,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_374,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_375,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_376,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_377,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_378,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_379,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_380,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_381,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_382,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_383,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_384,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_385,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_386,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_387,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_388,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_389,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_390,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_391,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_392,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_393,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_394,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_395,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_396,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_397,type,
esk52_2: $i > $i > $i ).
thf(decl_398,type,
esk53_2: $i > $i > $i ).
thf(decl_399,type,
esk54_2: $i > $i > $i ).
thf(decl_400,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_401,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_402,type,
esk57_2: $i > $i > $i ).
thf(decl_403,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_404,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_405,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_406,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_407,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_408,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_409,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_410,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_411,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_412,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_413,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_414,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_415,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_416,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_417,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_418,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_419,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_420,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_421,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_422,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_423,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_424,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_425,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_426,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_427,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_428,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_429,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_430,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_431,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_432,type,
esk87_0: $i ).
thf(decl_433,type,
esk88_0: $i ).
thf(decl_434,type,
epred2_0: $i > $o ).
thf(decl_435,type,
esk89_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(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(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
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(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(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(breln1,axiom,
( breln1
= ( ^ [X4: $i,X33: $i] : ( breln @ X4 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(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(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(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(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,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(breln1all2,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1all2) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(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(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(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(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(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(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(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(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(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(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(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(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(intersectInPowersetIntersectUnions,axiom,
( intersectInPowersetIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(inComplementUnionImpNotIn1,axiom,
( inComplementUnionImpNotIn1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inComplementUnionImpInComplement1,axiom,
( inComplementUnionImpInComplement1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(binunionTE,axiom,
( binunionTE
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X50: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ( ( ( in @ X2 @ X21 )
=> X50 )
=> ( ( ( in @ X2 @ X48 )
=> X50 )
=> X50 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionTEcontra,axiom,
( binunionTEcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(demorgan2a1,axiom,
( demorgan2a1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1) ).
thf(complementUnionInPowersetComplement,axiom,
( complementUnionInPowersetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) @ ( powerset @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementUnionInPowersetComplement) ).
thf(demorgan2a2,axiom,
( demorgan2a2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a2) ).
thf(demorgan1a,axiom,
( demorgan1a
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(demorgan1b,axiom,
( demorgan1b
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(demorgan1,axiom,
( demorgan1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) )
= ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
thf(demorgan2a,axiom,
( demorgan2a
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a) ).
thf(demorgan2b2,axiom,
( demorgan2b2
<=> ! [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 @ X48 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
thf(demorgan2b,axiom,
( demorgan2b
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b) ).
thf(demorgan2,axiom,
( demorgan2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binunion @ X21 @ X48 ) )
= ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).
thf(woz13rule0,axiom,
( woz13rule0
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule0) ).
thf(woz13rule1,axiom,
( woz13rule1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X49 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1) ).
thf(woz13rule2,axiom,
( woz13rule2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X48 @ X49 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule2) ).
thf(woz13rule3,axiom,
( woz13rule3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( ( subset @ X21 @ X49 )
=> ( subset @ X21 @ ( binintersect @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule3) ).
thf(woz13rule4,axiom,
( woz13rule4
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X51: $i] :
( ( in @ X51 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X49 )
=> ( ( subset @ X48 @ X51 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ ( binintersect @ X49 @ X51 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule4) ).
thf(woz1_1,axiom,
( woz1_1
<=> ! [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',woz1_1) ).
thf(woz1_2,axiom,
( woz1_2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X51: $i] :
( ( in @ X51 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binintersect @ ( binunion @ X21 @ X48 ) @ ( binunion @ X49 @ X51 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) @ ( binintersect @ ( setminus @ X4 @ X49 ) @ ( setminus @ X4 @ X51 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_2) ).
thf(woz1_3,axiom,
( woz1_3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_3) ).
thf(woz1_4,axiom,
( woz1_4
<=> ! [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',woz1_4) ).
thf(woz1_5,axiom,
( woz1_5
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) @ ( powerset @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_5) ).
thf(c_0_290,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_291,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_292,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_293,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_294,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_295,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_307,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_308,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_309,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_310,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_311,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_312,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_313,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X965: $i] :
( ( X6 @ X2 @ X965 )
& ! [X966: $i] :
( ( X6 @ X2 @ X966 )
=> ( X965 = X966 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_290,c_0_291]) ).
thf(c_0_314,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X967: $i] :
( ( X1 @ X967 )
& ! [X968: $i] :
( ( X1 @ X968 )
=> ( X967 = X968 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_292,c_0_291]) ).
thf(c_0_315,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_316,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_317,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_318,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X969: $i] :
( ( X1 @ X969 )
& ! [X970: $i] :
( ( X1 @ X970 )
=> ( X969 = X970 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_293,c_0_291]) ).
thf(c_0_319,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X971: $i] :
( ( X1 @ X971 )
& ! [X972: $i] :
( ( X1 @ X972 )
=> ( X971 = X972 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_294,c_0_291]) ).
thf(c_0_320,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_321,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_295]) ).
thf(c_0_322,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_296,c_0_295]) ).
thf(c_0_323,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_295]) ).
thf(c_0_324,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_325,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X973: $i] :
( ( X1 @ X973 )
& ! [X974: $i] :
( ( X1 @ X974 )
=> ( X973 = X974 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_297,c_0_291]) ).
thf(c_0_326,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_295]) ).
thf(c_0_327,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_328,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X975: $i] :
( ( X1 @ X975 )
& ! [X976: $i] :
( ( X1 @ X976 )
=> ( X975 = X976 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_298,c_0_291]) ).
thf(c_0_329,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X977: $i] :
( ( X1 @ X977 )
& ! [X978: $i] :
( ( X1 @ X978 )
=> ( X977 = X978 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_299,c_0_291]) ).
thf(c_0_330,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X979: $i] :
( ( X1 @ X979 )
& ! [X980: $i] :
( ( X1 @ X980 )
=> ( X979 = X980 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_300,c_0_291]) ).
thf(c_0_331,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X981: $i] :
( ( X1 @ X981 )
& ! [X982: $i] :
( ( X1 @ X982 )
=> ( X981 = X982 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_301,c_0_291]) ).
thf(c_0_332,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X983: $i] :
( ( X1 @ X983 )
& ! [X984: $i] :
( ( X1 @ X984 )
=> ( X983 = X984 ) ) )
<=> ? [X985: $i] :
( ( X17 @ X985 )
& ! [X986: $i] :
( ( X17 @ X986 )
=> ( X985 = X986 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_302,c_0_291]) ).
thf(c_0_333,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X987: $i] :
( ( X1 @ X987 )
& ! [X988: $i] :
( ( X1 @ X988 )
=> ( X987 = X988 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_303,c_0_291]) ).
thf(c_0_334,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X989: $i] :
( ( X1 @ X989 )
& ! [X990: $i] :
( ( X1 @ X990 )
=> ( X989 = X990 ) ) )
=> ( ? [X991: $i] :
( ( X17 @ X991 )
& ! [X992: $i] :
( ( X17 @ X992 )
=> ( X991 = X992 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_304,c_0_291]) ).
thf(c_0_335,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_336,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_337,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_338,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_339,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_305,c_0_306]) ).
thf(c_0_340,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_307,c_0_306]) ).
thf(c_0_341,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 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_308,c_0_306]) ).
thf(c_0_342,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_343,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_344,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_345,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_346,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_309,c_0_310]) ).
thf(c_0_347,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_348,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_349,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_350,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_351,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_352,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_353,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_354,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_355,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_356,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_310]) ).
thf(c_0_357,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_310]) ).
thf(c_0_358,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_311,c_0_306]) ).
thf(c_0_359,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_310]) ).
thf(c_0_360,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_310]) ).
thf(c_0_361,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_362,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_363,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_364,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_365,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_366,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_367,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_368,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_369,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_370,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_371,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_312,c_0_310]) ).
thf(c_0_372,plain,
( epred1_0
<=> ! [X1022: $i] :
? [X1023: $i] :
( ! [X1024: $i] :
( ( in @ X1024 @ X1023 )
=> ! [X1025: $i] :
( ( in @ X1025 @ X1024 )
=> ( in @ X1025 @ X1022 ) ) )
& ! [X1026: $i,X1027: $i] :
( ( ( in @ X1026 @ X1022 )
& ( in @ X1027 @ X1022 ) )
=> ( ! [X1028: $i] :
( ( in @ X1028 @ X1023 )
=> ( ( in @ X1026 @ X1028 )
<=> ( in @ X1027 @ X1028 ) ) )
=> ( X1026 = X1027 ) ) )
& ! [X1029: $i,X1030: $i] :
( ( ( in @ X1029 @ X1023 )
& ( in @ X1030 @ X1023 ) )
=> ( ! [X1031: $i] :
( ( in @ X1031 @ X1029 )
=> ( in @ X1031 @ X1030 ) )
| ! [X1032: $i] :
( ( in @ X1032 @ X1030 )
=> ( in @ X1032 @ X1029 ) ) ) )
& ! [X1033: $i] :
( ( ! [X1034: $i] :
( ( in @ X1034 @ X1033 )
=> ( in @ X1034 @ X1022 ) )
& ? [X1035: $i] : ( in @ X1035 @ X1033 ) )
=> ? [X1036: $i,X1037: $i] :
( ( in @ X1036 @ X1023 )
& ( in @ X1037 @ X1033 )
& ~ ? [X1038: $i] :
( ( in @ X1038 @ X1036 )
& ( in @ X1038 @ X1033 ) )
& ! [X1039: $i] :
( ( in @ X1039 @ X1023 )
=> ( ! [X1040: $i] :
( ( in @ X1040 @ X1039 )
=> ( in @ X1040 @ X1036 ) )
| ( in @ X1037 @ X1039 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_373,negated_conjecture,
~ ( ! [X993: $i,X994: $i] :
( ! [X995: $i] :
( ( in @ X995 @ X993 )
<=> ( in @ X995 @ X994 ) )
=> ( X993 = X994 ) )
=> ( ! [X996: $i] :
~ ( in @ X996 @ emptyset )
=> ( ! [X997: $i,X998: $i,X999: $i] :
( ( in @ X999 @ ( setadjoin @ X997 @ X998 ) )
<=> ( ( X999 = X997 )
| ( in @ X999 @ X998 ) ) )
=> ( ! [X1000: $i,X1001: $i] :
( ( in @ X1001 @ ( powerset @ X1000 ) )
<=> ! [X1002: $i] :
( ( in @ X1002 @ X1001 )
=> ( in @ X1002 @ X1000 ) ) )
=> ( ! [X1003: $i,X1004: $i] :
( ( in @ X1004 @ ( setunion @ X1003 ) )
<=> ? [X1005: $i] :
( ( in @ X1004 @ X1005 )
& ( in @ X1005 @ X1003 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X1006: $i] :
( ( in @ X1006 @ omega )
=> ( in @ ( setadjoin @ X1006 @ X1006 ) @ omega ) )
=> ( ! [X1007: $i] :
( ( ( in @ emptyset @ X1007 )
& ! [X1008: $i] :
( ( ( in @ X1008 @ omega )
& ( in @ X1008 @ X1007 ) )
=> ( in @ ( setadjoin @ X1008 @ X1008 ) @ X1007 ) ) )
=> ! [X1009: $i] :
( ( in @ X1009 @ omega )
=> ( in @ X1009 @ X1007 ) ) )
=> ( ! [X1010: $i > $i > $o,X1011: $i] :
( ! [X1012: $i] :
( ( in @ X1012 @ X1011 )
=> ? [X1013: $i] :
( ( X1010 @ X1012 @ X1013 )
& ! [X1014: $i] :
( ( X1010 @ X1012 @ X1014 )
=> ( X1013 = X1014 ) ) ) )
=> ? [X1015: $i] :
! [X1016: $i] :
( ( in @ X1016 @ X1015 )
<=> ? [X1017: $i] :
( ( in @ X1017 @ X1011 )
& ( X1010 @ X1017 @ X1016 ) ) ) )
=> ( ! [X1018: $i] :
( ? [X1019: $i] : ( in @ X1019 @ X1018 )
=> ? [X1020: $i] :
( ( in @ X1020 @ X1018 )
& ~ ? [X1021: $i] :
( ( in @ X1021 @ X1020 )
& ( in @ X1021 @ X1018 ) ) ) )
=> ( epred1_0
=> ( ! [X1041: $i > $o] :
( ? [X1042: $i] :
( ( X1041 @ X1042 )
& ! [X1043: $i] :
( ( X1041 @ X1043 )
=> ( X1042 = X1043 ) ) )
=> ( X1041
@ ( descr
@ ^ [Z0: $i] : ( X1041 @ Z0 ) ) ) )
=> ( ! [X1044: $i,X1045: $i > $o,X1046: $i] :
( ( in @ X1046 @ X1044 )
=> ( ( X1045 @ X1046 )
=> ( in @ X1046 @ ( dsetconstr @ X1044 @ X1045 ) ) ) )
=> ( ! [X1047: $i,X1048: $i > $o,X1049: $i] :
( ( in @ X1049 @ ( dsetconstr @ X1047 @ X1048 ) )
=> ( in @ X1049 @ X1047 ) )
=> ( ! [X1050: $i,X1051: $i > $o,X1052: $i] :
( ( in @ X1052 @ ( dsetconstr @ X1050 @ X1051 ) )
=> ( X1051 @ X1052 ) )
=> ( ! [X1053: $i > $o] :
( ? [X1054: $i] :
( ( X1053 @ X1054 )
& ! [X1055: $i] :
( ( X1053 @ X1055 )
=> ( X1054 = X1055 ) ) )
=> ? [X1056: $i] :
( ( X1053 @ X1056 )
& ! [X1057: $i] :
( ( X1053 @ X1057 )
=> ( X1056 = X1057 ) ) ) )
=> ( ! [X1058: $o,X1059: $i] :
( ( in @ X1059 @ ( prop2set @ X1058 ) )
=> X1058 )
=> ( ! [X1060: $i] :
( ( in @ X1060 @ emptyset )
=> ! [X1061: $o] : X1061 )
=> ( ! [X1062: $i] :
( ( in @ X1062 @ emptyset )
=> ~ $true )
=> ( ! [X1063: $i] :
~ ( in @ X1063 @ emptyset )
=> ( ! [X1064: $i > $o] :
( ? [X1065: $i] :
( ( X1064 @ X1065 )
& ! [X1066: $i] :
( ( X1064 @ X1066 )
=> ( X1065 = X1066 ) ) )
=> ? [X1067: $i] : ( X1064 @ X1067 ) )
=> ( ! [X1068: $i,X1069: $i] :
( ! [X1070: $i] :
( ( in @ X1070 @ X1068 )
=> ( in @ X1070 @ X1069 ) )
=> ( ! [X1071: $i] :
( ( in @ X1071 @ X1069 )
=> ( in @ X1071 @ X1068 ) )
=> ( X1068 = X1069 ) ) )
=> ( ! [X1072: $i] :
( ! [X1073: $i] :
~ ( in @ X1073 @ X1072 )
=> ( X1072 = emptyset ) )
=> ( ! [X1074: $i] :
( ! [X1075: $i] :
~ ( in @ X1075 @ X1074 )
=> ( X1074 = emptyset ) )
=> ( ! [X1076: $i,X1077: $i > $o,X1078: $i] :
( ( in @ X1078 @ X1076 )
=> ( ( in @ X1078 @ ( dsetconstr @ X1076 @ X1077 ) )
<=> ( X1077 @ X1078 ) ) )
=> ( ! [X1079: $i] :
( ( X1079 != emptyset )
=> ? [X1080: $i] : ( in @ X1080 @ X1079 ) )
=> ( ! [X1081: $i,X1082: $i > $o,X1083: $i] :
( ( in @ X1083 @ X1081 )
=> ( ( X1082 @ X1083 )
=> ( ( dsetconstr @ X1081 @ X1082 )
!= emptyset ) ) )
=> ( ! [X1084: $i] :
( ? [X1085: $i] : ( in @ X1085 @ X1084 )
=> ( X1084 != emptyset ) )
=> ( ! [X1086: $i,X1087: $i] : ( in @ X1086 @ ( setadjoin @ X1086 @ X1087 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1088: $i,X1089: $i,X1090: $i] :
( ( in @ X1090 @ X1089 )
=> ( in @ X1090 @ ( setadjoin @ X1088 @ X1089 ) ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( in @ X1093 @ ( setadjoin @ X1091 @ X1092 ) )
=> ! [X1094: $o] :
( ( ( X1093 = X1091 )
=> X1094 )
=> ( ( ( in @ X1093 @ X1092 )
=> X1094 )
=> X1094 ) ) )
=> ( ! [X1095: $i,X1096: $i,X1097: $i] :
( ( in @ X1097 @ ( setadjoin @ X1095 @ X1096 ) )
=> ( ( X1097 = X1095 )
| ( in @ X1097 @ X1096 ) ) )
=> ( ! [X1098: $i] :
( ( dsetconstr @ X1098
@ ^ [Z0: $i] : $true )
= X1098 )
=> ( ! [X1099: $i,X1100: $i] :
( ! [X1101: $i] :
( ( in @ X1101 @ X1100 )
=> ( in @ X1101 @ X1099 ) )
=> ( in @ X1100 @ ( powerset @ X1099 ) ) )
=> ( ! [X1102: $i] : ( in @ emptyset @ ( powerset @ X1102 ) )
=> ( ! [X1103: $i] : ( in @ emptyset @ ( powerset @ X1103 ) )
=> ( ! [X1104: $i,X1105: $i,X1106: $i] :
( ( in @ X1105 @ ( powerset @ X1104 ) )
=> ( ( in @ X1106 @ X1105 )
=> ( in @ X1106 @ X1104 ) ) )
=> ( ! [X1107: $i,X1108: $i,X1109: $i] :
( ( in @ X1108 @ X1109 )
=> ( ( in @ X1109 @ X1107 )
=> ( in @ X1108 @ ( setunion @ X1107 ) ) ) )
=> ( ! [X1110: $i,X1111: $i] :
( ( in @ X1111 @ ( setunion @ X1110 ) )
=> ! [X1112: $o] :
( ! [X1113: $i] :
( ( in @ X1111 @ X1113 )
=> ( ( in @ X1113 @ X1110 )
=> X1112 ) )
=> X1112 ) )
=> ( ! [X1114: $i,X1115: $i] :
( ( in @ X1115 @ X1114 )
=> ( in @ X1115 @ ( powerset @ ( setunion @ X1114 ) ) ) )
=> ( ! [X1116: $i > $o] :
( ? [X1117: $i] :
( ( X1116 @ X1117 )
& ! [X1118: $i] :
( ( X1116 @ X1118 )
=> ( X1117 = X1118 ) ) )
=> ? [X1119: $i] :
! [X1120: $i] :
( ( X1116 @ X1120 )
<=> ( X1120 = X1119 ) ) )
=> ( ! [X1121: $i] :
( ( X1121 != emptyset )
=> ? [X1122: $i] :
( ( in @ X1122 @ X1121 )
& $true ) )
=> ( ! [X1123: $i,X1124: $i] :
( ( in @ X1123 @ ( setadjoin @ X1124 @ emptyset ) )
=> ( X1123 = X1124 ) )
=> ( ! [X1125: $i,X1126: $i] :
( ( X1125 != X1126 )
=> ~ ( in @ X1126 @ ( setadjoin @ X1125 @ emptyset ) ) )
=> ( ! [X1127: $i,X1128: $i] :
( ( X1127 = X1128 )
=> ( in @ X1127 @ ( setadjoin @ X1128 @ emptyset ) ) )
=> ( ! [X1129: $i,X1130: $i] :
( ( in @ X1129 @ ( setadjoin @ X1130 @ emptyset ) )
=> ( in @ X1130 @ ( setadjoin @ X1129 @ emptyset ) ) )
=> ( ! [X1131: $i,X1132: $i,X1133: $i] :
( ( in @ X1133 @ ( setadjoin @ X1131 @ ( setadjoin @ X1132 @ emptyset ) ) )
=> ( ( X1133 = X1131 )
| ( X1133 = X1132 ) ) )
=> ( ! [X1134: $i,X1135: $i] : ( in @ X1134 @ ( setadjoin @ X1134 @ ( setadjoin @ X1135 @ emptyset ) ) )
=> ( ! [X1136: $i,X1137: $i] : ( in @ X1137 @ ( setadjoin @ X1136 @ ( setadjoin @ X1137 @ emptyset ) ) )
=> ( ! [X1138: $i,X1139: $i > $o] :
( ? [X1140: $i] :
( ( in @ X1140 @ X1138 )
& ( X1139 @ X1140 ) )
=> ( ( ( dsetconstr @ X1138 @ X1139 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1141: $i > $o,X1142: $i] :
( ( in @ X1142 @ emptyset )
=> ( X1141 @ X1142 ) )
=> ( ! [X1143: $i,X1144: $i > $o] :
( ~ ! [X1145: $i] :
( ( in @ X1145 @ X1143 )
=> ( X1144 @ X1145 ) )
=> ? [X1146: $i] :
( ( in @ X1146 @ X1143 )
& ~ ( X1144 @ X1146 ) ) )
=> ( ! [X1147: $i,X1148: $i > $o] :
( ! [X1149: $i] :
( ( in @ X1149 @ X1147 )
=> ~ ( X1148 @ X1149 ) )
=> ~ ? [X1150: $i] :
( ( in @ X1150 @ X1147 )
& ( X1148 @ X1150 ) ) )
=> ( ! [X1151: $i,X1152: $i > $o] :
( ~ ? [X1153: $i] :
( ( in @ X1153 @ X1151 )
& ( X1152 @ X1153 ) )
=> ! [X1154: $i] :
( ( in @ X1154 @ X1151 )
=> ~ ( X1152 @ X1154 ) ) )
=> ( ! [X1155: $i,X1156: $i > $o] :
( ? [X1157: $i] :
( ( in @ X1157 @ X1155 )
& ~ ( X1156 @ X1157 ) )
=> ~ ! [X1158: $i] :
( ( in @ X1158 @ X1155 )
=> ( X1156 @ X1158 ) ) )
=> ( ! [X1159: $o] :
( X1159
=> ( in @ emptyset @ ( prop2set @ X1159 ) ) )
=> ( ! [X1160: $o] :
( X1160
=> ( set2prop @ ( prop2set @ X1160 ) ) )
=> ( ! [X1161: $i,X1162: $i > $o] :
( ~ ? [X1163: $i] :
( ( in @ X1163 @ X1161 )
& ( X1162 @ X1163 ) )
=> ! [X1164: $i] :
( ( in @ X1164 @ X1161 )
=> ~ ( X1162 @ X1164 ) ) )
=> ( ! [X1165: $i,X1166: $i > $o] :
( ~ ! [X1167: $i] :
( ( in @ X1167 @ X1165 )
=> ( X1166 @ X1167 ) )
=> ? [X1168: $i] :
( ( in @ X1168 @ X1165 )
& ~ ( X1166 @ X1168 ) ) )
=> ( ! [X1169: $i > $o] :
( ? [X1170: $i] :
( ( X1169 @ X1170 )
& ! [X1171: $i] :
( ( X1169 @ X1171 )
=> ( X1170 = X1171 ) ) )
=> ? [X1172: $i] :
( ( X1169 @ X1172 )
& ! [X1173: $i] :
( ( X1169 @ X1173 )
=> ( X1172 = X1173 ) ) ) )
=> ( ! [X1174: $i > $o] :
( ? [X1175: $i] : ( X1174 @ X1175 )
=> ( ! [X1176: $i,X1177: $i] :
( ( X1174 @ X1176 )
=> ( ( X1174 @ X1177 )
=> ( X1176 = X1177 ) ) )
=> ? [X1178: $i] :
( ( X1174 @ X1178 )
& ! [X1179: $i] :
( ( X1174 @ X1179 )
=> ( X1178 = X1179 ) ) ) ) )
=> ( ! [X1180: $i > $o] :
( ? [X1181: $i] :
! [X1182: $i] :
( ( X1180 @ X1182 )
<=> ( X1182 = X1181 ) )
=> ? [X1183: $i] :
( ( X1180 @ X1183 )
& ! [X1184: $i] :
( ( X1180 @ X1184 )
=> ( X1183 = X1184 ) ) ) )
=> ( ! [X1185: $i,X1186: $i] :
( ( X1185 = X1186 )
=> ! [X1187: $i,X1188: $i] :
( ( X1187 = X1188 )
=> ( ( in @ X1187 @ X1185 )
=> ( in @ X1188 @ X1186 ) ) ) )
=> ( ! [X1189: $i,X1190: $i] :
( ( X1189 = X1190 )
=> ! [X1191: $i,X1192: $i] :
( ( X1191 = X1192 )
=> ( ( in @ X1191 @ X1189 )
<=> ( in @ X1192 @ X1190 ) ) ) )
=> ( ! [X1193: $i > $o] :
( ? [X1194: $i] :
( ( X1193 @ X1194 )
& ! [X1195: $i] :
( ( X1193 @ X1195 )
=> ( X1194 = X1195 ) ) )
=> ! [X1196: $i,X1197: $i] :
( ( X1193 @ X1196 )
=> ( ( X1193 @ X1197 )
=> ( X1196 = X1197 ) ) ) )
=> ( ! [X1198: $i > $o,X1199: $i > $o] :
( ! [X1200: $i,X1201: $i] :
( ( X1200 = X1201 )
=> ( ( X1198 @ X1200 )
<=> ( X1199 @ X1201 ) ) )
=> ( ? [X1202: $i] :
( ( X1198 @ X1202 )
& ! [X1203: $i] :
( ( X1198 @ X1203 )
=> ( X1202 = X1203 ) ) )
<=> ? [X1204: $i] :
( ( X1199 @ X1204 )
& ! [X1205: $i] :
( ( X1199 @ X1205 )
=> ( X1204 = X1205 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1206: $i,X1207: $i] :
( ( X1206 = X1207 )
=> ! [X1208: $i,X1209: $i] :
( ( X1208 = X1209 )
=> ( ( setadjoin @ X1206 @ X1208 )
= ( setadjoin @ X1207 @ X1209 ) ) ) )
=> ( ! [X1210: $i,X1211: $i] :
( ( X1210 = X1211 )
=> ( ( powerset @ X1210 )
= ( powerset @ X1211 ) ) )
=> ( ! [X1212: $i,X1213: $i] :
( ( X1212 = X1213 )
=> ( ( setunion @ X1212 )
= ( setunion @ X1213 ) ) )
=> ( ( omega = omega )
=> ( ! [X1214: $i > $o] :
( ? [X1215: $i] :
( ( X1214 @ X1215 )
& ! [X1216: $i] :
( ( X1214 @ X1216 )
=> ( X1215 = X1216 ) ) )
=> ! [X1217: $i,X1218: $i] :
( ( X1214 @ X1217 )
=> ( ( X1214 @ X1218 )
=> ( X1217 = X1218 ) ) ) )
=> ( ! [X1219: $i > $o,X1220: $i > $o] :
( ! [X1221: $i,X1222: $i] :
( ( X1221 = X1222 )
=> ( ( X1219 @ X1221 )
<=> ( X1220 @ X1222 ) ) )
=> ( ? [X1223: $i] :
( ( X1219 @ X1223 )
& ! [X1224: $i] :
( ( X1219 @ X1224 )
=> ( X1223 = X1224 ) ) )
=> ( ? [X1225: $i] :
( ( X1220 @ X1225 )
& ! [X1226: $i] :
( ( X1220 @ X1226 )
=> ( X1225 = X1226 ) ) )
=> ( ( descr @ X1219 )
= ( descr @ X1220 ) ) ) ) )
=> ( ! [X1227: $i,X1228: $i] :
( ( X1227 = X1228 )
=> ! [X1229: $i > $o,X1230: $i > $o] :
( ! [X1231: $i] :
( ( in @ X1231 @ X1227 )
=> ! [X1232: $i] :
( ( in @ X1232 @ X1228 )
=> ( ( X1231 = X1232 )
=> ( ( X1229 @ X1231 )
<=> ( X1230 @ X1232 ) ) ) ) )
=> ( ( dsetconstr @ X1227 @ X1229 )
= ( dsetconstr @ X1228 @ X1230 ) ) ) )
=> ( ! [X1233: $i,X1234: $i] :
( ! [X1235: $i] :
( ( in @ X1235 @ X1233 )
=> ( in @ X1235 @ X1234 ) )
=> ( subset @ X1233 @ X1234 ) )
=> ( ! [X1236: $i,X1237: $i] :
( ( X1236 = X1237 )
=> ( subset @ X1237 @ X1236 ) )
=> ( ! [X1238: $i,X1239: $i] :
( ( X1238 = X1239 )
=> ( subset @ X1238 @ X1239 ) )
=> ( ! [X1240: $i,X1241: $i] :
( ! [X1242: $i] :
( ( in @ X1242 @ X1240 )
=> ( in @ X1242 @ X1241 ) )
=> ( subset @ X1240 @ X1241 ) )
=> ( ! [X1243: $i] : ( subset @ emptyset @ X1243 )
=> ( ! [X1244: $i,X1245: $i,X1246: $i] :
( ( subset @ X1244 @ X1245 )
=> ( ( in @ X1246 @ X1244 )
=> ( in @ X1246 @ X1245 ) ) )
=> ( ! [X1247: $i,X1248: $i,X1249: $i] :
( ( subset @ X1247 @ X1248 )
=> ( ~ ( in @ X1249 @ X1248 )
=> ~ ( in @ X1249 @ X1247 ) ) )
=> ( ! [X1250: $i,X1251: $i,X1252: $i] :
( ( in @ X1252 @ X1250 )
=> ( ~ ( in @ X1252 @ X1251 )
=> ~ ( subset @ X1250 @ X1251 ) ) )
=> ( ! [X1253: $i,X1254: $i] :
( ~ ( subset @ X1253 @ X1254 )
=> ( X1253 != X1254 ) )
=> ( ! [X1255: $i,X1256: $i,X1257: $i] :
( ( in @ X1257 @ X1255 )
=> ( ~ ( in @ X1257 @ X1256 )
=> ( X1255 != X1256 ) ) )
=> ( ! [X1258: $i] : ( subset @ X1258 @ X1258 )
=> ( ! [X1259: $i,X1260: $i,X1261: $i] :
( ( subset @ X1259 @ X1260 )
=> ( ( subset @ X1260 @ X1261 )
=> ( subset @ X1259 @ X1261 ) ) )
=> ( ! [X1262: $i,X1263: $i] : ( subset @ X1263 @ ( setadjoin @ X1262 @ X1263 ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i] :
( ( subset @ X1264 @ X1266 )
=> ( subset @ X1264 @ ( setadjoin @ X1265 @ X1266 ) ) )
=> ( ! [X1267: $i,X1268: $i] :
( ( subset @ X1267 @ X1268 )
=> ( in @ X1267 @ ( powerset @ X1268 ) ) )
=> ( ! [X1269: $i,X1270: $i] :
( ( subset @ X1269 @ X1270 )
=> ( ( subset @ X1270 @ X1269 )
=> ( X1269 = X1270 ) ) )
=> ( ! [X1271: $i] :
( ( subset @ X1271 @ emptyset )
=> ( X1271 = emptyset ) )
=> ( ! [X1272: $i,X1273: $i] :
( ( subset @ X1273 @ X1272 )
=> ( in @ X1273 @ ( powerset @ X1272 ) ) )
=> ( ! [X1274: $i,X1275: $i] :
( ( in @ X1275 @ ( powerset @ X1274 ) )
=> ( subset @ X1275 @ X1274 ) )
=> ( ! [X1276: $i] : ( in @ X1276 @ ( powerset @ X1276 ) )
=> ( ! [X1277: $i,X1278: $i] :
( ( subset @ X1277 @ X1278 )
=> ( subset @ ( powerset @ X1277 ) @ ( powerset @ X1278 ) ) )
=> ( ! [X1279: $i,X1280: $i > $o] : ( in @ ( dsetconstr @ X1279 @ X1280 ) @ ( powerset @ X1279 ) )
=> ( ! [X1281: $i,X1282: $i > $o] : ( subset @ ( dsetconstr @ X1281 @ X1282 ) @ X1281 )
=> ( ! [X1283: $i,X1284: $i,X1285: $i] :
( ( in @ X1285 @ X1283 )
=> ( in @ X1285 @ ( binunion @ X1283 @ X1284 ) ) )
=> ( ! [X1286: $i,X1287: $i] : ( in @ X1287 @ ( setadjoin @ X1286 @ ( setadjoin @ X1287 @ emptyset ) ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i] :
( ( in @ X1290 @ X1289 )
=> ( in @ X1290 @ ( binunion @ X1288 @ X1289 ) ) )
=> ( ! [X1291: $i,X1292: $i,X1293: $i,X1294: $o] :
( ( in @ X1293 @ ( binunion @ X1291 @ X1292 ) )
=> ( ( ( in @ X1293 @ X1291 )
=> X1294 )
=> ( ( ( in @ X1293 @ X1292 )
=> X1294 )
=> X1294 ) ) )
=> ( ! [X1295: $i,X1296: $i,X1297: $i] :
( ( in @ X1297 @ ( binunion @ X1295 @ X1296 ) )
=> ( ( in @ X1297 @ X1295 )
| ( in @ X1297 @ X1296 ) ) )
=> ( ! [X1298: $i,X1299: $i] : ( subset @ X1298 @ ( binunion @ X1298 @ X1299 ) )
=> ( ! [X1300: $i,X1301: $i] : ( subset @ X1301 @ ( binunion @ X1300 @ X1301 ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i] :
( ( in @ X1304 @ X1302 )
=> ( ( in @ X1304 @ X1303 )
=> ( in @ X1304 @ ( binintersect @ X1302 @ X1303 ) ) ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( subset @ X1307 @ X1305 )
=> ( ( subset @ X1307 @ X1306 )
=> ( subset @ X1307 @ ( binintersect @ X1305 @ X1306 ) ) ) )
=> ( ! [X1308: $i,X1309: $i,X1310: $i] :
( ( in @ X1310 @ ( binintersect @ X1308 @ X1309 ) )
=> ( in @ X1310 @ X1308 ) )
=> ( ! [X1311: $i,X1312: $i] : ( subset @ ( binintersect @ X1311 @ X1312 ) @ X1311 )
=> ( ! [X1313: $i,X1314: $i] :
( ( subset @ X1313 @ X1314 )
=> ( ( binintersect @ X1313 @ X1314 )
= X1313 ) )
=> ( ! [X1315: $i,X1316: $i] :
( ( ( binintersect @ X1315 @ X1316 )
= X1316 )
=> ( subset @ X1316 @ X1315 ) )
=> ( ! [X1317: $i,X1318: $i,X1319: $i] :
( ( in @ X1319 @ ( binintersect @ X1317 @ X1318 ) )
=> ( in @ X1319 @ X1318 ) )
=> ( ! [X1320: $i,X1321: $i] :
( ~ ? [X1322: $i] :
( ( in @ X1322 @ X1320 )
& ( in @ X1322 @ X1321 ) )
=> ( ( binintersect @ X1320 @ X1321 )
= emptyset ) )
=> ( ! [X1323: $i,X1324: $i] : ( subset @ ( binintersect @ X1323 @ X1324 ) @ X1324 )
=> ( ! [X1325: $i,X1326: $i] :
( ( subset @ X1326 @ X1325 )
=> ( ( binintersect @ X1325 @ X1326 )
= X1326 ) )
=> ( ! [X1327: $i,X1328: $i] :
( ( ( binintersect @ X1327 @ X1328 )
= X1327 )
=> ( subset @ X1327 @ X1328 ) )
=> ( ! [X1329: $i,X1330: $i,X1331: $i] :
( ( binintersect @ X1329 @ ( binunion @ X1330 @ X1331 ) )
= ( binunion @ ( binintersect @ X1329 @ X1330 ) @ ( binintersect @ X1329 @ X1331 ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( in @ X1334 @ X1332 )
=> ( ~ ( in @ X1334 @ X1333 )
=> ( in @ X1334 @ ( setminus @ X1332 @ X1333 ) ) ) )
=> ( ! [X1335: $i,X1336: $i,X1337: $i] :
( ( in @ X1337 @ ( setminus @ X1335 @ X1336 ) )
=> ( in @ X1337 @ X1335 ) )
=> ( ! [X1338: $i,X1339: $i,X1340: $i] :
( ( in @ X1340 @ ( setminus @ X1338 @ X1339 ) )
=> ~ ( in @ X1340 @ X1339 ) )
=> ( ! [X1341: $i,X1342: $i] :
( ( subset @ X1341 @ X1342 )
=> ( ( setminus @ X1341 @ X1342 )
= emptyset ) )
=> ( ! [X1343: $i,X1344: $i,X1345: $i] :
( ~ ( in @ X1345 @ ( setminus @ X1343 @ X1344 ) )
=> ( ( in @ X1345 @ X1343 )
=> ( in @ X1345 @ X1344 ) ) )
=> ( ! [X1346: $i,X1347: $i,X1348: $i] :
( ~ ( in @ X1348 @ ( setminus @ X1346 @ X1347 ) )
=> ( ~ ( in @ X1348 @ X1347 )
=> ~ ( in @ X1348 @ X1346 ) ) )
=> ( ! [X1349: $i,X1350: $i,X1351: $i] :
( ~ ( in @ X1351 @ X1349 )
=> ~ ( in @ X1351 @ ( setminus @ X1349 @ X1350 ) ) )
=> ( ! [X1352: $i,X1353: $i,X1354: $i] :
( ( in @ X1354 @ X1353 )
=> ~ ( in @ X1354 @ ( setminus @ X1352 @ X1353 ) ) )
=> ( ! [X1355: $i,X1356: $i] : ( subset @ ( setminus @ X1355 @ X1356 ) @ X1355 )
=> ( ! [X1357: $i,X1358: $i] :
( ( ( setminus @ X1357 @ X1358 )
= emptyset )
=> ( subset @ X1357 @ X1358 ) )
=> ( ! [X1359: $i,X1360: $i,X1361: $i] :
( ( in @ X1361 @ ( symdiff @ X1359 @ X1360 ) )
=> ! [X1362: $o] :
( ( ( in @ X1361 @ X1359 )
=> ( ~ ( in @ X1361 @ X1360 )
=> X1362 ) )
=> ( ( ~ ( in @ X1361 @ X1359 )
=> ( ( in @ X1361 @ X1360 )
=> X1362 ) )
=> X1362 ) ) )
=> ( ! [X1363: $i,X1364: $i,X1365: $i] :
( ( in @ X1365 @ X1363 )
=> ( ~ ( in @ X1365 @ X1364 )
=> ( in @ X1365 @ ( symdiff @ X1363 @ X1364 ) ) ) )
=> ( ! [X1366: $i,X1367: $i,X1368: $i] :
( ~ ( in @ X1368 @ X1366 )
=> ( ( in @ X1368 @ X1367 )
=> ( in @ X1368 @ ( symdiff @ X1366 @ X1367 ) ) ) )
=> ( ! [X1369: $i,X1370: $i,X1371: $i] :
( ( in @ X1371 @ X1369 )
=> ( ( in @ X1371 @ X1370 )
=> ~ ( in @ X1371 @ ( symdiff @ X1369 @ X1370 ) ) ) )
=> ( ! [X1372: $i,X1373: $i,X1374: $i] :
( ~ ( in @ X1374 @ X1372 )
=> ( ~ ( in @ X1374 @ X1373 )
=> ~ ( in @ X1374 @ ( symdiff @ X1372 @ X1373 ) ) ) )
=> ( ! [X1375: $i,X1376: $i] : ( in @ X1376 @ ( setadjoin @ X1375 @ ( setadjoin @ X1376 @ emptyset ) ) )
=> ( ! [X1377: $i,X1378: $i] : ( in @ X1377 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1377 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1377 @ ( setadjoin @ X1378 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1379: $i,X1380: $i] : ( in @ X1380 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1379 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1379 @ ( setadjoin @ X1380 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1381: $i,X1382: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1381 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1381 @ ( setadjoin @ X1382 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1383: $i,X1384: $i] : ( iskpair @ ( kpair @ X1383 @ X1384 ) )
=> ( ! [X1385: $i,X1386: $i] :
( ( in @ X1386 @ X1385 )
=> ( subset @ ( setadjoin @ X1386 @ emptyset ) @ X1385 ) )
=> ( ! [X1387: $i,X1388: $i] :
( ( in @ X1388 @ X1387 )
=> ( in @ ( setadjoin @ X1388 @ emptyset ) @ ( powerset @ X1387 ) ) )
=> ( ! [X1389: $i,X1390: $i,X1391: $i] :
( ( in @ X1391 @ X1389 )
=> ( in @ ( setadjoin @ X1391 @ emptyset ) @ ( powerset @ ( binunion @ X1389 @ X1390 ) ) ) )
=> ( ! [X1392: $i,X1393: $i,X1394: $i] :
( ( in @ X1394 @ ( setadjoin @ X1392 @ ( setadjoin @ X1393 @ emptyset ) ) )
=> ( ( X1394 = X1392 )
| ( X1394 = X1393 ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i] :
( ( in @ X1397 @ X1395 )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1396 )
=> ( subset @ ( setadjoin @ X1397 @ ( setadjoin @ X1398 @ emptyset ) ) @ ( binunion @ X1395 @ X1396 ) ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( in @ X1401 @ X1399 )
=> ! [X1402: $i] :
( ( in @ X1402 @ X1400 )
=> ( in @ ( setadjoin @ X1401 @ ( setadjoin @ X1402 @ emptyset ) ) @ ( powerset @ ( binunion @ X1399 @ X1400 ) ) ) ) )
=> ( ! [X1403: $i,X1404: $i,X1405: $i] :
( ( in @ X1405 @ X1403 )
=> ! [X1406: $i] :
( ( in @ X1406 @ X1404 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1405 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1405 @ ( setadjoin @ X1406 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1403 @ X1404 ) ) ) ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i] :
( ( in @ X1409 @ X1407 )
=> ! [X1410: $i] :
( ( in @ X1410 @ X1408 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1409 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1409 @ ( setadjoin @ X1410 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1407 @ X1408 ) ) ) ) ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i] :
( ( in @ X1413 @ X1411 )
=> ! [X1414: $i] :
( ( in @ X1414 @ X1412 )
=> ( in @ ( kpair @ X1413 @ X1414 ) @ ( powerset @ ( powerset @ ( binunion @ X1411 @ X1412 ) ) ) ) ) )
=> ( ! [X1415: $i,X1416: $i,X1417: $i] :
( ( in @ X1417 @ X1415 )
=> ! [X1418: $i] :
( ( in @ X1418 @ X1416 )
=> ( in @ ( kpair @ X1417 @ X1418 ) @ ( cartprod @ X1415 @ X1416 ) ) ) )
=> ( ! [X1419: $i,X1420: $i,X1421: $i] :
( ( in @ X1421 @ ( cartprod @ X1419 @ X1420 ) )
=> ? [X1422: $i] :
( ( in @ X1422 @ X1419 )
& ? [X1423: $i] :
( ( in @ X1423 @ X1420 )
& ( X1421
= ( kpair @ X1422 @ X1423 ) ) ) ) )
=> ( ! [X1424: $i,X1425: $i,X1426: $i] :
( ( in @ X1426 @ ( cartprod @ X1424 @ X1425 ) )
=> ( iskpair @ X1426 ) )
=> ( ! [X1427: $i,X1428: $i] :
( ( in @ X1428 @ ( setunion @ X1427 ) )
=> ? [X1429: $i] :
( ( in @ X1429 @ X1427 )
& ( in @ X1428 @ X1429 ) ) )
=> ( ! [X1430: $i] : ( subset @ ( setunion @ ( setadjoin @ X1430 @ emptyset ) ) @ X1430 )
=> ( ! [X1431: $i] : ( subset @ X1431 @ ( setunion @ ( setadjoin @ X1431 @ emptyset ) ) )
=> ( ! [X1432: $i] :
( ( setunion @ ( setadjoin @ X1432 @ emptyset ) )
= X1432 )
=> ( ! [X1433: $i,X1434: $i > $o] :
( ! [X1435: $i] :
( ( in @ X1435 @ X1433 )
=> ! [X1436: $i] :
( ( in @ X1436 @ X1433 )
=> ( ( X1434 @ X1435 )
=> ( ( X1434 @ X1436 )
=> ( X1435 = X1436 ) ) ) ) )
=> ( ? [X1437: $i] :
( ( in @ X1437 @ X1433 )
& ( X1434 @ X1437 ) )
=> ( singleton @ ( dsetconstr @ X1433 @ X1434 ) ) ) )
=> ( ! [X1438: $i,X1439: $i > $o] :
( ( singleton @ ( dsetconstr @ X1438 @ X1439 ) )
=> ? [X1440: $i] :
( ( in @ X1440 @ X1438 )
& ( X1439 @ X1440 ) ) )
=> ( ! [X1441: $i,X1442: $i > $o,X1443: $i] :
( ( in @ X1443 @ X1441 )
=> ( ( X1442 @ X1443 )
=> ( ! [X1444: $i] :
( ( in @ X1444 @ X1441 )
=> ( ( X1442 @ X1444 )
=> ( X1444 = X1443 ) ) )
=> ( singleton @ ( dsetconstr @ X1441 @ X1442 ) ) ) ) )
=> ( ! [X1445: $i,X1446: $i > $o] :
( ! [X1447: $i] :
( ( in @ X1447 @ X1445 )
=> ! [X1448: $i] :
( ( in @ X1448 @ X1445 )
=> ( ( X1446 @ X1447 )
=> ( ( X1446 @ X1448 )
=> ( X1447 = X1448 ) ) ) ) )
=> ( ? [X1449: $i] :
( ( in @ X1449 @ X1445 )
& ( X1446 @ X1449 ) )
=> ( singleton @ ( dsetconstr @ X1445 @ X1446 ) ) ) )
=> ( ! [X1450: $i,X1451: $i] :
( ( ( setadjoin @ X1450 @ emptyset )
= ( setadjoin @ X1451 @ emptyset ) )
=> ( X1450 = X1451 ) )
=> ( ! [X1452: $i,X1453: $i,X1454: $i] :
( ( in @ ( setadjoin @ X1454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1452 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1452 @ ( setadjoin @ X1453 @ emptyset ) ) @ emptyset ) ) )
=> ( X1452 = X1454 ) )
=> ( ! [X1455: $i] :
( ( iskpair @ X1455 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1455 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1455 ) ) ) )
=> ( ! [X1456: $i] :
( ( singleton @ X1456 )
=> ( in @ ( setunion @ X1456 ) @ X1456 ) )
=> ( ! [X1457: $i,X1458: $i] :
( ( kfst @ ( kpair @ X1457 @ X1458 ) )
= X1457 )
=> ( ! [X1459: $i,X1460: $i,X1461: $i] :
( ( in @ X1461 @ ( cartprod @ X1459 @ X1460 ) )
=> ( in @ ( kfst @ X1461 ) @ X1459 ) )
=> ( ! [X1462: $i,X1463: $i,X1464: $i,X1465: $i] :
( ( ( setadjoin @ ( setadjoin @ X1462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1462 @ ( setadjoin @ X1463 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1464 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1464 @ ( setadjoin @ X1465 @ emptyset ) ) @ emptyset ) ) )
=> ( X1462 = X1464 ) )
=> ( ! [X1466: $i,X1467: $i,X1468: $i,X1469: $i] :
( ( ( kpair @ X1466 @ X1467 )
= ( kpair @ X1468 @ X1469 ) )
=> ( X1466 = X1468 ) )
=> ( ! [X1470: $i,X1471: $i] :
( ( X1470 = X1471 )
=> ( ( setadjoin @ X1470 @ ( setadjoin @ X1471 @ emptyset ) )
= ( setadjoin @ X1470 @ emptyset ) ) )
=> ( ! [X1472: $i,X1473: $i] :
( ( X1472 = X1473 )
=> ( ( setadjoin @ ( setadjoin @ X1472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1472 @ ( setadjoin @ X1473 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1472 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1474: $i,X1475: $i,X1476: $i,X1477: $i] :
( ( ( setadjoin @ ( setadjoin @ X1474 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1474 @ ( setadjoin @ X1475 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1476 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1476 @ ( setadjoin @ X1477 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1476 = X1477 )
=> ( X1475 = X1477 ) ) )
=> ( ! [X1478: $i,X1479: $i,X1480: $i] :
( ( ( setadjoin @ X1478 @ ( setadjoin @ X1479 @ emptyset ) )
= ( setadjoin @ X1480 @ emptyset ) )
=> ( X1478 = X1479 ) )
=> ( ! [X1481: $i,X1482: $i,X1483: $i,X1484: $i] :
( ( ( setadjoin @ ( setadjoin @ X1481 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1481 @ ( setadjoin @ X1482 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1483 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1483 @ ( setadjoin @ X1484 @ emptyset ) ) @ emptyset ) ) )
=> ( X1482 = X1484 ) )
=> ( ! [X1485: $i,X1486: $i,X1487: $i,X1488: $i] :
( ( ( kpair @ X1485 @ X1486 )
= ( kpair @ X1487 @ X1488 ) )
=> ( X1486 = X1488 ) )
=> ( ! [X1489: $i] :
( ( iskpair @ X1489 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1489 )
@ ^ [Z0: $i] :
( X1489
= ( kpair @ ( kfst @ X1489 ) @ Z0 ) ) ) ) )
=> ( ! [X1490: $i,X1491: $i] :
( ( ksnd @ ( kpair @ X1490 @ X1491 ) )
= X1491 )
=> ( ! [X1492: $i] :
( ( iskpair @ X1492 )
=> ( ( kpair @ ( kfst @ X1492 ) @ ( ksnd @ X1492 ) )
= X1492 ) )
=> ( ! [X1493: $i,X1494: $i,X1495: $i] :
( ( in @ X1495 @ ( cartprod @ X1493 @ X1494 ) )
=> ( in @ ( ksnd @ X1495 ) @ X1494 ) )
=> ( ! [X1496: $i,X1497: $i,X1498: $i,X1499: $i] :
( ( in @ ( kpair @ X1498 @ X1499 ) @ ( cartprod @ X1496 @ X1497 ) )
=> ( in @ X1498 @ X1496 ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i,X1503: $i] :
( ( in @ ( kpair @ X1502 @ X1503 ) @ ( cartprod @ X1500 @ X1501 ) )
=> ( in @ X1503 @ X1501 ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i] :
( ( in @ X1506 @ X1504 )
=> ! [X1507: $i] :
( ( in @ X1507 @ X1505 )
=> ( ( kpair @ X1506 @ X1507 )
= ( kpair @ X1506 @ X1507 ) ) ) )
=> ( ! [X1508: $i,X1509: $i,X1510: $i] :
( ( in @ X1510 @ X1508 )
=> ! [X1511: $i] :
( ( in @ X1511 @ X1509 )
=> ( ( kfst @ ( kpair @ X1510 @ X1511 ) )
= X1510 ) ) )
=> ( ! [X1512: $i,X1513: $i,X1514: $i] :
( ( in @ X1514 @ X1512 )
=> ! [X1515: $i] :
( ( in @ X1515 @ X1513 )
=> ( ( ksnd @ ( kpair @ X1514 @ X1515 ) )
= X1515 ) ) )
=> ( ! [X1516: $i,X1517: $i,X1518: $i] :
( ( in @ X1518 @ ( cartprod @ X1516 @ X1517 ) )
=> ( ( kpair @ ( kfst @ X1518 ) @ ( ksnd @ X1518 ) )
= X1518 ) )
=> ( ! [X1519: $i,X1520: $i,X1521: $i > $i > $o,X1522: $i] :
( ( in @ X1522 @ X1519 )
=> ! [X1523: $i] :
( ( in @ X1523 @ X1520 )
=> ( ( X1521 @ X1522 @ X1523 )
=> ( in @ ( kpair @ X1522 @ X1523 ) @ ( dpsetconstr @ X1519 @ X1520 @ X1521 ) ) ) ) )
=> ( ! [X1524: $i,X1525: $i,X1526: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1524 @ X1525 @ X1526 ) @ ( cartprod @ X1524 @ X1525 ) )
=> ( ! [X1527: $i,X1528: $i,X1529: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1527 @ X1528 @ X1529 ) @ ( cartprod @ X1527 @ X1528 ) )
=> ( ! [X1530: $i,X1531: $i,X1532: $i > $i > $o,X1533: $i] :
( ( in @ X1533 @ X1530 )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1531 )
=> ( ( in @ ( kpair @ X1533 @ X1534 ) @ ( dpsetconstr @ X1530 @ X1531 @ X1532 ) )
=> ( X1532 @ X1533 @ X1534 ) ) ) )
=> ( ! [X1535: $i,X1536: $i,X1537: $i > $i > $o,X1538: $i,X1539: $i] :
( ( in @ ( kpair @ X1538 @ X1539 ) @ ( dpsetconstr @ X1535 @ X1536 @ X1537 ) )
=> ( in @ X1538 @ X1535 ) )
=> ( ! [X1540: $i,X1541: $i,X1542: $i > $i > $o,X1543: $i,X1544: $i] :
( ( in @ ( kpair @ X1543 @ X1544 ) @ ( dpsetconstr @ X1540 @ X1541 @ X1542 ) )
=> ( in @ X1544 @ X1541 ) )
=> ( ! [X1545: $i,X1546: $i,X1547: $i > $i > $o,X1548: $i,X1549: $i] :
( ( in @ ( kpair @ X1548 @ X1549 ) @ ( dpsetconstr @ X1545 @ X1546 @ X1547 ) )
=> ( X1547 @ X1548 @ X1549 ) )
=> ( ! [X1550: $i,X1551: $i,X1552: $i] :
( ( func @ X1550 @ X1551 @ X1552 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1550 )
=> ( singleton
@ ( dsetconstr @ X1551
@ ^ [Z0: $i] : ( in @ ( kpair @ X1553 @ Z0 ) @ X1552 ) ) ) ) )
=> ( ! [X1554: $i,X1555: $i,X1556: $i] :
( ( func @ X1554 @ X1555 @ X1556 )
=> ! [X1557: $i] :
( ( in @ X1557 @ X1554 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1555
@ ^ [Z0: $i] : ( in @ ( kpair @ X1557 @ Z0 ) @ X1556 ) ) )
@ X1555 ) ) )
=> ( ! [X1558: $i,X1559: $i,X1560: $i] :
( ( func @ X1558 @ X1559 @ X1560 )
=> ! [X1561: $i] :
( ( in @ X1561 @ X1558 )
=> ( in @ ( ap @ X1558 @ X1559 @ X1560 @ X1561 ) @ X1559 ) ) )
=> ( ! [X1562: $i,X1563: $i,X1564: $i] :
( ( in @ X1564 @ ( funcSet @ X1562 @ X1563 ) )
=> ( func @ X1562 @ X1563 @ X1564 ) )
=> ( ! [X1565: $i,X1566: $i,X1567: $i] :
( ( in @ X1567 @ ( funcSet @ X1565 @ X1566 ) )
=> ! [X1568: $i] :
( ( in @ X1568 @ X1565 )
=> ( in @ ( ap @ X1565 @ X1566 @ X1567 @ X1568 ) @ X1566 ) ) )
=> ( ! [X1569: $i,X1570: $i,X1571: $i] :
( ( func @ X1569 @ X1570 @ X1571 )
=> ( in @ X1571 @ ( funcSet @ X1569 @ X1570 ) ) )
=> ( ! [X1572: $i,X1573: $i,X1574: $i > $i] :
( ! [X1575: $i] :
( ( in @ X1575 @ X1572 )
=> ( in @ ( X1574 @ X1575 ) @ X1573 ) )
=> ( func @ X1572 @ X1573
@ ( dpsetconstr @ X1572 @ X1573
@ ^ [Z0: $i] : ( $eq @ ( X1574 @ Z0 ) ) ) ) )
=> ( ! [X1576: $i,X1577: $i,X1578: $i > $i] :
( ! [X1579: $i] :
( ( in @ X1579 @ X1576 )
=> ( in @ ( X1578 @ X1579 ) @ X1577 ) )
=> ( func @ X1576 @ X1577 @ ( lam @ X1576 @ X1577 @ X1578 ) ) )
=> ( ! [X1580: $i,X1581: $i,X1582: $i > $i] :
( ! [X1583: $i] :
( ( in @ X1583 @ X1580 )
=> ( in @ ( X1582 @ X1583 ) @ X1581 ) )
=> ( in @ ( lam @ X1580 @ X1581 @ X1582 ) @ ( funcSet @ X1580 @ X1581 ) ) )
=> ( ! [X1584: $i,X1585: $i,X1586: $i] :
( ( subset @ X1586 @ ( cartprod @ X1584 @ X1585 ) )
=> ! [X1587: $i > $o] :
( ! [X1588: $i] :
( ( in @ X1588 @ X1584 )
=> ! [X1589: $i] :
( ( in @ X1589 @ X1585 )
=> ( ( in @ ( kpair @ X1588 @ X1589 ) @ X1586 )
=> ( X1587 @ ( kpair @ X1588 @ X1589 ) ) ) ) )
=> ! [X1590: $i] :
( ( in @ X1590 @ X1586 )
=> ( X1587 @ X1590 ) ) ) )
=> ( ! [X1591: $i,X1592: $i,X1593: $i] :
( ( subset @ X1593 @ ( cartprod @ X1591 @ X1592 ) )
=> ! [X1594: $i > $o] :
( ! [X1595: $i] :
( ( in @ X1595 @ X1591 )
=> ! [X1596: $i] :
( ( in @ X1596 @ X1592 )
=> ( ( in @ ( kpair @ X1595 @ X1596 ) @ X1593 )
=> ( X1594 @ ( kpair @ X1595 @ X1596 ) ) ) ) )
=> ! [X1597: $i] :
( ( in @ X1597 @ X1593 )
=> ( X1594 @ X1597 ) ) ) )
=> ( ! [X1598: $i,X1599: $i > $o] :
( ( singleton @ ( dsetconstr @ X1598 @ X1599 ) )
=> ! [X1600: $i] :
( ( in @ X1600 @ X1598 )
=> ! [X1601: $i] :
( ( in @ X1601 @ X1598 )
=> ( ( X1599 @ X1600 )
=> ( ( X1599 @ X1601 )
=> ( X1600 = X1601 ) ) ) ) ) )
=> ( ! [X1602: $i,X1603: $i,X1604: $i] :
( ( func @ X1602 @ X1603 @ X1604 )
=> ! [X1605: $i] :
( ( in @ X1605 @ X1602 )
=> ( in @ ( kpair @ X1605 @ ( ap @ X1602 @ X1603 @ X1604 @ X1605 ) ) @ X1604 ) ) )
=> ( ! [X1606: $i,X1607: $i,X1608: $i] :
( ( in @ X1608 @ ( funcSet @ X1606 @ X1607 ) )
=> ! [X1609: $i] :
( ( in @ X1609 @ X1606 )
=> ( in @ ( kpair @ X1609 @ ( ap @ X1606 @ X1607 @ X1608 @ X1609 ) ) @ X1608 ) ) )
=> ( ! [X1610: $i,X1611: $i,X1612: $i] :
( ( func @ X1610 @ X1611 @ X1612 )
=> ! [X1613: $i] :
( ( in @ X1613 @ X1610 )
=> ! [X1614: $i] :
( ( in @ X1614 @ X1611 )
=> ( ( in @ ( kpair @ X1613 @ X1614 ) @ X1612 )
=> ( ( ap @ X1610 @ X1611 @ X1612 @ X1613 )
= X1614 ) ) ) ) )
=> ( ! [X1615: $i,X1616: $i,X1617: $i] :
( ( func @ X1615 @ X1616 @ X1617 )
=> ! [X1618: $i] :
( ( func @ X1615 @ X1616 @ X1618 )
=> ( ! [X1619: $i] :
( ( in @ X1619 @ X1615 )
=> ( ( ap @ X1615 @ X1616 @ X1617 @ X1619 )
= ( ap @ X1615 @ X1616 @ X1618 @ X1619 ) ) )
=> ! [X1620: $i] :
( ( in @ X1620 @ X1615 )
=> ! [X1621: $i] :
( ( in @ X1621 @ X1616 )
=> ( ( in @ ( kpair @ X1620 @ X1621 ) @ X1618 )
=> ( in @ ( kpair @ X1620 @ X1621 ) @ X1617 ) ) ) ) ) ) )
=> ( ! [X1622: $i,X1623: $i,X1624: $i] :
( ( in @ X1624 @ ( funcSet @ X1622 @ X1623 ) )
=> ! [X1625: $i] :
( ( in @ X1625 @ X1622 )
=> ! [X1626: $i] :
( ( in @ X1626 @ X1623 )
=> ( ( in @ ( kpair @ X1625 @ X1626 ) @ X1624 )
=> ( ( ap @ X1622 @ X1623 @ X1624 @ X1625 )
= X1626 ) ) ) ) )
=> ( ! [X1627: $i,X1628: $i,X1629: $i] :
( ( subset @ X1629 @ ( cartprod @ X1627 @ X1628 ) )
=> ! [X1630: $i] :
( ( subset @ X1630 @ ( cartprod @ X1627 @ X1628 ) )
=> ( ! [X1631: $i] :
( ( in @ X1631 @ X1627 )
=> ! [X1632: $i] :
( ( in @ X1632 @ X1628 )
=> ( ( in @ ( kpair @ X1631 @ X1632 ) @ X1629 )
=> ( in @ ( kpair @ X1631 @ X1632 ) @ X1630 ) ) ) )
=> ( subset @ X1629 @ X1630 ) ) ) )
=> ( ! [X1633: $i,X1634: $i,X1635: $i] :
( ( subset @ X1635 @ ( cartprod @ X1633 @ X1634 ) )
=> ! [X1636: $i] :
( ( subset @ X1636 @ ( cartprod @ X1633 @ X1634 ) )
=> ( ! [X1637: $i] :
( ( in @ X1637 @ X1633 )
=> ! [X1638: $i] :
( ( in @ X1638 @ X1634 )
=> ( ( in @ ( kpair @ X1637 @ X1638 ) @ X1635 )
=> ( in @ ( kpair @ X1637 @ X1638 ) @ X1636 ) ) ) )
=> ( ! [X1639: $i] :
( ( in @ X1639 @ X1633 )
=> ! [X1640: $i] :
( ( in @ X1640 @ X1634 )
=> ( ( in @ ( kpair @ X1639 @ X1640 ) @ X1636 )
=> ( in @ ( kpair @ X1639 @ X1640 ) @ X1635 ) ) ) )
=> ( X1635 = X1636 ) ) ) ) )
=> ( ! [X1641: $i,X1642: $i,X1643: $i] :
( ( func @ X1641 @ X1642 @ X1643 )
=> ! [X1644: $i] :
( ( func @ X1641 @ X1642 @ X1644 )
=> ( ! [X1645: $i] :
( ( in @ X1645 @ X1641 )
=> ( ( ap @ X1641 @ X1642 @ X1643 @ X1645 )
= ( ap @ X1641 @ X1642 @ X1644 @ X1645 ) ) )
=> ( X1643 = X1644 ) ) ) )
=> ( ! [X1646: $i,X1647: $i,X1648: $i] :
( ( in @ X1648 @ ( funcSet @ X1646 @ X1647 ) )
=> ! [X1649: $i] :
( ( in @ X1649 @ ( funcSet @ X1646 @ X1647 ) )
=> ( ! [X1650: $i] :
( ( in @ X1650 @ X1646 )
=> ( ( ap @ X1646 @ X1647 @ X1648 @ X1650 )
= ( ap @ X1646 @ X1647 @ X1649 @ X1650 ) ) )
=> ( X1648 = X1649 ) ) ) )
=> ( ! [X1651: $i,X1652: $i,X1653: $i] :
( ( in @ X1653 @ ( funcSet @ X1651 @ X1652 ) )
=> ! [X1654: $i] :
( ( in @ X1654 @ X1651 )
=> ( ( ap @ X1651 @ X1652 @ X1653 @ X1654 )
= ( ap @ X1651 @ X1652 @ X1653 @ X1654 ) ) ) )
=> ( ! [X1655: $i,X1656: $i,X1657: $i] :
( ( func @ X1655 @ X1656 @ X1657 )
=> ! [X1658: $i] :
( ( in @ X1658 @ X1655 )
=> ( ( ap @ X1655 @ X1656 @ X1657 @ X1658 )
= ( ap @ X1655 @ X1656 @ X1657 @ X1658 ) ) ) )
=> ( ! [X1659: $i,X1660: $i,X1661: $i > $i] :
( ! [X1662: $i] :
( ( in @ X1662 @ X1659 )
=> ( in @ ( X1661 @ X1662 ) @ X1660 ) )
=> ! [X1663: $i] :
( ( in @ X1663 @ X1659 )
=> ( ( ap @ X1659 @ X1660 @ ( lam @ X1659 @ X1660 @ X1661 ) @ X1663 )
= ( X1661 @ X1663 ) ) ) )
=> ( ! [X1664: $i,X1665: $i,X1666: $i] :
( ( func @ X1664 @ X1665 @ X1666 )
=> ( ( lam @ X1664 @ X1665 @ ( ap @ X1664 @ X1665 @ X1666 ) )
= X1666 ) )
=> ( ! [X1667: $i,X1668: $i,X1669: $i > $i] :
( ! [X1670: $i] :
( ( in @ X1670 @ X1667 )
=> ( in @ ( X1669 @ X1670 ) @ X1668 ) )
=> ( ( lam @ X1667 @ X1668 @ X1669 )
= ( lam @ X1667 @ X1668 @ X1669 ) ) )
=> ( ! [X1671: $i,X1672: $i,X1673: $i > $i] :
( ! [X1674: $i] :
( ( in @ X1674 @ X1671 )
=> ( in @ ( X1673 @ X1674 ) @ X1672 ) )
=> ! [X1675: $i] :
( ( in @ X1675 @ X1671 )
=> ( ( ap @ X1671 @ X1672 @ ( lam @ X1671 @ X1672 @ X1673 ) @ X1675 )
= ( X1673 @ X1675 ) ) ) )
=> ( ! [X1676: $i,X1677: $i,X1678: $i] :
( ( in @ X1678 @ ( funcSet @ X1676 @ X1677 ) )
=> ( ( lam @ X1676 @ X1677 @ ( ap @ X1676 @ X1677 @ X1678 ) )
= X1678 ) )
=> ( ! [X1679: $i,X1680: $o,X1681: $i] :
( ( in @ X1681 @ X1679 )
=> ! [X1682: $i] :
( ( in @ X1682 @ X1679 )
=> ( ~ X1680
=> ( in @ X1682
@ ( dsetconstr @ X1679
@ ^ [Z0: $i] :
( ( X1680
& ( Z0 = X1681 ) )
| ( ~ X1680
& ( Z0 = X1682 ) ) ) ) ) ) ) )
=> ( ! [X1683: $i,X1684: $o,X1685: $i] :
( ( in @ X1685 @ X1683 )
=> ! [X1686: $i] :
( ( in @ X1686 @ X1683 )
=> ( ~ X1684
=> ( ( dsetconstr @ X1683
@ ^ [Z0: $i] :
( ( X1684
& ( Z0 = X1685 ) )
| ( ~ X1684
& ( Z0 = X1686 ) ) ) )
= ( setadjoin @ X1686 @ emptyset ) ) ) ) )
=> ( ! [X1687: $i,X1688: $o,X1689: $i] :
( ( in @ X1689 @ X1687 )
=> ! [X1690: $i] :
( ( in @ X1690 @ X1687 )
=> ( X1688
=> ( in @ X1689
@ ( dsetconstr @ X1687
@ ^ [Z0: $i] :
( ( X1688
& ( Z0 = X1689 ) )
| ( ~ X1688
& ( Z0 = X1690 ) ) ) ) ) ) ) )
=> ( ! [X1691: $i,X1692: $o,X1693: $i] :
( ( in @ X1693 @ X1691 )
=> ! [X1694: $i] :
( ( in @ X1694 @ X1691 )
=> ( X1692
=> ( ( dsetconstr @ X1691
@ ^ [Z0: $i] :
( ( X1692
& ( Z0 = X1693 ) )
| ( ~ X1692
& ( Z0 = X1694 ) ) ) )
= ( setadjoin @ X1693 @ emptyset ) ) ) ) )
=> ( ! [X1695: $i,X1696: $o,X1697: $i] :
( ( in @ X1697 @ X1695 )
=> ! [X1698: $i] :
( ( in @ X1698 @ X1695 )
=> ( singleton
@ ( dsetconstr @ X1695
@ ^ [Z0: $i] :
( ( X1696
& ( Z0 = X1697 ) )
| ( ~ X1696
& ( Z0 = X1698 ) ) ) ) ) ) )
=> ( ! [X1699: $i,X1700: $o,X1701: $i] :
( ( in @ X1701 @ X1699 )
=> ! [X1702: $i] :
( ( in @ X1702 @ X1699 )
=> ( in @ ( if @ X1699 @ X1700 @ X1701 @ X1702 ) @ X1699 ) ) )
=> ( ! [X1703: $i] :
( ( singleton @ X1703 )
=> ! [X1704: $i] :
( ( in @ X1704 @ X1703 )
=> ( ( setunion @ X1703 )
= X1704 ) ) )
=> ( ! [X1705: $i,X1706: $o,X1707: $i] :
( ( in @ X1707 @ X1705 )
=> ! [X1708: $i] :
( ( in @ X1708 @ X1705 )
=> ( X1706
=> ( ( if @ X1705 @ X1706 @ X1707 @ X1708 )
= X1707 ) ) ) )
=> ( ! [X1709: $i,X1710: $o,X1711: $i] :
( ( in @ X1711 @ X1709 )
=> ! [X1712: $i] :
( ( in @ X1712 @ X1709 )
=> ( ~ X1710
=> ( ( if @ X1709 @ X1710 @ X1711 @ X1712 )
= X1712 ) ) ) )
=> ( ! [X1713: $i,X1714: $o,X1715: $i] :
( ( in @ X1715 @ X1713 )
=> ! [X1716: $i] :
( ( in @ X1716 @ X1713 )
=> ( in @ ( if @ X1713 @ X1714 @ X1715 @ X1716 ) @ ( setadjoin @ X1715 @ ( setadjoin @ X1716 @ emptyset ) ) ) ) )
=> ( ! [X1717: $i,X1718: $i] :
( ( in @ X1718 @ ( powerset @ X1717 ) )
=> ! [X1719: $i] :
( ( in @ X1719 @ ( powerset @ X1717 ) )
=> ( in @ ( binintersect @ X1718 @ X1719 ) @ ( powerset @ X1717 ) ) ) )
=> ( ! [X1720: $i,X1721: $i] :
( ( in @ X1721 @ ( powerset @ X1720 ) )
=> ! [X1722: $i] :
( ( in @ X1722 @ ( powerset @ X1720 ) )
=> ( in @ ( binunion @ X1721 @ X1722 ) @ ( powerset @ X1720 ) ) ) )
=> ( ! [X1723: $i,X1724: $i] :
( ( in @ X1724 @ ( powerset @ X1723 ) )
=> ( in @ ( powerset @ X1724 ) @ ( powerset @ ( powerset @ X1723 ) ) ) )
=> ( ! [X1725: $i,X1726: $i] :
( ( in @ X1726 @ ( powerset @ X1725 ) )
=> ! [X1727: $i] :
( ( in @ X1727 @ ( powerset @ X1725 ) )
=> ( in @ ( setminus @ X1726 @ X1727 ) @ ( powerset @ X1725 ) ) ) )
=> ( ! [X1728: $i,X1729: $i] :
( ( in @ X1729 @ ( powerset @ X1728 ) )
=> ( in @ ( setminus @ X1728 @ X1729 ) @ ( powerset @ X1728 ) ) )
=> ( ! [X1730: $i,X1731: $i] :
( ( in @ X1731 @ ( powerset @ X1730 ) )
=> ! [X1732: $i] :
( ( in @ X1732 @ ( powerset @ X1730 ) )
=> ( ! [X1733: $i] :
( ( in @ X1733 @ X1730 )
=> ( ( in @ X1733 @ X1731 )
=> ( in @ X1733 @ X1732 ) ) )
=> ( ! [X1734: $i] :
( ( in @ X1734 @ X1730 )
=> ( ( in @ X1734 @ X1732 )
=> ( in @ X1734 @ X1731 ) ) )
=> ( X1731 = X1732 ) ) ) ) )
=> ( ! [X1735: $i,X1736: $i] :
( ( in @ X1736 @ ( powerset @ X1735 ) )
=> ! [X1737: $i] :
( ( in @ X1737 @ ( powerset @ X1735 ) )
=> ( ! [X1738: $i] :
( ( in @ X1738 @ X1735 )
=> ( ( in @ X1738 @ X1736 )
=> ( in @ X1738 @ X1737 ) ) )
=> ( subset @ X1736 @ X1737 ) ) ) )
=> ( ! [X1739: $i,X1740: $i] :
( ( in @ X1740 @ ( powerset @ X1739 ) )
=> ! [X1741: $i] :
( ( in @ X1741 @ ( powerset @ X1739 ) )
=> ( ! [X1742: $i] :
( ( in @ X1742 @ X1739 )
=> ( ( in @ X1742 @ X1740 )
=> ( in @ X1742 @ X1741 ) ) )
=> ( in @ X1740 @ ( powerset @ X1741 ) ) ) ) )
=> ( ! [X1743: $i,X1744: $i] :
( ( in @ X1744 @ ( powerset @ X1743 ) )
=> ! [X1745: $i] :
( ( in @ X1745 @ ( powerset @ X1743 ) )
=> ! [X1746: $i] :
( ( in @ X1746 @ X1743 )
=> ( ( in @ X1744 @ ( powerset @ X1745 ) )
=> ( ( in @ X1746 @ X1744 )
=> ( in @ X1746 @ X1745 ) ) ) ) ) )
=> ( ! [X1747: $i,X1748: $i] :
( ( in @ X1748 @ ( powerset @ X1747 ) )
=> ! [X1749: $i] :
( ( in @ X1749 @ X1747 )
=> ( ( in @ X1749 @ X1748 )
=> ~ ( in @ X1749 @ ( setminus @ X1747 @ X1748 ) ) ) ) )
=> ( ! [X1750: $i,X1751: $i] :
( ( in @ X1751 @ ( powerset @ X1750 ) )
=> ! [X1752: $i] :
( ( in @ X1752 @ X1750 )
=> ( ~ ( in @ X1752 @ ( setminus @ X1750 @ X1751 ) )
=> ( in @ X1752 @ X1751 ) ) ) )
=> ( ! [X1753: $i,X1754: $i] :
( ( in @ X1754 @ ( powerset @ X1753 ) )
=> ! [X1755: $i] :
( ( in @ X1755 @ ( powerset @ X1753 ) )
=> ! [X1756: $i] :
( ( in @ X1756 @ X1753 )
=> ( ~ ( in @ X1756 @ X1754 )
=> ~ ( in @ X1756 @ ( binintersect @ X1754 @ X1755 ) ) ) ) ) )
=> ( ! [X1757: $i,X1758: $i] :
( ( in @ X1758 @ ( powerset @ X1757 ) )
=> ! [X1759: $i] :
( ( in @ X1759 @ ( powerset @ X1757 ) )
=> ! [X1760: $i] :
( ( in @ X1760 @ X1757 )
=> ( ~ ( in @ X1760 @ X1759 )
=> ~ ( in @ X1760 @ ( binintersect @ X1758 @ X1759 ) ) ) ) ) )
=> ( ! [X1761: $i,X1762: $i] :
( ( in @ X1762 @ ( powerset @ X1761 ) )
=> ! [X1763: $i] :
( ( in @ X1763 @ ( powerset @ X1761 ) )
=> ! [X1764: $i] :
( ( in @ X1764 @ X1761 )
=> ( ( subset @ X1762 @ ( setminus @ X1761 @ X1763 ) )
=> ( ( in @ X1764 @ X1763 )
=> ~ ( in @ X1764 @ X1762 ) ) ) ) ) )
=> ( ! [X1765: $i,X1766: $i] :
( ( in @ X1766 @ ( powerset @ X1765 ) )
=> ! [X1767: $i] :
( ( in @ X1767 @ ( powerset @ X1765 ) )
=> ! [X1768: $i] :
( ( in @ X1768 @ X1765 )
=> ( ( subset @ X1766 @ X1767 )
=> ( ~ ( in @ X1768 @ X1767 )
=> ~ ( in @ X1768 @ X1766 ) ) ) ) ) )
=> ( ! [X1769: $i,X1770: $i] :
( ( in @ X1770 @ ( powerset @ X1769 ) )
=> ! [X1771: $i] :
( ( in @ X1771 @ ( powerset @ X1769 ) )
=> ( ( subset @ X1770 @ X1771 )
=> ( subset @ ( setminus @ X1769 @ X1771 ) @ ( setminus @ X1769 @ X1770 ) ) ) ) )
=> ( ! [X1772: $i,X1773: $i] :
( ( in @ X1773 @ ( powerset @ X1772 ) )
=> ! [X1774: $i] :
( ( in @ X1774 @ ( powerset @ X1772 ) )
=> ( ( subset @ ( setminus @ X1772 @ X1774 ) @ ( setminus @ X1772 @ X1773 ) )
=> ( subset @ X1773 @ X1774 ) ) ) )
=> ( ! [X1775: $i,X1776: $i] :
( ( in @ X1776 @ ( powerset @ X1775 ) )
=> ! [X1777: $i] :
( ( in @ X1777 @ X1775 )
=> ( ( in @ X1777 @ X1776 )
=> ( in @ X1777 @ ( setminus @ X1775 @ ( setminus @ X1775 @ X1776 ) ) ) ) ) )
=> ( ! [X1778: $i,X1779: $i] :
( ( in @ X1779 @ ( powerset @ X1778 ) )
=> ! [X1780: $i] :
( ( in @ X1780 @ X1778 )
=> ( ( in @ X1780 @ ( setminus @ X1778 @ ( setminus @ X1778 @ X1779 ) ) )
=> ( in @ X1780 @ X1779 ) ) ) )
=> ( ! [X1781: $i,X1782: $i] :
( ( in @ X1782 @ ( powerset @ X1781 ) )
=> ( subset @ X1782 @ ( setminus @ X1781 @ ( setminus @ X1781 @ X1782 ) ) ) )
=> ( ! [X1783: $i,X1784: $i] :
( ( in @ X1784 @ ( powerset @ X1783 ) )
=> ( subset @ ( setminus @ X1783 @ ( setminus @ X1783 @ X1784 ) ) @ X1784 ) )
=> ( ! [X1785: $i,X1786: $i] :
( ( in @ X1786 @ ( powerset @ X1785 ) )
=> ( X1786
= ( setminus @ X1785 @ ( setminus @ X1785 @ X1786 ) ) ) )
=> ( ! [X1787: $i,X1788: $i] :
( ( in @ X1788 @ ( powerset @ X1787 ) )
=> ! [X1789: $i] :
( ( in @ X1789 @ ( powerset @ X1787 ) )
=> ! [X1790: $i] :
( ( in @ X1790 @ X1787 )
=> ( ( in @ X1790 @ ( setminus @ X1787 @ X1788 ) )
=> ~ ( in @ X1790 @ ( binintersect @ X1788 @ X1789 ) ) ) ) ) )
=> ( ! [X1791: $i,X1792: $i] :
( ( in @ X1792 @ ( powerset @ X1791 ) )
=> ! [X1793: $i] :
( ( in @ X1793 @ ( powerset @ X1791 ) )
=> ! [X1794: $i] :
( ( in @ X1794 @ X1791 )
=> ( ( in @ X1794 @ ( setminus @ X1791 @ X1792 ) )
=> ( in @ X1794 @ ( setminus @ X1791 @ ( binintersect @ X1792 @ X1793 ) ) ) ) ) ) )
=> ( ! [X1795: $i,X1796: $i] :
( ( in @ X1796 @ ( powerset @ X1795 ) )
=> ! [X1797: $i] :
( ( in @ X1797 @ ( powerset @ X1795 ) )
=> ( subset @ ( setminus @ X1795 @ X1796 ) @ ( setminus @ X1795 @ ( binintersect @ X1796 @ X1797 ) ) ) ) )
=> ( ! [X1798: $i,X1799: $i] :
( ( in @ X1799 @ ( powerset @ X1798 ) )
=> ! [X1800: $i] :
( ( in @ X1800 @ ( powerset @ X1798 ) )
=> ( in @ ( setminus @ X1798 @ X1799 ) @ ( powerset @ ( setminus @ X1798 @ ( binintersect @ X1799 @ X1800 ) ) ) ) ) )
=> ( ! [X1801: $i,X1802: $i] :
( ( in @ X1802 @ ( powerset @ X1801 ) )
=> ! [X1803: $i] :
( ( in @ X1803 @ ( powerset @ X1801 ) )
=> ( ( subset @ X1802 @ ( setminus @ X1801 @ X1803 ) )
=> ! [X1804: $i] :
( ( in @ X1804 @ X1801 )
=> ( ( in @ X1804 @ X1803 )
=> ( in @ X1804 @ ( setminus @ X1801 @ X1802 ) ) ) ) ) ) )
=> ( ! [X1805: $i,X1806: $i] :
( ( in @ X1806 @ ( powerset @ X1805 ) )
=> ! [X1807: $i] :
( ( in @ X1807 @ ( powerset @ X1805 ) )
=> ( ( subset @ X1806 @ ( setminus @ X1805 @ X1807 ) )
=> ( subset @ X1807 @ ( setminus @ X1805 @ X1806 ) ) ) ) )
=> ( ! [X1808: $i,X1809: $i] :
( ( in @ X1809 @ ( powerset @ X1808 ) )
=> ! [X1810: $i] :
( ( in @ X1810 @ ( powerset @ X1808 ) )
=> ! [X1811: $i] :
( ( in @ X1811 @ X1808 )
=> ( ~ ( in @ X1811 @ ( binunion @ X1809 @ X1810 ) )
=> ~ ( in @ X1811 @ X1809 ) ) ) ) )
=> ( ! [X1812: $i,X1813: $i] :
( ( in @ X1813 @ ( powerset @ X1812 ) )
=> ! [X1814: $i] :
( ( in @ X1814 @ ( powerset @ X1812 ) )
=> ! [X1815: $i] :
( ( in @ X1815 @ X1812 )
=> ( ~ ( in @ X1815 @ ( binunion @ X1813 @ X1814 ) )
=> ~ ( in @ X1815 @ X1814 ) ) ) ) )
=> ( ! [X1816: $i,X1817: $i] :
( ( in @ X1817 @ ( powerset @ X1816 ) )
=> ! [X1818: $i] :
( ( in @ X1818 @ ( powerset @ X1816 ) )
=> ! [X1819: $i] :
( ( in @ X1819 @ ( powerset @ X1816 ) )
=> ! [X1820: $i] :
( ( in @ X1820 @ X1816 )
=> ( ( in @ X1820 @ ( binintersect @ X1817 @ X1818 ) )
=> ( in @ X1820 @ ( binunion @ X1817 @ X1819 ) ) ) ) ) ) )
=> ( ! [X1821: $i,X1822: $i] :
( ( in @ X1822 @ ( powerset @ X1821 ) )
=> ! [X1823: $i] :
( ( in @ X1823 @ ( powerset @ X1821 ) )
=> ! [X1824: $i] :
( ( in @ X1824 @ ( powerset @ X1821 ) )
=> ! [X1825: $i] :
( ( in @ X1825 @ X1821 )
=> ( ( in @ X1825 @ ( binintersect @ X1822 @ X1823 ) )
=> ( in @ X1825 @ ( binunion @ X1823 @ X1824 ) ) ) ) ) ) )
=> ( ! [X1826: $i,X1827: $i] :
( ( in @ X1827 @ ( powerset @ X1826 ) )
=> ! [X1828: $i] :
( ( in @ X1828 @ ( powerset @ X1826 ) )
=> ! [X1829: $i] :
( ( in @ X1829 @ ( powerset @ X1826 ) )
=> ! [X1830: $i] :
( ( in @ X1830 @ X1826 )
=> ( ( in @ X1830 @ ( binintersect @ X1827 @ X1828 ) )
=> ( in @ X1830 @ ( binintersect @ ( binunion @ X1827 @ X1829 ) @ ( binunion @ X1828 @ X1829 ) ) ) ) ) ) ) )
=> ( ! [X1831: $i,X1832: $i] :
( ( in @ X1832 @ ( powerset @ X1831 ) )
=> ! [X1833: $i] :
( ( in @ X1833 @ ( powerset @ X1831 ) )
=> ! [X1834: $i] :
( ( in @ X1834 @ ( powerset @ X1831 ) )
=> ( in @ ( binintersect @ X1832 @ X1833 ) @ ( powerset @ ( binintersect @ ( binunion @ X1832 @ X1834 ) @ ( binunion @ X1833 @ X1834 ) ) ) ) ) ) )
=> ( ! [X1835: $i,X1836: $i] :
( ( in @ X1836 @ ( powerset @ X1835 ) )
=> ! [X1837: $i] :
( ( in @ X1837 @ ( powerset @ X1835 ) )
=> ! [X1838: $i] :
( ( in @ X1838 @ X1835 )
=> ( ( in @ X1838 @ ( setminus @ X1835 @ ( binunion @ X1836 @ X1837 ) ) )
=> ~ ( in @ X1838 @ X1836 ) ) ) ) )
=> ( ! [X1839: $i,X1840: $i] :
( ( in @ X1840 @ ( powerset @ X1839 ) )
=> ! [X1841: $i] :
( ( in @ X1841 @ ( powerset @ X1839 ) )
=> ! [X1842: $i] :
( ( in @ X1842 @ X1839 )
=> ( ( in @ X1842 @ ( setminus @ X1839 @ ( binunion @ X1840 @ X1841 ) ) )
=> ( in @ X1842 @ ( setminus @ X1839 @ X1840 ) ) ) ) ) )
=> ( ! [X1843: $i,X1844: $i] :
( ( in @ X1844 @ ( powerset @ X1843 ) )
=> ! [X1845: $i] :
( ( in @ X1845 @ ( powerset @ X1843 ) )
=> ! [X1846: $o,X1847: $i] :
( ( in @ X1847 @ X1843 )
=> ( ( in @ X1847 @ ( binunion @ X1844 @ X1845 ) )
=> ( ( ( in @ X1847 @ X1844 )
=> X1846 )
=> ( ( ( in @ X1847 @ X1845 )
=> X1846 )
=> X1846 ) ) ) ) ) )
=> ( ! [X1848: $i,X1849: $i] :
( ( in @ X1849 @ ( powerset @ X1848 ) )
=> ! [X1850: $i] :
( ( in @ X1850 @ ( powerset @ X1848 ) )
=> ! [X1851: $i] :
( ( in @ X1851 @ X1848 )
=> ( ~ ( in @ X1851 @ X1849 )
=> ( ~ ( in @ X1851 @ X1850 )
=> ~ ( in @ X1851 @ ( binunion @ X1849 @ X1850 ) ) ) ) ) ) )
=> ( ! [X1852: $i,X1853: $i] :
( ( in @ X1853 @ ( powerset @ X1852 ) )
=> ! [X1854: $i] :
( ( in @ X1854 @ ( powerset @ X1852 ) )
=> ! [X1855: $i] :
( ( in @ X1855 @ X1852 )
=> ( ( in @ X1855 @ ( setminus @ X1852 @ ( binunion @ X1853 @ X1854 ) ) )
=> ( in @ X1855 @ ( setminus @ X1852 @ X1853 ) ) ) ) ) )
=> ( ! [X1856: $i,X1857: $i] :
( ( in @ X1857 @ ( powerset @ X1856 ) )
=> ! [X1858: $i] :
( ( in @ X1858 @ ( powerset @ X1856 ) )
=> ( in @ ( setminus @ X1856 @ ( binunion @ X1857 @ X1858 ) ) @ ( powerset @ ( setminus @ X1856 @ X1857 ) ) ) ) )
=> ( ! [X1859: $i,X1860: $i] :
( ( in @ X1860 @ ( powerset @ X1859 ) )
=> ! [X1861: $i] :
( ( in @ X1861 @ ( powerset @ X1859 ) )
=> ! [X1862: $i] :
( ( in @ X1862 @ X1859 )
=> ( ( in @ X1862 @ ( setminus @ X1859 @ ( binunion @ X1860 @ X1861 ) ) )
=> ( in @ X1862 @ ( setminus @ X1859 @ X1861 ) ) ) ) ) )
=> ( ! [X1863: $i,X1864: $i] :
( ( in @ X1864 @ ( powerset @ X1863 ) )
=> ! [X1865: $i] :
( ( in @ X1865 @ ( powerset @ X1863 ) )
=> ! [X1866: $i] :
( ( in @ X1866 @ X1863 )
=> ( ( in @ X1866 @ ( setminus @ X1863 @ ( binintersect @ X1864 @ X1865 ) ) )
=> ( in @ X1866 @ ( binunion @ ( setminus @ X1863 @ X1864 ) @ ( setminus @ X1863 @ X1865 ) ) ) ) ) ) )
=> ( ! [X1867: $i,X1868: $i] :
( ( in @ X1868 @ ( powerset @ X1867 ) )
=> ! [X1869: $i] :
( ( in @ X1869 @ ( powerset @ X1867 ) )
=> ! [X1870: $i] :
( ( in @ X1870 @ X1867 )
=> ( ( in @ X1870 @ ( binunion @ ( setminus @ X1867 @ X1868 ) @ ( setminus @ X1867 @ X1869 ) ) )
=> ( in @ X1870 @ ( setminus @ X1867 @ ( binintersect @ X1868 @ X1869 ) ) ) ) ) ) )
=> ( ! [X1871: $i,X1872: $i] :
( ( in @ X1872 @ ( powerset @ X1871 ) )
=> ! [X1873: $i] :
( ( in @ X1873 @ ( powerset @ X1871 ) )
=> ( ( setminus @ X1871 @ ( binintersect @ X1872 @ X1873 ) )
= ( binunion @ ( setminus @ X1871 @ X1872 ) @ ( setminus @ X1871 @ X1873 ) ) ) ) )
=> ( ! [X1874: $i,X1875: $i] :
( ( in @ X1875 @ ( powerset @ X1874 ) )
=> ! [X1876: $i] :
( ( in @ X1876 @ ( powerset @ X1874 ) )
=> ! [X1877: $i] :
( ( in @ X1877 @ X1874 )
=> ( ( in @ X1877 @ ( setminus @ X1874 @ ( binunion @ X1875 @ X1876 ) ) )
=> ( in @ X1877 @ ( binintersect @ ( setminus @ X1874 @ X1875 ) @ ( setminus @ X1874 @ X1876 ) ) ) ) ) ) )
=> ( ! [X1878: $i,X1879: $i] :
( ( in @ X1879 @ ( powerset @ X1878 ) )
=> ! [X1880: $i] :
( ( in @ X1880 @ ( powerset @ X1878 ) )
=> ! [X1881: $i] :
( ( in @ X1881 @ X1878 )
=> ( ( in @ X1881 @ ( setminus @ X1878 @ X1879 ) )
=> ( ( in @ X1881 @ ( setminus @ X1878 @ X1880 ) )
=> ( in @ X1881 @ ( setminus @ X1878 @ ( binunion @ X1879 @ X1880 ) ) ) ) ) ) ) )
=> ( ! [X1882: $i,X1883: $i] :
( ( in @ X1883 @ ( powerset @ X1882 ) )
=> ! [X1884: $i] :
( ( in @ X1884 @ ( powerset @ X1882 ) )
=> ! [X1885: $i] :
( ( in @ X1885 @ X1882 )
=> ( ( in @ X1885 @ ( binintersect @ ( setminus @ X1882 @ X1883 ) @ ( setminus @ X1882 @ X1884 ) ) )
=> ( in @ X1885 @ ( setminus @ X1882 @ ( binunion @ X1883 @ X1884 ) ) ) ) ) ) )
=> ( ! [X1886: $i,X1887: $i] :
( ( in @ X1887 @ ( powerset @ X1886 ) )
=> ! [X1888: $i] :
( ( in @ X1888 @ ( powerset @ X1886 ) )
=> ( ( setminus @ X1886 @ ( binunion @ X1887 @ X1888 ) )
= ( binintersect @ ( setminus @ X1886 @ X1887 ) @ ( setminus @ X1886 @ X1888 ) ) ) ) )
=> ( ! [X1889: $i,X1890: $i] :
( ( in @ X1890 @ ( powerset @ X1889 ) )
=> ! [X1891: $i] :
( ( in @ X1891 @ ( powerset @ X1889 ) )
=> ! [X1892: $i] :
( ( in @ X1892 @ ( binintersect @ X1890 @ X1891 ) )
=> ( in @ X1892 @ X1889 ) ) ) )
=> ( ! [X1893: $i,X1894: $i] :
( ( in @ X1894 @ ( powerset @ X1893 ) )
=> ! [X1895: $i] :
( ( in @ X1895 @ ( powerset @ X1893 ) )
=> ! [X1896: $i] :
( ( in @ X1896 @ ( powerset @ X1893 ) )
=> ( ( subset @ X1894 @ X1896 )
=> ( subset @ ( binintersect @ X1894 @ X1895 ) @ X1896 ) ) ) ) )
=> ( ! [X1897: $i,X1898: $i] :
( ( in @ X1898 @ ( powerset @ X1897 ) )
=> ! [X1899: $i] :
( ( in @ X1899 @ ( powerset @ X1897 ) )
=> ! [X1900: $i] :
( ( in @ X1900 @ ( powerset @ X1897 ) )
=> ( ( subset @ X1899 @ X1900 )
=> ( subset @ ( binintersect @ X1898 @ X1899 ) @ X1900 ) ) ) ) )
=> ( ! [X1901: $i,X1902: $i] :
( ( in @ X1902 @ ( powerset @ X1901 ) )
=> ! [X1903: $i] :
( ( in @ X1903 @ ( powerset @ X1901 ) )
=> ! [X1904: $i] :
( ( in @ X1904 @ ( powerset @ X1901 ) )
=> ( ( subset @ X1902 @ X1903 )
=> ( ( subset @ X1902 @ X1904 )
=> ( subset @ X1902 @ ( binintersect @ X1903 @ X1904 ) ) ) ) ) ) )
=> ( ! [X1905: $i,X1906: $i] :
( ( in @ X1906 @ ( powerset @ X1905 ) )
=> ! [X1907: $i] :
( ( in @ X1907 @ ( powerset @ X1905 ) )
=> ! [X1908: $i] :
( ( in @ X1908 @ ( powerset @ X1905 ) )
=> ! [X1909: $i] :
( ( in @ X1909 @ ( powerset @ X1905 ) )
=> ( ( subset @ X1906 @ X1908 )
=> ( ( subset @ X1907 @ X1909 )
=> ( subset @ ( binintersect @ X1906 @ X1907 ) @ ( binintersect @ X1908 @ X1909 ) ) ) ) ) ) ) )
=> ( ! [X1910: $i,X1911: $i] :
( ( in @ X1911 @ ( powerset @ X1910 ) )
=> ! [X1912: $i] :
( ( in @ X1912 @ ( powerset @ X1910 ) )
=> ( in @ ( setminus @ X1910 @ X1911 ) @ ( powerset @ ( setminus @ X1910 @ ( binintersect @ X1911 @ X1912 ) ) ) ) ) )
=> ( ! [X1913: $i,X1914: $i] :
( ( in @ X1914 @ ( powerset @ X1913 ) )
=> ! [X1915: $i] :
( ( in @ X1915 @ ( powerset @ X1913 ) )
=> ! [X1916: $i] :
( ( in @ X1916 @ ( powerset @ X1913 ) )
=> ! [X1917: $i] :
( ( in @ X1917 @ ( powerset @ X1913 ) )
=> ( ( setminus @ X1913 @ ( binintersect @ ( binunion @ X1914 @ X1915 ) @ ( binunion @ X1916 @ X1917 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1913 @ X1914 ) @ ( setminus @ X1913 @ X1915 ) ) @ ( binintersect @ ( setminus @ X1913 @ X1916 ) @ ( setminus @ X1913 @ X1917 ) ) ) ) ) ) ) )
=> ( ! [X1918: $i,X1919: $i] :
( ( in @ X1919 @ ( powerset @ X1918 ) )
=> ! [X1920: $i] :
( ( in @ X1920 @ ( powerset @ X1918 ) )
=> ! [X1921: $i] :
( ( in @ X1921 @ ( powerset @ X1918 ) )
=> ( in @ ( binintersect @ X1919 @ X1920 ) @ ( powerset @ ( binintersect @ ( binunion @ X1919 @ X1921 ) @ ( binunion @ X1920 @ X1921 ) ) ) ) ) ) )
=> ( ! [X1922: $i,X1923: $i] :
( ( in @ X1923 @ ( powerset @ X1922 ) )
=> ! [X1924: $i] :
( ( in @ X1924 @ ( powerset @ X1922 ) )
=> ( ( subset @ X1923 @ ( setminus @ X1922 @ X1924 ) )
=> ( subset @ X1924 @ ( setminus @ X1922 @ X1923 ) ) ) ) )
=> ( ! [X1925: $i,X1926: $i] :
( ( in @ X1926 @ ( powerset @ X1925 ) )
=> ! [X1927: $i] :
( ( in @ X1927 @ ( powerset @ X1925 ) )
=> ( in @ ( setminus @ X1925 @ ( binunion @ X1926 @ X1927 ) ) @ ( powerset @ ( setminus @ X1925 @ X1926 ) ) ) ) )
=> ! [X4: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X4 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1all2]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_313]),foundationAx]),wellorderingAx]),c_0_314]),c_0_315]),c_0_316]),c_0_317]),c_0_318]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_319]),setext]),emptyI]),noeltsimpempty]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_324]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_325]),c_0_326]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_327]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_328]),c_0_329]),c_0_330]),inCongP]),in__Cong]),c_0_331]),c_0_332]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_333]),c_0_334]),c_0_335]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_336]),c_0_337]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_338]),c_0_339]),c_0_340]),c_0_341]),singletonsuniq]),setukpairinjL1]),c_0_342]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_343]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_344]),c_0_345]),c_0_346]),c_0_347]),c_0_348]),c_0_349]),c_0_350]),c_0_351]),c_0_352]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_353]),c_0_354]),c_0_355]),c_0_356]),c_0_357]),c_0_358]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_359]),c_0_360]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_361]),c_0_362]),c_0_363]),c_0_364]),c_0_365]),c_0_366]),c_0_367]),c_0_368]),c_0_369]),c_0_370]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),setminusT_lem]),complementT_lem]),setextT]),subsetTI]),powersetTI1]),powersetTE1]),complementTI1]),complementTE1]),binintersectTELcontra]),binintersectTERcontra]),contrasubsetT]),contrasubsetT1]),contrasubsetT2]),contrasubsetT3]),doubleComplementI1]),doubleComplementE1]),doubleComplementSub1]),doubleComplementSub2]),doubleComplementEq]),complementTnotintersectT]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),complementInPowersetComplementIntersect]),contraSubsetComplement]),complementTcontraSubset]),binunionTILcontra]),binunionTIRcontra]),inIntersectImpInUnion]),inIntersectImpInUnion2]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),inComplementUnionImpNotIn1]),inComplementUnionImpInComplement1]),binunionTE]),binunionTEcontra]),demorgan2a1]),complementUnionInPowersetComplement]),demorgan2a2]),demorgan1a]),demorgan1b]),demorgan1]),demorgan2a]),demorgan2b2]),demorgan2b]),demorgan2]),woz13rule0]),woz13rule1]),woz13rule2]),woz13rule3]),woz13rule4]),woz1_1]),woz1_2]),woz1_3]),woz1_4]),woz1_5]),c_0_371])])]),c_0_372]) ).
thf(c_0_374,negated_conjecture,
! 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$i,X2045: $i,X2046: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i > $o,X2065: $i,X2066: $i > $o,X2067: $i,X2068: $i,X2069: $i > $o,X2070: $i,X2072: $i,X2073: $i > $o,X2075: $i,X2076: $i,X2077: $i > $o,X2079: $i,X2080: $i,X2081: $i > $o,X2082: $i,X2084: $o,X2085: $o,X2086: $i,X2087: $i > $o,X2089: $i,X2090: $i,X2091: $i > $o,X2092: $i,X2094: $i > $o,X2095: $i,X2098: $i,X2099: $i > $o,X2100: $i,X2104: $i,X2105: $i > $o,X2106: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i > $o,X2119: $i,X2121: $i,X2122: $i,X2123: $i > $o,X2124: $i > $o,X2127: $i,X2130: $i,X2131: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i > $o,X2144: $i,X2146: $i,X2147: $i,X2148: $i > $o,X2149: $i > $o,X2152: $i,X2154: $i,X2156: $i,X2157: $i,X2158: $i > $o,X2159: $i > $o,X2162: 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$o,X2370: $i,X2371: $i > $o,X2372: $i,X2374: $i,X2375: $i > $o,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 > $i > $o,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i > $i > $o,X2456: $i,X2457: $i,X2458: $i > $i > $o,X2459: $i,X2460: $i,X2461: $i > $i > $o,X2462: $i,X2463: $i,X2464: $i,X2465: $i,X2466: $i > $i > $o,X2467: $i,X2468: $i,X2469: $i,X2470: $i,X2471: $i > $i > $o,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i > $i > $o,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2490: $i,X2491: $i,X2492: $i,X2493: $i,X2494: $i,X2495: $i,X2496: $i,X2497: $i,X2498: $i,X2499: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i > $i,X2505: $i,X2506: $i,X2507: $i > $i,X2509: $i,X2510: $i,X2511: $i > $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i > $o,X2519: $i,X2520: $i,X2521: $i,X2522: $i,X2523: $i > $o,X2526: $i,X2527: $i,X2528: $i > $o,X2529: $i,X2530: $i,X2531: $i,X2532: $i,X2533: $i,X2534: $i,X2535: $i,X2536: $i,X2537: $i,X2538: $i,X2539: $i,X2540: $i,X2541: $i,X2542: $i,X2543: $i,X2544: $i,X2545: $i,X2546: $i,X2547: $i,X2549: $i,X2550: $i,X2551: $i,X2552: $i,X2553: $i,X2554: $i,X2555: $i,X2556: $i,X2557: $i,X2558: $i,X2559: $i,X2562: $i,X2563: $i,X2564: $i,X2565: $i,X2570: $i,X2571: $i,X2572: $i,X2573: $i,X2575: $i,X2576: 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( ( ~ ( in @ ( esk1_2 @ X1928 @ X1929 ) @ X1928 )
| ~ ( in @ ( esk1_2 @ X1928 @ X1929 ) @ X1929 )
| ( X1928 = X1929 ) )
& ( ( in @ ( esk1_2 @ X1928 @ X1929 ) @ X1928 )
| ( in @ ( esk1_2 @ X1928 @ X1929 ) @ X1929 )
| ( X1928 = X1929 ) )
& ~ ( in @ X1931 @ emptyset )
& ( ~ ( in @ X1934 @ ( setadjoin @ X1932 @ X1933 ) )
| ( X1934 = X1932 )
| ( in @ X1934 @ X1933 ) )
& ( ( X1934 != X1932 )
| ( in @ X1934 @ ( setadjoin @ X1932 @ X1933 ) ) )
& ( ~ ( in @ X1934 @ X1933 )
| ( in @ X1934 @ ( setadjoin @ X1932 @ X1933 ) ) )
& ( ~ ( in @ X1936 @ ( powerset @ X1935 ) )
| ~ ( in @ X1937 @ X1936 )
| ( in @ X1937 @ X1935 ) )
& ( ( in @ ( esk2_2 @ X1938 @ X1939 ) @ X1939 )
| ( in @ X1939 @ ( powerset @ X1938 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1938 @ X1939 ) @ X1938 )
| ( in @ X1939 @ ( powerset @ X1938 ) ) )
& ( ( in @ X1942 @ ( esk3_2 @ X1941 @ X1942 ) )
| ~ ( in @ X1942 @ ( setunion @ X1941 ) ) )
& ( ( in @ ( esk3_2 @ X1941 @ X1942 ) @ X1941 )
| ~ ( in @ X1942 @ ( setunion @ X1941 ) ) )
& ( ~ ( in @ X1945 @ X1946 )
| ~ ( in @ X1946 @ X1944 )
| ( in @ X1945 @ ( setunion @ X1944 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1947 @ omega )
| ( in @ ( setadjoin @ X1947 @ X1947 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1948 ) @ omega )
| ~ ( in @ emptyset @ X1948 )
| ~ ( in @ X1950 @ omega )
| ( in @ X1950 @ X1948 ) )
& ( ( in @ ( esk4_1 @ X1948 ) @ X1948 )
| ~ ( in @ emptyset @ X1948 )
| ~ ( in @ X1950 @ omega )
| ( in @ X1950 @ X1948 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1948 ) @ ( esk4_1 @ X1948 ) ) @ X1948 )
| ~ ( in @ emptyset @ X1948 )
| ~ ( in @ X1950 @ omega )
| ( in @ X1950 @ X1948 ) )
& ( ( in @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1952 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( in @ ( esk5_2 @ X1951 @ X1952 ) @ X1952 ) )
& ( ( X1951 @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1957 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( in @ ( esk5_2 @ X1951 @ X1952 ) @ X1952 ) )
& ( ~ ( in @ X1960 @ X1952 )
| ~ ( X1951 @ X1960 @ X1959 )
| ( in @ X1959 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( in @ ( esk5_2 @ X1951 @ X1952 ) @ X1952 ) )
& ( ( in @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1952 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ( X1951 @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1957 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ~ ( in @ X1960 @ X1952 )
| ~ ( X1951 @ X1960 @ X1959 )
| ( in @ X1959 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ( in @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1952 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1954
!= ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ( X1951 @ ( esk8_3 @ X1951 @ X1952 @ X1957 ) @ X1957 )
| ~ ( in @ X1957 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1954
!= ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ~ ( in @ X1960 @ X1952 )
| ~ ( X1951 @ X1960 @ X1959 )
| ( in @ X1959 @ ( esk7_2 @ X1951 @ X1952 ) )
| ( X1954
!= ( esk6_3 @ X1951 @ X1952 @ X1954 ) )
| ~ ( X1951 @ ( esk5_2 @ X1951 @ X1952 ) @ X1954 ) )
& ( ( in @ ( esk9_1 @ X1961 ) @ X1961 )
| ~ ( in @ X1962 @ X1961 ) )
& ( ~ ( in @ X1964 @ ( esk9_1 @ X1961 ) )
| ~ ( in @ X1964 @ X1961 )
| ~ ( in @ X1962 @ X1961 ) )
& epred1_0
& ( ( X1965 @ ( esk10_2 @ X1965 @ X1966 ) )
| ~ ( X1965 @ X1966 )
| ( X1965 @ ( descr @ X1965 ) ) )
& ( ( X1966
!= ( esk10_2 @ X1965 @ X1966 ) )
| ~ ( X1965 @ X1966 )
| ( X1965 @ ( descr @ X1965 ) ) )
& ( ~ ( in @ X1970 @ X1968 )
| ~ ( X1969 @ X1970 )
| ( in @ X1970 @ ( dsetconstr @ X1968 @ X1969 ) ) )
& ( ~ ( in @ X1973 @ ( dsetconstr @ X1971 @ X1972 ) )
| ( in @ X1973 @ X1971 ) )
& ( ~ ( in @ X1976 @ ( dsetconstr @ X1974 @ X1975 ) )
| ( X1975 @ X1976 ) )
& ( ( X1977 @ ( esk12_1 @ X1977 ) )
| ( X1977 @ ( esk11_2 @ X1977 @ X1978 ) )
| ~ ( X1977 @ X1978 ) )
& ( ~ ( X1977 @ X1981 )
| ( ( esk12_1 @ X1977 )
= X1981 )
| ( X1977 @ ( esk11_2 @ X1977 @ X1978 ) )
| ~ ( X1977 @ X1978 ) )
& ( ( X1977 @ ( esk12_1 @ X1977 ) )
| ( X1978
!= ( esk11_2 @ X1977 @ X1978 ) )
| ~ ( X1977 @ X1978 ) )
& ( ~ ( X1977 @ X1981 )
| ( ( esk12_1 @ X1977 )
= X1981 )
| ( X1978
!= ( esk11_2 @ X1977 @ X1978 ) )
| ~ ( X1977 @ X1978 ) )
& ( ~ ( in @ X1983 @ ( prop2set @ X1982 ) )
| X1982 )
& ( ~ ( in @ X1984 @ emptyset )
| X1985 )
& ( ~ ( in @ X1986 @ emptyset )
| ~ $true )
& ~ ( in @ X1987 @ emptyset )
& ( ( X1988 @ ( esk13_2 @ X1988 @ X1989 ) )
| ~ ( X1988 @ X1989 )
| ( X1988 @ ( esk14_1 @ X1988 ) ) )
& ( ( X1989
!= ( esk13_2 @ X1988 @ X1989 ) )
| ~ ( X1988 @ X1989 )
| ( X1988 @ ( esk14_1 @ X1988 ) ) )
& ( ( in @ ( esk16_2 @ X1992 @ X1993 ) @ X1993 )
| ( X1992 = X1993 )
| ( in @ ( esk15_2 @ X1992 @ X1993 ) @ X1992 ) )
& ( ~ ( in @ ( esk16_2 @ X1992 @ X1993 ) @ X1992 )
| ( X1992 = X1993 )
| ( in @ ( esk15_2 @ X1992 @ X1993 ) @ X1992 ) )
& ( ( in @ ( esk16_2 @ X1992 @ X1993 ) @ X1993 )
| ( X1992 = X1993 )
| ~ ( in @ ( esk15_2 @ X1992 @ X1993 ) @ X1993 ) )
& ( ~ ( in @ ( esk16_2 @ X1992 @ X1993 ) @ X1992 )
| ( X1992 = X1993 )
| ~ ( in @ ( esk15_2 @ X1992 @ X1993 ) @ X1993 ) )
& ( ( in @ ( esk17_1 @ X1996 ) @ X1996 )
| ( X1996 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1998 ) @ X1998 )
| ( X1998 = emptyset ) )
& ( ~ ( in @ X2002 @ ( dsetconstr @ X2000 @ X2001 ) )
| ( X2001 @ X2002 )
| ~ ( in @ X2002 @ X2000 ) )
& ( ~ ( X2001 @ X2002 )
| ( in @ X2002 @ ( dsetconstr @ X2000 @ X2001 ) )
| ~ ( in @ X2002 @ X2000 ) )
& ( ( X2003 = emptyset )
| ( in @ ( esk19_1 @ X2003 ) @ X2003 ) )
& ( ~ ( in @ X2007 @ X2005 )
| ~ ( X2006 @ X2007 )
| ( ( dsetconstr @ X2005 @ X2006 )
!= emptyset ) )
& ( ~ ( in @ X2009 @ X2008 )
| ( X2008 != emptyset ) )
& ( in @ X2010 @ ( setadjoin @ X2010 @ X2011 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X2014 @ X2013 )
| ( in @ X2014 @ ( setadjoin @ X2012 @ X2013 ) ) )
& ( ( in @ X2017 @ X2016 )
| X2018
| ( X2017 = X2015 )
| ~ ( in @ X2017 @ ( setadjoin @ X2015 @ X2016 ) ) )
& ( ~ X2018
| X2018
| ( X2017 = X2015 )
| ~ ( in @ X2017 @ ( setadjoin @ X2015 @ X2016 ) ) )
& ( ( in @ X2017 @ X2016 )
| X2018
| ~ X2018
| ~ ( in @ X2017 @ ( setadjoin @ X2015 @ X2016 ) ) )
& ( ~ X2018
| X2018
| ~ X2018
| ~ ( in @ X2017 @ ( setadjoin @ X2015 @ X2016 ) ) )
& ( ~ ( in @ X2021 @ ( setadjoin @ X2019 @ X2020 ) )
| ( X2021 = X2019 )
| ( in @ X2021 @ X2020 ) )
& ( ( dsetconstr @ X2022
@ ^ [Z0: $i] : $true )
= X2022 )
& ( ( in @ ( esk20_2 @ X2023 @ X2024 ) @ X2024 )
| ( in @ X2024 @ ( powerset @ X2023 ) ) )
& ( ~ ( in @ ( esk20_2 @ X2023 @ X2024 ) @ X2023 )
| ( in @ X2024 @ ( powerset @ X2023 ) ) )
& ( in @ emptyset @ ( powerset @ X2026 ) )
& ( in @ emptyset @ ( powerset @ X2027 ) )
& ( ~ ( in @ X2029 @ ( powerset @ X2028 ) )
| ~ ( in @ X2030 @ X2029 )
| ( in @ X2030 @ X2028 ) )
& ( ~ ( in @ X2032 @ X2033 )
| ~ ( in @ X2033 @ X2031 )
| ( in @ X2032 @ ( setunion @ X2031 ) ) )
& ( ( in @ X2035 @ ( esk21_3 @ X2034 @ X2035 @ X2036 ) )
| X2036
| ~ ( in @ X2035 @ ( setunion @ X2034 ) ) )
& ( ( in @ ( esk21_3 @ X2034 @ X2035 @ X2036 ) @ X2034 )
| X2036
| ~ ( in @ X2035 @ ( setunion @ X2034 ) ) )
& ( ~ X2036
| X2036
| ~ ( in @ X2035 @ ( setunion @ X2034 ) ) )
& ( ~ ( in @ X2039 @ X2038 )
| ( in @ X2039 @ ( powerset @ ( setunion @ X2038 ) ) ) )
& ( ~ ( X2040 @ X2044 )
| ( X2044
= ( esk23_1 @ X2040 ) )
| ( X2040 @ ( esk22_2 @ X2040 @ X2041 ) )
| ~ ( X2040 @ X2041 ) )
& ( ( X2045
!= ( esk23_1 @ X2040 ) )
| ( X2040 @ X2045 )
| ( X2040 @ ( esk22_2 @ X2040 @ X2041 ) )
| ~ ( X2040 @ X2041 ) )
& ( ~ ( X2040 @ X2044 )
| ( X2044
= ( esk23_1 @ X2040 ) )
| ( X2041
!= ( esk22_2 @ X2040 @ X2041 ) )
| ~ ( X2040 @ X2041 ) )
& ( ( X2045
!= ( esk23_1 @ X2040 ) )
| ( X2040 @ X2045 )
| ( X2041
!= ( esk22_2 @ X2040 @ X2041 ) )
| ~ ( X2040 @ X2041 ) )
& ( ( in @ ( esk24_1 @ X2046 ) @ X2046 )
| ( X2046 = emptyset ) )
& ( $true
| ( X2046 = emptyset ) )
& ( ~ ( in @ X2048 @ ( setadjoin @ X2049 @ emptyset ) )
| ( X2048 = X2049 ) )
& ( ( X2050 = X2051 )
| ~ ( in @ X2051 @ ( setadjoin @ X2050 @ emptyset ) ) )
& ( ( X2052 != X2053 )
| ( in @ X2052 @ ( setadjoin @ X2053 @ emptyset ) ) )
& ( ~ ( in @ X2054 @ ( setadjoin @ X2055 @ emptyset ) )
| ( in @ X2055 @ ( setadjoin @ X2054 @ emptyset ) ) )
& ( ~ ( in @ X2058 @ ( setadjoin @ X2056 @ ( setadjoin @ X2057 @ emptyset ) ) )
| ( X2058 = X2056 )
| ( X2058 = X2057 ) )
& ( in @ X2059 @ ( setadjoin @ X2059 @ ( setadjoin @ X2060 @ emptyset ) ) )
& ( in @ X2062 @ ( setadjoin @ X2061 @ ( setadjoin @ X2062 @ emptyset ) ) )
& ( ~ ( in @ X2065 @ X2063 )
| ~ ( X2064 @ X2065 )
| ( ( dsetconstr @ X2063 @ X2064 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X2067 @ emptyset )
| ( X2066 @ X2067 ) )
& ( ( in @ ( esk25_2 @ X2068 @ X2069 ) @ X2068 )
| ~ ( in @ X2070 @ X2068 )
| ( X2069 @ X2070 ) )
& ( ~ ( X2069 @ ( esk25_2 @ X2068 @ X2069 ) )
| ~ ( in @ X2070 @ X2068 )
| ( X2069 @ X2070 ) )
& ( ( in @ ( esk26_2 @ X2072 @ X2073 ) @ X2072 )
| ~ ( in @ X2075 @ X2072 )
| ~ ( X2073 @ X2075 ) )
& ( ( X2073 @ ( esk26_2 @ X2072 @ X2073 ) )
| ~ ( in @ X2075 @ X2072 )
| ~ ( X2073 @ X2075 ) )
& ( ( in @ ( esk27_2 @ X2076 @ X2077 ) @ X2076 )
| ~ ( in @ X2079 @ X2076 )
| ~ ( X2077 @ X2079 ) )
& ( ( X2077 @ ( esk27_2 @ X2076 @ X2077 ) )
| ~ ( in @ X2079 @ X2076 )
| ~ ( X2077 @ X2079 ) )
& ( ( in @ ( esk28_2 @ X2080 @ X2081 ) @ X2080 )
| ~ ( in @ X2082 @ X2080 )
| ( X2081 @ X2082 ) )
& ( ~ ( X2081 @ ( esk28_2 @ X2080 @ X2081 ) )
| ~ ( in @ X2082 @ X2080 )
| ( X2081 @ X2082 ) )
& ( ~ X2084
| ( in @ emptyset @ ( prop2set @ X2084 ) ) )
& ( ~ X2085
| ( set2prop @ ( prop2set @ X2085 ) ) )
& ( ( in @ ( esk29_2 @ X2086 @ X2087 ) @ X2086 )
| ~ ( in @ X2089 @ X2086 )
| ~ ( X2087 @ X2089 ) )
& ( ( X2087 @ ( esk29_2 @ X2086 @ X2087 ) )
| ~ ( in @ X2089 @ X2086 )
| ~ ( X2087 @ X2089 ) )
& ( ( in @ ( esk30_2 @ X2090 @ X2091 ) @ X2090 )
| ~ ( in @ X2092 @ X2090 )
| ( X2091 @ X2092 ) )
& ( ~ ( X2091 @ ( esk30_2 @ X2090 @ X2091 ) )
| ~ ( in @ X2092 @ X2090 )
| ( X2091 @ X2092 ) )
& ( ( X2094 @ ( esk32_1 @ X2094 ) )
| ( X2094 @ ( esk31_2 @ X2094 @ X2095 ) )
| ~ ( X2094 @ X2095 ) )
& ( ~ ( X2094 @ X2098 )
| ( ( esk32_1 @ X2094 )
= X2098 )
| ( X2094 @ ( esk31_2 @ X2094 @ X2095 ) )
| ~ ( X2094 @ X2095 ) )
& ( ( X2094 @ ( esk32_1 @ X2094 ) )
| ( X2095
!= ( esk31_2 @ X2094 @ X2095 ) )
| ~ ( X2094 @ X2095 ) )
& ( ~ ( X2094 @ X2098 )
| ( ( esk32_1 @ X2094 )
= X2098 )
| ( X2095
!= ( esk31_2 @ X2094 @ X2095 ) )
| ~ ( X2094 @ X2095 ) )
& ( ( X2099 @ ( esk35_1 @ X2099 ) )
| ( X2099 @ ( esk33_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ~ ( X2099 @ X2104 )
| ( ( esk35_1 @ X2099 )
= X2104 )
| ( X2099 @ ( esk33_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ( X2099 @ ( esk35_1 @ X2099 ) )
| ( X2099 @ ( esk34_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ~ ( X2099 @ X2104 )
| ( ( esk35_1 @ X2099 )
= X2104 )
| ( X2099 @ ( esk34_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ( X2099 @ ( esk35_1 @ X2099 ) )
| ( ( esk33_1 @ X2099 )
!= ( esk34_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ~ ( X2099 @ X2104 )
| ( ( esk35_1 @ X2099 )
= X2104 )
| ( ( esk33_1 @ X2099 )
!= ( esk34_1 @ X2099 ) )
| ~ ( X2099 @ X2100 ) )
& ( ( X2105 @ ( esk37_1 @ X2105 ) )
| ~ ( X2105 @ ( esk36_2 @ X2105 @ X2106 ) )
| ( ( esk36_2 @ X2105 @ X2106 )
!= X2106 ) )
& ( ~ ( X2105 @ X2109 )
| ( ( esk37_1 @ X2105 )
= X2109 )
| ~ ( X2105 @ ( esk36_2 @ X2105 @ X2106 ) )
| ( ( esk36_2 @ X2105 @ X2106 )
!= X2106 ) )
& ( ( X2105 @ ( esk37_1 @ X2105 ) )
| ( X2105 @ ( esk36_2 @ X2105 @ X2106 ) )
| ( ( esk36_2 @ X2105 @ X2106 )
= X2106 ) )
& ( ~ ( X2105 @ X2109 )
| ( ( esk37_1 @ X2105 )
= X2109 )
| ( X2105 @ ( esk36_2 @ X2105 @ X2106 ) )
| ( ( esk36_2 @ X2105 @ X2106 )
= X2106 ) )
& ( ( X2110 != X2111 )
| ( X2112 != X2113 )
| ~ ( in @ X2112 @ X2110 )
| ( in @ X2113 @ X2111 ) )
& ( ~ ( in @ X2116 @ X2114 )
| ( in @ X2117 @ X2115 )
| ( X2116 != X2117 )
| ( X2114 != X2115 ) )
& ( ~ ( in @ X2117 @ X2115 )
| ( in @ X2116 @ X2114 )
| ( X2116 != X2117 )
| ( X2114 != X2115 ) )
& ( ( X2118 @ ( esk38_2 @ X2118 @ X2119 ) )
| ~ ( X2118 @ X2119 )
| ~ ( X2118 @ X2121 )
| ~ ( X2118 @ X2122 )
| ( X2121 = X2122 ) )
& ( ( X2119
!= ( esk38_2 @ X2118 @ X2119 ) )
| ~ ( X2118 @ X2119 )
| ~ ( X2118 @ X2121 )
| ~ ( X2118 @ X2122 )
| ( X2121 = X2122 ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( ( esk39_2 @ X2123 @ X2124 )
= ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ~ ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ~ ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2123 @ ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2124 @ ( esk42_2 @ X2123 @ X2124 ) )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2124 @ X2130 )
| ( ( esk42_2 @ X2123 @ X2124 )
= X2130 )
| ( X2127
!= ( esk41_3 @ X2123 @ X2124 @ X2127 ) )
| ~ ( X2123 @ X2127 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2124 @ ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ( X2123 @ ( esk44_2 @ X2123 @ X2124 ) )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( ~ ( X2123 @ X2134 )
| ( ( esk44_2 @ X2123 @ X2124 )
= X2134 )
| ( X2131
!= ( esk43_3 @ X2123 @ X2124 @ X2131 ) )
| ~ ( X2124 @ X2131 )
| ( X2123 @ ( esk39_2 @ X2123 @ X2124 ) )
| ( X2124 @ ( esk40_2 @ X2123 @ X2124 ) ) )
& ( emptyset = emptyset )
& ( ( X2135 != X2136 )
| ( X2137 != X2138 )
| ( ( setadjoin @ X2135 @ X2137 )
= ( setadjoin @ X2136 @ X2138 ) ) )
& ( ( X2139 != X2140 )
| ( ( powerset @ X2139 )
= ( powerset @ X2140 ) ) )
& ( ( X2141 != X2142 )
| ( ( setunion @ X2141 )
= ( setunion @ X2142 ) ) )
& ( omega = omega )
& ( ( X2143 @ ( esk45_2 @ X2143 @ X2144 ) )
| ~ ( X2143 @ X2144 )
| ~ ( X2143 @ X2146 )
| ~ ( X2143 @ X2147 )
| ( X2146 = X2147 ) )
& ( ( X2144
!= ( esk45_2 @ X2143 @ X2144 ) )
| ~ ( X2143 @ X2144 )
| ~ ( X2143 @ X2146 )
| ~ ( X2143 @ X2147 )
| ( X2146 = X2147 ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( ( esk46_2 @ X2148 @ X2149 )
= ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( ( esk46_2 @ X2148 @ X2149 )
= ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( ( esk46_2 @ X2148 @ X2149 )
= ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( ( esk46_2 @ X2148 @ X2149 )
= ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ~ ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ~ ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ~ ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ~ ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ~ ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ~ ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ~ ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ~ ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2148 @ ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2149 @ ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( X2154
!= ( esk49_3 @ X2148 @ X2149 @ X2154 ) )
| ~ ( X2149 @ X2154 )
| ( ( descr @ X2148 )
= ( descr @ X2149 ) )
| ( X2152
!= ( esk48_3 @ X2148 @ X2149 @ X2152 ) )
| ~ ( X2148 @ X2152 )
| ( X2148 @ ( esk46_2 @ X2148 @ X2149 ) )
| ( X2149 @ ( esk47_2 @ X2148 @ X2149 ) ) )
& ( ( in @ ( esk50_4 @ X2156 @ X2157 @ X2158 @ X2159 ) @ X2156 )
| ( ( dsetconstr @ X2156 @ X2158 )
= ( dsetconstr @ X2157 @ X2159 ) )
| ( X2156 != X2157 ) )
& ( ( in @ ( esk51_4 @ X2156 @ X2157 @ X2158 @ X2159 ) @ X2157 )
| ( ( dsetconstr @ X2156 @ X2158 )
= ( dsetconstr @ X2157 @ X2159 ) )
| ( X2156 != X2157 ) )
& ( ( ( esk50_4 @ X2156 @ X2157 @ X2158 @ X2159 )
= ( esk51_4 @ X2156 @ X2157 @ X2158 @ X2159 ) )
| ( ( dsetconstr @ X2156 @ X2158 )
= ( dsetconstr @ X2157 @ X2159 ) )
| ( X2156 != X2157 ) )
& ( ~ ( X2158 @ ( esk50_4 @ X2156 @ X2157 @ X2158 @ X2159 ) )
| ~ ( X2159 @ ( esk51_4 @ X2156 @ X2157 @ X2158 @ X2159 ) )
| ( ( dsetconstr @ X2156 @ X2158 )
= ( dsetconstr @ X2157 @ X2159 ) )
| ( X2156 != X2157 ) )
& ( ( X2158 @ ( esk50_4 @ X2156 @ X2157 @ X2158 @ X2159 ) )
| ( X2159 @ ( esk51_4 @ X2156 @ X2157 @ X2158 @ X2159 ) )
| ( ( dsetconstr @ X2156 @ X2158 )
= ( dsetconstr @ X2157 @ X2159 ) )
| ( X2156 != X2157 ) )
& ( ( in @ ( esk52_2 @ X2162 @ X2163 ) @ X2162 )
| ( subset @ X2162 @ X2163 ) )
& ( ~ ( in @ ( esk52_2 @ X2162 @ X2163 ) @ X2163 )
| ( subset @ X2162 @ X2163 ) )
& ( ( X2165 != X2166 )
| ( subset @ X2166 @ X2165 ) )
& ( ( X2167 != X2168 )
| ( subset @ X2167 @ X2168 ) )
& ( ( in @ ( esk53_2 @ X2169 @ X2170 ) @ X2169 )
| ( subset @ X2169 @ X2170 ) )
& ( ~ ( in @ ( esk53_2 @ X2169 @ X2170 ) @ X2170 )
| ( subset @ X2169 @ X2170 ) )
& ( subset @ emptyset @ X2172 )
& ( ~ ( subset @ X2173 @ X2174 )
| ~ ( in @ X2175 @ X2173 )
| ( in @ X2175 @ X2174 ) )
& ( ~ ( subset @ X2176 @ X2177 )
| ( in @ X2178 @ X2177 )
| ~ ( in @ X2178 @ X2176 ) )
& ( ~ ( in @ X2181 @ X2179 )
| ( in @ X2181 @ X2180 )
| ~ ( subset @ X2179 @ X2180 ) )
& ( ( subset @ X2182 @ X2183 )
| ( X2182 != X2183 ) )
& ( ~ ( in @ X2186 @ X2184 )
| ( in @ X2186 @ X2185 )
| ( X2184 != X2185 ) )
& ( subset @ X2187 @ X2187 )
& ( ~ ( subset @ X2188 @ X2189 )
| ~ ( subset @ X2189 @ X2190 )
| ( subset @ X2188 @ X2190 ) )
& ( subset @ X2192 @ ( setadjoin @ X2191 @ X2192 ) )
& ( ~ ( subset @ X2193 @ X2195 )
| ( subset @ X2193 @ ( setadjoin @ X2194 @ X2195 ) ) )
& ( ~ ( subset @ X2196 @ X2197 )
| ( in @ X2196 @ ( powerset @ X2197 ) ) )
& ( ~ ( subset @ X2198 @ X2199 )
| ~ ( subset @ X2199 @ X2198 )
| ( X2198 = X2199 ) )
& ( ~ ( subset @ X2200 @ emptyset )
| ( X2200 = emptyset ) )
& ( ~ ( subset @ X2202 @ X2201 )
| ( in @ X2202 @ ( powerset @ X2201 ) ) )
& ( ~ ( in @ X2204 @ ( powerset @ X2203 ) )
| ( subset @ X2204 @ X2203 ) )
& ( in @ X2205 @ ( powerset @ X2205 ) )
& ( ~ ( subset @ X2206 @ X2207 )
| ( subset @ ( powerset @ X2206 ) @ ( powerset @ X2207 ) ) )
& ( in @ ( dsetconstr @ X2208 @ X2209 ) @ ( powerset @ X2208 ) )
& ( subset @ ( dsetconstr @ X2210 @ X2211 ) @ X2210 )
& ( ~ ( in @ X2214 @ X2212 )
| ( in @ X2214 @ ( binunion @ X2212 @ X2213 ) ) )
& ( in @ X2216 @ ( setadjoin @ X2215 @ ( setadjoin @ X2216 @ emptyset ) ) )
& ( ~ ( in @ X2219 @ X2218 )
| ( in @ X2219 @ ( binunion @ X2217 @ X2218 ) ) )
& ( ( in @ X2222 @ X2221 )
| X2223
| ( in @ X2222 @ X2220 )
| ~ ( in @ X2222 @ ( binunion @ X2220 @ X2221 ) ) )
& ( ~ X2223
| X2223
| ( in @ X2222 @ X2220 )
| ~ ( in @ X2222 @ ( binunion @ X2220 @ X2221 ) ) )
& ( ( in @ X2222 @ X2221 )
| X2223
| ~ X2223
| ~ ( in @ X2222 @ ( binunion @ X2220 @ X2221 ) ) )
& ( ~ X2223
| X2223
| ~ X2223
| ~ ( in @ X2222 @ ( binunion @ X2220 @ X2221 ) ) )
& ( ~ ( in @ X2226 @ ( binunion @ X2224 @ X2225 ) )
| ( in @ X2226 @ X2224 )
| ( in @ X2226 @ X2225 ) )
& ( subset @ X2227 @ ( binunion @ X2227 @ X2228 ) )
& ( subset @ X2230 @ ( binunion @ X2229 @ X2230 ) )
& ( ~ ( in @ X2233 @ X2231 )
| ~ ( in @ X2233 @ X2232 )
| ( in @ X2233 @ ( binintersect @ X2231 @ X2232 ) ) )
& ( ~ ( subset @ X2236 @ X2234 )
| ~ ( subset @ X2236 @ X2235 )
| ( subset @ X2236 @ ( binintersect @ X2234 @ X2235 ) ) )
& ( ~ ( in @ X2239 @ ( binintersect @ X2237 @ X2238 ) )
| ( in @ X2239 @ X2237 ) )
& ( subset @ ( binintersect @ X2240 @ X2241 ) @ X2240 )
& ( ~ ( subset @ X2242 @ X2243 )
| ( ( binintersect @ X2242 @ X2243 )
= X2242 ) )
& ( ( ( binintersect @ X2244 @ X2245 )
!= X2245 )
| ( subset @ X2245 @ X2244 ) )
& ( ~ ( in @ X2248 @ ( binintersect @ X2246 @ X2247 ) )
| ( in @ X2248 @ X2247 ) )
& ( ( in @ ( esk54_2 @ X2249 @ X2250 ) @ X2249 )
| ( ( binintersect @ X2249 @ X2250 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X2249 @ X2250 ) @ X2250 )
| ( ( binintersect @ X2249 @ X2250 )
= emptyset ) )
& ( subset @ ( binintersect @ X2252 @ X2253 ) @ X2253 )
& ( ~ ( subset @ X2255 @ X2254 )
| ( ( binintersect @ X2254 @ X2255 )
= X2255 ) )
& ( ( ( binintersect @ X2256 @ X2257 )
!= X2256 )
| ( subset @ X2256 @ X2257 ) )
& ( ( binintersect @ X2258 @ ( binunion @ X2259 @ X2260 ) )
= ( binunion @ ( binintersect @ X2258 @ X2259 ) @ ( binintersect @ X2258 @ X2260 ) ) )
& ( ~ ( in @ X2263 @ X2261 )
| ( in @ X2263 @ X2262 )
| ( in @ X2263 @ ( setminus @ X2261 @ X2262 ) ) )
& ( ~ ( in @ X2266 @ ( setminus @ X2264 @ X2265 ) )
| ( in @ X2266 @ X2264 ) )
& ( ~ ( in @ X2269 @ ( setminus @ X2267 @ X2268 ) )
| ~ ( in @ X2269 @ X2268 ) )
& ( ~ ( subset @ X2270 @ X2271 )
| ( ( setminus @ X2270 @ X2271 )
= emptyset ) )
& ( ( in @ X2274 @ ( setminus @ X2272 @ X2273 ) )
| ~ ( in @ X2274 @ X2272 )
| ( in @ X2274 @ X2273 ) )
& ( ( in @ X2277 @ ( setminus @ X2275 @ X2276 ) )
| ( in @ X2277 @ X2276 )
| ~ ( in @ X2277 @ X2275 ) )
& ( ( in @ X2280 @ X2278 )
| ~ ( in @ X2280 @ ( setminus @ X2278 @ X2279 ) ) )
& ( ~ ( in @ X2283 @ X2282 )
| ~ ( in @ X2283 @ ( setminus @ X2281 @ X2282 ) ) )
& ( subset @ ( setminus @ X2284 @ X2285 ) @ X2284 )
& ( ( ( setminus @ X2286 @ X2287 )
!= emptyset )
| ( subset @ X2286 @ X2287 ) )
& ( ~ ( in @ X2290 @ X2288 )
| X2291
| ( in @ X2290 @ X2288 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ( in @ X2290 @ X2289 )
| X2291
| ( in @ X2290 @ X2288 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ X2291
| X2291
| ( in @ X2290 @ X2288 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ ( in @ X2290 @ X2288 )
| X2291
| ~ ( in @ X2290 @ X2289 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ( in @ X2290 @ X2289 )
| X2291
| ~ ( in @ X2290 @ X2289 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ X2291
| X2291
| ~ ( in @ X2290 @ X2289 )
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ ( in @ X2290 @ X2288 )
| X2291
| ~ X2291
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ( in @ X2290 @ X2289 )
| X2291
| ~ X2291
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ X2291
| X2291
| ~ X2291
| ~ ( in @ X2290 @ ( symdiff @ X2288 @ X2289 ) ) )
& ( ~ ( in @ X2294 @ X2292 )
| ( in @ X2294 @ X2293 )
| ( in @ X2294 @ ( symdiff @ X2292 @ X2293 ) ) )
& ( ( in @ X2297 @ X2295 )
| ~ ( in @ X2297 @ X2296 )
| ( in @ X2297 @ ( symdiff @ X2295 @ X2296 ) ) )
& ( ~ ( in @ X2300 @ X2298 )
| ~ ( in @ X2300 @ X2299 )
| ~ ( in @ X2300 @ ( symdiff @ X2298 @ X2299 ) ) )
& ( ( in @ X2303 @ X2301 )
| ( in @ X2303 @ X2302 )
| ~ ( in @ X2303 @ ( symdiff @ X2301 @ X2302 ) ) )
& ( in @ X2305 @ ( setadjoin @ X2304 @ ( setadjoin @ X2305 @ emptyset ) ) )
& ( in @ X2306 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2306 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2306 @ ( setadjoin @ X2307 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2309 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2308 @ ( setadjoin @ X2309 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2310 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2310 @ ( setadjoin @ X2311 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2312 @ X2313 ) )
& ( ~ ( in @ X2315 @ X2314 )
| ( subset @ ( setadjoin @ X2315 @ emptyset ) @ X2314 ) )
& ( ~ ( in @ X2317 @ X2316 )
| ( in @ ( setadjoin @ X2317 @ emptyset ) @ ( powerset @ X2316 ) ) )
& ( ~ ( in @ X2320 @ X2318 )
| ( in @ ( setadjoin @ X2320 @ emptyset ) @ ( powerset @ ( binunion @ X2318 @ X2319 ) ) ) )
& ( ~ ( in @ X2323 @ ( setadjoin @ X2321 @ ( setadjoin @ X2322 @ emptyset ) ) )
| ( X2323 = X2321 )
| ( X2323 = X2322 ) )
& ( ~ ( in @ X2326 @ X2324 )
| ~ ( in @ X2327 @ X2325 )
| ( subset @ ( setadjoin @ X2326 @ ( setadjoin @ X2327 @ emptyset ) ) @ ( binunion @ X2324 @ X2325 ) ) )
& ( ~ ( in @ X2330 @ X2328 )
| ~ ( in @ X2331 @ X2329 )
| ( in @ ( setadjoin @ X2330 @ ( setadjoin @ X2331 @ emptyset ) ) @ ( powerset @ ( binunion @ X2328 @ X2329 ) ) ) )
& ( ~ ( in @ X2334 @ X2332 )
| ~ ( in @ X2335 @ X2333 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2334 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2334 @ ( setadjoin @ X2335 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2332 @ X2333 ) ) ) )
& ( ~ ( in @ X2338 @ X2336 )
| ~ ( in @ X2339 @ X2337 )
| ( in @ ( setadjoin @ ( setadjoin @ X2338 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2338 @ ( setadjoin @ X2339 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2336 @ X2337 ) ) ) ) )
& ( ~ ( in @ X2342 @ X2340 )
| ~ ( in @ X2343 @ X2341 )
| ( in @ ( kpair @ X2342 @ X2343 ) @ ( powerset @ ( powerset @ ( binunion @ X2340 @ X2341 ) ) ) ) )
& ( ~ ( in @ X2346 @ X2344 )
| ~ ( in @ X2347 @ X2345 )
| ( in @ ( kpair @ X2346 @ X2347 ) @ ( cartprod @ X2344 @ X2345 ) ) )
& ( ( in @ ( esk55_3 @ X2348 @ X2349 @ X2350 ) @ X2348 )
| ~ ( in @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ( in @ ( esk56_3 @ X2348 @ X2349 @ X2350 ) @ X2349 )
| ~ ( in @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ( X2350
= ( kpair @ ( esk55_3 @ X2348 @ X2349 @ X2350 ) @ ( esk56_3 @ X2348 @ X2349 @ X2350 ) ) )
| ~ ( in @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ~ ( in @ X2355 @ ( cartprod @ X2353 @ X2354 ) )
| ( iskpair @ X2355 ) )
& ( ( in @ ( esk57_2 @ X2356 @ X2357 ) @ X2356 )
| ~ ( in @ X2357 @ ( setunion @ X2356 ) ) )
& ( ( in @ X2357 @ ( esk57_2 @ X2356 @ X2357 ) )
| ~ ( in @ X2357 @ ( setunion @ X2356 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2359 @ emptyset ) ) @ X2359 )
& ( subset @ X2360 @ ( setunion @ ( setadjoin @ X2360 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2361 @ emptyset ) )
= X2361 )
& ( ( in @ ( esk58_2 @ X2362 @ X2363 ) @ X2362 )
| ~ ( in @ X2366 @ X2362 )
| ~ ( X2363 @ X2366 )
| ( singleton @ ( dsetconstr @ X2362 @ X2363 ) ) )
& ( ( in @ ( esk59_2 @ X2362 @ X2363 ) @ X2362 )
| ~ ( in @ X2366 @ X2362 )
| ~ ( X2363 @ X2366 )
| ( singleton @ ( dsetconstr @ X2362 @ X2363 ) ) )
& ( ( X2363 @ ( esk58_2 @ X2362 @ X2363 ) )
| ~ ( in @ X2366 @ X2362 )
| ~ ( X2363 @ X2366 )
| ( singleton @ ( dsetconstr @ X2362 @ X2363 ) ) )
& ( ( X2363 @ ( esk59_2 @ X2362 @ X2363 ) )
| ~ ( in @ X2366 @ X2362 )
| ~ ( X2363 @ X2366 )
| ( singleton @ ( dsetconstr @ X2362 @ X2363 ) ) )
& ( ( ( esk58_2 @ X2362 @ X2363 )
!= ( esk59_2 @ X2362 @ X2363 ) )
| ~ ( in @ X2366 @ X2362 )
| ~ ( X2363 @ X2366 )
| ( singleton @ ( dsetconstr @ X2362 @ X2363 ) ) )
& ( ( in @ ( esk60_2 @ X2367 @ X2368 ) @ X2367 )
| ~ ( singleton @ ( dsetconstr @ X2367 @ X2368 ) ) )
& ( ( X2368 @ ( esk60_2 @ X2367 @ X2368 ) )
| ~ ( singleton @ ( dsetconstr @ X2367 @ X2368 ) ) )
& ( ( in @ ( esk61_3 @ X2370 @ X2371 @ X2372 ) @ X2370 )
| ( singleton @ ( dsetconstr @ X2370 @ X2371 ) )
| ~ ( X2371 @ X2372 )
| ~ ( in @ X2372 @ X2370 ) )
& ( ( X2371 @ ( esk61_3 @ X2370 @ X2371 @ X2372 ) )
| ( singleton @ ( dsetconstr @ X2370 @ X2371 ) )
| ~ ( X2371 @ X2372 )
| ~ ( in @ X2372 @ X2370 ) )
& ( ( ( esk61_3 @ X2370 @ X2371 @ X2372 )
!= X2372 )
| ( singleton @ ( dsetconstr @ X2370 @ X2371 ) )
| ~ ( X2371 @ X2372 )
| ~ ( in @ X2372 @ X2370 ) )
& ( ( in @ ( esk62_2 @ X2374 @ X2375 ) @ X2374 )
| ~ ( in @ X2378 @ X2374 )
| ~ ( X2375 @ X2378 )
| ( singleton @ ( dsetconstr @ X2374 @ X2375 ) ) )
& ( ( in @ ( esk63_2 @ X2374 @ X2375 ) @ X2374 )
| ~ ( in @ X2378 @ X2374 )
| ~ ( X2375 @ X2378 )
| ( singleton @ ( dsetconstr @ X2374 @ X2375 ) ) )
& ( ( X2375 @ ( esk62_2 @ X2374 @ X2375 ) )
| ~ ( in @ X2378 @ X2374 )
| ~ ( X2375 @ X2378 )
| ( singleton @ ( dsetconstr @ X2374 @ X2375 ) ) )
& ( ( X2375 @ ( esk63_2 @ X2374 @ X2375 ) )
| ~ ( in @ X2378 @ X2374 )
| ~ ( X2375 @ X2378 )
| ( singleton @ ( dsetconstr @ X2374 @ X2375 ) ) )
& ( ( ( esk62_2 @ X2374 @ X2375 )
!= ( esk63_2 @ X2374 @ X2375 ) )
| ~ ( in @ X2378 @ X2374 )
| ~ ( X2375 @ X2378 )
| ( singleton @ ( dsetconstr @ X2374 @ X2375 ) ) )
& ( ( ( setadjoin @ X2379 @ emptyset )
!= ( setadjoin @ X2380 @ emptyset ) )
| ( X2379 = X2380 ) )
& ( ~ ( in @ ( setadjoin @ X2383 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2381 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2381 @ ( setadjoin @ X2382 @ emptyset ) ) @ emptyset ) ) )
| ( X2381 = X2383 ) )
& ( ~ ( iskpair @ X2384 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2384 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2384 ) ) ) )
& ( ~ ( singleton @ X2385 )
| ( in @ ( setunion @ X2385 ) @ X2385 ) )
& ( ( kfst @ ( kpair @ X2386 @ X2387 ) )
= X2386 )
& ( ~ ( in @ X2390 @ ( cartprod @ X2388 @ X2389 ) )
| ( in @ ( kfst @ X2390 ) @ X2388 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2391 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2391 @ ( setadjoin @ X2392 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2393 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2393 @ ( setadjoin @ X2394 @ emptyset ) ) @ emptyset ) ) )
| ( X2391 = X2393 ) )
& ( ( ( kpair @ X2395 @ X2396 )
!= ( kpair @ X2397 @ X2398 ) )
| ( X2395 = X2397 ) )
& ( ( X2399 != X2400 )
| ( ( setadjoin @ X2399 @ ( setadjoin @ X2400 @ emptyset ) )
= ( setadjoin @ X2399 @ emptyset ) ) )
& ( ( X2401 != X2402 )
| ( ( setadjoin @ ( setadjoin @ X2401 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2401 @ ( setadjoin @ X2402 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2401 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2403 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2403 @ ( setadjoin @ X2404 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2405 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2405 @ ( setadjoin @ X2406 @ emptyset ) ) @ emptyset ) ) )
| ( X2405 != X2406 )
| ( X2404 = X2406 ) )
& ( ( ( setadjoin @ X2407 @ ( setadjoin @ X2408 @ emptyset ) )
!= ( setadjoin @ X2409 @ emptyset ) )
| ( X2407 = X2408 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2410 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2410 @ ( setadjoin @ X2411 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2412 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2412 @ ( setadjoin @ X2413 @ emptyset ) ) @ emptyset ) ) )
| ( X2411 = X2413 ) )
& ( ( ( kpair @ X2414 @ X2415 )
!= ( kpair @ X2416 @ X2417 ) )
| ( X2415 = X2417 ) )
& ( ~ ( iskpair @ X2418 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2418 )
@ ^ [Z0: $i] :
( X2418
= ( kpair @ ( kfst @ X2418 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2419 @ X2420 ) )
= X2420 )
& ( ~ ( iskpair @ X2421 )
| ( ( kpair @ ( kfst @ X2421 ) @ ( ksnd @ X2421 ) )
= X2421 ) )
& ( ~ ( in @ X2424 @ ( cartprod @ X2422 @ X2423 ) )
| ( in @ ( ksnd @ X2424 ) @ X2423 ) )
& ( ~ ( in @ ( kpair @ X2427 @ X2428 ) @ ( cartprod @ X2425 @ X2426 ) )
| ( in @ X2427 @ X2425 ) )
& ( ~ ( in @ ( kpair @ X2431 @ X2432 ) @ ( cartprod @ X2429 @ X2430 ) )
| ( in @ X2432 @ X2430 ) )
& ( ~ ( in @ X2435 @ X2433 )
| ~ ( in @ X2436 @ X2434 )
| ( ( kpair @ X2435 @ X2436 )
= ( kpair @ X2435 @ X2436 ) ) )
& ( ~ ( in @ X2439 @ X2437 )
| ~ ( in @ X2440 @ X2438 )
| ( ( kfst @ ( kpair @ X2439 @ X2440 ) )
= X2439 ) )
& ( ~ ( in @ X2443 @ X2441 )
| ~ ( in @ X2444 @ X2442 )
| ( ( ksnd @ ( kpair @ X2443 @ X2444 ) )
= X2444 ) )
& ( ~ ( in @ X2447 @ ( cartprod @ X2445 @ X2446 ) )
| ( ( kpair @ ( kfst @ X2447 ) @ ( ksnd @ X2447 ) )
= X2447 ) )
& ( ~ ( in @ X2451 @ X2448 )
| ~ ( in @ X2452 @ X2449 )
| ~ ( X2450 @ X2451 @ X2452 )
| ( in @ ( kpair @ X2451 @ X2452 ) @ ( dpsetconstr @ X2448 @ X2449 @ X2450 ) ) )
& ( subset @ ( dpsetconstr @ X2453 @ X2454 @ X2455 ) @ ( cartprod @ X2453 @ X2454 ) )
& ( subset @ ( dpsetconstr @ X2456 @ X2457 @ X2458 ) @ ( cartprod @ X2456 @ X2457 ) )
& ( ~ ( in @ X2462 @ X2459 )
| ~ ( in @ X2463 @ X2460 )
| ~ ( in @ ( kpair @ X2462 @ X2463 ) @ ( dpsetconstr @ X2459 @ X2460 @ X2461 ) )
| ( X2461 @ X2462 @ X2463 ) )
& ( ~ ( in @ ( kpair @ X2467 @ X2468 ) @ ( dpsetconstr @ X2464 @ X2465 @ X2466 ) )
| ( in @ X2467 @ X2464 ) )
& ( ~ ( in @ ( kpair @ X2472 @ X2473 ) @ ( dpsetconstr @ X2469 @ X2470 @ X2471 ) )
| ( in @ X2473 @ X2470 ) )
& ( ~ ( in @ ( kpair @ X2477 @ X2478 ) @ ( dpsetconstr @ X2474 @ X2475 @ X2476 ) )
| ( X2476 @ X2477 @ X2478 ) )
& ( ~ ( func @ X2479 @ X2480 @ X2481 )
| ~ ( in @ X2482 @ X2479 )
| ( singleton
@ ( dsetconstr @ X2480
@ ^ [Z0: $i] : ( in @ ( kpair @ X2482 @ Z0 ) @ X2481 ) ) ) )
& ( ~ ( func @ X2483 @ X2484 @ X2485 )
| ~ ( in @ X2486 @ X2483 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2484
@ ^ [Z0: $i] : ( in @ ( kpair @ X2486 @ Z0 ) @ X2485 ) ) )
@ X2484 ) )
& ( ~ ( func @ X2487 @ X2488 @ X2489 )
| ~ ( in @ X2490 @ X2487 )
| ( in @ ( ap @ X2487 @ X2488 @ X2489 @ X2490 ) @ X2488 ) )
& ( ~ ( in @ X2493 @ ( funcSet @ X2491 @ X2492 ) )
| ( func @ X2491 @ X2492 @ X2493 ) )
& ( ~ ( in @ X2496 @ ( funcSet @ X2494 @ X2495 ) )
| ~ ( in @ X2497 @ X2494 )
| ( in @ ( ap @ X2494 @ X2495 @ X2496 @ X2497 ) @ X2495 ) )
& ( ~ ( func @ X2498 @ X2499 @ X2500 )
| ( in @ X2500 @ ( funcSet @ X2498 @ X2499 ) ) )
& ( ( in @ ( esk64_3 @ X2501 @ X2502 @ X2503 ) @ X2501 )
| ( func @ X2501 @ X2502
@ ( dpsetconstr @ X2501 @ X2502
@ ^ [Z0: $i] : ( $eq @ ( X2503 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2503 @ ( esk64_3 @ X2501 @ X2502 @ X2503 ) ) @ X2502 )
| ( func @ X2501 @ X2502
@ ( dpsetconstr @ X2501 @ X2502
@ ^ [Z0: $i] : ( $eq @ ( X2503 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2505 @ X2506 @ X2507 ) @ X2505 )
| ( func @ X2505 @ X2506 @ ( lam @ X2505 @ X2506 @ X2507 ) ) )
& ( ~ ( in @ ( X2507 @ ( esk65_3 @ X2505 @ X2506 @ X2507 ) ) @ X2506 )
| ( func @ X2505 @ X2506 @ ( lam @ X2505 @ X2506 @ X2507 ) ) )
& ( ( in @ ( esk66_3 @ X2509 @ X2510 @ X2511 ) @ X2509 )
| ( in @ ( lam @ X2509 @ X2510 @ X2511 ) @ ( funcSet @ X2509 @ X2510 ) ) )
& ( ~ ( in @ ( X2511 @ ( esk66_3 @ X2509 @ X2510 @ X2511 ) ) @ X2510 )
| ( in @ ( lam @ X2509 @ X2510 @ X2511 ) @ ( funcSet @ X2509 @ X2510 ) ) )
& ( ( in @ ( esk67_4 @ X2513 @ X2514 @ X2515 @ X2516 ) @ X2513 )
| ~ ( in @ X2519 @ X2515 )
| ( X2516 @ X2519 )
| ~ ( subset @ X2515 @ ( cartprod @ X2513 @ X2514 ) ) )
& ( ( in @ ( esk68_4 @ X2513 @ X2514 @ X2515 @ X2516 ) @ X2514 )
| ~ ( in @ X2519 @ X2515 )
| ( X2516 @ X2519 )
| ~ ( subset @ X2515 @ ( cartprod @ X2513 @ X2514 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2513 @ X2514 @ X2515 @ X2516 ) @ ( esk68_4 @ X2513 @ X2514 @ X2515 @ X2516 ) ) @ X2515 )
| ~ ( in @ X2519 @ X2515 )
| ( X2516 @ X2519 )
| ~ ( subset @ X2515 @ ( cartprod @ X2513 @ X2514 ) ) )
& ( ~ ( X2516 @ ( kpair @ ( esk67_4 @ X2513 @ X2514 @ X2515 @ X2516 ) @ ( esk68_4 @ X2513 @ X2514 @ X2515 @ X2516 ) ) )
| ~ ( in @ X2519 @ X2515 )
| ( X2516 @ X2519 )
| ~ ( subset @ X2515 @ ( cartprod @ X2513 @ X2514 ) ) )
& ( ( in @ ( esk69_4 @ X2520 @ X2521 @ X2522 @ X2523 ) @ X2520 )
| ~ ( in @ X2526 @ X2522 )
| ( X2523 @ X2526 )
| ~ ( subset @ X2522 @ ( cartprod @ X2520 @ X2521 ) ) )
& ( ( in @ ( esk70_4 @ X2520 @ X2521 @ X2522 @ X2523 ) @ X2521 )
| ~ ( in @ X2526 @ X2522 )
| ( X2523 @ X2526 )
| ~ ( subset @ X2522 @ ( cartprod @ X2520 @ X2521 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2520 @ X2521 @ X2522 @ X2523 ) @ ( esk70_4 @ X2520 @ X2521 @ X2522 @ X2523 ) ) @ X2522 )
| ~ ( in @ X2526 @ X2522 )
| ( X2523 @ X2526 )
| ~ ( subset @ X2522 @ ( cartprod @ X2520 @ X2521 ) ) )
& ( ~ ( X2523 @ ( kpair @ ( esk69_4 @ X2520 @ X2521 @ X2522 @ X2523 ) @ ( esk70_4 @ X2520 @ X2521 @ X2522 @ X2523 ) ) )
| ~ ( in @ X2526 @ X2522 )
| ( X2523 @ X2526 )
| ~ ( subset @ X2522 @ ( cartprod @ X2520 @ X2521 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2527 @ X2528 ) )
| ~ ( in @ X2529 @ X2527 )
| ~ ( in @ X2530 @ X2527 )
| ~ ( X2528 @ X2529 )
| ~ ( X2528 @ X2530 )
| ( X2529 = X2530 ) )
& ( ~ ( func @ X2531 @ X2532 @ X2533 )
| ~ ( in @ X2534 @ X2531 )
| ( in @ ( kpair @ X2534 @ ( ap @ X2531 @ X2532 @ X2533 @ X2534 ) ) @ X2533 ) )
& ( ~ ( in @ X2537 @ ( funcSet @ X2535 @ X2536 ) )
| ~ ( in @ X2538 @ X2535 )
| ( in @ ( kpair @ X2538 @ ( ap @ X2535 @ X2536 @ X2537 @ X2538 ) ) @ X2537 ) )
& ( ~ ( func @ X2539 @ X2540 @ X2541 )
| ~ ( in @ X2542 @ X2539 )
| ~ ( in @ X2543 @ X2540 )
| ~ ( in @ ( kpair @ X2542 @ X2543 ) @ X2541 )
| ( ( ap @ X2539 @ X2540 @ X2541 @ X2542 )
= X2543 ) )
& ( ( in @ ( esk71_4 @ X2544 @ X2545 @ X2546 @ X2547 ) @ X2544 )
| ~ ( in @ X2549 @ X2544 )
| ~ ( in @ X2550 @ X2545 )
| ~ ( in @ ( kpair @ X2549 @ X2550 ) @ X2547 )
| ( in @ ( kpair @ X2549 @ X2550 ) @ X2546 )
| ~ ( func @ X2544 @ X2545 @ X2547 )
| ~ ( func @ X2544 @ X2545 @ X2546 ) )
& ( ( ( ap @ X2544 @ X2545 @ X2546 @ ( esk71_4 @ X2544 @ X2545 @ X2546 @ X2547 ) )
!= ( ap @ X2544 @ X2545 @ X2547 @ ( esk71_4 @ X2544 @ X2545 @ X2546 @ X2547 ) ) )
| ~ ( in @ X2549 @ X2544 )
| ~ ( in @ X2550 @ X2545 )
| ~ ( in @ ( kpair @ X2549 @ X2550 ) @ X2547 )
| ( in @ ( kpair @ X2549 @ X2550 ) @ X2546 )
| ~ ( func @ X2544 @ X2545 @ X2547 )
| ~ ( func @ X2544 @ X2545 @ X2546 ) )
& ( ~ ( in @ X2553 @ ( funcSet @ X2551 @ X2552 ) )
| ~ ( in @ X2554 @ X2551 )
| ~ ( in @ X2555 @ X2552 )
| ~ ( in @ ( kpair @ X2554 @ X2555 ) @ X2553 )
| ( ( ap @ X2551 @ X2552 @ X2553 @ X2554 )
= X2555 ) )
& ( ( in @ ( esk72_4 @ X2556 @ X2557 @ X2558 @ X2559 ) @ X2556 )
| ( subset @ X2558 @ X2559 )
| ~ ( subset @ X2559 @ ( cartprod @ X2556 @ X2557 ) )
| ~ ( subset @ X2558 @ ( cartprod @ X2556 @ X2557 ) ) )
& ( ( in @ ( esk73_4 @ X2556 @ X2557 @ X2558 @ X2559 ) @ X2557 )
| ( subset @ X2558 @ X2559 )
| ~ ( subset @ X2559 @ ( cartprod @ X2556 @ X2557 ) )
| ~ ( subset @ X2558 @ ( cartprod @ X2556 @ X2557 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2556 @ X2557 @ X2558 @ X2559 ) @ ( esk73_4 @ X2556 @ X2557 @ X2558 @ X2559 ) ) @ X2558 )
| ( subset @ X2558 @ X2559 )
| ~ ( subset @ X2559 @ ( cartprod @ X2556 @ X2557 ) )
| ~ ( subset @ X2558 @ ( cartprod @ X2556 @ X2557 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2556 @ X2557 @ X2558 @ X2559 ) @ ( esk73_4 @ X2556 @ X2557 @ X2558 @ X2559 ) ) @ X2559 )
| ( subset @ X2558 @ X2559 )
| ~ ( subset @ X2559 @ ( cartprod @ X2556 @ X2557 ) )
| ~ ( subset @ X2558 @ ( cartprod @ X2556 @ X2557 ) ) )
& ( ( in @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ( X2564 = X2565 )
| ( in @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ( X2564 = X2565 )
| ( in @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ( X2564 = X2565 )
| ( in @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ( X2564 = X2565 )
| ( in @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ( X2564 = X2565 )
| ( in @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ( X2564 = X2565 )
| ( in @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ( X2564 = X2565 )
| ( in @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ( X2564 = X2565 )
| ( in @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ( X2564 = X2565 )
| ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ( X2564 = X2565 )
| ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ( X2564 = X2565 )
| ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ( X2564 = X2565 )
| ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2562 )
| ( X2564 = X2565 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ X2563 )
| ( X2564 = X2565 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ( X2564 = X2565 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk77_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2564 )
| ( X2564 = X2565 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2562 @ X2563 @ X2564 @ X2565 ) @ ( esk75_4 @ X2562 @ X2563 @ X2564 @ X2565 ) ) @ X2565 )
| ~ ( subset @ X2565 @ ( cartprod @ X2562 @ X2563 ) )
| ~ ( subset @ X2564 @ ( cartprod @ X2562 @ X2563 ) ) )
& ( ( in @ ( esk78_4 @ X2570 @ X2571 @ X2572 @ X2573 ) @ X2570 )
| ( X2572 = X2573 )
| ~ ( func @ X2570 @ X2571 @ X2573 )
| ~ ( func @ X2570 @ X2571 @ X2572 ) )
& ( ( ( ap @ X2570 @ X2571 @ X2572 @ ( esk78_4 @ X2570 @ X2571 @ X2572 @ X2573 ) )
!= ( ap @ X2570 @ X2571 @ X2573 @ ( esk78_4 @ X2570 @ X2571 @ X2572 @ X2573 ) ) )
| ( X2572 = X2573 )
| ~ ( func @ X2570 @ X2571 @ X2573 )
| ~ ( func @ X2570 @ X2571 @ X2572 ) )
& ( ( in @ ( esk79_4 @ X2575 @ X2576 @ X2577 @ X2578 ) @ X2575 )
| ( X2577 = X2578 )
| ~ ( in @ X2578 @ ( funcSet @ X2575 @ X2576 ) )
| ~ ( in @ X2577 @ ( funcSet @ X2575 @ X2576 ) ) )
& ( ( ( ap @ X2575 @ X2576 @ X2577 @ ( esk79_4 @ X2575 @ X2576 @ X2577 @ X2578 ) )
!= ( ap @ X2575 @ X2576 @ X2578 @ ( esk79_4 @ X2575 @ X2576 @ X2577 @ X2578 ) ) )
| ( X2577 = X2578 )
| ~ ( in @ X2578 @ ( funcSet @ X2575 @ X2576 ) )
| ~ ( in @ X2577 @ ( funcSet @ X2575 @ X2576 ) ) )
& ( ~ ( in @ X2582 @ ( funcSet @ X2580 @ X2581 ) )
| ~ ( in @ X2583 @ X2580 )
| ( ( ap @ X2580 @ X2581 @ X2582 @ X2583 )
= ( ap @ X2580 @ X2581 @ X2582 @ X2583 ) ) )
& ( ~ ( func @ X2584 @ X2585 @ X2586 )
| ~ ( in @ X2587 @ X2584 )
| ( ( ap @ X2584 @ X2585 @ X2586 @ X2587 )
= ( ap @ X2584 @ X2585 @ X2586 @ X2587 ) ) )
& ( ( in @ ( esk80_3 @ X2588 @ X2589 @ X2590 ) @ X2588 )
| ~ ( in @ X2592 @ X2588 )
| ( ( ap @ X2588 @ X2589 @ ( lam @ X2588 @ X2589 @ X2590 ) @ X2592 )
= ( X2590 @ X2592 ) ) )
& ( ~ ( in @ ( X2590 @ ( esk80_3 @ X2588 @ X2589 @ X2590 ) ) @ X2589 )
| ~ ( in @ X2592 @ X2588 )
| ( ( ap @ X2588 @ X2589 @ ( lam @ X2588 @ X2589 @ X2590 ) @ X2592 )
= ( X2590 @ X2592 ) ) )
& ( ~ ( func @ X2593 @ X2594 @ X2595 )
| ( ( lam @ X2593 @ X2594 @ ( ap @ X2593 @ X2594 @ X2595 ) )
= X2595 ) )
& ( ( in @ ( esk81_3 @ X2596 @ X2597 @ X2598 ) @ X2596 )
| ( ( lam @ X2596 @ X2597 @ X2598 )
= ( lam @ X2596 @ X2597 @ X2598 ) ) )
& ( ~ ( in @ ( X2598 @ ( esk81_3 @ X2596 @ X2597 @ X2598 ) ) @ X2597 )
| ( ( lam @ X2596 @ X2597 @ X2598 )
= ( lam @ X2596 @ X2597 @ X2598 ) ) )
& ( ( in @ ( esk82_3 @ X2600 @ X2601 @ X2602 ) @ X2600 )
| ~ ( in @ X2604 @ X2600 )
| ( ( ap @ X2600 @ X2601 @ ( lam @ X2600 @ X2601 @ X2602 ) @ X2604 )
= ( X2602 @ X2604 ) ) )
& ( ~ ( in @ ( X2602 @ ( esk82_3 @ X2600 @ X2601 @ X2602 ) ) @ X2601 )
| ~ ( in @ X2604 @ X2600 )
| ( ( ap @ X2600 @ X2601 @ ( lam @ X2600 @ X2601 @ X2602 ) @ X2604 )
= ( X2602 @ X2604 ) ) )
& ( ~ ( in @ X2607 @ ( funcSet @ X2605 @ X2606 ) )
| ( ( lam @ X2605 @ X2606 @ ( ap @ X2605 @ X2606 @ X2607 ) )
= X2607 ) )
& ( ~ ( in @ X2610 @ X2608 )
| ~ ( in @ X2611 @ X2608 )
| X2609
| ( in @ X2611
@ ( dsetconstr @ X2608
@ ^ [Z0: $i] :
( ( X2609
& ( Z0 = X2610 ) )
| ( ~ X2609
& ( Z0 = X2611 ) ) ) ) ) )
& ( ~ ( in @ X2614 @ X2612 )
| ~ ( in @ X2615 @ X2612 )
| X2613
| ( ( dsetconstr @ X2612
@ ^ [Z0: $i] :
( ( X2613
& ( Z0 = X2614 ) )
| ( ~ X2613
& ( Z0 = X2615 ) ) ) )
= ( setadjoin @ X2615 @ emptyset ) ) )
& ( ~ ( in @ X2618 @ X2616 )
| ~ ( in @ X2619 @ X2616 )
| ~ X2617
| ( in @ X2618
@ ( dsetconstr @ X2616
@ ^ [Z0: $i] :
( ( X2617
& ( Z0 = X2618 ) )
| ( ~ X2617
& ( Z0 = X2619 ) ) ) ) ) )
& ( ~ ( in @ X2622 @ X2620 )
| ~ ( in @ X2623 @ X2620 )
| ~ X2621
| ( ( dsetconstr @ X2620
@ ^ [Z0: $i] :
( ( X2621
& ( Z0 = X2622 ) )
| ( ~ X2621
& ( Z0 = X2623 ) ) ) )
= ( setadjoin @ X2622 @ emptyset ) ) )
& ( ~ ( in @ X2626 @ X2624 )
| ~ ( in @ X2627 @ X2624 )
| ( singleton
@ ( dsetconstr @ X2624
@ ^ [Z0: $i] :
( ( X2625
& ( Z0 = X2626 ) )
| ( ~ X2625
& ( Z0 = X2627 ) ) ) ) ) )
& ( ~ ( in @ X2630 @ X2628 )
| ~ ( in @ X2631 @ X2628 )
| ( in @ ( if @ X2628 @ X2629 @ X2630 @ X2631 ) @ X2628 ) )
& ( ~ ( singleton @ X2632 )
| ~ ( in @ X2633 @ X2632 )
| ( ( setunion @ X2632 )
= X2633 ) )
& ( ~ ( in @ X2636 @ X2634 )
| ~ ( in @ X2637 @ X2634 )
| ~ X2635
| ( ( if @ X2634 @ X2635 @ X2636 @ X2637 )
= X2636 ) )
& ( ~ ( in @ X2640 @ X2638 )
| ~ ( in @ X2641 @ X2638 )
| X2639
| ( ( if @ X2638 @ X2639 @ X2640 @ X2641 )
= X2641 ) )
& ( ~ ( in @ X2644 @ X2642 )
| ~ ( in @ X2645 @ X2642 )
| ( in @ ( if @ X2642 @ X2643 @ X2644 @ X2645 ) @ ( setadjoin @ X2644 @ ( setadjoin @ X2645 @ emptyset ) ) ) )
& ( ~ ( in @ X2647 @ ( powerset @ X2646 ) )
| ~ ( in @ X2648 @ ( powerset @ X2646 ) )
| ( in @ ( binintersect @ X2647 @ X2648 ) @ ( powerset @ X2646 ) ) )
& ( ~ ( in @ X2650 @ ( powerset @ X2649 ) )
| ~ ( in @ X2651 @ ( powerset @ X2649 ) )
| ( in @ ( binunion @ X2650 @ X2651 ) @ ( powerset @ X2649 ) ) )
& ( ~ ( in @ X2653 @ ( powerset @ X2652 ) )
| ( in @ ( powerset @ X2653 ) @ ( powerset @ ( powerset @ X2652 ) ) ) )
& ( ~ ( in @ X2655 @ ( powerset @ X2654 ) )
| ~ ( in @ X2656 @ ( powerset @ X2654 ) )
| ( in @ ( setminus @ X2655 @ X2656 ) @ ( powerset @ X2654 ) ) )
& ( ~ ( in @ X2658 @ ( powerset @ X2657 ) )
| ( in @ ( setminus @ X2657 @ X2658 ) @ ( powerset @ X2657 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ( X2660 = X2661 )
| ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2659 )
| ( X2660 = X2661 )
| ~ ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ( X2660 = X2661 )
| ~ ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2659 @ X2660 @ X2661 ) @ X2660 )
| ( X2660 = X2661 )
| ~ ( in @ ( esk83_3 @ X2659 @ X2660 @ X2661 ) @ X2661 )
| ~ ( in @ X2661 @ ( powerset @ X2659 ) )
| ~ ( in @ X2660 @ ( powerset @ X2659 ) ) )
& ( ( in @ ( esk85_3 @ X2664 @ X2665 @ X2666 ) @ X2664 )
| ( subset @ X2665 @ X2666 )
| ~ ( in @ X2666 @ ( powerset @ X2664 ) )
| ~ ( in @ X2665 @ ( powerset @ X2664 ) ) )
& ( ( in @ ( esk85_3 @ X2664 @ X2665 @ X2666 ) @ X2665 )
| ( subset @ X2665 @ X2666 )
| ~ ( in @ X2666 @ ( powerset @ X2664 ) )
| ~ ( in @ X2665 @ ( powerset @ X2664 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2664 @ X2665 @ X2666 ) @ X2666 )
| ( subset @ X2665 @ X2666 )
| ~ ( in @ X2666 @ ( powerset @ X2664 ) )
| ~ ( in @ X2665 @ ( powerset @ X2664 ) ) )
& ( ( in @ ( esk86_3 @ X2668 @ X2669 @ X2670 ) @ X2668 )
| ( in @ X2669 @ ( powerset @ X2670 ) )
| ~ ( in @ X2670 @ ( powerset @ X2668 ) )
| ~ ( in @ X2669 @ ( powerset @ X2668 ) ) )
& ( ( in @ ( esk86_3 @ X2668 @ X2669 @ X2670 ) @ X2669 )
| ( in @ X2669 @ ( powerset @ X2670 ) )
| ~ ( in @ X2670 @ ( powerset @ X2668 ) )
| ~ ( in @ X2669 @ ( powerset @ X2668 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2668 @ X2669 @ X2670 ) @ X2670 )
| ( in @ X2669 @ ( powerset @ X2670 ) )
| ~ ( in @ X2670 @ ( powerset @ X2668 ) )
| ~ ( in @ X2669 @ ( powerset @ X2668 ) ) )
& ( ~ ( in @ X2673 @ ( powerset @ X2672 ) )
| ~ ( in @ X2674 @ ( powerset @ X2672 ) )
| ~ ( in @ X2675 @ X2672 )
| ~ ( in @ X2673 @ ( powerset @ X2674 ) )
| ~ ( in @ X2675 @ X2673 )
| ( in @ X2675 @ X2674 ) )
& ( ~ ( in @ X2677 @ ( powerset @ X2676 ) )
| ~ ( in @ X2678 @ X2676 )
| ~ ( in @ X2678 @ X2677 )
| ~ ( in @ X2678 @ ( setminus @ X2676 @ X2677 ) ) )
& ( ~ ( in @ X2680 @ ( powerset @ X2679 ) )
| ~ ( in @ X2681 @ X2679 )
| ( in @ X2681 @ ( setminus @ X2679 @ X2680 ) )
| ( in @ X2681 @ X2680 ) )
& ( ~ ( in @ X2683 @ ( powerset @ X2682 ) )
| ~ ( in @ X2684 @ ( powerset @ X2682 ) )
| ~ ( in @ X2685 @ X2682 )
| ( in @ X2685 @ X2683 )
| ~ ( in @ X2685 @ ( binintersect @ X2683 @ X2684 ) ) )
& ( ~ ( in @ X2687 @ ( powerset @ X2686 ) )
| ~ ( in @ X2688 @ ( powerset @ X2686 ) )
| ~ ( in @ X2689 @ X2686 )
| ( in @ X2689 @ X2688 )
| ~ ( in @ X2689 @ ( binintersect @ X2687 @ X2688 ) ) )
& ( ~ ( in @ X2691 @ ( powerset @ X2690 ) )
| ~ ( in @ X2692 @ ( powerset @ X2690 ) )
| ~ ( in @ X2693 @ X2690 )
| ~ ( subset @ X2691 @ ( setminus @ X2690 @ X2692 ) )
| ~ ( in @ X2693 @ X2692 )
| ~ ( in @ X2693 @ X2691 ) )
& ( ~ ( in @ X2695 @ ( powerset @ X2694 ) )
| ~ ( in @ X2696 @ ( powerset @ X2694 ) )
| ~ ( in @ X2697 @ X2694 )
| ~ ( subset @ X2695 @ X2696 )
| ( in @ X2697 @ X2696 )
| ~ ( in @ X2697 @ X2695 ) )
& ( ~ ( in @ X2699 @ ( powerset @ X2698 ) )
| ~ ( in @ X2700 @ ( powerset @ X2698 ) )
| ~ ( subset @ X2699 @ X2700 )
| ( subset @ ( setminus @ X2698 @ X2700 ) @ ( setminus @ X2698 @ X2699 ) ) )
& ( ~ ( in @ X2702 @ ( powerset @ X2701 ) )
| ~ ( in @ X2703 @ ( powerset @ X2701 ) )
| ~ ( subset @ ( setminus @ X2701 @ X2703 ) @ ( setminus @ X2701 @ X2702 ) )
| ( subset @ X2702 @ X2703 ) )
& ( ~ ( in @ X2705 @ ( powerset @ X2704 ) )
| ~ ( in @ X2706 @ X2704 )
| ~ ( in @ X2706 @ X2705 )
| ( in @ X2706 @ ( setminus @ X2704 @ ( setminus @ X2704 @ X2705 ) ) ) )
& ( ~ ( in @ X2708 @ ( powerset @ X2707 ) )
| ~ ( in @ X2709 @ X2707 )
| ~ ( in @ X2709 @ ( setminus @ X2707 @ ( setminus @ X2707 @ X2708 ) ) )
| ( in @ X2709 @ X2708 ) )
& ( ~ ( in @ X2711 @ ( powerset @ X2710 ) )
| ( subset @ X2711 @ ( setminus @ X2710 @ ( setminus @ X2710 @ X2711 ) ) ) )
& ( ~ ( in @ X2713 @ ( powerset @ X2712 ) )
| ( subset @ ( setminus @ X2712 @ ( setminus @ X2712 @ X2713 ) ) @ X2713 ) )
& ( ~ ( in @ X2715 @ ( powerset @ X2714 ) )
| ( X2715
= ( setminus @ X2714 @ ( setminus @ X2714 @ X2715 ) ) ) )
& ( ~ ( in @ X2717 @ ( powerset @ X2716 ) )
| ~ ( in @ X2718 @ ( powerset @ X2716 ) )
| ~ ( in @ X2719 @ X2716 )
| ~ ( in @ X2719 @ ( setminus @ X2716 @ X2717 ) )
| ~ ( in @ X2719 @ ( binintersect @ X2717 @ X2718 ) ) )
& ( ~ ( in @ X2721 @ ( powerset @ X2720 ) )
| ~ ( in @ X2722 @ ( powerset @ X2720 ) )
| ~ ( in @ X2723 @ X2720 )
| ~ ( in @ X2723 @ ( setminus @ X2720 @ X2721 ) )
| ( in @ X2723 @ ( setminus @ X2720 @ ( binintersect @ X2721 @ X2722 ) ) ) )
& ( ~ ( in @ X2725 @ ( powerset @ X2724 ) )
| ~ ( in @ X2726 @ ( powerset @ X2724 ) )
| ( subset @ ( setminus @ X2724 @ X2725 ) @ ( setminus @ X2724 @ ( binintersect @ X2725 @ X2726 ) ) ) )
& ( ~ ( in @ X2728 @ ( powerset @ X2727 ) )
| ~ ( in @ X2729 @ ( powerset @ X2727 ) )
| ( in @ ( setminus @ X2727 @ X2728 ) @ ( powerset @ ( setminus @ X2727 @ ( binintersect @ X2728 @ X2729 ) ) ) ) )
& ( ~ ( in @ X2731 @ ( powerset @ X2730 ) )
| ~ ( in @ X2732 @ ( powerset @ X2730 ) )
| ~ ( subset @ X2731 @ ( setminus @ X2730 @ X2732 ) )
| ~ ( in @ X2733 @ X2730 )
| ~ ( in @ X2733 @ X2732 )
| ( in @ X2733 @ ( setminus @ X2730 @ X2731 ) ) )
& ( ~ ( in @ X2735 @ ( powerset @ X2734 ) )
| ~ ( in @ X2736 @ ( powerset @ X2734 ) )
| ~ ( subset @ X2735 @ ( setminus @ X2734 @ X2736 ) )
| ( subset @ X2736 @ ( setminus @ X2734 @ X2735 ) ) )
& ( ~ ( in @ X2738 @ ( powerset @ X2737 ) )
| ~ ( in @ X2739 @ ( powerset @ X2737 ) )
| ~ ( in @ X2740 @ X2737 )
| ( in @ X2740 @ ( binunion @ X2738 @ X2739 ) )
| ~ ( in @ X2740 @ X2738 ) )
& ( ~ ( in @ X2742 @ ( powerset @ X2741 ) )
| ~ ( in @ X2743 @ ( powerset @ X2741 ) )
| ~ ( in @ X2744 @ X2741 )
| ( in @ X2744 @ ( binunion @ X2742 @ X2743 ) )
| ~ ( in @ X2744 @ X2743 ) )
& ( ~ ( in @ X2746 @ ( powerset @ X2745 ) )
| ~ ( in @ X2747 @ ( powerset @ X2745 ) )
| ~ ( in @ X2748 @ ( powerset @ X2745 ) )
| ~ ( in @ X2749 @ X2745 )
| ~ ( in @ X2749 @ ( binintersect @ X2746 @ X2747 ) )
| ( in @ X2749 @ ( binunion @ X2746 @ X2748 ) ) )
& ( ~ ( in @ X2751 @ ( powerset @ X2750 ) )
| ~ ( in @ X2752 @ ( powerset @ X2750 ) )
| ~ ( in @ X2753 @ ( powerset @ X2750 ) )
| ~ ( in @ X2754 @ X2750 )
| ~ ( in @ X2754 @ ( binintersect @ X2751 @ X2752 ) )
| ( in @ X2754 @ ( binunion @ X2752 @ X2753 ) ) )
& ( ~ ( in @ X2756 @ ( powerset @ X2755 ) )
| ~ ( in @ X2757 @ ( powerset @ X2755 ) )
| ~ ( in @ X2758 @ ( powerset @ X2755 ) )
| ~ ( in @ X2759 @ X2755 )
| ~ ( in @ X2759 @ ( binintersect @ X2756 @ X2757 ) )
| ( in @ X2759 @ ( binintersect @ ( binunion @ X2756 @ X2758 ) @ ( binunion @ X2757 @ X2758 ) ) ) )
& ( ~ ( in @ X2761 @ ( powerset @ X2760 ) )
| ~ ( in @ X2762 @ ( powerset @ X2760 ) )
| ~ ( in @ X2763 @ ( powerset @ X2760 ) )
| ( in @ ( binintersect @ X2761 @ X2762 ) @ ( powerset @ ( binintersect @ ( binunion @ X2761 @ X2763 ) @ ( binunion @ X2762 @ X2763 ) ) ) ) )
& ( ~ ( in @ X2765 @ ( powerset @ X2764 ) )
| ~ ( in @ X2766 @ ( powerset @ X2764 ) )
| ~ ( in @ X2767 @ X2764 )
| ~ ( in @ X2767 @ ( setminus @ X2764 @ ( binunion @ X2765 @ X2766 ) ) )
| ~ ( in @ X2767 @ X2765 ) )
& ( ~ ( in @ X2769 @ ( powerset @ X2768 ) )
| ~ ( in @ X2770 @ ( powerset @ X2768 ) )
| ~ ( in @ X2771 @ X2768 )
| ~ ( in @ X2771 @ ( setminus @ X2768 @ ( binunion @ X2769 @ X2770 ) ) )
| ( in @ X2771 @ ( setminus @ X2768 @ X2769 ) ) )
& ( ( in @ X2776 @ X2774 )
| X2775
| ( in @ X2776 @ X2773 )
| ~ ( in @ X2776 @ ( binunion @ X2773 @ X2774 ) )
| ~ ( in @ X2776 @ X2772 )
| ~ ( in @ X2774 @ ( powerset @ X2772 ) )
| ~ ( in @ X2773 @ ( powerset @ X2772 ) ) )
& ( ~ X2775
| X2775
| ( in @ X2776 @ X2773 )
| ~ ( in @ X2776 @ ( binunion @ X2773 @ X2774 ) )
| ~ ( in @ X2776 @ X2772 )
| ~ ( in @ X2774 @ ( powerset @ X2772 ) )
| ~ ( in @ X2773 @ ( powerset @ X2772 ) ) )
& ( ( in @ X2776 @ X2774 )
| X2775
| ~ X2775
| ~ ( in @ X2776 @ ( binunion @ X2773 @ X2774 ) )
| ~ ( in @ X2776 @ X2772 )
| ~ ( in @ X2774 @ ( powerset @ X2772 ) )
| ~ ( in @ X2773 @ ( powerset @ X2772 ) ) )
& ( ~ X2775
| X2775
| ~ X2775
| ~ ( in @ X2776 @ ( binunion @ X2773 @ X2774 ) )
| ~ ( in @ X2776 @ X2772 )
| ~ ( in @ X2774 @ ( powerset @ X2772 ) )
| ~ ( in @ X2773 @ ( powerset @ X2772 ) ) )
& ( ~ ( in @ X2778 @ ( powerset @ X2777 ) )
| ~ ( in @ X2779 @ ( powerset @ X2777 ) )
| ~ ( in @ X2780 @ X2777 )
| ( in @ X2780 @ X2778 )
| ( in @ X2780 @ X2779 )
| ~ ( in @ X2780 @ ( binunion @ X2778 @ X2779 ) ) )
& ( ~ ( in @ X2782 @ ( powerset @ X2781 ) )
| ~ ( in @ X2783 @ ( powerset @ X2781 ) )
| ~ ( in @ X2784 @ X2781 )
| ~ ( in @ X2784 @ ( setminus @ X2781 @ ( binunion @ X2782 @ X2783 ) ) )
| ( in @ X2784 @ ( setminus @ X2781 @ X2782 ) ) )
& ( ~ ( in @ X2786 @ ( powerset @ X2785 ) )
| ~ ( in @ X2787 @ ( powerset @ X2785 ) )
| ( in @ ( setminus @ X2785 @ ( binunion @ X2786 @ X2787 ) ) @ ( powerset @ ( setminus @ X2785 @ X2786 ) ) ) )
& ( ~ ( in @ X2789 @ ( powerset @ X2788 ) )
| ~ ( in @ X2790 @ ( powerset @ X2788 ) )
| ~ ( in @ X2791 @ X2788 )
| ~ ( in @ X2791 @ ( setminus @ X2788 @ ( binunion @ X2789 @ X2790 ) ) )
| ( in @ X2791 @ ( setminus @ X2788 @ X2790 ) ) )
& ( ~ ( in @ X2793 @ ( powerset @ X2792 ) )
| ~ ( in @ X2794 @ ( powerset @ X2792 ) )
| ~ ( in @ X2795 @ X2792 )
| ~ ( in @ X2795 @ ( setminus @ X2792 @ ( binintersect @ X2793 @ X2794 ) ) )
| ( in @ X2795 @ ( binunion @ ( setminus @ X2792 @ X2793 ) @ ( setminus @ X2792 @ X2794 ) ) ) )
& ( ~ ( in @ X2797 @ ( powerset @ X2796 ) )
| ~ ( in @ X2798 @ ( powerset @ X2796 ) )
| ~ ( in @ X2799 @ X2796 )
| ~ ( in @ X2799 @ ( binunion @ ( setminus @ X2796 @ X2797 ) @ ( setminus @ X2796 @ X2798 ) ) )
| ( in @ X2799 @ ( setminus @ X2796 @ ( binintersect @ X2797 @ X2798 ) ) ) )
& ( ~ ( in @ X2801 @ ( powerset @ X2800 ) )
| ~ ( in @ X2802 @ ( powerset @ X2800 ) )
| ( ( setminus @ X2800 @ ( binintersect @ X2801 @ X2802 ) )
= ( binunion @ ( setminus @ X2800 @ X2801 ) @ ( setminus @ X2800 @ X2802 ) ) ) )
& ( ~ ( in @ X2804 @ ( powerset @ X2803 ) )
| ~ ( in @ X2805 @ ( powerset @ X2803 ) )
| ~ ( in @ X2806 @ X2803 )
| ~ ( in @ X2806 @ ( setminus @ X2803 @ ( binunion @ X2804 @ X2805 ) ) )
| ( in @ X2806 @ ( binintersect @ ( setminus @ X2803 @ X2804 ) @ ( setminus @ X2803 @ X2805 ) ) ) )
& ( ~ ( in @ X2808 @ ( powerset @ X2807 ) )
| ~ ( in @ X2809 @ ( powerset @ X2807 ) )
| ~ ( in @ X2810 @ X2807 )
| ~ ( in @ X2810 @ ( setminus @ X2807 @ X2808 ) )
| ~ ( in @ X2810 @ ( setminus @ X2807 @ X2809 ) )
| ( in @ X2810 @ ( setminus @ X2807 @ ( binunion @ X2808 @ X2809 ) ) ) )
& ( ~ ( in @ X2812 @ ( powerset @ X2811 ) )
| ~ ( in @ X2813 @ ( powerset @ X2811 ) )
| ~ ( in @ X2814 @ X2811 )
| ~ ( in @ X2814 @ ( binintersect @ ( setminus @ X2811 @ X2812 ) @ ( setminus @ X2811 @ X2813 ) ) )
| ( in @ X2814 @ ( setminus @ X2811 @ ( binunion @ X2812 @ X2813 ) ) ) )
& ( ~ ( in @ X2816 @ ( powerset @ X2815 ) )
| ~ ( in @ X2817 @ ( powerset @ X2815 ) )
| ( ( setminus @ X2815 @ ( binunion @ X2816 @ X2817 ) )
= ( binintersect @ ( setminus @ X2815 @ X2816 ) @ ( setminus @ X2815 @ X2817 ) ) ) )
& ( ~ ( in @ X2819 @ ( powerset @ X2818 ) )
| ~ ( in @ X2820 @ ( powerset @ X2818 ) )
| ~ ( in @ X2821 @ ( binintersect @ X2819 @ X2820 ) )
| ( in @ X2821 @ X2818 ) )
& ( ~ ( in @ X2823 @ ( powerset @ X2822 ) )
| ~ ( in @ X2824 @ ( powerset @ X2822 ) )
| ~ ( in @ X2825 @ ( powerset @ X2822 ) )
| ~ ( subset @ X2823 @ X2825 )
| ( subset @ ( binintersect @ X2823 @ X2824 ) @ X2825 ) )
& ( ~ ( in @ X2827 @ ( powerset @ X2826 ) )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2829 @ ( powerset @ X2826 ) )
| ~ ( subset @ X2828 @ X2829 )
| ( subset @ ( binintersect @ X2827 @ X2828 ) @ X2829 ) )
& ( ~ ( in @ X2831 @ ( powerset @ X2830 ) )
| ~ ( in @ X2832 @ ( powerset @ X2830 ) )
| ~ ( in @ X2833 @ ( powerset @ X2830 ) )
| ~ ( subset @ X2831 @ X2832 )
| ~ ( subset @ X2831 @ X2833 )
| ( subset @ X2831 @ ( binintersect @ X2832 @ X2833 ) ) )
& ( ~ ( in @ X2835 @ ( powerset @ X2834 ) )
| ~ ( in @ X2836 @ ( powerset @ X2834 ) )
| ~ ( in @ X2837 @ ( powerset @ X2834 ) )
| ~ ( in @ X2838 @ ( powerset @ X2834 ) )
| ~ ( subset @ X2835 @ X2837 )
| ~ ( subset @ X2836 @ X2838 )
| ( subset @ ( binintersect @ X2835 @ X2836 ) @ ( binintersect @ X2837 @ X2838 ) ) )
& ( ~ ( in @ X2840 @ ( powerset @ X2839 ) )
| ~ ( in @ X2841 @ ( powerset @ X2839 ) )
| ( in @ ( setminus @ X2839 @ X2840 ) @ ( powerset @ ( setminus @ X2839 @ ( binintersect @ X2840 @ X2841 ) ) ) ) )
& ( ~ ( in @ X2843 @ ( powerset @ X2842 ) )
| ~ ( in @ X2844 @ ( powerset @ X2842 ) )
| ~ ( in @ X2845 @ ( powerset @ X2842 ) )
| ~ ( in @ X2846 @ ( powerset @ X2842 ) )
| ( ( setminus @ X2842 @ ( binintersect @ ( binunion @ X2843 @ X2844 ) @ ( binunion @ X2845 @ X2846 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X2842 @ X2843 ) @ ( setminus @ X2842 @ X2844 ) ) @ ( binintersect @ ( setminus @ X2842 @ X2845 ) @ ( setminus @ X2842 @ X2846 ) ) ) ) )
& ( ~ ( in @ X2848 @ ( powerset @ X2847 ) )
| ~ ( in @ X2849 @ ( powerset @ X2847 ) )
| ~ ( in @ X2850 @ ( powerset @ X2847 ) )
| ( in @ ( binintersect @ X2848 @ X2849 ) @ ( powerset @ ( binintersect @ ( binunion @ X2848 @ X2850 ) @ ( binunion @ X2849 @ X2850 ) ) ) ) )
& ( ~ ( in @ X2852 @ ( powerset @ X2851 ) )
| ~ ( in @ X2853 @ ( powerset @ X2851 ) )
| ~ ( subset @ X2852 @ ( setminus @ X2851 @ X2853 ) )
| ( subset @ X2853 @ ( setminus @ X2851 @ X2852 ) ) )
& ( ~ ( in @ X2855 @ ( powerset @ X2854 ) )
| ~ ( in @ X2856 @ ( powerset @ X2854 ) )
| ( in @ ( setminus @ X2854 @ ( binunion @ X2855 @ X2856 ) ) @ ( powerset @ ( setminus @ X2854 @ X2855 ) ) ) )
& ( subset @ esk88_0 @ ( cartprod @ esk87_0 @ esk87_0 ) )
& ( ~ ( in @ X2860 @ esk87_0 )
| ~ ( in @ X2861 @ esk87_0 )
| ~ ( in @ ( kpair @ X2860 @ X2861 ) @ esk88_0 )
| ( epred2_0 @ ( kpair @ X2860 @ X2861 ) ) )
& ( in @ esk89_0 @ esk88_0 )
& ~ ( epred2_0 @ esk89_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_373])])])])])])]) ).
thf(c_0_375,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_376,negated_conjecture,
in @ esk89_0 @ esk88_0,
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_377,negated_conjecture,
! [X2: $i] :
( ( in @ esk89_0 @ X2 )
| ~ ( subset @ esk88_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_375,c_0_376]) ).
thf(c_0_378,negated_conjecture,
subset @ esk88_0 @ ( cartprod @ esk87_0 @ esk87_0 ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_379,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_380,negated_conjecture,
in @ esk89_0 @ ( cartprod @ esk87_0 @ esk87_0 ),
inference(spm,[status(thm)],[c_0_377,c_0_378]) ).
thf(c_0_381,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ ( ksnd @ X2 ) @ X4 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_382,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ ( kfst @ X2 ) @ X3 )
| ~ ( in @ X2 @ ( cartprod @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_383,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_0 @ ( kpair @ X2 @ X3 ) )
| ~ ( in @ X2 @ esk87_0 )
| ~ ( in @ X3 @ esk87_0 )
| ~ ( in @ ( kpair @ X2 @ X3 ) @ esk88_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_384,negated_conjecture,
( ( kpair @ ( kfst @ esk89_0 ) @ ( ksnd @ esk89_0 ) )
= esk89_0 ),
inference(spm,[status(thm)],[c_0_379,c_0_380]) ).
thf(c_0_385,negated_conjecture,
in @ ( ksnd @ esk89_0 ) @ esk87_0,
inference(spm,[status(thm)],[c_0_381,c_0_380]) ).
thf(c_0_386,negated_conjecture,
in @ ( kfst @ esk89_0 ) @ esk87_0,
inference(spm,[status(thm)],[c_0_382,c_0_380]) ).
thf(c_0_387,negated_conjecture,
~ ( epred2_0 @ esk89_0 ),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
thf(c_0_388,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383,c_0_384]),c_0_376]),c_0_385]),c_0_386])]),c_0_387]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SEU768^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.10 % Command : run_E %s %d THM
% 0.10/0.29 % Computer : n029.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sun May 19 16:58:07 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.14/0.39 Running higher-order theorem proving
% 0.14/0.39 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
% 1.09/0.69 # Version: 3.1.0-ho
% 1.09/0.69 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.09/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.09/0.69 # Starting pre_casc_3 with 300s (1) cores
% 1.09/0.69 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.09/0.69 # Starting full_lambda_10 with 300s (1) cores
% 1.09/0.69 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.09/0.69 # full_lambda_10 with pid 19580 completed with status 8
% 1.09/0.69 # ho_unfolding_5 with pid 19577 completed with status 0
% 1.09/0.69 # Result found by ho_unfolding_5
% 1.09/0.69 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.09/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.09/0.69 # No SInE strategy applied
% 1.09/0.69 # Search class: HGHSM-FSLM32-MHSMMSBN
% 1.09/0.69 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.09/0.69 # Starting full_lambda_5 with 99s (1) cores
% 1.09/0.69 # Starting ho_unfolding_5 with 121s (1) cores
% 1.09/0.69 # Starting pre_casc_4 with 99s (1) cores
% 1.09/0.69 # Starting pre_casc_3 with 99s (1) cores
% 1.09/0.69 # ho_unfolding_5 with pid 19598 completed with status 0
% 1.09/0.69 # Result found by ho_unfolding_5
% 1.09/0.69 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.09/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.69 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.09/0.69 # No SInE strategy applied
% 1.09/0.69 # Search class: HGHSM-FSLM32-MHSMMSBN
% 1.09/0.69 # Scheduled 12 strats onto 4 cores with 1200 seconds (1200 total)
% 1.09/0.69 # Starting full_lambda_5 with 99s (1) cores
% 1.09/0.69 # Starting ho_unfolding_5 with 121s (1) cores
% 1.09/0.69 # Preprocessing time : 0.008 s
% 1.09/0.69 # Presaturation interreduction done
% 1.09/0.69
% 1.09/0.69 # Proof found!
% 1.09/0.69 # SZS status Theorem
% 1.09/0.69 # SZS output start CNFRefutation
% See solution above
% 1.09/0.69 # Parsed axioms : 613
% 1.09/0.69 # Removed by relevancy pruning/SinE : 0
% 1.09/0.69 # Initial clauses : 816
% 1.09/0.69 # Removed in clause preprocessing : 362
% 1.09/0.69 # Initial clauses in saturation : 454
% 1.09/0.69 # Processed clauses : 986
% 1.09/0.69 # ...of these trivial : 11
% 1.09/0.69 # ...subsumed : 238
% 1.09/0.69 # ...remaining for further processing : 737
% 1.09/0.69 # Other redundant clauses eliminated : 37
% 1.09/0.69 # Clauses deleted for lack of memory : 0
% 1.09/0.69 # Backward-subsumed : 11
% 1.09/0.69 # Backward-rewritten : 7
% 1.09/0.69 # Generated clauses : 2449
% 1.09/0.69 # ...of the previous two non-redundant : 2244
% 1.09/0.69 # ...aggressively subsumed : 0
% 1.09/0.69 # Contextual simplify-reflections : 16
% 1.09/0.69 # Paramodulations : 2388
% 1.09/0.69 # Factorizations : 0
% 1.09/0.69 # NegExts : 4
% 1.09/0.69 # Equation resolutions : 40
% 1.09/0.69 # Disequality decompositions : 0
% 1.09/0.69 # Total rewrite steps : 251
% 1.09/0.69 # ...of those cached : 171
% 1.09/0.69 # Propositional unsat checks : 0
% 1.09/0.69 # Propositional check models : 0
% 1.09/0.69 # Propositional check unsatisfiable : 0
% 1.09/0.69 # Propositional clauses : 0
% 1.09/0.69 # Propositional clauses after purity: 0
% 1.09/0.69 # Propositional unsat core size : 0
% 1.09/0.69 # Propositional preprocessing time : 0.000
% 1.09/0.69 # Propositional encoding time : 0.000
% 1.09/0.69 # Propositional solver time : 0.000
% 1.09/0.69 # Success case prop preproc time : 0.000
% 1.09/0.69 # Success case prop encoding time : 0.000
% 1.09/0.69 # Success case prop solver time : 0.000
% 1.09/0.69 # Current number of processed clauses : 307
% 1.09/0.69 # Positive orientable unit clauses : 65
% 1.09/0.69 # Positive unorientable unit clauses: 0
% 1.09/0.69 # Negative unit clauses : 8
% 1.09/0.69 # Non-unit-clauses : 234
% 1.09/0.69 # Current number of unprocessed clauses: 2082
% 1.09/0.69 # ...number of literals in the above : 5713
% 1.09/0.69 # Current number of archived formulas : 0
% 1.09/0.69 # Current number of archived clauses : 414
% 1.09/0.69 # Clause-clause subsumption calls (NU) : 49865
% 1.09/0.69 # Rec. Clause-clause subsumption calls : 20431
% 1.09/0.69 # Non-unit clause-clause subsumptions : 153
% 1.09/0.69 # Unit Clause-clause subsumption calls : 282
% 1.09/0.69 # Rewrite failures with RHS unbound : 0
% 1.09/0.69 # BW rewrite match attempts : 42
% 1.09/0.69 # BW rewrite match successes : 6
% 1.09/0.69 # Condensation attempts : 0
% 1.09/0.69 # Condensation successes : 0
% 1.09/0.69 # Termbank termtop insertions : 129665
% 1.09/0.69 # Search garbage collected termcells : 30732
% 1.09/0.69
% 1.09/0.69 # -------------------------------------------------
% 1.09/0.69 # User time : 0.252 s
% 1.09/0.69 # System time : 0.016 s
% 1.09/0.69 # Total time : 0.268 s
% 1.09/0.69 # Maximum resident set size: 9284 pages
% 1.09/0.69
% 1.09/0.69 # -------------------------------------------------
% 1.09/0.69 # User time : 0.749 s
% 1.09/0.69 # System time : 0.080 s
% 1.09/0.69 # Total time : 0.829 s
% 1.09/0.69 # Maximum resident set size: 2748 pages
% 1.09/0.69 % E---3.1 exiting
% 1.09/0.70 % E exiting
%------------------------------------------------------------------------------