%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU813^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.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 03:30:29 EDT 2024
% Result : Theorem 4.53s 1.16s
% Output : CNFRefutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 794
% Syntax : Number of formulae : 866 ( 9 unt; 464 typ; 0 def)
% Number of atoms : 4473 ( 539 equ; 0 cnn)
% Maximal formula atoms : 1486 ( 11 avg)
% Number of connectives : 17730 (1150 ~;1188 |; 635 &;12125 @)
% ( 429 <=>;2203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1480 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 640 ( 640 >; 0 *; 0 +; 0 <<)
% Number of symbols : 468 ( 464 usr; 338 con; 0-6 aty)
% Number of variables : 3506 ( 172 ^3233 !; 101 ?;3506 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
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,
breln1all2: $o ).
thf(decl_346,type,
breln1Set: $i > $i ).
thf(decl_347,type,
breln1SetBreln1: $o ).
thf(decl_354,type,
choice2fnsingleton: $o ).
thf(decl_355,type,
setOfPairsIsBReln1: $o ).
thf(decl_356,type,
breln1all1: $o ).
thf(decl_357,type,
subbreln1: $o ).
thf(decl_358,type,
eqbreln1: $o ).
thf(decl_359,type,
breln1invset: $i > $i > $i ).
thf(decl_360,type,
breln1invprop: $o ).
thf(decl_361,type,
breln1invI: $o ).
thf(decl_362,type,
breln1invE: $o ).
thf(decl_363,type,
breln1compset: $i > $i > $i > $i ).
thf(decl_364,type,
breln1compprop: $o ).
thf(decl_365,type,
breln1compI: $o ).
thf(decl_366,type,
breln1compE: $o ).
thf(decl_367,type,
breln1compEex: $o ).
thf(decl_368,type,
breln1unionprop: $o ).
thf(decl_369,type,
breln1unionIL: $o ).
thf(decl_370,type,
breln1unionIR: $o ).
thf(decl_371,type,
breln1unionI: $o ).
thf(decl_372,type,
breln1unionE: $o ).
thf(decl_373,type,
breln1unionEcases: $o ).
thf(decl_374,type,
breln1unionCommutes: $o ).
thf(decl_375,type,
woz2Ex: $o ).
thf(decl_376,type,
woz2W: $o ).
thf(decl_377,type,
woz2A: $o ).
thf(decl_378,type,
woz2B: $o ).
thf(decl_379,type,
image1Ex: $o ).
thf(decl_380,type,
image1Ex1: $o ).
thf(decl_381,type,
image1: $i > ( $i > $i ) > $i ).
thf(decl_382,type,
image1Equiv: $o ).
thf(decl_383,type,
image1E: $o ).
thf(decl_384,type,
image1I: $o ).
thf(decl_385,type,
injective: $i > $i > $i > $o ).
thf(decl_386,type,
injFuncSet: $i > $i > $i ).
thf(decl_387,type,
injFuncInInjFuncSet: $o ).
thf(decl_388,type,
injFuncSetFuncIn: $o ).
thf(decl_389,type,
injFuncSetFuncInj: $o ).
thf(decl_390,type,
surjective: $i > $i > $i > $o ).
thf(decl_391,type,
surjFuncSet: $i > $i > $i ).
thf(decl_392,type,
surjFuncSetFuncIn: $o ).
thf(decl_393,type,
surjFuncSetFuncSurj: $o ).
thf(decl_394,type,
leftInvIsSurj: $o ).
thf(decl_395,type,
surjCantorThm: $o ).
thf(decl_396,type,
foundation2: $o ).
thf(decl_397,type,
notinself: $o ).
thf(decl_398,type,
notinself2: $o ).
thf(decl_399,type,
omegaS: $i > $i ).
thf(decl_400,type,
omegaSp: $o ).
thf(decl_401,type,
omegaSclos: $o ).
thf(decl_402,type,
peano0notS: $o ).
thf(decl_406,type,
peanoSinj: $o ).
thf(decl_408,type,
transitiveset: $i > $o ).
thf(decl_409,type,
transitivesetOp1: $o ).
thf(decl_410,type,
epred1_0: $o ).
thf(decl_411,type,
esk1_2: $i > $i > $i ).
thf(decl_412,type,
esk2_2: $i > $i > $i ).
thf(decl_413,type,
esk3_2: $i > $i > $i ).
thf(decl_414,type,
esk4_1: $i > $i ).
thf(decl_415,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_416,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_417,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_418,type,
esk8_1: $i > $i ).
thf(decl_419,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_420,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_421,type,
esk11_2: $i > $i > $i ).
thf(decl_422,type,
esk12_2: $i > $i > $i ).
thf(decl_423,type,
esk13_1: $i > $i ).
thf(decl_424,type,
esk14_1: $i > $i ).
thf(decl_425,type,
esk15_1: $i > $i ).
thf(decl_426,type,
esk16_2: $i > $i > $i ).
thf(decl_427,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_428,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_429,type,
esk19_1: $i > $i ).
thf(decl_430,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_431,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_432,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_433,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_434,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_435,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_436,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_437,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_438,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_439,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_440,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_441,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_442,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_443,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_444,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_445,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_446,type,
esk36_2: $i > $i > $i ).
thf(decl_447,type,
esk37_2: $i > $i > $i ).
thf(decl_448,type,
esk38_2: $i > $i > $i ).
thf(decl_449,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_450,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_451,type,
esk41_2: $i > $i > $i ).
thf(decl_452,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_453,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_454,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_455,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_456,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_457,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_458,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_459,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_460,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_461,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_462,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_463,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_464,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_465,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_466,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_467,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_468,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_469,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_470,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_471,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_472,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_473,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_474,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_475,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_476,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_477,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_478,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_479,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_480,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_481,type,
esk71_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_482,type,
esk72_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_483,type,
esk73_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_484,type,
esk74_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_485,type,
esk75_3: $i > $i > $i > $i ).
thf(decl_486,type,
esk76_3: $i > $i > $i > $i ).
thf(decl_487,type,
esk77_3: $i > $i > $i > $i ).
thf(decl_488,type,
esk78_3: $i > $i > $i > $i ).
thf(decl_489,type,
esk79_3: $i > $i > $i > $i ).
thf(decl_490,type,
esk80_3: $i > $i > $i > $i ).
thf(decl_491,type,
esk81_5: $i > $i > $i > $i > $i > $i ).
thf(decl_492,type,
esk82_6: $i > $i > $i > $i > $i > $o > $i ).
thf(decl_493,type,
esk83_2: $i > ( $i > $i ) > $i ).
thf(decl_494,type,
esk84_3: $i > ( $i > $i ) > $i > $i ).
thf(decl_495,type,
esk85_3: $i > ( $i > $i ) > $i > $i ).
thf(decl_496,type,
esk86_3: $i > ( $i > $i ) > $i > $i ).
thf(decl_497,type,
esk87_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_498,type,
esk88_4: $i > $i > ( $i > $i ) > $i > $i ).
thf(decl_499,type,
esk89_1: $i > $i ).
thf(decl_500,type,
esk90_1: $i > $i ).
thf(decl_501,type,
esk91_0: $i ).
thf(decl_502,type,
esk92_0: $i ).
thf(decl_503,type,
esk93_0: $i ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X4: $i] :
! [X21: $i] :
( ( in @ X21 @ X4 )
=> ( subset @ X21 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(transitivesetOp1,axiom,
( transitivesetOp1
<=> ! [X21: $i] :
( ( transitiveset @ X21 )
=> ! [X4: $i] :
( ( in @ X4 @ X21 )
=> ( subset @ X4 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp1) ).
thf(setOfPairsIsBReln1,axiom,
( setOfPairsIsBReln1
<=> ! [X4: $i,X53: $i > $i > $o] :
( breln1 @ X4
@ ( dpsetconstr @ X4 @ X4
@ ^ [X2: $i,X3: $i] : ( X53 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(image1Ex1,axiom,
( image1Ex1
<=> ! [X4: $i,X58: $i > $i] :
( exu
@ ^ [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X58 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex1) ).
thf(image1Equiv,axiom,
( image1Equiv
<=> ! [X4: $i,X59: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X4
@ ^ [X3: $i] : ( X59 @ X3 ) ) )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X59 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv) ).
thf(image1E,axiom,
( image1E
<=> ! [X4: $i,X60: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X4
@ ^ [X3: $i] : ( X60 @ X3 ) ) )
=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X60 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1E) ).
thf(image1I,axiom,
( image1I
<=> ! [X4: $i,X61: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X61 @ X3 ) ) )
=> ( in @ X2
@ ( image1 @ X4
@ ^ [X3: $i] : ( X61 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1I) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(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(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(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(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(binintTransitive,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
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ! [X21: $i] :
( ( transitiveset @ X21 )
=> ! [X48: $i] :
( ( transitiveset @ X48 )
=> ( transitiveset @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
thf(breln1SetBreln1,axiom,
( breln1SetBreln1
<=> ! [X4: $i,X33: $i] :
( ( in @ X33 @ ( breln1Set @ X4 ) )
=> ( breln1 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1SetBreln1) ).
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(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(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(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
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(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
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(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
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(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(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(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(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(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(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(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(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(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
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(breln1all2,axiom,
( breln1all2
<=> ! [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(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(peanoSinj,axiom,
( peanoSinj
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ! [X3: $i] :
( ( in @ X3 @ omega )
=> ( ( ( omegaS @ X2 )
= ( omegaS @ X3 ) )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peanoSinj) ).
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(breln1all1,axiom,
( breln1all1
<=> ! [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',breln1all1) ).
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(subbreln1,axiom,
( subbreln1
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln1) ).
thf(eqbreln1,axiom,
( eqbreln1
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln1) ).
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(breln1invprop,axiom,
( breln1invprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ( breln1 @ X4 @ ( breln1invset @ X4 @ X33 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).
thf(breln1invI,axiom,
( breln1invI
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X4 @ X33 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invI) ).
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(breln1invE,axiom,
( breln1invE
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X4 @ X33 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invE) ).
thf(breln1compprop,axiom,
( breln1compprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( breln1 @ X4 @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compprop) ).
thf(breln1compI,axiom,
( breln1compI
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compI) ).
thf(breln1compE,axiom,
( breln1compE
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ? [X14: $i] :
( ( in @ X14 @ X4 )
& ( in @ ( kpair @ X2 @ X14 ) @ X33 )
& ( in @ ( kpair @ X14 @ X3 ) @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(breln1compEex,axiom,
( breln1compEex
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
=> ! [X54: $o] :
( ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
=> ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
=> X54 ) ) )
=> X54 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compEex) ).
thf(breln1unionprop,axiom,
( breln1unionprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( breln1 @ X4 @ ( binunion @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionprop) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(breln1unionIL,axiom,
( breln1unionIL
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIL) ).
thf(breln1unionIR,axiom,
( breln1unionIR
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIR) ).
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(breln1unionI,axiom,
( breln1unionI
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
| ( in @ ( kpair @ X2 @ X3 ) @ X35 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionI) ).
thf(breln1unionE,axiom,
( breln1unionE
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
| ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionE) ).
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(breln1unionEcases,axiom,
( breln1unionEcases
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) )
=> ! [X55: $o] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> X55 )
=> ( ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> X55 )
=> X55 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases) ).
thf(breln1unionCommutes,axiom,
( breln1unionCommutes
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( ( binunion @ X33 @ X35 )
= ( binunion @ X35 @ X33 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionCommutes) ).
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(woz2Ex,axiom,
( woz2Ex
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ( X33
= ( breln1invset @ X4 @ ( breln1invset @ X4 @ X33 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2Ex) ).
thf(woz2W,axiom,
( woz2W
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( ( breln1invset @ X4 @ ( breln1compset @ X4 @ X33 @ X35 ) )
= ( breln1compset @ X4 @ ( breln1invset @ X4 @ X35 ) @ ( breln1invset @ X4 @ X33 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2W) ).
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(woz2A,axiom,
( woz2A
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X56: $i] :
( ( breln1 @ X4 @ X56 )
=> ( ( breln1compset @ X4 @ ( binunion @ X33 @ X35 ) @ X56 )
= ( binunion @ ( breln1compset @ X4 @ X33 @ X56 ) @ ( breln1compset @ X4 @ X35 @ X56 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2A) ).
thf(woz2B,axiom,
( woz2B
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ! [X56: $i] :
( ( breln1 @ X4 @ X56 )
=> ( ( breln1compset @ X4 @ ( binunion @ X33 @ X35 ) @ X56 )
= ( binunion @ ( breln1invset @ X4 @ ( breln1compset @ X4 @ ( breln1invset @ X4 @ X56 ) @ ( breln1invset @ X4 @ X35 ) ) ) @ ( breln1invset @ X4 @ ( breln1compset @ X4 @ ( breln1invset @ X4 @ X56 ) @ ( breln1invset @ X4 @ X33 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2B) ).
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(image1Ex,axiom,
( image1Ex
<=> ! [X4: $i,X57: $i > $i] :
? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X57 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex) ).
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(injFuncInInjFuncSet,axiom,
( injFuncInInjFuncSet
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( injective @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( injFuncSet @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncInInjFuncSet) ).
thf(injFuncSetFuncIn,axiom,
( injFuncSetFuncIn
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( injFuncSet @ X4 @ X5 ) )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSetFuncIn) ).
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(injFuncSetFuncInj,axiom,
( injFuncSetFuncInj
<=> ! [X2: $i,X3: $i,X29: $i] :
( ( in @ X29 @ ( injFuncSet @ X2 @ X3 ) )
=> ( injective @ X2 @ X3 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSetFuncInj) ).
thf(surjFuncSetFuncIn,axiom,
( surjFuncSetFuncIn
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( surjFuncSet @ X4 @ X5 ) )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjFuncSetFuncIn) ).
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(surjFuncSetFuncSurj,axiom,
( surjFuncSetFuncSurj
<=> ! [X2: $i,X3: $i,X29: $i] :
( ( in @ X29 @ ( surjFuncSet @ X2 @ X3 ) )
=> ( surjective @ X2 @ X3 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjFuncSetFuncSurj) ).
thf(leftInvIsSurj,axiom,
( leftInvIsSurj
<=> ! [X4: $i,X5: $i,X62: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X62 @ X2 ) @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X5 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X5 @ X4 @ X34 @ ( X62 @ X2 ) )
= X2 ) )
=> ( surjective @ X5 @ X4 @ X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leftInvIsSurj) ).
thf(surjCantorThm,axiom,
( surjCantorThm
<=> ! [X4: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ ( powerset @ X4 ) ) )
=> ~ ( surjective @ X4 @ ( powerset @ X4 ) @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjCantorThm) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(foundation2,axiom,
( foundation2
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( ( binintersect @ X21 @ X4 )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2) ).
thf(notinself,axiom,
( notinself
<=> ! [X4: $i] :
~ ( in @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself) ).
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(notinself2,axiom,
( notinself2
<=> ! [X4: $i,X5: $i] :
( ( in @ X4 @ X5 )
=> ~ ( in @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(omegaSp,axiom,
( omegaSp
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( omegaS @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSp) ).
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(omegaSclos,axiom,
( omegaSclos
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSclos) ).
thf(peano0notS,axiom,
( peano0notS
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( omegaS @ X2 )
!= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peano0notS) ).
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(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(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(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
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(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(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
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(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(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(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(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(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(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
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(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(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(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(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(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(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(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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
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(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_329,plain,
( transitiveset
= ( ^ [Z0: $i] :
! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ( subset @ X21 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitiveset]) ).
thf(c_0_330,axiom,
( transitivesetOp1
= ( ! [X21: $i] :
( ! [X1130: $i] :
( ( in @ X1130 @ X21 )
=> ( subset @ X1130 @ X21 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X21 )
=> ( subset @ X4 @ X21 ) ) ) ) ),
inference(apply_def,[status(thm)],[transitivesetOp1,c_0_329]) ).
thf(c_0_331,plain,
( setOfPairsIsBReln1
<=> ! [X4: $i,X53: $i > $i > $o] :
( breln1 @ X4
@ ( dpsetconstr @ X4 @ X4
@ ^ [Z0: $i,Z1: $i] : ( X53 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1]) ).
thf(c_0_332,plain,
( image1Ex1
<=> ! [X4: $i,X58: $i > $i] :
( exu
@ ^ [Z0: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X58 @ X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1Ex1]) ).
thf(c_0_333,plain,
( image1Equiv
<=> ! [X4: $i,X59: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X4
@ ^ [Z0: $i] : ( X59 @ Z0 ) ) )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X59 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1Equiv]) ).
thf(c_0_334,plain,
( image1E
<=> ! [X4: $i,X60: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X4
@ ^ [Z0: $i] : ( X60 @ Z0 ) ) )
=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X60 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1E]) ).
thf(c_0_335,plain,
( image1I
<=> ! [X4: $i,X61: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X61 @ X3 ) ) )
=> ( in @ X2
@ ( image1 @ X4
@ ^ [Z0: $i] : ( X61 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1I]) ).
thf(c_0_336,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_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,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_345,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_346,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_347,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_348,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_349,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_350,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_351,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_352,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_353,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_354,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_355,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_356,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_357,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_358,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_359,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_360,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_361,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_362,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_363,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_364,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_365,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_366,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_367,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_368,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_369,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_370,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_371,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_372,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_373,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_374,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_375,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_376,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_377,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_378,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_379,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_380,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_381,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_382,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_383,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_384,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_385,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_386,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_387,plain,
( epred1_0
<=> ! [X1158: $i] :
? [X1159: $i] :
( ! [X1160: $i] :
( ( in @ X1160 @ X1159 )
=> ! [X1161: $i] :
( ( in @ X1161 @ X1160 )
=> ( in @ X1161 @ X1158 ) ) )
& ! [X1162: $i,X1163: $i] :
( ( ( in @ X1162 @ X1158 )
& ( in @ X1163 @ X1158 ) )
=> ( ! [X1164: $i] :
( ( in @ X1164 @ X1159 )
=> ( ( in @ X1162 @ X1164 )
<=> ( in @ X1163 @ X1164 ) ) )
=> ( X1162 = X1163 ) ) )
& ! [X1165: $i,X1166: $i] :
( ( ( in @ X1165 @ X1159 )
& ( in @ X1166 @ X1159 ) )
=> ( ! [X1167: $i] :
( ( in @ X1167 @ X1165 )
=> ( in @ X1167 @ X1166 ) )
| ! [X1168: $i] :
( ( in @ X1168 @ X1166 )
=> ( in @ X1168 @ X1165 ) ) ) )
& ! [X1169: $i] :
( ( ! [X1170: $i] :
( ( in @ X1170 @ X1169 )
=> ( in @ X1170 @ X1158 ) )
& ? [X1171: $i] : ( in @ X1171 @ X1169 ) )
=> ? [X1172: $i,X1173: $i] :
( ( in @ X1172 @ X1159 )
& ( in @ X1173 @ X1169 )
& ~ ? [X1174: $i] :
( ( in @ X1174 @ X1172 )
& ( in @ X1174 @ X1169 ) )
& ! [X1175: $i] :
( ( in @ X1175 @ X1159 )
=> ( ! [X1176: $i] :
( ( in @ X1176 @ X1175 )
=> ( in @ X1176 @ X1172 ) )
| ( in @ X1173 @ X1175 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_388,negated_conjecture,
~ ( ! [X1131: $i,X1132: $i] :
( ! [X1133: $i] :
( ( in @ X1133 @ X1131 )
<=> ( in @ X1133 @ X1132 ) )
=> ( X1131 = X1132 ) )
=> ( ! [X1134: $i] :
~ ( in @ X1134 @ emptyset )
=> ( ! [X1135: $i,X1136: $i,X1137: $i] :
( ( in @ X1137 @ ( setadjoin @ X1135 @ X1136 ) )
<=> ( ( X1137 = X1135 )
| ( in @ X1137 @ X1136 ) ) )
=> ( ! [X1138: $i,X1139: $i] :
( ( in @ X1139 @ ( powerset @ X1138 ) )
<=> ! [X1140: $i] :
( ( in @ X1140 @ X1139 )
=> ( in @ X1140 @ X1138 ) ) )
=> ( ! [X1141: $i,X1142: $i] :
( ( in @ X1142 @ ( setunion @ X1141 ) )
<=> ? [X1143: $i] :
( ( in @ X1142 @ X1143 )
& ( in @ X1143 @ X1141 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X1144: $i] :
( ( in @ X1144 @ omega )
=> ( in @ ( setadjoin @ X1144 @ X1144 ) @ omega ) )
=> ( ! [X1145: $i] :
( ( ( in @ emptyset @ X1145 )
& ! [X1146: $i] :
( ( ( in @ X1146 @ omega )
& ( in @ X1146 @ X1145 ) )
=> ( in @ ( setadjoin @ X1146 @ X1146 ) @ X1145 ) ) )
=> ! [X1147: $i] :
( ( in @ X1147 @ omega )
=> ( in @ X1147 @ X1145 ) ) )
=> ( ! [X1148: $i > $i > $o,X1149: $i] :
( ! [X1150: $i] :
( ( in @ X1150 @ X1149 )
=> ( exu @ ( X1148 @ X1150 ) ) )
=> ? [X1151: $i] :
! [X1152: $i] :
( ( in @ X1152 @ X1151 )
<=> ? [X1153: $i] :
( ( in @ X1153 @ X1149 )
& ( X1148 @ X1153 @ X1152 ) ) ) )
=> ( ! [X1154: $i] :
( ? [X1155: $i] : ( in @ X1155 @ X1154 )
=> ? [X1156: $i] :
( ( in @ X1156 @ X1154 )
& ~ ? [X1157: $i] :
( ( in @ X1157 @ X1156 )
& ( in @ X1157 @ X1154 ) ) ) )
=> ( epred1_0
=> ( ! [X1177: $i > $o] :
( ( exu @ X1177 )
=> ( X1177
@ ( descr
@ ^ [Z0: $i] : ( X1177 @ Z0 ) ) ) )
=> ( ! [X1178: $i,X1179: $i > $o,X1180: $i] :
( ( in @ X1180 @ X1178 )
=> ( ( X1179 @ X1180 )
=> ( in @ X1180 @ ( dsetconstr @ X1178 @ X1179 ) ) ) )
=> ( ! [X1181: $i,X1182: $i > $o,X1183: $i] :
( ( in @ X1183 @ ( dsetconstr @ X1181 @ X1182 ) )
=> ( in @ X1183 @ X1181 ) )
=> ( ! [X1184: $i,X1185: $i > $o,X1186: $i] :
( ( in @ X1186 @ ( dsetconstr @ X1184 @ X1185 ) )
=> ( X1185 @ X1186 ) )
=> ( ! [X1187: $i > $o] :
( ( exu @ X1187 )
=> ? [X1188: $i] :
( ( X1187 @ X1188 )
& ! [X1189: $i] :
( ( X1187 @ X1189 )
=> ( X1188 = X1189 ) ) ) )
=> ( ! [X1190: $o,X1191: $i] :
( ( in @ X1191 @ ( prop2set @ X1190 ) )
=> X1190 )
=> ( ! [X1192: $i] :
( ( in @ X1192 @ emptyset )
=> ! [X1193: $o] : X1193 )
=> ( ! [X1194: $i] :
( ( in @ X1194 @ emptyset )
=> ~ $true )
=> ( ! [X1195: $i] :
~ ( in @ X1195 @ emptyset )
=> ( ! [X1196: $i > $o] :
( ( exu @ X1196 )
=> ? [X1197: $i] : ( X1196 @ X1197 ) )
=> ( ! [X1198: $i,X1199: $i] :
( ! [X1200: $i] :
( ( in @ X1200 @ X1198 )
=> ( in @ X1200 @ X1199 ) )
=> ( ! [X1201: $i] :
( ( in @ X1201 @ X1199 )
=> ( in @ X1201 @ X1198 ) )
=> ( X1198 = X1199 ) ) )
=> ( ! [X1202: $i] :
( ! [X1203: $i] :
~ ( in @ X1203 @ X1202 )
=> ( X1202 = emptyset ) )
=> ( ! [X1204: $i] :
( ! [X1205: $i] :
~ ( in @ X1205 @ X1204 )
=> ( X1204 = emptyset ) )
=> ( ! [X1206: $i,X1207: $i > $o,X1208: $i] :
( ( in @ X1208 @ X1206 )
=> ( ( in @ X1208 @ ( dsetconstr @ X1206 @ X1207 ) )
<=> ( X1207 @ X1208 ) ) )
=> ( ! [X1209: $i] :
( ( nonempty @ X1209 )
=> ? [X1210: $i] : ( in @ X1210 @ X1209 ) )
=> ( ! [X1211: $i,X1212: $i > $o,X1213: $i] :
( ( in @ X1213 @ X1211 )
=> ( ( X1212 @ X1213 )
=> ( nonempty @ ( dsetconstr @ X1211 @ X1212 ) ) ) )
=> ( ! [X1214: $i] :
( ? [X1215: $i] : ( in @ X1215 @ X1214 )
=> ( nonempty @ X1214 ) )
=> ( ! [X1216: $i,X1217: $i] : ( in @ X1216 @ ( setadjoin @ X1216 @ X1217 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( in @ X1220 @ X1219 )
=> ( in @ X1220 @ ( setadjoin @ X1218 @ X1219 ) ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i] :
( ( in @ X1223 @ ( setadjoin @ X1221 @ X1222 ) )
=> ! [X1224: $o] :
( ( ( X1223 = X1221 )
=> X1224 )
=> ( ( ( in @ X1223 @ X1222 )
=> X1224 )
=> X1224 ) ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i] :
( ( in @ X1227 @ ( setadjoin @ X1225 @ X1226 ) )
=> ( ( X1227 = X1225 )
| ( in @ X1227 @ X1226 ) ) )
=> ( ! [X1228: $i] :
( ( dsetconstr @ X1228
@ ^ [Z0: $i] : $true )
= X1228 )
=> ( ! [X1229: $i,X1230: $i] :
( ! [X1231: $i] :
( ( in @ X1231 @ X1230 )
=> ( in @ X1231 @ X1229 ) )
=> ( in @ X1230 @ ( powerset @ X1229 ) ) )
=> ( ! [X1232: $i] : ( in @ emptyset @ ( powerset @ X1232 ) )
=> ( ! [X1233: $i] : ( in @ emptyset @ ( powerset @ X1233 ) )
=> ( ! [X1234: $i,X1235: $i,X1236: $i] :
( ( in @ X1235 @ ( powerset @ X1234 ) )
=> ( ( in @ X1236 @ X1235 )
=> ( in @ X1236 @ X1234 ) ) )
=> ( ! [X1237: $i,X1238: $i,X1239: $i] :
( ( in @ X1238 @ X1239 )
=> ( ( in @ X1239 @ X1237 )
=> ( in @ X1238 @ ( setunion @ X1237 ) ) ) )
=> ( ! [X1240: $i,X1241: $i] :
( ( in @ X1241 @ ( setunion @ X1240 ) )
=> ! [X1242: $o] :
( ! [X1243: $i] :
( ( in @ X1241 @ X1243 )
=> ( ( in @ X1243 @ X1240 )
=> X1242 ) )
=> X1242 ) )
=> ( ! [X1244: $i,X1245: $i] :
( ( in @ X1245 @ X1244 )
=> ( in @ X1245 @ ( powerset @ ( setunion @ X1244 ) ) ) )
=> ( ! [X1246: $i > $o] :
( ( exu @ X1246 )
=> ? [X1247: $i] :
! [X1248: $i] :
( ( X1246 @ X1248 )
<=> ( X1248 = X1247 ) ) )
=> ( ! [X1249: $i] :
( ( nonempty @ X1249 )
=> ? [X1250: $i] :
( ( in @ X1250 @ X1249 )
& $true ) )
=> ( ! [X1251: $i,X1252: $i] :
( ( in @ X1251 @ ( setadjoin @ X1252 @ emptyset ) )
=> ( X1251 = X1252 ) )
=> ( ! [X1253: $i,X1254: $i] :
( ( X1253 != X1254 )
=> ~ ( in @ X1254 @ ( setadjoin @ X1253 @ emptyset ) ) )
=> ( ! [X1255: $i,X1256: $i] :
( ( X1255 = X1256 )
=> ( in @ X1255 @ ( setadjoin @ X1256 @ emptyset ) ) )
=> ( ! [X1257: $i,X1258: $i] :
( ( in @ X1257 @ ( setadjoin @ X1258 @ emptyset ) )
=> ( in @ X1258 @ ( setadjoin @ X1257 @ emptyset ) ) )
=> ( ! [X1259: $i,X1260: $i,X1261: $i] :
( ( in @ X1261 @ ( setadjoin @ X1259 @ ( setadjoin @ X1260 @ emptyset ) ) )
=> ( ( X1261 = X1259 )
| ( X1261 = X1260 ) ) )
=> ( ! [X1262: $i,X1263: $i] : ( in @ X1262 @ ( setadjoin @ X1262 @ ( setadjoin @ X1263 @ emptyset ) ) )
=> ( ! [X1264: $i,X1265: $i] : ( in @ X1265 @ ( setadjoin @ X1264 @ ( setadjoin @ X1265 @ emptyset ) ) )
=> ( ! [X1266: $i,X1267: $i > $o] :
( ? [X1268: $i] :
( ( in @ X1268 @ X1266 )
& ( X1267 @ X1268 ) )
=> ( ( ( dsetconstr @ X1266 @ X1267 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1269: $i > $o,X1270: $i] :
( ( in @ X1270 @ emptyset )
=> ( X1269 @ X1270 ) )
=> ( ! [X1271: $i,X1272: $i > $o] :
( ~ ! [X1273: $i] :
( ( in @ X1273 @ X1271 )
=> ( X1272 @ X1273 ) )
=> ? [X1274: $i] :
( ( in @ X1274 @ X1271 )
& ~ ( X1272 @ X1274 ) ) )
=> ( ! [X1275: $i,X1276: $i > $o] :
( ! [X1277: $i] :
( ( in @ X1277 @ X1275 )
=> ~ ( X1276 @ X1277 ) )
=> ~ ? [X1278: $i] :
( ( in @ X1278 @ X1275 )
& ( X1276 @ X1278 ) ) )
=> ( ! [X1279: $i,X1280: $i > $o] :
( ~ ? [X1281: $i] :
( ( in @ X1281 @ X1279 )
& ( X1280 @ X1281 ) )
=> ! [X1282: $i] :
( ( in @ X1282 @ X1279 )
=> ~ ( X1280 @ X1282 ) ) )
=> ( ! [X1283: $i,X1284: $i > $o] :
( ? [X1285: $i] :
( ( in @ X1285 @ X1283 )
& ~ ( X1284 @ X1285 ) )
=> ~ ! [X1286: $i] :
( ( in @ X1286 @ X1283 )
=> ( X1284 @ X1286 ) ) )
=> ( ! [X1287: $o] :
( X1287
=> ( in @ emptyset @ ( prop2set @ X1287 ) ) )
=> ( prop2set2propI
=> ( ! [X1288: $i,X1289: $i > $o] :
( ~ ? [X1290: $i] :
( ( in @ X1290 @ X1288 )
& ( X1289 @ X1290 ) )
=> ! [X1291: $i] :
( ( in @ X1291 @ X1288 )
=> ~ ( X1289 @ X1291 ) ) )
=> ( ! [X1292: $i,X1293: $i > $o] :
( ~ ! [X1294: $i] :
( ( in @ X1294 @ X1292 )
=> ( X1293 @ X1294 ) )
=> ? [X1295: $i] :
( ( in @ X1295 @ X1292 )
& ~ ( X1293 @ X1295 ) ) )
=> ( ! [X1296: $i > $o] :
( ? [X1297: $i] :
( ( X1296 @ X1297 )
& ! [X1298: $i] :
( ( X1296 @ X1298 )
=> ( X1297 = X1298 ) ) )
=> ( exu @ X1296 ) )
=> ( ! [X1299: $i > $o] :
( ? [X1300: $i] : ( X1299 @ X1300 )
=> ( ! [X1301: $i,X1302: $i] :
( ( X1299 @ X1301 )
=> ( ( X1299 @ X1302 )
=> ( X1301 = X1302 ) ) )
=> ( exu @ X1299 ) ) )
=> ( ! [X1303: $i > $o] :
( ? [X1304: $i] :
! [X1305: $i] :
( ( X1303 @ X1305 )
<=> ( X1305 = X1304 ) )
=> ( exu @ X1303 ) )
=> ( ! [X1306: $i,X1307: $i] :
( ( X1306 = X1307 )
=> ! [X1308: $i,X1309: $i] :
( ( X1308 = X1309 )
=> ( ( in @ X1308 @ X1306 )
=> ( in @ X1309 @ X1307 ) ) ) )
=> ( ! [X1310: $i,X1311: $i] :
( ( X1310 = X1311 )
=> ! [X1312: $i,X1313: $i] :
( ( X1312 = X1313 )
=> ( ( in @ X1312 @ X1310 )
<=> ( in @ X1313 @ X1311 ) ) ) )
=> ( ! [X1314: $i > $o] :
( ( exu @ X1314 )
=> ! [X1315: $i,X1316: $i] :
( ( X1314 @ X1315 )
=> ( ( X1314 @ X1316 )
=> ( X1315 = X1316 ) ) ) )
=> ( ! [X1317: $i > $o,X1318: $i > $o] :
( ! [X1319: $i,X1320: $i] :
( ( X1319 = X1320 )
=> ( ( X1317 @ X1319 )
<=> ( X1318 @ X1320 ) ) )
=> ( ( exu @ X1317 )
<=> ( exu @ X1318 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1321: $i,X1322: $i] :
( ( X1321 = X1322 )
=> ! [X1323: $i,X1324: $i] :
( ( X1323 = X1324 )
=> ( ( setadjoin @ X1321 @ X1323 )
= ( setadjoin @ X1322 @ X1324 ) ) ) )
=> ( ! [X1325: $i,X1326: $i] :
( ( X1325 = X1326 )
=> ( ( powerset @ X1325 )
= ( powerset @ X1326 ) ) )
=> ( ! [X1327: $i,X1328: $i] :
( ( X1327 = X1328 )
=> ( ( setunion @ X1327 )
= ( setunion @ X1328 ) ) )
=> ( ( omega = omega )
=> ( ! [X1329: $i > $o] :
( ( exu @ X1329 )
=> ! [X1330: $i,X1331: $i] :
( ( X1329 @ X1330 )
=> ( ( X1329 @ X1331 )
=> ( X1330 = X1331 ) ) ) )
=> ( ! [X1332: $i > $o,X1333: $i > $o] :
( ! [X1334: $i,X1335: $i] :
( ( X1334 = X1335 )
=> ( ( X1332 @ X1334 )
<=> ( X1333 @ X1335 ) ) )
=> ( ( exu @ X1332 )
=> ( ( exu @ X1333 )
=> ( ( descr @ X1332 )
= ( descr @ X1333 ) ) ) ) )
=> ( ! [X1336: $i,X1337: $i] :
( ( X1336 = X1337 )
=> ! [X1338: $i > $o,X1339: $i > $o] :
( ! [X1340: $i] :
( ( in @ X1340 @ X1336 )
=> ! [X1341: $i] :
( ( in @ X1341 @ X1337 )
=> ( ( X1340 = X1341 )
=> ( ( X1338 @ X1340 )
<=> ( X1339 @ X1341 ) ) ) ) )
=> ( ( dsetconstr @ X1336 @ X1338 )
= ( dsetconstr @ X1337 @ X1339 ) ) ) )
=> ( ! [X1342: $i,X1343: $i] :
( ! [X1344: $i] :
( ( in @ X1344 @ X1342 )
=> ( in @ X1344 @ X1343 ) )
=> ( subset @ X1342 @ X1343 ) )
=> ( ! [X1345: $i,X1346: $i] :
( ( X1345 = X1346 )
=> ( subset @ X1346 @ X1345 ) )
=> ( ! [X1347: $i,X1348: $i] :
( ( X1347 = X1348 )
=> ( subset @ X1347 @ X1348 ) )
=> ( ! [X1349: $i,X1350: $i] :
( ! [X1351: $i] :
( ( in @ X1351 @ X1349 )
=> ( in @ X1351 @ X1350 ) )
=> ( subset @ X1349 @ X1350 ) )
=> ( ! [X1352: $i] : ( subset @ emptyset @ X1352 )
=> ( ! [X1353: $i,X1354: $i,X1355: $i] :
( ( subset @ X1353 @ X1354 )
=> ( ( in @ X1355 @ X1353 )
=> ( in @ X1355 @ X1354 ) ) )
=> ( ! [X1356: $i,X1357: $i,X1358: $i] :
( ( subset @ X1356 @ X1357 )
=> ( ~ ( in @ X1358 @ X1357 )
=> ~ ( in @ X1358 @ X1356 ) ) )
=> ( ! [X1359: $i,X1360: $i,X1361: $i] :
( ( in @ X1361 @ X1359 )
=> ( ~ ( in @ X1361 @ X1360 )
=> ~ ( subset @ X1359 @ X1360 ) ) )
=> ( ! [X1362: $i,X1363: $i] :
( ~ ( subset @ X1362 @ X1363 )
=> ( X1362 != X1363 ) )
=> ( ! [X1364: $i,X1365: $i,X1366: $i] :
( ( in @ X1366 @ X1364 )
=> ( ~ ( in @ X1366 @ X1365 )
=> ( X1364 != X1365 ) ) )
=> ( ! [X1367: $i] : ( subset @ X1367 @ X1367 )
=> ( ! [X1368: $i,X1369: $i,X1370: $i] :
( ( subset @ X1368 @ X1369 )
=> ( ( subset @ X1369 @ X1370 )
=> ( subset @ X1368 @ X1370 ) ) )
=> ( ! [X1371: $i,X1372: $i] : ( subset @ X1372 @ ( setadjoin @ X1371 @ X1372 ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( subset @ X1373 @ X1375 )
=> ( subset @ X1373 @ ( setadjoin @ X1374 @ X1375 ) ) )
=> ( ! [X1376: $i,X1377: $i] :
( ( subset @ X1376 @ X1377 )
=> ( in @ X1376 @ ( powerset @ X1377 ) ) )
=> ( ! [X1378: $i,X1379: $i] :
( ( subset @ X1378 @ X1379 )
=> ( ( subset @ X1379 @ X1378 )
=> ( X1378 = X1379 ) ) )
=> ( ! [X1380: $i] :
( ( subset @ X1380 @ emptyset )
=> ( X1380 = emptyset ) )
=> ( ! [X1381: $i,X1382: $i] :
( ( subset @ X1382 @ X1381 )
=> ( in @ X1382 @ ( powerset @ X1381 ) ) )
=> ( ! [X1383: $i,X1384: $i] :
( ( in @ X1384 @ ( powerset @ X1383 ) )
=> ( subset @ X1384 @ X1383 ) )
=> ( ! [X1385: $i] : ( in @ X1385 @ ( powerset @ X1385 ) )
=> ( ! [X1386: $i,X1387: $i] :
( ( subset @ X1386 @ X1387 )
=> ( subset @ ( powerset @ X1386 ) @ ( powerset @ X1387 ) ) )
=> ( ! [X1388: $i,X1389: $i > $o] : ( in @ ( dsetconstr @ X1388 @ X1389 ) @ ( powerset @ X1388 ) )
=> ( ! [X1390: $i,X1391: $i > $o] : ( subset @ ( dsetconstr @ X1390 @ X1391 ) @ X1390 )
=> ( ! [X1392: $i,X1393: $i,X1394: $i] :
( ( in @ X1394 @ X1392 )
=> ( in @ X1394 @ ( binunion @ X1392 @ X1393 ) ) )
=> ( ! [X1395: $i,X1396: $i] : ( in @ X1396 @ ( setadjoin @ X1395 @ ( setadjoin @ X1396 @ emptyset ) ) )
=> ( ! [X1397: $i,X1398: $i,X1399: $i] :
( ( in @ X1399 @ X1398 )
=> ( in @ X1399 @ ( binunion @ X1397 @ X1398 ) ) )
=> ( ! [X1400: $i,X1401: $i,X1402: $i,X1403: $o] :
( ( in @ X1402 @ ( binunion @ X1400 @ X1401 ) )
=> ( ( ( in @ X1402 @ X1400 )
=> X1403 )
=> ( ( ( in @ X1402 @ X1401 )
=> X1403 )
=> X1403 ) ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i] :
( ( in @ X1406 @ ( binunion @ X1404 @ X1405 ) )
=> ( ( in @ X1406 @ X1404 )
| ( in @ X1406 @ X1405 ) ) )
=> ( ! [X1407: $i,X1408: $i] : ( subset @ X1407 @ ( binunion @ X1407 @ X1408 ) )
=> ( ! [X1409: $i,X1410: $i] : ( subset @ X1410 @ ( binunion @ X1409 @ X1410 ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i] :
( ( in @ X1413 @ X1411 )
=> ( ( in @ X1413 @ X1412 )
=> ( in @ X1413 @ ( binintersect @ X1411 @ X1412 ) ) ) )
=> ( ! [X1414: $i,X1415: $i,X1416: $i] :
( ( subset @ X1416 @ X1414 )
=> ( ( subset @ X1416 @ X1415 )
=> ( subset @ X1416 @ ( binintersect @ X1414 @ X1415 ) ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( in @ X1419 @ ( binintersect @ X1417 @ X1418 ) )
=> ( in @ X1419 @ X1417 ) )
=> ( ! [X1420: $i,X1421: $i] : ( subset @ ( binintersect @ X1420 @ X1421 ) @ X1420 )
=> ( ! [X1422: $i,X1423: $i] :
( ( subset @ X1422 @ X1423 )
=> ( ( binintersect @ X1422 @ X1423 )
= X1422 ) )
=> ( ! [X1424: $i,X1425: $i] :
( ( ( binintersect @ X1424 @ X1425 )
= X1425 )
=> ( subset @ X1425 @ X1424 ) )
=> ( ! [X1426: $i,X1427: $i,X1428: $i] :
( ( in @ X1428 @ ( binintersect @ X1426 @ X1427 ) )
=> ( in @ X1428 @ X1427 ) )
=> ( ! [X1429: $i,X1430: $i] :
( ~ ? [X1431: $i] :
( ( in @ X1431 @ X1429 )
& ( in @ X1431 @ X1430 ) )
=> ( ( binintersect @ X1429 @ X1430 )
= emptyset ) )
=> ( ! [X1432: $i,X1433: $i] : ( subset @ ( binintersect @ X1432 @ X1433 ) @ X1433 )
=> ( ! [X1434: $i,X1435: $i] :
( ( subset @ X1435 @ X1434 )
=> ( ( binintersect @ X1434 @ X1435 )
= X1435 ) )
=> ( ! [X1436: $i,X1437: $i] :
( ( ( binintersect @ X1436 @ X1437 )
= X1436 )
=> ( subset @ X1436 @ X1437 ) )
=> ( ! [X1438: $i,X1439: $i,X1440: $i] :
( ( binintersect @ X1438 @ ( binunion @ X1439 @ X1440 ) )
= ( binunion @ ( binintersect @ X1438 @ X1439 ) @ ( binintersect @ X1438 @ X1440 ) ) )
=> ( ! [X1441: $i,X1442: $i,X1443: $i] :
( ( in @ X1443 @ X1441 )
=> ( ~ ( in @ X1443 @ X1442 )
=> ( in @ X1443 @ ( setminus @ X1441 @ X1442 ) ) ) )
=> ( ! [X1444: $i,X1445: $i,X1446: $i] :
( ( in @ X1446 @ ( setminus @ X1444 @ X1445 ) )
=> ( in @ X1446 @ X1444 ) )
=> ( ! [X1447: $i,X1448: $i,X1449: $i] :
( ( in @ X1449 @ ( setminus @ X1447 @ X1448 ) )
=> ~ ( in @ X1449 @ X1448 ) )
=> ( ! [X1450: $i,X1451: $i] :
( ( subset @ X1450 @ X1451 )
=> ( ( setminus @ X1450 @ X1451 )
= emptyset ) )
=> ( ! [X1452: $i,X1453: $i,X1454: $i] :
( ~ ( in @ X1454 @ ( setminus @ X1452 @ X1453 ) )
=> ( ( in @ X1454 @ X1452 )
=> ( in @ X1454 @ X1453 ) ) )
=> ( ! [X1455: $i,X1456: $i,X1457: $i] :
( ~ ( in @ X1457 @ ( setminus @ X1455 @ X1456 ) )
=> ( ~ ( in @ X1457 @ X1456 )
=> ~ ( in @ X1457 @ X1455 ) ) )
=> ( ! [X1458: $i,X1459: $i,X1460: $i] :
( ~ ( in @ X1460 @ X1458 )
=> ~ ( in @ X1460 @ ( setminus @ X1458 @ X1459 ) ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i] :
( ( in @ X1463 @ X1462 )
=> ~ ( in @ X1463 @ ( setminus @ X1461 @ X1462 ) ) )
=> ( ! [X1464: $i,X1465: $i] : ( subset @ ( setminus @ X1464 @ X1465 ) @ X1464 )
=> ( ! [X1466: $i,X1467: $i] :
( ( ( setminus @ X1466 @ X1467 )
= emptyset )
=> ( subset @ X1466 @ X1467 ) )
=> ( ! [X1468: $i,X1469: $i,X1470: $i] :
( ( in @ X1470 @ ( symdiff @ X1468 @ X1469 ) )
=> ! [X1471: $o] :
( ( ( in @ X1470 @ X1468 )
=> ( ~ ( in @ X1470 @ X1469 )
=> X1471 ) )
=> ( ( ~ ( in @ X1470 @ X1468 )
=> ( ( in @ X1470 @ X1469 )
=> X1471 ) )
=> X1471 ) ) )
=> ( ! [X1472: $i,X1473: $i,X1474: $i] :
( ( in @ X1474 @ X1472 )
=> ( ~ ( in @ X1474 @ X1473 )
=> ( in @ X1474 @ ( symdiff @ X1472 @ X1473 ) ) ) )
=> ( ! [X1475: $i,X1476: $i,X1477: $i] :
( ~ ( in @ X1477 @ X1475 )
=> ( ( in @ X1477 @ X1476 )
=> ( in @ X1477 @ ( symdiff @ X1475 @ X1476 ) ) ) )
=> ( ! [X1478: $i,X1479: $i,X1480: $i] :
( ( in @ X1480 @ X1478 )
=> ( ( in @ X1480 @ X1479 )
=> ~ ( in @ X1480 @ ( symdiff @ X1478 @ X1479 ) ) ) )
=> ( ! [X1481: $i,X1482: $i,X1483: $i] :
( ~ ( in @ X1483 @ X1481 )
=> ( ~ ( in @ X1483 @ X1482 )
=> ~ ( in @ X1483 @ ( symdiff @ X1481 @ X1482 ) ) ) )
=> ( ! [X1484: $i,X1485: $i] : ( in @ X1485 @ ( setadjoin @ X1484 @ ( setadjoin @ X1485 @ emptyset ) ) )
=> ( ! [X1486: $i,X1487: $i] : ( in @ X1486 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1486 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1486 @ ( setadjoin @ X1487 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1488: $i,X1489: $i] : ( in @ X1489 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1488 @ ( setadjoin @ X1489 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1490: $i,X1491: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1490 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1490 @ ( setadjoin @ X1491 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1492: $i,X1493: $i] : ( iskpair @ ( kpair @ X1492 @ X1493 ) )
=> ( ! [X1494: $i,X1495: $i] :
( ( in @ X1495 @ X1494 )
=> ( subset @ ( setadjoin @ X1495 @ emptyset ) @ X1494 ) )
=> ( ! [X1496: $i,X1497: $i] :
( ( in @ X1497 @ X1496 )
=> ( in @ ( setadjoin @ X1497 @ emptyset ) @ ( powerset @ X1496 ) ) )
=> ( ! [X1498: $i,X1499: $i,X1500: $i] :
( ( in @ X1500 @ X1498 )
=> ( in @ ( setadjoin @ X1500 @ emptyset ) @ ( powerset @ ( binunion @ X1498 @ X1499 ) ) ) )
=> ( ! [X1501: $i,X1502: $i,X1503: $i] :
( ( in @ X1503 @ ( setadjoin @ X1501 @ ( setadjoin @ X1502 @ emptyset ) ) )
=> ( ( X1503 = X1501 )
| ( X1503 = X1502 ) ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i] :
( ( in @ X1506 @ X1504 )
=> ! [X1507: $i] :
( ( in @ X1507 @ X1505 )
=> ( subset @ ( setadjoin @ X1506 @ ( setadjoin @ X1507 @ emptyset ) ) @ ( binunion @ X1504 @ X1505 ) ) ) )
=> ( ! [X1508: $i,X1509: $i,X1510: $i] :
( ( in @ X1510 @ X1508 )
=> ! [X1511: $i] :
( ( in @ X1511 @ X1509 )
=> ( in @ ( setadjoin @ X1510 @ ( setadjoin @ X1511 @ emptyset ) ) @ ( powerset @ ( binunion @ X1508 @ X1509 ) ) ) ) )
=> ( ! [X1512: $i,X1513: $i,X1514: $i] :
( ( in @ X1514 @ X1512 )
=> ! [X1515: $i] :
( ( in @ X1515 @ X1513 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1514 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1514 @ ( setadjoin @ X1515 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1512 @ X1513 ) ) ) ) )
=> ( ! [X1516: $i,X1517: $i,X1518: $i] :
( ( in @ X1518 @ X1516 )
=> ! [X1519: $i] :
( ( in @ X1519 @ X1517 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1518 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1518 @ ( setadjoin @ X1519 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1516 @ X1517 ) ) ) ) ) )
=> ( ! [X1520: $i,X1521: $i,X1522: $i] :
( ( in @ X1522 @ X1520 )
=> ! [X1523: $i] :
( ( in @ X1523 @ X1521 )
=> ( in @ ( kpair @ X1522 @ X1523 ) @ ( powerset @ ( powerset @ ( binunion @ X1520 @ X1521 ) ) ) ) ) )
=> ( ! [X1524: $i,X1525: $i,X1526: $i] :
( ( in @ X1526 @ X1524 )
=> ! [X1527: $i] :
( ( in @ X1527 @ X1525 )
=> ( in @ ( kpair @ X1526 @ X1527 ) @ ( cartprod @ X1524 @ X1525 ) ) ) )
=> ( ! [X1528: $i,X1529: $i,X1530: $i] :
( ( in @ X1530 @ ( cartprod @ X1528 @ X1529 ) )
=> ? [X1531: $i] :
( ( in @ X1531 @ X1528 )
& ? [X1532: $i] :
( ( in @ X1532 @ X1529 )
& ( X1530
= ( kpair @ X1531 @ X1532 ) ) ) ) )
=> ( ! [X1533: $i,X1534: $i,X1535: $i] :
( ( in @ X1535 @ ( cartprod @ X1533 @ X1534 ) )
=> ( iskpair @ X1535 ) )
=> ( ! [X1536: $i,X1537: $i] :
( ( in @ X1537 @ ( setunion @ X1536 ) )
=> ? [X1538: $i] :
( ( in @ X1538 @ X1536 )
& ( in @ X1537 @ X1538 ) ) )
=> ( ! [X1539: $i] : ( subset @ ( setunion @ ( setadjoin @ X1539 @ emptyset ) ) @ X1539 )
=> ( ! [X1540: $i] : ( subset @ X1540 @ ( setunion @ ( setadjoin @ X1540 @ emptyset ) ) )
=> ( ! [X1541: $i] :
( ( setunion @ ( setadjoin @ X1541 @ emptyset ) )
= X1541 )
=> ( ! [X1542: $i,X1543: $i > $o] :
( ! [X1544: $i] :
( ( in @ X1544 @ X1542 )
=> ! [X1545: $i] :
( ( in @ X1545 @ X1542 )
=> ( ( X1543 @ X1544 )
=> ( ( X1543 @ X1545 )
=> ( X1544 = X1545 ) ) ) ) )
=> ( ? [X1546: $i] :
( ( in @ X1546 @ X1542 )
& ( X1543 @ X1546 ) )
=> ( singleton @ ( dsetconstr @ X1542 @ X1543 ) ) ) )
=> ( ! [X1547: $i,X1548: $i > $o] :
( ( ex1 @ X1547 @ X1548 )
=> ? [X1549: $i] :
( ( in @ X1549 @ X1547 )
& ( X1548 @ X1549 ) ) )
=> ( ! [X1550: $i,X1551: $i > $o,X1552: $i] :
( ( in @ X1552 @ X1550 )
=> ( ( X1551 @ X1552 )
=> ( ! [X1553: $i] :
( ( in @ X1553 @ X1550 )
=> ( ( X1551 @ X1553 )
=> ( X1553 = X1552 ) ) )
=> ( ex1 @ X1550 @ X1551 ) ) ) )
=> ( ! [X1554: $i,X1555: $i > $o] :
( ! [X1556: $i] :
( ( in @ X1556 @ X1554 )
=> ! [X1557: $i] :
( ( in @ X1557 @ X1554 )
=> ( ( X1555 @ X1556 )
=> ( ( X1555 @ X1557 )
=> ( X1556 = X1557 ) ) ) ) )
=> ( ? [X1558: $i] :
( ( in @ X1558 @ X1554 )
& ( X1555 @ X1558 ) )
=> ( ex1 @ X1554 @ X1555 ) ) )
=> ( ! [X1559: $i,X1560: $i] :
( ( ( setadjoin @ X1559 @ emptyset )
= ( setadjoin @ X1560 @ emptyset ) )
=> ( X1559 = X1560 ) )
=> ( ! [X1561: $i,X1562: $i,X1563: $i] :
( ( in @ ( setadjoin @ X1563 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1561 @ ( setadjoin @ X1562 @ emptyset ) ) @ emptyset ) ) )
=> ( X1561 = X1563 ) )
=> ( ! [X1564: $i] :
( ( iskpair @ X1564 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1564 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1564 ) ) ) )
=> ( ! [X1565: $i] :
( ( singleton @ X1565 )
=> ( in @ ( setunion @ X1565 ) @ X1565 ) )
=> ( ! [X1566: $i,X1567: $i] :
( ( kfst @ ( kpair @ X1566 @ X1567 ) )
= X1566 )
=> ( ! [X1568: $i,X1569: $i,X1570: $i] :
( ( in @ X1570 @ ( cartprod @ X1568 @ X1569 ) )
=> ( in @ ( kfst @ X1570 ) @ X1568 ) )
=> ( ! [X1571: $i,X1572: $i,X1573: $i,X1574: $i] :
( ( ( setadjoin @ ( setadjoin @ X1571 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1571 @ ( setadjoin @ X1572 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1573 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1573 @ ( setadjoin @ X1574 @ emptyset ) ) @ emptyset ) ) )
=> ( X1571 = X1573 ) )
=> ( ! [X1575: $i,X1576: $i,X1577: $i,X1578: $i] :
( ( ( kpair @ X1575 @ X1576 )
= ( kpair @ X1577 @ X1578 ) )
=> ( X1575 = X1577 ) )
=> ( ! [X1579: $i,X1580: $i] :
( ( X1579 = X1580 )
=> ( ( setadjoin @ X1579 @ ( setadjoin @ X1580 @ emptyset ) )
= ( setadjoin @ X1579 @ emptyset ) ) )
=> ( ! [X1581: $i,X1582: $i] :
( ( X1581 = X1582 )
=> ( ( setadjoin @ ( setadjoin @ X1581 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1581 @ ( setadjoin @ X1582 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1581 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1583: $i,X1584: $i,X1585: $i,X1586: $i] :
( ( ( setadjoin @ ( setadjoin @ X1583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1583 @ ( setadjoin @ X1584 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1585 @ ( setadjoin @ X1586 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1585 = X1586 )
=> ( X1584 = X1586 ) ) )
=> ( ! [X1587: $i,X1588: $i,X1589: $i] :
( ( ( setadjoin @ X1587 @ ( setadjoin @ X1588 @ emptyset ) )
= ( setadjoin @ X1589 @ emptyset ) )
=> ( X1587 = X1588 ) )
=> ( ! [X1590: $i,X1591: $i,X1592: $i,X1593: $i] :
( ( ( setadjoin @ ( setadjoin @ X1590 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1590 @ ( setadjoin @ X1591 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1592 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1592 @ ( setadjoin @ X1593 @ emptyset ) ) @ emptyset ) ) )
=> ( X1591 = X1593 ) )
=> ( ! [X1594: $i,X1595: $i,X1596: $i,X1597: $i] :
( ( ( kpair @ X1594 @ X1595 )
= ( kpair @ X1596 @ X1597 ) )
=> ( X1595 = X1597 ) )
=> ( ! [X1598: $i] :
( ( iskpair @ X1598 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1598 )
@ ^ [Z0: $i] :
( X1598
= ( kpair @ ( kfst @ X1598 ) @ Z0 ) ) ) ) )
=> ( ! [X1599: $i,X1600: $i] :
( ( ksnd @ ( kpair @ X1599 @ X1600 ) )
= X1600 )
=> ( ! [X1601: $i] :
( ( iskpair @ X1601 )
=> ( ( kpair @ ( kfst @ X1601 ) @ ( ksnd @ X1601 ) )
= X1601 ) )
=> ( ! [X1602: $i,X1603: $i,X1604: $i] :
( ( in @ X1604 @ ( cartprod @ X1602 @ X1603 ) )
=> ( in @ ( ksnd @ X1604 ) @ X1603 ) )
=> ( ! [X1605: $i,X1606: $i,X1607: $i,X1608: $i] :
( ( in @ ( kpair @ X1607 @ X1608 ) @ ( cartprod @ X1605 @ X1606 ) )
=> ( in @ X1607 @ X1605 ) )
=> ( ! [X1609: $i,X1610: $i,X1611: $i,X1612: $i] :
( ( in @ ( kpair @ X1611 @ X1612 ) @ ( cartprod @ X1609 @ X1610 ) )
=> ( in @ X1612 @ X1610 ) )
=> ( ! [X1613: $i,X1614: $i,X1615: $i] :
( ( in @ X1615 @ X1613 )
=> ! [X1616: $i] :
( ( in @ X1616 @ X1614 )
=> ( ( kpair @ X1615 @ X1616 )
= ( kpair @ X1615 @ X1616 ) ) ) )
=> ( ! [X1617: $i,X1618: $i,X1619: $i] :
( ( in @ X1619 @ X1617 )
=> ! [X1620: $i] :
( ( in @ X1620 @ X1618 )
=> ( ( kfst @ ( kpair @ X1619 @ X1620 ) )
= X1619 ) ) )
=> ( ! [X1621: $i,X1622: $i,X1623: $i] :
( ( in @ X1623 @ X1621 )
=> ! [X1624: $i] :
( ( in @ X1624 @ X1622 )
=> ( ( ksnd @ ( kpair @ X1623 @ X1624 ) )
= X1624 ) ) )
=> ( ! [X1625: $i,X1626: $i,X1627: $i] :
( ( in @ X1627 @ ( cartprod @ X1625 @ X1626 ) )
=> ( ( kpair @ ( kfst @ X1627 ) @ ( ksnd @ X1627 ) )
= X1627 ) )
=> ( ! [X1628: $i,X1629: $i,X1630: $i > $i > $o,X1631: $i] :
( ( in @ X1631 @ X1628 )
=> ! [X1632: $i] :
( ( in @ X1632 @ X1629 )
=> ( ( X1630 @ X1631 @ X1632 )
=> ( in @ ( kpair @ X1631 @ X1632 ) @ ( dpsetconstr @ X1628 @ X1629 @ X1630 ) ) ) ) )
=> ( ! [X1633: $i,X1634: $i,X1635: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1633 @ X1634 @ X1635 ) @ ( cartprod @ X1633 @ X1634 ) )
=> ( ! [X1636: $i,X1637: $i,X1638: $i > $i > $o] : ( breln @ X1636 @ X1637 @ ( dpsetconstr @ X1636 @ X1637 @ X1638 ) )
=> ( ! [X1639: $i,X1640: $i,X1641: $i > $i > $o,X1642: $i] :
( ( in @ X1642 @ X1639 )
=> ! [X1643: $i] :
( ( in @ X1643 @ X1640 )
=> ( ( in @ ( kpair @ X1642 @ X1643 ) @ ( dpsetconstr @ X1639 @ X1640 @ X1641 ) )
=> ( X1641 @ X1642 @ X1643 ) ) ) )
=> ( ! [X1644: $i,X1645: $i,X1646: $i > $i > $o,X1647: $i,X1648: $i] :
( ( in @ ( kpair @ X1647 @ X1648 ) @ ( dpsetconstr @ X1644 @ X1645 @ X1646 ) )
=> ( in @ X1647 @ X1644 ) )
=> ( ! [X1649: $i,X1650: $i,X1651: $i > $i > $o,X1652: $i,X1653: $i] :
( ( in @ ( kpair @ X1652 @ X1653 ) @ ( dpsetconstr @ X1649 @ X1650 @ X1651 ) )
=> ( in @ X1653 @ X1650 ) )
=> ( ! [X1654: $i,X1655: $i,X1656: $i > $i > $o,X1657: $i,X1658: $i] :
( ( in @ ( kpair @ X1657 @ X1658 ) @ ( dpsetconstr @ X1654 @ X1655 @ X1656 ) )
=> ( X1656 @ X1657 @ X1658 ) )
=> ( ! [X1659: $i,X1660: $i,X1661: $i] :
( ( func @ X1659 @ X1660 @ X1661 )
=> ! [X1662: $i] :
( ( in @ X1662 @ X1659 )
=> ( singleton
@ ( dsetconstr @ X1660
@ ^ [Z0: $i] : ( in @ ( kpair @ X1662 @ Z0 ) @ X1661 ) ) ) ) )
=> ( ! [X1663: $i,X1664: $i,X1665: $i] :
( ( func @ X1663 @ X1664 @ X1665 )
=> ! [X1666: $i] :
( ( in @ X1666 @ X1663 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1664
@ ^ [Z0: $i] : ( in @ ( kpair @ X1666 @ Z0 ) @ X1665 ) ) )
@ X1664 ) ) )
=> ( ! [X1667: $i,X1668: $i,X1669: $i] :
( ( func @ X1667 @ X1668 @ X1669 )
=> ! [X1670: $i] :
( ( in @ X1670 @ X1667 )
=> ( in @ ( ap @ X1667 @ X1668 @ X1669 @ X1670 ) @ X1668 ) ) )
=> ( ! [X1671: $i,X1672: $i,X1673: $i] :
( ( in @ X1673 @ ( funcSet @ X1671 @ X1672 ) )
=> ( func @ X1671 @ X1672 @ X1673 ) )
=> ( ! [X1674: $i,X1675: $i,X1676: $i] :
( ( in @ X1676 @ ( funcSet @ X1674 @ X1675 ) )
=> ! [X1677: $i] :
( ( in @ X1677 @ X1674 )
=> ( in @ ( ap @ X1674 @ X1675 @ X1676 @ X1677 ) @ X1675 ) ) )
=> ( ! [X1678: $i,X1679: $i,X1680: $i] :
( ( func @ X1678 @ X1679 @ X1680 )
=> ( in @ X1680 @ ( funcSet @ X1678 @ X1679 ) ) )
=> ( ! [X1681: $i,X1682: $i,X1683: $i > $i] :
( ! [X1684: $i] :
( ( in @ X1684 @ X1681 )
=> ( in @ ( X1683 @ X1684 ) @ X1682 ) )
=> ( func @ X1681 @ X1682
@ ( dpsetconstr @ X1681 @ X1682
@ ^ [Z0: $i] : ( $eq @ ( X1683 @ Z0 ) ) ) ) )
=> ( ! [X1685: $i,X1686: $i,X1687: $i > $i] :
( ! [X1688: $i] :
( ( in @ X1688 @ X1685 )
=> ( in @ ( X1687 @ X1688 ) @ X1686 ) )
=> ( func @ X1685 @ X1686 @ ( lam @ X1685 @ X1686 @ X1687 ) ) )
=> ( ! [X1689: $i,X1690: $i,X1691: $i > $i] :
( ! [X1692: $i] :
( ( in @ X1692 @ X1689 )
=> ( in @ ( X1691 @ X1692 ) @ X1690 ) )
=> ( in @ ( lam @ X1689 @ X1690 @ X1691 ) @ ( funcSet @ X1689 @ X1690 ) ) )
=> ( ! [X1693: $i,X1694: $i,X1695: $i] :
( ( breln @ X1693 @ X1694 @ X1695 )
=> ! [X1696: $i > $o] :
( ! [X1697: $i] :
( ( in @ X1697 @ X1693 )
=> ! [X1698: $i] :
( ( in @ X1698 @ X1694 )
=> ( ( in @ ( kpair @ X1697 @ X1698 ) @ X1695 )
=> ( X1696 @ ( kpair @ X1697 @ X1698 ) ) ) ) )
=> ! [X1699: $i] :
( ( in @ X1699 @ X1695 )
=> ( X1696 @ X1699 ) ) ) )
=> ( ! [X1700: $i,X1701: $i,X1702: $i] :
( ( breln @ X1700 @ X1701 @ X1702 )
=> ! [X1703: $i > $o] :
( ! [X1704: $i] :
( ( in @ X1704 @ X1700 )
=> ! [X1705: $i] :
( ( in @ X1705 @ X1701 )
=> ( ( in @ ( kpair @ X1704 @ X1705 ) @ X1702 )
=> ( X1703 @ ( kpair @ X1704 @ X1705 ) ) ) ) )
=> ! [X1706: $i] :
( ( in @ X1706 @ X1702 )
=> ( X1703 @ X1706 ) ) ) )
=> ( ! [X1707: $i,X1708: $i > $o] :
( ( ex1 @ X1707 @ X1708 )
=> ! [X1709: $i] :
( ( in @ X1709 @ X1707 )
=> ! [X1710: $i] :
( ( in @ X1710 @ X1707 )
=> ( ( X1708 @ X1709 )
=> ( ( X1708 @ X1710 )
=> ( X1709 = X1710 ) ) ) ) ) )
=> ( ! [X1711: $i,X1712: $i,X1713: $i] :
( ( func @ X1711 @ X1712 @ X1713 )
=> ! [X1714: $i] :
( ( in @ X1714 @ X1711 )
=> ( in @ ( kpair @ X1714 @ ( ap @ X1711 @ X1712 @ X1713 @ X1714 ) ) @ X1713 ) ) )
=> ( ! [X1715: $i,X1716: $i,X1717: $i] :
( ( in @ X1717 @ ( funcSet @ X1715 @ X1716 ) )
=> ! [X1718: $i] :
( ( in @ X1718 @ X1715 )
=> ( in @ ( kpair @ X1718 @ ( ap @ X1715 @ X1716 @ X1717 @ X1718 ) ) @ X1717 ) ) )
=> ( ! [X1719: $i,X1720: $i,X1721: $i] :
( ( func @ X1719 @ X1720 @ X1721 )
=> ! [X1722: $i] :
( ( in @ X1722 @ X1719 )
=> ! [X1723: $i] :
( ( in @ X1723 @ X1720 )
=> ( ( in @ ( kpair @ X1722 @ X1723 ) @ X1721 )
=> ( ( ap @ X1719 @ X1720 @ X1721 @ X1722 )
= X1723 ) ) ) ) )
=> ( ! [X1724: $i,X1725: $i,X1726: $i] :
( ( func @ X1724 @ X1725 @ X1726 )
=> ! [X1727: $i] :
( ( func @ X1724 @ X1725 @ X1727 )
=> ( ! [X1728: $i] :
( ( in @ X1728 @ X1724 )
=> ( ( ap @ X1724 @ X1725 @ X1726 @ X1728 )
= ( ap @ X1724 @ X1725 @ X1727 @ X1728 ) ) )
=> ! [X1729: $i] :
( ( in @ X1729 @ X1724 )
=> ! [X1730: $i] :
( ( in @ X1730 @ X1725 )
=> ( ( in @ ( kpair @ X1729 @ X1730 ) @ X1727 )
=> ( in @ ( kpair @ X1729 @ X1730 ) @ X1726 ) ) ) ) ) ) )
=> ( ! [X1731: $i,X1732: $i,X1733: $i] :
( ( in @ X1733 @ ( funcSet @ X1731 @ X1732 ) )
=> ! [X1734: $i] :
( ( in @ X1734 @ X1731 )
=> ! [X1735: $i] :
( ( in @ X1735 @ X1732 )
=> ( ( in @ ( kpair @ X1734 @ X1735 ) @ X1733 )
=> ( ( ap @ X1731 @ X1732 @ X1733 @ X1734 )
= X1735 ) ) ) ) )
=> ( ! [X1736: $i,X1737: $i,X1738: $i] :
( ( breln @ X1736 @ X1737 @ X1738 )
=> ! [X1739: $i] :
( ( breln @ X1736 @ X1737 @ X1739 )
=> ( ! [X1740: $i] :
( ( in @ X1740 @ X1736 )
=> ! [X1741: $i] :
( ( in @ X1741 @ X1737 )
=> ( ( in @ ( kpair @ X1740 @ X1741 ) @ X1738 )
=> ( in @ ( kpair @ X1740 @ X1741 ) @ X1739 ) ) ) )
=> ( subset @ X1738 @ X1739 ) ) ) )
=> ( ! [X1742: $i,X1743: $i,X1744: $i] :
( ( breln @ X1742 @ X1743 @ X1744 )
=> ! [X1745: $i] :
( ( breln @ X1742 @ X1743 @ X1745 )
=> ( ! [X1746: $i] :
( ( in @ X1746 @ X1742 )
=> ! [X1747: $i] :
( ( in @ X1747 @ X1743 )
=> ( ( in @ ( kpair @ X1746 @ X1747 ) @ X1744 )
=> ( in @ ( kpair @ X1746 @ X1747 ) @ X1745 ) ) ) )
=> ( ! [X1748: $i] :
( ( in @ X1748 @ X1742 )
=> ! [X1749: $i] :
( ( in @ X1749 @ X1743 )
=> ( ( in @ ( kpair @ X1748 @ X1749 ) @ X1745 )
=> ( in @ ( kpair @ X1748 @ X1749 ) @ X1744 ) ) ) )
=> ( X1744 = X1745 ) ) ) ) )
=> ( ! [X1750: $i,X1751: $i,X1752: $i] :
( ( func @ X1750 @ X1751 @ X1752 )
=> ! [X1753: $i] :
( ( func @ X1750 @ X1751 @ X1753 )
=> ( ! [X1754: $i] :
( ( in @ X1754 @ X1750 )
=> ( ( ap @ X1750 @ X1751 @ X1752 @ X1754 )
= ( ap @ X1750 @ X1751 @ X1753 @ X1754 ) ) )
=> ( X1752 = X1753 ) ) ) )
=> ( ! [X1755: $i,X1756: $i,X1757: $i] :
( ( in @ X1757 @ ( funcSet @ X1755 @ X1756 ) )
=> ! [X1758: $i] :
( ( in @ X1758 @ ( funcSet @ X1755 @ X1756 ) )
=> ( ! [X1759: $i] :
( ( in @ X1759 @ X1755 )
=> ( ( ap @ X1755 @ X1756 @ X1757 @ X1759 )
= ( ap @ X1755 @ X1756 @ X1758 @ X1759 ) ) )
=> ( X1757 = X1758 ) ) ) )
=> ( ! [X1760: $i,X1761: $i,X1762: $i] :
( ( in @ X1762 @ ( funcSet @ X1760 @ X1761 ) )
=> ! [X1763: $i] :
( ( in @ X1763 @ X1760 )
=> ( ( ap @ X1760 @ X1761 @ X1762 @ X1763 )
= ( ap @ X1760 @ X1761 @ X1762 @ X1763 ) ) ) )
=> ( ! [X1764: $i,X1765: $i,X1766: $i] :
( ( func @ X1764 @ X1765 @ X1766 )
=> ! [X1767: $i] :
( ( in @ X1767 @ X1764 )
=> ( ( ap @ X1764 @ X1765 @ X1766 @ X1767 )
= ( ap @ X1764 @ X1765 @ X1766 @ X1767 ) ) ) )
=> ( ! [X1768: $i,X1769: $i,X1770: $i > $i] :
( ! [X1771: $i] :
( ( in @ X1771 @ X1768 )
=> ( in @ ( X1770 @ X1771 ) @ X1769 ) )
=> ! [X1772: $i] :
( ( in @ X1772 @ X1768 )
=> ( ( ap @ X1768 @ X1769 @ ( lam @ X1768 @ X1769 @ X1770 ) @ X1772 )
= ( X1770 @ X1772 ) ) ) )
=> ( ! [X1773: $i,X1774: $i,X1775: $i] :
( ( func @ X1773 @ X1774 @ X1775 )
=> ( ( lam @ X1773 @ X1774 @ ( ap @ X1773 @ X1774 @ X1775 ) )
= X1775 ) )
=> ( ! [X1776: $i,X1777: $i,X1778: $i > $i] :
( ! [X1779: $i] :
( ( in @ X1779 @ X1776 )
=> ( in @ ( X1778 @ X1779 ) @ X1777 ) )
=> ( ( lam @ X1776 @ X1777 @ X1778 )
= ( lam @ X1776 @ X1777 @ X1778 ) ) )
=> ( ! [X1780: $i,X1781: $i,X1782: $i > $i] :
( ! [X1783: $i] :
( ( in @ X1783 @ X1780 )
=> ( in @ ( X1782 @ X1783 ) @ X1781 ) )
=> ! [X1784: $i] :
( ( in @ X1784 @ X1780 )
=> ( ( ap @ X1780 @ X1781 @ ( lam @ X1780 @ X1781 @ X1782 ) @ X1784 )
= ( X1782 @ X1784 ) ) ) )
=> ( ! [X1785: $i,X1786: $i,X1787: $i] :
( ( in @ X1787 @ ( funcSet @ X1785 @ X1786 ) )
=> ( ( lam @ X1785 @ X1786 @ ( ap @ X1785 @ X1786 @ X1787 ) )
= X1787 ) )
=> ( ! [X1788: $i,X1789: $o,X1790: $i] :
( ( in @ X1790 @ X1788 )
=> ! [X1791: $i] :
( ( in @ X1791 @ X1788 )
=> ( ~ X1789
=> ( in @ X1791
@ ( dsetconstr @ X1788
@ ^ [Z0: $i] :
( ( X1789
& ( Z0 = X1790 ) )
| ( ~ X1789
& ( Z0 = X1791 ) ) ) ) ) ) ) )
=> ( ! [X1792: $i,X1793: $o,X1794: $i] :
( ( in @ X1794 @ X1792 )
=> ! [X1795: $i] :
( ( in @ X1795 @ X1792 )
=> ( ~ X1793
=> ( ( dsetconstr @ X1792
@ ^ [Z0: $i] :
( ( X1793
& ( Z0 = X1794 ) )
| ( ~ X1793
& ( Z0 = X1795 ) ) ) )
= ( setadjoin @ X1795 @ emptyset ) ) ) ) )
=> ( ! [X1796: $i,X1797: $o,X1798: $i] :
( ( in @ X1798 @ X1796 )
=> ! [X1799: $i] :
( ( in @ X1799 @ X1796 )
=> ( X1797
=> ( in @ X1798
@ ( dsetconstr @ X1796
@ ^ [Z0: $i] :
( ( X1797
& ( Z0 = X1798 ) )
| ( ~ X1797
& ( Z0 = X1799 ) ) ) ) ) ) ) )
=> ( ! [X1800: $i,X1801: $o,X1802: $i] :
( ( in @ X1802 @ X1800 )
=> ! [X1803: $i] :
( ( in @ X1803 @ X1800 )
=> ( X1801
=> ( ( dsetconstr @ X1800
@ ^ [Z0: $i] :
( ( X1801
& ( Z0 = X1802 ) )
| ( ~ X1801
& ( Z0 = X1803 ) ) ) )
= ( setadjoin @ X1802 @ emptyset ) ) ) ) )
=> ( ! [X1804: $i,X1805: $o,X1806: $i] :
( ( in @ X1806 @ X1804 )
=> ! [X1807: $i] :
( ( in @ X1807 @ X1804 )
=> ( singleton
@ ( dsetconstr @ X1804
@ ^ [Z0: $i] :
( ( X1805
& ( Z0 = X1806 ) )
| ( ~ X1805
& ( Z0 = X1807 ) ) ) ) ) ) )
=> ( ! [X1808: $i,X1809: $o,X1810: $i] :
( ( in @ X1810 @ X1808 )
=> ! [X1811: $i] :
( ( in @ X1811 @ X1808 )
=> ( in @ ( if @ X1808 @ X1809 @ X1810 @ X1811 ) @ X1808 ) ) )
=> ( ! [X1812: $i] :
( ( singleton @ X1812 )
=> ! [X1813: $i] :
( ( in @ X1813 @ X1812 )
=> ( ( setunion @ X1812 )
= X1813 ) ) )
=> ( ! [X1814: $i,X1815: $o,X1816: $i] :
( ( in @ X1816 @ X1814 )
=> ! [X1817: $i] :
( ( in @ X1817 @ X1814 )
=> ( X1815
=> ( ( if @ X1814 @ X1815 @ X1816 @ X1817 )
= X1816 ) ) ) )
=> ( ! [X1818: $i,X1819: $o,X1820: $i] :
( ( in @ X1820 @ X1818 )
=> ! [X1821: $i] :
( ( in @ X1821 @ X1818 )
=> ( ~ X1819
=> ( ( if @ X1818 @ X1819 @ X1820 @ X1821 )
= X1821 ) ) ) )
=> ( ! [X1822: $i,X1823: $o,X1824: $i] :
( ( in @ X1824 @ X1822 )
=> ! [X1825: $i] :
( ( in @ X1825 @ X1822 )
=> ( in @ ( if @ X1822 @ X1823 @ X1824 @ X1825 ) @ ( setadjoin @ X1824 @ ( setadjoin @ X1825 @ emptyset ) ) ) ) )
=> ( ! [X1826: $i,X1827: $i] :
( ( in @ X1827 @ ( powerset @ X1826 ) )
=> ! [X1828: $i] :
( ( in @ X1828 @ ( powerset @ X1826 ) )
=> ( in @ ( binintersect @ X1827 @ X1828 ) @ ( powerset @ X1826 ) ) ) )
=> ( ! [X1829: $i,X1830: $i] :
( ( in @ X1830 @ ( powerset @ X1829 ) )
=> ! [X1831: $i] :
( ( in @ X1831 @ ( powerset @ X1829 ) )
=> ( in @ ( binunion @ X1830 @ X1831 ) @ ( powerset @ X1829 ) ) ) )
=> ( ! [X1832: $i,X1833: $i] :
( ( in @ X1833 @ ( powerset @ X1832 ) )
=> ( in @ ( powerset @ X1833 ) @ ( powerset @ ( powerset @ X1832 ) ) ) )
=> ( ! [X1834: $i,X1835: $i] :
( ( in @ X1835 @ ( powerset @ X1834 ) )
=> ! [X1836: $i] :
( ( in @ X1836 @ ( powerset @ X1834 ) )
=> ( in @ ( setminus @ X1835 @ X1836 ) @ ( powerset @ X1834 ) ) ) )
=> ( ! [X1837: $i,X1838: $i] :
( ( in @ X1838 @ ( powerset @ X1837 ) )
=> ( in @ ( setminus @ X1837 @ X1838 ) @ ( powerset @ X1837 ) ) )
=> ( ! [X1839: $i,X1840: $i] :
( ( in @ X1840 @ ( powerset @ X1839 ) )
=> ! [X1841: $i] :
( ( in @ X1841 @ ( powerset @ X1839 ) )
=> ( ! [X1842: $i] :
( ( in @ X1842 @ X1839 )
=> ( ( in @ X1842 @ X1840 )
=> ( in @ X1842 @ X1841 ) ) )
=> ( ! [X1843: $i] :
( ( in @ X1843 @ X1839 )
=> ( ( in @ X1843 @ X1841 )
=> ( in @ X1843 @ X1840 ) ) )
=> ( X1840 = X1841 ) ) ) ) )
=> ( ! [X1844: $i,X1845: $i] :
( ( in @ X1845 @ ( powerset @ X1844 ) )
=> ! [X1846: $i] :
( ( in @ X1846 @ ( powerset @ X1844 ) )
=> ( ! [X1847: $i] :
( ( in @ X1847 @ X1844 )
=> ( ( in @ X1847 @ X1845 )
=> ( in @ X1847 @ X1846 ) ) )
=> ( subset @ X1845 @ 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 @ X1849 @ ( powerset @ X1850 ) ) ) ) )
=> ( ! [X1852: $i,X1853: $i] :
( ( in @ X1853 @ ( powerset @ X1852 ) )
=> ! [X1854: $i] :
( ( in @ X1854 @ ( powerset @ X1852 ) )
=> ! [X1855: $i] :
( ( in @ X1855 @ X1852 )
=> ( ( in @ X1853 @ ( powerset @ X1854 ) )
=> ( ( in @ X1855 @ X1853 )
=> ( in @ X1855 @ X1854 ) ) ) ) ) )
=> ( ! [X1856: $i,X1857: $i] :
( ( in @ X1857 @ ( powerset @ X1856 ) )
=> ! [X1858: $i] :
( ( in @ X1858 @ X1856 )
=> ( ( in @ X1858 @ X1857 )
=> ~ ( in @ X1858 @ ( setminus @ X1856 @ X1857 ) ) ) ) )
=> ( ! [X1859: $i,X1860: $i] :
( ( in @ X1860 @ ( powerset @ X1859 ) )
=> ! [X1861: $i] :
( ( in @ X1861 @ X1859 )
=> ( ~ ( in @ X1861 @ ( setminus @ X1859 @ X1860 ) )
=> ( in @ X1861 @ X1860 ) ) ) )
=> ( ! [X1862: $i,X1863: $i] :
( ( in @ X1863 @ ( powerset @ X1862 ) )
=> ! [X1864: $i] :
( ( in @ X1864 @ ( powerset @ X1862 ) )
=> ! [X1865: $i] :
( ( in @ X1865 @ X1862 )
=> ( ~ ( in @ X1865 @ X1863 )
=> ~ ( in @ X1865 @ ( binintersect @ X1863 @ X1864 ) ) ) ) ) )
=> ( ! [X1866: $i,X1867: $i] :
( ( in @ X1867 @ ( powerset @ X1866 ) )
=> ! [X1868: $i] :
( ( in @ X1868 @ ( powerset @ X1866 ) )
=> ! [X1869: $i] :
( ( in @ X1869 @ X1866 )
=> ( ~ ( in @ X1869 @ X1868 )
=> ~ ( in @ X1869 @ ( binintersect @ X1867 @ X1868 ) ) ) ) ) )
=> ( ! [X1870: $i,X1871: $i] :
( ( in @ X1871 @ ( powerset @ X1870 ) )
=> ! [X1872: $i] :
( ( in @ X1872 @ ( powerset @ X1870 ) )
=> ! [X1873: $i] :
( ( in @ X1873 @ X1870 )
=> ( ( subset @ X1871 @ ( setminus @ X1870 @ X1872 ) )
=> ( ( in @ X1873 @ X1872 )
=> ~ ( in @ X1873 @ X1871 ) ) ) ) ) )
=> ( ! [X1874: $i,X1875: $i] :
( ( in @ X1875 @ ( powerset @ X1874 ) )
=> ! [X1876: $i] :
( ( in @ X1876 @ ( powerset @ X1874 ) )
=> ! [X1877: $i] :
( ( in @ X1877 @ X1874 )
=> ( ( subset @ X1875 @ X1876 )
=> ( ~ ( in @ X1877 @ X1876 )
=> ~ ( in @ X1877 @ X1875 ) ) ) ) ) )
=> ( ! [X1878: $i,X1879: $i] :
( ( in @ X1879 @ ( powerset @ X1878 ) )
=> ! [X1880: $i] :
( ( in @ X1880 @ ( powerset @ X1878 ) )
=> ( ( subset @ X1879 @ X1880 )
=> ( subset @ ( setminus @ X1878 @ X1880 ) @ ( setminus @ X1878 @ X1879 ) ) ) ) )
=> ( ! [X1881: $i,X1882: $i] :
( ( in @ X1882 @ ( powerset @ X1881 ) )
=> ! [X1883: $i] :
( ( in @ X1883 @ ( powerset @ X1881 ) )
=> ( ( subset @ ( setminus @ X1881 @ X1883 ) @ ( setminus @ X1881 @ X1882 ) )
=> ( subset @ X1882 @ X1883 ) ) ) )
=> ( ! [X1884: $i,X1885: $i] :
( ( in @ X1885 @ ( powerset @ X1884 ) )
=> ! [X1886: $i] :
( ( in @ X1886 @ X1884 )
=> ( ( in @ X1886 @ X1885 )
=> ( in @ X1886 @ ( setminus @ X1884 @ ( setminus @ X1884 @ X1885 ) ) ) ) ) )
=> ( ! [X1887: $i,X1888: $i] :
( ( in @ X1888 @ ( powerset @ X1887 ) )
=> ! [X1889: $i] :
( ( in @ X1889 @ X1887 )
=> ( ( in @ X1889 @ ( setminus @ X1887 @ ( setminus @ X1887 @ X1888 ) ) )
=> ( in @ X1889 @ X1888 ) ) ) )
=> ( ! [X1890: $i,X1891: $i] :
( ( in @ X1891 @ ( powerset @ X1890 ) )
=> ( subset @ X1891 @ ( setminus @ X1890 @ ( setminus @ X1890 @ X1891 ) ) ) )
=> ( ! [X1892: $i,X1893: $i] :
( ( in @ X1893 @ ( powerset @ X1892 ) )
=> ( subset @ ( setminus @ X1892 @ ( setminus @ X1892 @ X1893 ) ) @ X1893 ) )
=> ( ! [X1894: $i,X1895: $i] :
( ( in @ X1895 @ ( powerset @ X1894 ) )
=> ( X1895
= ( setminus @ X1894 @ ( setminus @ X1894 @ X1895 ) ) ) )
=> ( ! [X1896: $i,X1897: $i] :
( ( in @ X1897 @ ( powerset @ X1896 ) )
=> ! [X1898: $i] :
( ( in @ X1898 @ ( powerset @ X1896 ) )
=> ! [X1899: $i] :
( ( in @ X1899 @ X1896 )
=> ( ( in @ X1899 @ ( setminus @ X1896 @ X1897 ) )
=> ~ ( in @ X1899 @ ( binintersect @ X1897 @ X1898 ) ) ) ) ) )
=> ( ! [X1900: $i,X1901: $i] :
( ( in @ X1901 @ ( powerset @ X1900 ) )
=> ! [X1902: $i] :
( ( in @ X1902 @ ( powerset @ X1900 ) )
=> ! [X1903: $i] :
( ( in @ X1903 @ X1900 )
=> ( ( in @ X1903 @ ( setminus @ X1900 @ X1901 ) )
=> ( in @ X1903 @ ( setminus @ X1900 @ ( binintersect @ X1901 @ X1902 ) ) ) ) ) ) )
=> ( ! [X1904: $i,X1905: $i] :
( ( in @ X1905 @ ( powerset @ X1904 ) )
=> ! [X1906: $i] :
( ( in @ X1906 @ ( powerset @ X1904 ) )
=> ( subset @ ( setminus @ X1904 @ X1905 ) @ ( setminus @ X1904 @ ( binintersect @ X1905 @ X1906 ) ) ) ) )
=> ( ! [X1907: $i,X1908: $i] :
( ( in @ X1908 @ ( powerset @ X1907 ) )
=> ! [X1909: $i] :
( ( in @ X1909 @ ( powerset @ X1907 ) )
=> ( in @ ( setminus @ X1907 @ X1908 ) @ ( powerset @ ( setminus @ X1907 @ ( binintersect @ X1908 @ X1909 ) ) ) ) ) )
=> ( ! [X1910: $i,X1911: $i] :
( ( in @ X1911 @ ( powerset @ X1910 ) )
=> ! [X1912: $i] :
( ( in @ X1912 @ ( powerset @ X1910 ) )
=> ( ( subset @ X1911 @ ( setminus @ X1910 @ X1912 ) )
=> ! [X1913: $i] :
( ( in @ X1913 @ X1910 )
=> ( ( in @ X1913 @ X1912 )
=> ( in @ X1913 @ ( setminus @ X1910 @ X1911 ) ) ) ) ) ) )
=> ( ! [X1914: $i,X1915: $i] :
( ( in @ X1915 @ ( powerset @ X1914 ) )
=> ! [X1916: $i] :
( ( in @ X1916 @ ( powerset @ X1914 ) )
=> ( ( subset @ X1915 @ ( setminus @ X1914 @ X1916 ) )
=> ( subset @ X1916 @ ( setminus @ X1914 @ X1915 ) ) ) ) )
=> ( ! [X1917: $i,X1918: $i] :
( ( in @ X1918 @ ( powerset @ X1917 ) )
=> ! [X1919: $i] :
( ( in @ X1919 @ ( powerset @ X1917 ) )
=> ! [X1920: $i] :
( ( in @ X1920 @ X1917 )
=> ( ~ ( in @ X1920 @ ( binunion @ X1918 @ X1919 ) )
=> ~ ( in @ X1920 @ X1918 ) ) ) ) )
=> ( ! [X1921: $i,X1922: $i] :
( ( in @ X1922 @ ( powerset @ X1921 ) )
=> ! [X1923: $i] :
( ( in @ X1923 @ ( powerset @ X1921 ) )
=> ! [X1924: $i] :
( ( in @ X1924 @ X1921 )
=> ( ~ ( in @ X1924 @ ( binunion @ X1922 @ X1923 ) )
=> ~ ( in @ X1924 @ X1923 ) ) ) ) )
=> ( ! [X1925: $i,X1926: $i] :
( ( in @ X1926 @ ( powerset @ X1925 ) )
=> ! [X1927: $i] :
( ( in @ X1927 @ ( powerset @ X1925 ) )
=> ! [X1928: $i] :
( ( in @ X1928 @ ( powerset @ X1925 ) )
=> ! [X1929: $i] :
( ( in @ X1929 @ X1925 )
=> ( ( in @ X1929 @ ( binintersect @ X1926 @ X1927 ) )
=> ( in @ X1929 @ ( binunion @ X1926 @ X1928 ) ) ) ) ) ) )
=> ( ! [X1930: $i,X1931: $i] :
( ( in @ X1931 @ ( powerset @ X1930 ) )
=> ! [X1932: $i] :
( ( in @ X1932 @ ( powerset @ X1930 ) )
=> ! [X1933: $i] :
( ( in @ X1933 @ ( powerset @ X1930 ) )
=> ! [X1934: $i] :
( ( in @ X1934 @ X1930 )
=> ( ( in @ X1934 @ ( binintersect @ X1931 @ X1932 ) )
=> ( in @ X1934 @ ( binunion @ X1932 @ X1933 ) ) ) ) ) ) )
=> ( ! [X1935: $i,X1936: $i] :
( ( in @ X1936 @ ( powerset @ X1935 ) )
=> ! [X1937: $i] :
( ( in @ X1937 @ ( powerset @ X1935 ) )
=> ! [X1938: $i] :
( ( in @ X1938 @ ( powerset @ X1935 ) )
=> ! [X1939: $i] :
( ( in @ X1939 @ X1935 )
=> ( ( in @ X1939 @ ( binintersect @ X1936 @ X1937 ) )
=> ( in @ X1939 @ ( binintersect @ ( binunion @ X1936 @ X1938 ) @ ( binunion @ X1937 @ X1938 ) ) ) ) ) ) ) )
=> ( ! [X1940: $i,X1941: $i] :
( ( in @ X1941 @ ( powerset @ X1940 ) )
=> ! [X1942: $i] :
( ( in @ X1942 @ ( powerset @ X1940 ) )
=> ! [X1943: $i] :
( ( in @ X1943 @ ( powerset @ X1940 ) )
=> ( in @ ( binintersect @ X1941 @ X1942 ) @ ( powerset @ ( binintersect @ ( binunion @ X1941 @ X1943 ) @ ( binunion @ X1942 @ X1943 ) ) ) ) ) ) )
=> ( ! [X1944: $i,X1945: $i] :
( ( in @ X1945 @ ( powerset @ X1944 ) )
=> ! [X1946: $i] :
( ( in @ X1946 @ ( powerset @ X1944 ) )
=> ! [X1947: $i] :
( ( in @ X1947 @ X1944 )
=> ( ( in @ X1947 @ ( setminus @ X1944 @ ( binunion @ X1945 @ X1946 ) ) )
=> ~ ( in @ X1947 @ X1945 ) ) ) ) )
=> ( ! [X1948: $i,X1949: $i] :
( ( in @ X1949 @ ( powerset @ X1948 ) )
=> ! [X1950: $i] :
( ( in @ X1950 @ ( powerset @ X1948 ) )
=> ! [X1951: $i] :
( ( in @ X1951 @ X1948 )
=> ( ( in @ X1951 @ ( setminus @ X1948 @ ( binunion @ X1949 @ X1950 ) ) )
=> ( in @ X1951 @ ( setminus @ X1948 @ X1949 ) ) ) ) ) )
=> ( ! [X1952: $i,X1953: $i] :
( ( in @ X1953 @ ( powerset @ X1952 ) )
=> ! [X1954: $i] :
( ( in @ X1954 @ ( powerset @ X1952 ) )
=> ! [X1955: $o,X1956: $i] :
( ( in @ X1956 @ X1952 )
=> ( ( in @ X1956 @ ( binunion @ X1953 @ X1954 ) )
=> ( ( ( in @ X1956 @ X1953 )
=> X1955 )
=> ( ( ( in @ X1956 @ X1954 )
=> X1955 )
=> X1955 ) ) ) ) ) )
=> ( ! [X1957: $i,X1958: $i] :
( ( in @ X1958 @ ( powerset @ X1957 ) )
=> ! [X1959: $i] :
( ( in @ X1959 @ ( powerset @ X1957 ) )
=> ! [X1960: $i] :
( ( in @ X1960 @ X1957 )
=> ( ~ ( in @ X1960 @ X1958 )
=> ( ~ ( in @ X1960 @ X1959 )
=> ~ ( in @ X1960 @ ( binunion @ X1958 @ X1959 ) ) ) ) ) ) )
=> ( ! [X1961: $i,X1962: $i] :
( ( in @ X1962 @ ( powerset @ X1961 ) )
=> ! [X1963: $i] :
( ( in @ X1963 @ ( powerset @ X1961 ) )
=> ! [X1964: $i] :
( ( in @ X1964 @ X1961 )
=> ( ( in @ X1964 @ ( setminus @ X1961 @ ( binunion @ X1962 @ X1963 ) ) )
=> ( in @ X1964 @ ( setminus @ X1961 @ X1962 ) ) ) ) ) )
=> ( ! [X1965: $i,X1966: $i] :
( ( in @ X1966 @ ( powerset @ X1965 ) )
=> ! [X1967: $i] :
( ( in @ X1967 @ ( powerset @ X1965 ) )
=> ( in @ ( setminus @ X1965 @ ( binunion @ X1966 @ X1967 ) ) @ ( powerset @ ( setminus @ X1965 @ X1966 ) ) ) ) )
=> ( ! [X1968: $i,X1969: $i] :
( ( in @ X1969 @ ( powerset @ X1968 ) )
=> ! [X1970: $i] :
( ( in @ X1970 @ ( powerset @ X1968 ) )
=> ! [X1971: $i] :
( ( in @ X1971 @ X1968 )
=> ( ( in @ X1971 @ ( setminus @ X1968 @ ( binunion @ X1969 @ X1970 ) ) )
=> ( in @ X1971 @ ( setminus @ X1968 @ X1970 ) ) ) ) ) )
=> ( ! [X1972: $i,X1973: $i] :
( ( in @ X1973 @ ( powerset @ X1972 ) )
=> ! [X1974: $i] :
( ( in @ X1974 @ ( powerset @ X1972 ) )
=> ! [X1975: $i] :
( ( in @ X1975 @ X1972 )
=> ( ( in @ X1975 @ ( setminus @ X1972 @ ( binintersect @ X1973 @ X1974 ) ) )
=> ( in @ X1975 @ ( binunion @ ( setminus @ X1972 @ X1973 ) @ ( setminus @ X1972 @ X1974 ) ) ) ) ) ) )
=> ( ! [X1976: $i,X1977: $i] :
( ( in @ X1977 @ ( powerset @ X1976 ) )
=> ! [X1978: $i] :
( ( in @ X1978 @ ( powerset @ X1976 ) )
=> ! [X1979: $i] :
( ( in @ X1979 @ X1976 )
=> ( ( in @ X1979 @ ( binunion @ ( setminus @ X1976 @ X1977 ) @ ( setminus @ X1976 @ X1978 ) ) )
=> ( in @ X1979 @ ( setminus @ X1976 @ ( binintersect @ X1977 @ X1978 ) ) ) ) ) ) )
=> ( ! [X1980: $i,X1981: $i] :
( ( in @ X1981 @ ( powerset @ X1980 ) )
=> ! [X1982: $i] :
( ( in @ X1982 @ ( powerset @ X1980 ) )
=> ( ( setminus @ X1980 @ ( binintersect @ X1981 @ X1982 ) )
= ( binunion @ ( setminus @ X1980 @ X1981 ) @ ( setminus @ X1980 @ X1982 ) ) ) ) )
=> ( ! [X1983: $i,X1984: $i] :
( ( in @ X1984 @ ( powerset @ X1983 ) )
=> ! [X1985: $i] :
( ( in @ X1985 @ ( powerset @ X1983 ) )
=> ! [X1986: $i] :
( ( in @ X1986 @ X1983 )
=> ( ( in @ X1986 @ ( setminus @ X1983 @ ( binunion @ X1984 @ X1985 ) ) )
=> ( in @ X1986 @ ( binintersect @ ( setminus @ X1983 @ X1984 ) @ ( setminus @ X1983 @ X1985 ) ) ) ) ) ) )
=> ( ! [X1987: $i,X1988: $i] :
( ( in @ X1988 @ ( powerset @ X1987 ) )
=> ! [X1989: $i] :
( ( in @ X1989 @ ( powerset @ X1987 ) )
=> ! [X1990: $i] :
( ( in @ X1990 @ X1987 )
=> ( ( in @ X1990 @ ( setminus @ X1987 @ X1988 ) )
=> ( ( in @ X1990 @ ( setminus @ X1987 @ X1989 ) )
=> ( in @ X1990 @ ( setminus @ X1987 @ ( binunion @ X1988 @ X1989 ) ) ) ) ) ) ) )
=> ( ! [X1991: $i,X1992: $i] :
( ( in @ X1992 @ ( powerset @ X1991 ) )
=> ! [X1993: $i] :
( ( in @ X1993 @ ( powerset @ X1991 ) )
=> ! [X1994: $i] :
( ( in @ X1994 @ X1991 )
=> ( ( in @ X1994 @ ( binintersect @ ( setminus @ X1991 @ X1992 ) @ ( setminus @ X1991 @ X1993 ) ) )
=> ( in @ X1994 @ ( setminus @ X1991 @ ( binunion @ X1992 @ X1993 ) ) ) ) ) ) )
=> ( ! [X1995: $i,X1996: $i] :
( ( in @ X1996 @ ( powerset @ X1995 ) )
=> ! [X1997: $i] :
( ( in @ X1997 @ ( powerset @ X1995 ) )
=> ( ( setminus @ X1995 @ ( binunion @ X1996 @ X1997 ) )
= ( binintersect @ ( setminus @ X1995 @ X1996 ) @ ( setminus @ X1995 @ X1997 ) ) ) ) )
=> ( ! [X1998: $i,X1999: $i] :
( ( in @ X1999 @ ( powerset @ X1998 ) )
=> ! [X2000: $i] :
( ( in @ X2000 @ ( powerset @ X1998 ) )
=> ! [X2001: $i] :
( ( in @ X2001 @ ( binintersect @ X1999 @ X2000 ) )
=> ( in @ X2001 @ X1998 ) ) ) )
=> ( ! [X2002: $i,X2003: $i] :
( ( in @ X2003 @ ( powerset @ X2002 ) )
=> ! [X2004: $i] :
( ( in @ X2004 @ ( powerset @ X2002 ) )
=> ! [X2005: $i] :
( ( in @ X2005 @ ( powerset @ X2002 ) )
=> ( ( subset @ X2003 @ X2005 )
=> ( subset @ ( binintersect @ X2003 @ X2004 ) @ X2005 ) ) ) ) )
=> ( ! [X2006: $i,X2007: $i] :
( ( in @ X2007 @ ( powerset @ X2006 ) )
=> ! [X2008: $i] :
( ( in @ X2008 @ ( powerset @ X2006 ) )
=> ! [X2009: $i] :
( ( in @ X2009 @ ( powerset @ X2006 ) )
=> ( ( subset @ X2008 @ X2009 )
=> ( subset @ ( binintersect @ X2007 @ X2008 ) @ X2009 ) ) ) ) )
=> ( ! [X2010: $i,X2011: $i] :
( ( in @ X2011 @ ( powerset @ X2010 ) )
=> ! [X2012: $i] :
( ( in @ X2012 @ ( powerset @ X2010 ) )
=> ! [X2013: $i] :
( ( in @ X2013 @ ( powerset @ X2010 ) )
=> ( ( subset @ X2011 @ X2012 )
=> ( ( subset @ X2011 @ X2013 )
=> ( subset @ X2011 @ ( binintersect @ X2012 @ X2013 ) ) ) ) ) ) )
=> ( ! [X2014: $i,X2015: $i] :
( ( in @ X2015 @ ( powerset @ X2014 ) )
=> ! [X2016: $i] :
( ( in @ X2016 @ ( powerset @ X2014 ) )
=> ! [X2017: $i] :
( ( in @ X2017 @ ( powerset @ X2014 ) )
=> ! [X2018: $i] :
( ( in @ X2018 @ ( powerset @ X2014 ) )
=> ( ( subset @ X2015 @ X2017 )
=> ( ( subset @ X2016 @ X2018 )
=> ( subset @ ( binintersect @ X2015 @ X2016 ) @ ( binintersect @ X2017 @ X2018 ) ) ) ) ) ) ) )
=> ( ! [X2019: $i,X2020: $i] :
( ( in @ X2020 @ ( powerset @ X2019 ) )
=> ! [X2021: $i] :
( ( in @ X2021 @ ( powerset @ X2019 ) )
=> ( in @ ( setminus @ X2019 @ X2020 ) @ ( powerset @ ( setminus @ X2019 @ ( binintersect @ X2020 @ X2021 ) ) ) ) ) )
=> ( ! [X2022: $i,X2023: $i] :
( ( in @ X2023 @ ( powerset @ X2022 ) )
=> ! [X2024: $i] :
( ( in @ X2024 @ ( powerset @ X2022 ) )
=> ! [X2025: $i] :
( ( in @ X2025 @ ( powerset @ X2022 ) )
=> ! [X2026: $i] :
( ( in @ X2026 @ ( powerset @ X2022 ) )
=> ( ( setminus @ X2022 @ ( binintersect @ ( binunion @ X2023 @ X2024 ) @ ( binunion @ X2025 @ X2026 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X2022 @ X2023 ) @ ( setminus @ X2022 @ X2024 ) ) @ ( binintersect @ ( setminus @ X2022 @ X2025 ) @ ( setminus @ X2022 @ X2026 ) ) ) ) ) ) ) )
=> ( ! [X2027: $i,X2028: $i] :
( ( in @ X2028 @ ( powerset @ X2027 ) )
=> ! [X2029: $i] :
( ( in @ X2029 @ ( powerset @ X2027 ) )
=> ! [X2030: $i] :
( ( in @ X2030 @ ( powerset @ X2027 ) )
=> ( in @ ( binintersect @ X2028 @ X2029 ) @ ( powerset @ ( binintersect @ ( binunion @ X2028 @ X2030 ) @ ( binunion @ X2029 @ X2030 ) ) ) ) ) ) )
=> ( ! [X2031: $i,X2032: $i] :
( ( in @ X2032 @ ( powerset @ X2031 ) )
=> ! [X2033: $i] :
( ( in @ X2033 @ ( powerset @ X2031 ) )
=> ( ( subset @ X2032 @ ( setminus @ X2031 @ X2033 ) )
=> ( subset @ X2033 @ ( setminus @ X2031 @ X2032 ) ) ) ) )
=> ( ! [X2034: $i,X2035: $i] :
( ( in @ X2035 @ ( powerset @ X2034 ) )
=> ! [X2036: $i] :
( ( in @ X2036 @ ( powerset @ X2034 ) )
=> ( in @ ( setminus @ X2034 @ ( binunion @ X2035 @ X2036 ) ) @ ( powerset @ ( setminus @ X2034 @ X2035 ) ) ) ) )
=> ( ! [X2037: $i,X2038: $i] :
( ( breln1 @ X2037 @ X2038 )
=> ! [X2039: $i > $o] :
( ! [X2040: $i] :
( ( in @ X2040 @ X2037 )
=> ! [X2041: $i] :
( ( in @ X2041 @ X2037 )
=> ( ( in @ ( kpair @ X2040 @ X2041 ) @ X2038 )
=> ( X2039 @ ( kpair @ X2040 @ X2041 ) ) ) ) )
=> ! [X2042: $i] :
( ( in @ X2042 @ X2038 )
=> ( X2039 @ X2042 ) ) ) )
=> ( ! [X2043: $i,X2044: $i] :
( ( in @ X2044 @ ( breln1Set @ X2043 ) )
=> ( breln1 @ X2043 @ X2044 ) )
=> ( choice2fnsingleton
=> ( ! [X2045: $i,X2046: $i > $i > $o] : ( breln1 @ X2045 @ ( dpsetconstr @ X2045 @ X2045 @ X2046 ) )
=> ( ! [X2047: $i,X2048: $i] :
( ( breln1 @ X2047 @ X2048 )
=> ! [X2049: $i > $o] :
( ! [X2050: $i] :
( ( in @ X2050 @ X2047 )
=> ! [X2051: $i] :
( ( in @ X2051 @ X2047 )
=> ( ( in @ ( kpair @ X2050 @ X2051 ) @ X2048 )
=> ( X2049 @ ( kpair @ X2050 @ X2051 ) ) ) ) )
=> ! [X2052: $i] :
( ( in @ X2052 @ X2048 )
=> ( X2049 @ X2052 ) ) ) )
=> ( ! [X2053: $i,X2054: $i] :
( ( breln1 @ X2053 @ X2054 )
=> ! [X2055: $i] :
( ( breln1 @ X2053 @ X2055 )
=> ( ! [X2056: $i] :
( ( in @ X2056 @ X2053 )
=> ! [X2057: $i] :
( ( in @ X2057 @ X2053 )
=> ( ( in @ ( kpair @ X2056 @ X2057 ) @ X2054 )
=> ( in @ ( kpair @ X2056 @ X2057 ) @ X2055 ) ) ) )
=> ( subset @ X2054 @ X2055 ) ) ) )
=> ( ! [X2058: $i,X2059: $i] :
( ( breln1 @ X2058 @ X2059 )
=> ! [X2060: $i] :
( ( breln1 @ X2058 @ X2060 )
=> ( ! [X2061: $i] :
( ( in @ X2061 @ X2058 )
=> ! [X2062: $i] :
( ( in @ X2062 @ X2058 )
=> ( ( in @ ( kpair @ X2061 @ X2062 ) @ X2059 )
=> ( in @ ( kpair @ X2061 @ X2062 ) @ X2060 ) ) ) )
=> ( ! [X2063: $i] :
( ( in @ X2063 @ X2058 )
=> ! [X2064: $i] :
( ( in @ X2064 @ X2058 )
=> ( ( in @ ( kpair @ X2063 @ X2064 ) @ X2060 )
=> ( in @ ( kpair @ X2063 @ X2064 ) @ X2059 ) ) ) )
=> ( X2059 = X2060 ) ) ) ) )
=> ( ! [X2065: $i,X2066: $i] :
( ( breln1 @ X2065 @ X2066 )
=> ( breln1 @ X2065 @ ( breln1invset @ X2065 @ X2066 ) ) )
=> ( ! [X2067: $i,X2068: $i] :
( ( breln1 @ X2067 @ X2068 )
=> ! [X2069: $i] :
( ( in @ X2069 @ X2067 )
=> ! [X2070: $i] :
( ( in @ X2070 @ X2067 )
=> ( ( in @ ( kpair @ X2069 @ X2070 ) @ X2068 )
=> ( in @ ( kpair @ X2070 @ X2069 ) @ ( breln1invset @ X2067 @ X2068 ) ) ) ) ) )
=> ( ! [X2071: $i,X2072: $i] :
( ( breln1 @ X2071 @ X2072 )
=> ! [X2073: $i] :
( ( in @ X2073 @ X2071 )
=> ! [X2074: $i] :
( ( in @ X2074 @ X2071 )
=> ( ( in @ ( kpair @ X2074 @ X2073 ) @ ( breln1invset @ X2071 @ X2072 ) )
=> ( in @ ( kpair @ X2073 @ X2074 ) @ X2072 ) ) ) ) )
=> ( ! [X2075: $i,X2076: $i] :
( ( breln1 @ X2075 @ X2076 )
=> ! [X2077: $i] :
( ( breln1 @ X2075 @ X2077 )
=> ( breln1 @ X2075 @ ( breln1compset @ X2075 @ X2076 @ X2077 ) ) ) )
=> ( ! [X2078: $i,X2079: $i] :
( ( breln1 @ X2078 @ X2079 )
=> ! [X2080: $i] :
( ( breln1 @ X2078 @ X2080 )
=> ! [X2081: $i] :
( ( in @ X2081 @ X2078 )
=> ! [X2082: $i] :
( ( in @ X2082 @ X2078 )
=> ! [X2083: $i] :
( ( in @ X2083 @ X2078 )
=> ( ( in @ ( kpair @ X2081 @ X2083 ) @ X2079 )
=> ( ( in @ ( kpair @ X2083 @ X2082 ) @ X2080 )
=> ( in @ ( kpair @ X2081 @ X2082 ) @ ( breln1compset @ X2078 @ X2079 @ X2080 ) ) ) ) ) ) ) ) )
=> ( ! [X2084: $i,X2085: $i] :
( ( breln1 @ X2084 @ X2085 )
=> ! [X2086: $i] :
( ( breln1 @ X2084 @ X2086 )
=> ! [X2087: $i] :
( ( in @ X2087 @ X2084 )
=> ! [X2088: $i] :
( ( in @ X2088 @ X2084 )
=> ( ( in @ ( kpair @ X2087 @ X2088 ) @ ( breln1compset @ X2084 @ X2085 @ X2086 ) )
=> ? [X2089: $i] :
( ( in @ X2089 @ X2084 )
& ( in @ ( kpair @ X2087 @ X2089 ) @ X2085 )
& ( in @ ( kpair @ X2089 @ X2088 ) @ X2086 ) ) ) ) ) ) )
=> ( ! [X2090: $i,X2091: $i] :
( ( breln1 @ X2090 @ X2091 )
=> ! [X2092: $i] :
( ( breln1 @ X2090 @ X2092 )
=> ! [X2093: $i] :
( ( in @ X2093 @ X2090 )
=> ! [X2094: $i] :
( ( in @ X2094 @ X2090 )
=> ( ( in @ ( kpair @ X2093 @ X2094 ) @ ( breln1compset @ X2090 @ X2091 @ X2092 ) )
=> ! [X2095: $o] :
( ! [X2096: $i] :
( ( in @ X2096 @ X2090 )
=> ( ( in @ ( kpair @ X2093 @ X2096 ) @ X2091 )
=> ( ( in @ ( kpair @ X2096 @ X2094 ) @ X2092 )
=> X2095 ) ) )
=> X2095 ) ) ) ) ) )
=> ( ! [X2097: $i,X2098: $i] :
( ( breln1 @ X2097 @ X2098 )
=> ! [X2099: $i] :
( ( breln1 @ X2097 @ X2099 )
=> ( breln1 @ X2097 @ ( binunion @ X2098 @ X2099 ) ) ) )
=> ( ! [X2100: $i,X2101: $i] :
( ( breln1 @ X2100 @ X2101 )
=> ! [X2102: $i] :
( ( breln1 @ X2100 @ X2102 )
=> ! [X2103: $i] :
( ( in @ X2103 @ X2100 )
=> ! [X2104: $i] :
( ( in @ X2104 @ X2100 )
=> ( ( in @ ( kpair @ X2103 @ X2104 ) @ X2101 )
=> ( in @ ( kpair @ X2103 @ X2104 ) @ ( binunion @ X2101 @ X2102 ) ) ) ) ) ) )
=> ( ! [X2105: $i,X2106: $i] :
( ( breln1 @ X2105 @ X2106 )
=> ! [X2107: $i] :
( ( breln1 @ X2105 @ X2107 )
=> ! [X2108: $i] :
( ( in @ X2108 @ X2105 )
=> ! [X2109: $i] :
( ( in @ X2109 @ X2105 )
=> ( ( in @ ( kpair @ X2108 @ X2109 ) @ X2107 )
=> ( in @ ( kpair @ X2108 @ X2109 ) @ ( binunion @ X2106 @ X2107 ) ) ) ) ) ) )
=> ( ! [X2110: $i,X2111: $i] :
( ( breln1 @ X2110 @ X2111 )
=> ! [X2112: $i] :
( ( breln1 @ X2110 @ X2112 )
=> ! [X2113: $i] :
( ( in @ X2113 @ X2110 )
=> ! [X2114: $i] :
( ( in @ X2114 @ X2110 )
=> ( ( ( in @ ( kpair @ X2113 @ X2114 ) @ X2111 )
| ( in @ ( kpair @ X2113 @ X2114 ) @ X2112 ) )
=> ( in @ ( kpair @ X2113 @ X2114 ) @ ( binunion @ X2111 @ X2112 ) ) ) ) ) ) )
=> ( ! [X2115: $i,X2116: $i] :
( ( breln1 @ X2115 @ X2116 )
=> ! [X2117: $i] :
( ( breln1 @ X2115 @ X2117 )
=> ! [X2118: $i] :
( ( in @ X2118 @ X2115 )
=> ! [X2119: $i] :
( ( in @ X2119 @ X2115 )
=> ( ( in @ ( kpair @ X2118 @ X2119 ) @ ( binunion @ X2116 @ X2117 ) )
=> ( ( in @ ( kpair @ X2118 @ X2119 ) @ X2116 )
| ( in @ ( kpair @ X2118 @ X2119 ) @ X2117 ) ) ) ) ) ) )
=> ( ! [X2120: $i,X2121: $i] :
( ( breln1 @ X2120 @ X2121 )
=> ! [X2122: $i] :
( ( breln1 @ X2120 @ X2122 )
=> ! [X2123: $i] :
( ( in @ X2123 @ X2120 )
=> ! [X2124: $i] :
( ( in @ X2124 @ X2120 )
=> ( ( in @ ( kpair @ X2123 @ X2124 ) @ ( binunion @ X2121 @ X2122 ) )
=> ! [X2125: $o] :
( ( ( in @ ( kpair @ X2123 @ X2124 ) @ X2121 )
=> X2125 )
=> ( ( ( in @ ( kpair @ X2123 @ X2124 ) @ X2122 )
=> X2125 )
=> X2125 ) ) ) ) ) ) )
=> ( ! [X2126: $i,X2127: $i] :
( ( breln1 @ X2126 @ X2127 )
=> ! [X2128: $i] :
( ( breln1 @ X2126 @ X2128 )
=> ( ( binunion @ X2127 @ X2128 )
= ( binunion @ X2128 @ X2127 ) ) ) )
=> ( ! [X2129: $i,X2130: $i] :
( ( breln1 @ X2129 @ X2130 )
=> ( X2130
= ( breln1invset @ X2129 @ ( breln1invset @ X2129 @ X2130 ) ) ) )
=> ( ! [X2131: $i,X2132: $i] :
( ( breln1 @ X2131 @ X2132 )
=> ! [X2133: $i] :
( ( breln1 @ X2131 @ X2133 )
=> ( ( breln1invset @ X2131 @ ( breln1compset @ X2131 @ X2132 @ X2133 ) )
= ( breln1compset @ X2131 @ ( breln1invset @ X2131 @ X2133 ) @ ( breln1invset @ X2131 @ X2132 ) ) ) ) )
=> ( ! [X2134: $i,X2135: $i] :
( ( breln1 @ X2134 @ X2135 )
=> ! [X2136: $i] :
( ( breln1 @ X2134 @ X2136 )
=> ! [X2137: $i] :
( ( breln1 @ X2134 @ X2137 )
=> ( ( breln1compset @ X2134 @ ( binunion @ X2135 @ X2136 ) @ X2137 )
= ( binunion @ ( breln1compset @ X2134 @ X2135 @ X2137 ) @ ( breln1compset @ X2134 @ X2136 @ X2137 ) ) ) ) ) )
=> ( ! [X2138: $i,X2139: $i] :
( ( breln1 @ X2138 @ X2139 )
=> ! [X2140: $i] :
( ( breln1 @ X2138 @ X2140 )
=> ! [X2141: $i] :
( ( breln1 @ X2138 @ X2141 )
=> ( ( breln1compset @ X2138 @ ( binunion @ X2139 @ X2140 ) @ X2141 )
= ( binunion @ ( breln1invset @ X2138 @ ( breln1compset @ X2138 @ ( breln1invset @ X2138 @ X2141 ) @ ( breln1invset @ X2138 @ X2140 ) ) ) @ ( breln1invset @ X2138 @ ( breln1compset @ X2138 @ ( breln1invset @ X2138 @ X2141 ) @ ( breln1invset @ X2138 @ X2139 ) ) ) ) ) ) ) )
=> ( ! [X2142: $i,X2143: $i > $i] :
? [X2144: $i] :
! [X2145: $i] :
( ( in @ X2145 @ X2144 )
<=> ? [X2146: $i] :
( ( in @ X2146 @ X2142 )
& ( X2145
= ( X2143 @ X2146 ) ) ) )
=> ( ! [X2147: $i,X2148: $i > $i] :
( exu
@ ^ [Z0: $i] :
! [X2149: $i] :
( ( in @ X2149 @ Z0 )
<=> ? [X2150: $i] :
( ( in @ X2150 @ X2147 )
& ( X2149
= ( X2148 @ X2150 ) ) ) ) )
=> ( ! [X2151: $i,X2152: $i > $i,X2153: $i] :
( ( in @ X2153 @ ( image1 @ X2151 @ X2152 ) )
<=> ? [X2154: $i] :
( ( in @ X2154 @ X2151 )
& ( X2153
= ( X2152 @ X2154 ) ) ) )
=> ( ! [X2155: $i,X2156: $i > $i,X2157: $i] :
( ( in @ X2157 @ ( image1 @ X2155 @ X2156 ) )
=> ? [X2158: $i] :
( ( in @ X2158 @ X2155 )
& ( X2157
= ( X2156 @ X2158 ) ) ) )
=> ( ! [X2159: $i,X2160: $i > $i,X2161: $i] :
( ? [X2162: $i] :
( ( in @ X2162 @ X2159 )
& ( X2161
= ( X2160 @ X2162 ) ) )
=> ( in @ X2161 @ ( image1 @ X2159 @ X2160 ) ) )
=> ( ! [X2163: $i,X2164: $i,X2165: $i] :
( ( in @ X2165 @ ( funcSet @ X2163 @ X2164 ) )
=> ( ( injective @ X2163 @ X2164 @ X2165 )
=> ( in @ X2165 @ ( injFuncSet @ X2163 @ X2164 ) ) ) )
=> ( ! [X2166: $i,X2167: $i,X2168: $i] :
( ( in @ X2168 @ ( injFuncSet @ X2166 @ X2167 ) )
=> ( in @ X2168 @ ( funcSet @ X2166 @ X2167 ) ) )
=> ( ! [X2169: $i,X2170: $i,X2171: $i] :
( ( in @ X2171 @ ( injFuncSet @ X2169 @ X2170 ) )
=> ( injective @ X2169 @ X2170 @ X2171 ) )
=> ( ! [X2172: $i,X2173: $i,X2174: $i] :
( ( in @ X2174 @ ( surjFuncSet @ X2172 @ X2173 ) )
=> ( in @ X2174 @ ( funcSet @ X2172 @ X2173 ) ) )
=> ( ! [X2175: $i,X2176: $i,X2177: $i] :
( ( in @ X2177 @ ( surjFuncSet @ X2175 @ X2176 ) )
=> ( surjective @ X2175 @ X2176 @ X2177 ) )
=> ( ! [X2178: $i,X2179: $i,X2180: $i > $i] :
( ! [X2181: $i] :
( ( in @ X2181 @ X2178 )
=> ( in @ ( X2180 @ X2181 ) @ X2179 ) )
=> ! [X2182: $i] :
( ( in @ X2182 @ ( funcSet @ X2179 @ X2178 ) )
=> ( ! [X2183: $i] :
( ( in @ X2183 @ X2178 )
=> ( ( ap @ X2179 @ X2178 @ X2182 @ ( X2180 @ X2183 ) )
= X2183 ) )
=> ( surjective @ X2179 @ X2178 @ X2182 ) ) ) )
=> ( ! [X2184: $i,X2185: $i] :
( ( in @ X2185 @ ( funcSet @ X2184 @ ( powerset @ X2184 ) ) )
=> ~ ( surjective @ X2184 @ ( powerset @ X2184 ) @ X2185 ) )
=> ( ! [X2186: $i] :
( ( nonempty @ X2186 )
=> ? [X2187: $i] :
( ( in @ X2187 @ X2186 )
& ( ( binintersect @ X2187 @ X2186 )
= emptyset ) ) )
=> ( ! [X2188: $i] :
~ ( in @ X2188 @ X2188 )
=> ( ! [X2189: $i,X2190: $i] :
( ( in @ X2189 @ X2190 )
=> ~ ( in @ X2190 @ X2189 ) )
=> ( ! [X2191: $i] :
( ( in @ X2191 @ omega )
=> ( in @ ( omegaS @ X2191 ) @ omega ) )
=> ( ! [X2192: $i] :
( ( in @ X2192 @ omega )
=> ( in @ ( setadjoin @ X2192 @ X2192 ) @ omega ) )
=> ( ! [X2193: $i] :
( ( in @ X2193 @ omega )
=> ( ( omegaS @ X2193 )
!= emptyset ) )
=> ( ! [X2194: $i] :
( ( in @ X2194 @ omega )
=> ! [X2195: $i] :
( ( in @ X2195 @ omega )
=> ( ( ( omegaS @ X2194 )
= ( omegaS @ X2195 ) )
=> ( X2194 = X2195 ) ) ) )
=> ( ! [X2196: $i] :
( ! [X2197: $i] :
( ( in @ X2197 @ X2196 )
=> ( subset @ X2197 @ X2196 ) )
=> ! [X2198: $i] :
( ( in @ X2198 @ X2196 )
=> ( subset @ X2198 @ X2196 ) ) )
=> ! [X21: $i] :
( ! [X2199: $i] :
( ( in @ X2199 @ X21 )
=> ( subset @ X2199 @ X21 ) )
=> ! [X48: $i] :
( ! [X2200: $i] :
( ( in @ X2200 @ X48 )
=> ( subset @ X2200 @ X48 ) )
=> ! [X2201: $i] :
( ( in @ X2201 @ ( binintersect @ X21 @ X48 ) )
=> ( subset @ X2201 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[binintTransitive]),breln1SetBreln1]),c_0_329]),demorgan2a1]),disjointsetsI1]),complementUnionInPowersetComplement]),demorgan2a2]),demorgan1a]),binintersectRsub]),demorgan1b]),demorgan1]),binintersectSubset4]),demorgan2a]),demorgan2b2]),binintersectSubset1]),demorgan2b]),demorgan2]),bs114d]),woz13rule0]),woz13rule1]),setminusI]),woz13rule2]),woz13rule3]),setminusEL]),woz13rule4]),setminusER]),woz1_1]),woz1_2]),woz1_3]),setminusSubset2]),woz1_4]),woz1_5]),breln1all2]),setminusERneg]),peanoSinj]),c_0_330]),upairset2E]),c_0_331]),breln1all1]),setminusELneg]),subbreln1]),eqbreln1]),setminusILneg]),breln1invprop]),breln1invI]),setminusIRneg]),breln1invE]),breln1compprop]),breln1compI]),breln1compE]),setminusLsub]),breln1compEex]),breln1unionprop]),setminusSubset1]),breln1unionIL]),breln1unionIR]),symdiffE]),breln1unionI]),breln1unionE]),symdiffI1]),breln1unionEcases]),breln1unionCommutes]),symdiffI2]),woz2Ex]),woz2W]),symdiffIneg1]),woz2A]),woz2B]),symdiffIneg2]),image1Ex]),c_0_332]),secondinupair]),c_0_333]),c_0_334]),c_0_335]),setukpairIL]),injFuncInInjFuncSet]),injFuncSetFuncIn]),setukpairIR]),injFuncSetFuncInj]),surjFuncSetFuncIn]),kpairiskpair]),surjFuncSetFuncSurj]),leftInvIsSurj]),surjCantorThm]),kpairp]),foundation2]),notinself]),singletonsubset]),notinself2]),omegaSp]),singletoninpowerset]),omegaSclos]),peano0notS]),singletoninpowunion]),cartprodpairmemER]),cartprodmempaircEq]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_336]),c_0_337]),c_0_338]),c_0_339]),singletonsuniq]),setukpairinjL1]),c_0_340]),theprop]),kfstpairEq]),cartprodfstin]),upairset2IR]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),binunionIR]),c_0_341]),ksndpairEq]),binunionEcases]),binunionE]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),complementTI1]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_342]),c_0_343]),c_0_344]),c_0_345]),c_0_346]),binunionLsub]),c_0_347]),c_0_348]),c_0_349]),c_0_350]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_351]),c_0_352]),c_0_353]),brelnall1]),brelnall2]),c_0_354]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_355]),c_0_356]),c_0_357]),c_0_358]),c_0_359]),c_0_360]),c_0_361]),c_0_362]),c_0_363]),c_0_364]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),setminusT_lem]),binunionRsub]),complementT_lem]),setextT]),subsetTI]),binintersectI]),powersetTI1]),binintersectSubset5]),binintersectEL]),binintersectLsub]),powersetTE1]),binintersectSubset2]),binintersectSubset3]),binintersectER]),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]),binunionIL]),c_0_365]),c_0_366]),powersetsubset]),inPowerset]),powersetE1]),powersetI1]),subsetemptysetimpeq]),setextsub]),subset2powerset]),setadjoinSub2]),setadjoinSub]),subsetTrans]),subsetRefl]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_367]),c_0_368]),c_0_369]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_370]),c_0_371]),in__Cong]),inCongP]),c_0_372]),c_0_373]),c_0_374]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_375]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_376]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_377]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_378]),nonemptyE1]),c_0_379]),noeltsimpempty]),emptyI]),setext]),c_0_380]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_381]),c_0_382]),c_0_383]),c_0_384]),c_0_385]),wellorderingAx]),foundationAx]),c_0_386]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_387]) ).
thf(c_0_389,negated_conjecture,
! 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$i,X2523: $i,X2524: $i,X2525: $i,X2526: $i,X2527: $i,X2528: $i,X2529: $i,X2530: $i,X2531: $i,X2532: $o,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,X2548: $i,X2549: $i,X2550: $i,X2551: $i,X2552: $i,X2553: $i,X2554: $i,X2555: $i,X2556: $i,X2557: $i,X2558: $i,X2559: $i,X2560: $i,X2561: $i,X2562: $i,X2563: $i,X2564: $i,X2565: $i,X2566: $i,X2567: $i,X2568: $i,X2569: $i,X2570: $i,X2571: $i,X2572: $i,X2573: $i,X2574: $i,X2575: $i,X2576: $i,X2577: $i,X2578: $i,X2579: $i,X2580: $i,X2581: $i,X2582: $i,X2583: $i,X2584: $i,X2585: $i,X2586: $i,X2587: $i,X2588: $i,X2589: $i,X2590: $i,X2591: $i,X2594: $i,X2595: $i,X2596: $i,X2597: $i,X2598: $i,X2600: $i,X2601: $i,X2602: $i,X2603: $i,X2604: $i > $o,X2607: $i,X2608: $i,X2609: $i > $o,X2611: $i,X2612: $i > $o,X2613: $i,X2615: $i,X2616: $i > $o,X2619: $i,X2620: $i,X2621: $i,X2622: $i,X2623: $i,X2624: $i,X2625: $i,X2626: $i,X2627: $i,X2628: $i,X2629: $i,X2630: $i,X2631: $i,X2632: $i,X2633: $i,X2634: $i,X2635: $i,X2636: $i,X2637: $i,X2638: $i,X2639: $i,X2640: $i,X2641: $i,X2642: $i,X2643: $i,X2644: $i,X2645: $i,X2646: $i,X2647: $i,X2648: $i,X2649: $i,X2650: $i,X2651: $i,X2652: $i,X2653: $i,X2654: $i,X2655: $i,X2656: $i,X2657: $i,X2658: $i,X2659: $i,X2660: $i,X2661: $i,X2662: $i,X2663: $i,X2664: $i,X2665: $i,X2666: $i,X2667: $i,X2668: $i,X2669: $i,X2670: $i,X2671: $i,X2672: $i,X2673: $i,X2674: $i,X2675: $i,X2676: $i,X2677: $i,X2678: $i,X2679: $i,X2680: $i,X2681: $i,X2682: $i,X2683: $i,X2684: $i,X2685: $i,X2686: $i,X2687: $i,X2688: $i,X2689: $i,X2690: $i,X2691: $i > $i > $o,X2692: $i,X2693: $i,X2694: $i,X2695: $i,X2696: $i > $i > $o,X2697: $i,X2698: $i,X2699: $i > $i > $o,X2700: $i,X2701: $i,X2702: $i > $i > $o,X2703: $i,X2704: $i,X2705: $i,X2706: $i,X2707: $i > $i > $o,X2708: $i,X2709: $i,X2710: $i,X2711: $i,X2712: $i > $i > $o,X2713: $i,X2714: $i,X2715: $i,X2716: $i,X2717: $i > $i > $o,X2718: $i,X2719: $i,X2720: $i,X2721: $i,X2722: $i,X2723: $i,X2724: $i,X2725: $i,X2726: $i,X2727: $i,X2728: $i,X2729: $i,X2730: $i,X2731: $i,X2732: $i,X2733: $i,X2734: $i,X2735: $i,X2736: $i,X2737: $i,X2738: $i,X2739: $i,X2740: $i,X2741: $i,X2742: $i,X2743: $i,X2744: $i > $i,X2746: $i,X2747: $i,X2748: $i > $i,X2750: $i,X2751: $i,X2752: $i > $i,X2754: $i,X2755: $i,X2756: $i,X2757: $i > $o,X2760: $i,X2761: $i,X2762: $i,X2763: $i,X2764: $i > $o,X2767: $i,X2768: $i,X2769: $i > $o,X2770: $i,X2771: $i,X2772: $i,X2773: $i,X2774: $i,X2775: $i,X2776: $i,X2777: $i,X2778: $i,X2779: $i,X2780: $i,X2781: $i,X2782: $i,X2783: $i,X2784: $i,X2785: $i,X2786: $i,X2787: $i,X2788: $i,X2790: $i,X2791: $i,X2792: $i,X2793: $i,X2794: $i,X2795: $i,X2796: $i,X2797: $i,X2798: $i,X2799: $i,X2800: $i,X2803: $i,X2804: $i,X2805: $i,X2806: $i,X2811: $i,X2812: $i,X2813: $i,X2814: $i,X2816: $i,X2817: $i,X2818: $i,X2819: $i,X2821: $i,X2822: $i,X2823: $i,X2824: $i,X2825: $i,X2826: $i,X2827: $i,X2828: $i,X2829: $i,X2830: $i,X2831: $i > $i,X2833: $i,X2834: $i,X2835: $i,X2836: $i,X2837: $i,X2838: $i,X2839: $i > $i,X2841: $i,X2842: $i,X2843: $i > $i,X2845: $i,X2846: $i,X2847: $i,X2848: $i,X2849: $i,X2850: $o,X2851: $i,X2852: $i,X2853: $i,X2854: $o,X2855: $i,X2856: $i,X2857: $i,X2858: $o,X2859: $i,X2860: $i,X2861: $i,X2862: $o,X2863: $i,X2864: $i,X2865: $i,X2866: $o,X2867: $i,X2868: $i,X2869: $i,X2870: $o,X2871: $i,X2872: $i,X2873: $i,X2874: $i,X2875: $i,X2876: $o,X2877: $i,X2878: $i,X2879: $i,X2880: $o,X2881: $i,X2882: $i,X2883: $i,X2884: $o,X2885: $i,X2886: $i,X2887: $i,X2888: $i,X2889: $i,X2890: $i,X2891: $i,X2892: $i,X2893: $i,X2894: $i,X2895: $i,X2896: $i,X2897: $i,X2898: $i,X2899: $i,X2900: $i,X2901: $i,X2902: $i,X2905: $i,X2906: $i,X2907: $i,X2909: $i,X2910: $i,X2911: $i,X2913: $i,X2914: $i,X2915: $i,X2916: $i,X2917: $i,X2918: $i,X2919: $i,X2920: $i,X2921: $i,X2922: $i,X2923: $i,X2924: $i,X2925: $i,X2926: $i,X2927: $i,X2928: $i,X2929: $i,X2930: $i,X2931: $i,X2932: $i,X2933: $i,X2934: $i,X2935: $i,X2936: $i,X2937: $i,X2938: $i,X2939: $i,X2940: $i,X2941: $i,X2942: $i,X2943: $i,X2944: $i,X2945: $i,X2946: $i,X2947: $i,X2948: $i,X2949: $i,X2950: $i,X2951: $i,X2952: $i,X2953: $i,X2954: $i,X2955: $i,X2956: $i,X2957: $i,X2958: $i,X2959: $i,X2960: $i,X2961: $i,X2962: $i,X2963: $i,X2964: $i,X2965: $i,X2966: $i,X2967: $i,X2968: $i,X2969: $i,X2970: $i,X2971: $i,X2972: $i,X2973: $i,X2974: $i,X2975: $i,X2976: $i,X2977: $i,X2978: $i,X2979: $i,X2980: $i,X2981: $i,X2982: $i,X2983: $i,X2984: $i,X2985: $i,X2986: $i,X2987: $i,X2988: $i,X2989: $i,X2990: $i,X2991: $i,X2992: $i,X2993: $i,X2994: $i,X2995: $i,X2996: $i,X2997: $i,X2998: $i,X2999: $i,X3000: $i,X3001: $i,X3002: $i,X3003: $i,X3004: $i,X3005: $i,X3006: $i,X3007: $i,X3008: $i,X3009: $i,X3010: $i,X3011: $i,X3012: $i,X3013: $i,X3014: $i,X3015: $i,X3016: $o,X3017: $i,X3018: $i,X3019: $i,X3020: $i,X3021: $i,X3022: $i,X3023: $i,X3024: $i,X3025: $i,X3026: $i,X3027: $i,X3028: $i,X3029: $i,X3030: $i,X3031: $i,X3032: $i,X3033: $i,X3034: $i,X3035: $i,X3036: $i,X3037: $i,X3038: $i,X3039: $i,X3040: $i,X3041: $i,X3042: $i,X3043: $i,X3044: $i,X3045: $i,X3046: $i,X3047: $i,X3048: $i,X3049: $i,X3050: $i,X3051: $i,X3052: $i,X3053: $i,X3054: $i,X3055: $i,X3056: $i,X3057: $i,X3058: $i,X3059: $i,X3060: $i,X3061: $i,X3062: $i,X3063: $i,X3064: $i,X3065: $i,X3066: $i,X3067: $i,X3068: $i,X3069: $i,X3070: $i,X3071: $i,X3072: $i,X3073: $i,X3074: $i,X3075: $i,X3076: $i,X3077: $i,X3078: $i,X3079: $i,X3080: $i,X3081: $i,X3082: $i,X3083: $i,X3084: $i,X3085: $i,X3086: $i,X3087: $i,X3088: $i,X3089: $i,X3090: $i,X3091: $i,X3092: $i,X3093: $i,X3094: $i,X3095: $i,X3096: $i,X3097: $i,X3098: $i,X3099: $i,X3100: $i > $o,X3103: $i,X3104: $i,X3105: $i,X3106: $i,X3107: $i > $i > $o,X3108: $i,X3109: $i,X3110: $i > $o,X3113: $i,X3114: $i,X3115: $i,X3116: $i,X3119: $i,X3120: $i,X3121: $i,X3126: $i,X3127: $i,X3128: $i,X3129: $i,X3130: $i,X3131: $i,X3132: $i,X3133: $i,X3134: $i,X3135: $i,X3136: $i,X3137: $i,X3138: $i,X3139: $i,X3140: $i,X3141: $i,X3142: $i,X3143: $i,X3144: $i,X3145: $i,X3146: $i,X3147: $i,X3148: $i,X3149: $i,X3151: $i,X3152: $i,X3153: $i,X3154: $i,X3155: $i,X3156: $o,X3158: $i,X3159: $i,X3160: $i,X3161: $i,X3162: $i,X3163: $i,X3164: $i,X3165: $i,X3166: $i,X3167: $i,X3168: $i,X3169: $i,X3170: $i,X3171: $i,X3172: $i,X3173: $i,X3174: $i,X3175: $i,X3176: $i,X3177: $i,X3178: $i,X3179: $i,X3180: $i,X3181: $i,X3182: $i,X3183: $i,X3184: $i,X3185: $i,X3186: $o,X3187: $i,X3188: $i,X3189: $i,X3190: $i,X3191: $i,X3192: $i,X3193: $i,X3194: $i,X3195: $i,X3196: $i,X3197: $i,X3198: $i,X3199: $i,X3200: $i,X3201: $i,X3202: $i,X3203: $i,X3204: $i > $i,X3206: $i,X3208: $i,X3209: $i,X3210: $i,X3211: $i > $i,X3212: $i,X3213: $i > $i,X3214: $i,X3216: $i,X3217: $i > $i,X3218: $i,X3219: $i,X3220: $i,X3221: $i > $i,X3222: $i,X3224: $i,X3225: $i > $i,X3226: $i,X3227: $i,X3228: $i,X3229: $i,X3230: $i,X3231: $i,X3232: $i,X3233: $i,X3234: $i,X3235: $i,X3236: $i,X3237: $i,X3238: $i,X3239: $i,X3240: $i,X3241: $i,X3242: $i,X3243: $i,X3244: $i,X3245: $i > $i,X3247: $i,X3249: $i,X3250: $i,X3251: $i,X3253: $i,X3254: $i,X3255: $i,X3256: $i,X3257: $i,X3258: $i,X3259: $i,X3260: $i,X3261: $i,X3263: $i,X3265: $i,X3267: $i] :
( ( ~ ( in @ ( esk1_2 @ X2202 @ X2203 ) @ X2202 )
| ~ ( in @ ( esk1_2 @ X2202 @ X2203 ) @ X2203 )
| ( X2202 = X2203 ) )
& ( ( in @ ( esk1_2 @ X2202 @ X2203 ) @ X2202 )
| ( in @ ( esk1_2 @ X2202 @ X2203 ) @ X2203 )
| ( X2202 = X2203 ) )
& ~ ( in @ X2205 @ emptyset )
& ( ~ ( in @ X2208 @ ( setadjoin @ X2206 @ X2207 ) )
| ( X2208 = X2206 )
| ( in @ X2208 @ X2207 ) )
& ( ( X2208 != X2206 )
| ( in @ X2208 @ ( setadjoin @ X2206 @ X2207 ) ) )
& ( ~ ( in @ X2208 @ X2207 )
| ( in @ X2208 @ ( setadjoin @ X2206 @ X2207 ) ) )
& ( ~ ( in @ X2210 @ ( powerset @ X2209 ) )
| ~ ( in @ X2211 @ X2210 )
| ( in @ X2211 @ X2209 ) )
& ( ( in @ ( esk2_2 @ X2212 @ X2213 ) @ X2213 )
| ( in @ X2213 @ ( powerset @ X2212 ) ) )
& ( ~ ( in @ ( esk2_2 @ X2212 @ X2213 ) @ X2212 )
| ( in @ X2213 @ ( powerset @ X2212 ) ) )
& ( ( in @ X2216 @ ( esk3_2 @ X2215 @ X2216 ) )
| ~ ( in @ X2216 @ ( setunion @ X2215 ) ) )
& ( ( in @ ( esk3_2 @ X2215 @ X2216 ) @ X2215 )
| ~ ( in @ X2216 @ ( setunion @ X2215 ) ) )
& ( ~ ( in @ X2219 @ X2220 )
| ~ ( in @ X2220 @ X2218 )
| ( in @ X2219 @ ( setunion @ X2218 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X2221 @ omega )
| ( in @ ( setadjoin @ X2221 @ X2221 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X2222 ) @ omega )
| ~ ( in @ emptyset @ X2222 )
| ~ ( in @ X2224 @ omega )
| ( in @ X2224 @ X2222 ) )
& ( ( in @ ( esk4_1 @ X2222 ) @ X2222 )
| ~ ( in @ emptyset @ X2222 )
| ~ ( in @ X2224 @ omega )
| ( in @ X2224 @ X2222 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X2222 ) @ ( esk4_1 @ X2222 ) ) @ X2222 )
| ~ ( in @ emptyset @ X2222 )
| ~ ( in @ X2224 @ omega )
| ( in @ X2224 @ X2222 ) )
& ( ( in @ ( esk7_3 @ X2225 @ X2226 @ X2229 ) @ X2226 )
| ~ ( in @ X2229 @ ( esk6_2 @ X2225 @ X2226 ) )
| ( in @ ( esk5_2 @ X2225 @ X2226 ) @ X2226 ) )
& ( ( X2225 @ ( esk7_3 @ X2225 @ X2226 @ X2229 ) @ X2229 )
| ~ ( in @ X2229 @ ( esk6_2 @ X2225 @ X2226 ) )
| ( in @ ( esk5_2 @ X2225 @ X2226 ) @ X2226 ) )
& ( ~ ( in @ X2232 @ X2226 )
| ~ ( X2225 @ X2232 @ X2231 )
| ( in @ X2231 @ ( esk6_2 @ X2225 @ X2226 ) )
| ( in @ ( esk5_2 @ X2225 @ X2226 ) @ X2226 ) )
& ( ( in @ ( esk7_3 @ X2225 @ X2226 @ X2229 ) @ X2226 )
| ~ ( in @ X2229 @ ( esk6_2 @ X2225 @ X2226 ) )
| ~ ( exu @ ( X2225 @ ( esk5_2 @ X2225 @ X2226 ) ) ) )
& ( ( X2225 @ ( esk7_3 @ X2225 @ X2226 @ X2229 ) @ X2229 )
| ~ ( in @ X2229 @ ( esk6_2 @ X2225 @ X2226 ) )
| ~ ( exu @ ( X2225 @ ( esk5_2 @ X2225 @ X2226 ) ) ) )
& ( ~ ( in @ X2232 @ X2226 )
| ~ ( X2225 @ X2232 @ X2231 )
| ( in @ X2231 @ ( esk6_2 @ X2225 @ X2226 ) )
| ~ ( exu @ ( X2225 @ ( esk5_2 @ X2225 @ X2226 ) ) ) )
& ( ( in @ ( esk8_1 @ X2233 ) @ X2233 )
| ~ ( in @ X2234 @ X2233 ) )
& ( ~ ( in @ X2236 @ ( esk8_1 @ X2233 ) )
| ~ ( in @ X2236 @ X2233 )
| ~ ( in @ X2234 @ X2233 ) )
& epred1_0
& ( ~ ( exu @ X2237 )
| ( X2237 @ ( descr @ X2237 ) ) )
& ( ~ ( in @ X2240 @ X2238 )
| ~ ( X2239 @ X2240 )
| ( in @ X2240 @ ( dsetconstr @ X2238 @ X2239 ) ) )
& ( ~ ( in @ X2243 @ ( dsetconstr @ X2241 @ X2242 ) )
| ( in @ X2243 @ X2241 ) )
& ( ~ ( in @ X2246 @ ( dsetconstr @ X2244 @ X2245 ) )
| ( X2245 @ X2246 ) )
& ( ( X2247 @ ( esk9_1 @ X2247 ) )
| ~ ( exu @ X2247 ) )
& ( ~ ( X2247 @ X2249 )
| ( ( esk9_1 @ X2247 )
= X2249 )
| ~ ( exu @ X2247 ) )
& ( ~ ( in @ X2251 @ ( prop2set @ X2250 ) )
| X2250 )
& ( ~ ( in @ X2252 @ emptyset )
| X2253 )
& ( ~ ( in @ X2254 @ emptyset )
| ~ $true )
& ~ ( in @ X2255 @ emptyset )
& ( ~ ( exu @ X2256 )
| ( X2256 @ ( esk10_1 @ X2256 ) ) )
& ( ( in @ ( esk12_2 @ X2258 @ X2259 ) @ X2259 )
| ( X2258 = X2259 )
| ( in @ ( esk11_2 @ X2258 @ X2259 ) @ X2258 ) )
& ( ~ ( in @ ( esk12_2 @ X2258 @ X2259 ) @ X2258 )
| ( X2258 = X2259 )
| ( in @ ( esk11_2 @ X2258 @ X2259 ) @ X2258 ) )
& ( ( in @ ( esk12_2 @ X2258 @ X2259 ) @ X2259 )
| ( X2258 = X2259 )
| ~ ( in @ ( esk11_2 @ X2258 @ X2259 ) @ X2259 ) )
& ( ~ ( in @ ( esk12_2 @ X2258 @ X2259 ) @ X2258 )
| ( X2258 = X2259 )
| ~ ( in @ ( esk11_2 @ X2258 @ X2259 ) @ X2259 ) )
& ( ( in @ ( esk13_1 @ X2262 ) @ X2262 )
| ( X2262 = emptyset ) )
& ( ( in @ ( esk14_1 @ X2264 ) @ X2264 )
| ( X2264 = emptyset ) )
& ( ~ ( in @ X2268 @ ( dsetconstr @ X2266 @ X2267 ) )
| ( X2267 @ X2268 )
| ~ ( in @ X2268 @ X2266 ) )
& ( ~ ( X2267 @ X2268 )
| ( in @ X2268 @ ( dsetconstr @ X2266 @ X2267 ) )
| ~ ( in @ X2268 @ X2266 ) )
& ( ~ ( nonempty @ X2269 )
| ( in @ ( esk15_1 @ X2269 ) @ X2269 ) )
& ( ~ ( in @ X2273 @ X2271 )
| ~ ( X2272 @ X2273 )
| ( nonempty @ ( dsetconstr @ X2271 @ X2272 ) ) )
& ( ~ ( in @ X2275 @ X2274 )
| ( nonempty @ X2274 ) )
& ( in @ X2276 @ ( setadjoin @ X2276 @ X2277 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X2280 @ X2279 )
| ( in @ X2280 @ ( setadjoin @ X2278 @ X2279 ) ) )
& ( ( in @ X2283 @ X2282 )
| X2284
| ( X2283 = X2281 )
| ~ ( in @ X2283 @ ( setadjoin @ X2281 @ X2282 ) ) )
& ( ~ X2284
| X2284
| ( X2283 = X2281 )
| ~ ( in @ X2283 @ ( setadjoin @ X2281 @ X2282 ) ) )
& ( ( in @ X2283 @ X2282 )
| X2284
| ~ X2284
| ~ ( in @ X2283 @ ( setadjoin @ X2281 @ X2282 ) ) )
& ( ~ X2284
| X2284
| ~ X2284
| ~ ( in @ X2283 @ ( setadjoin @ X2281 @ X2282 ) ) )
& ( ~ ( in @ X2287 @ ( setadjoin @ X2285 @ X2286 ) )
| ( X2287 = X2285 )
| ( in @ X2287 @ X2286 ) )
& ( ( dsetconstr @ X2288
@ ^ [Z0: $i] : $true )
= X2288 )
& ( ( in @ ( esk16_2 @ X2289 @ X2290 ) @ X2290 )
| ( in @ X2290 @ ( powerset @ X2289 ) ) )
& ( ~ ( in @ ( esk16_2 @ X2289 @ X2290 ) @ X2289 )
| ( in @ X2290 @ ( powerset @ X2289 ) ) )
& ( in @ emptyset @ ( powerset @ X2292 ) )
& ( in @ emptyset @ ( powerset @ X2293 ) )
& ( ~ ( in @ X2295 @ ( powerset @ X2294 ) )
| ~ ( in @ X2296 @ X2295 )
| ( in @ X2296 @ X2294 ) )
& ( ~ ( in @ X2298 @ X2299 )
| ~ ( in @ X2299 @ X2297 )
| ( in @ X2298 @ ( setunion @ X2297 ) ) )
& ( ( in @ X2301 @ ( esk17_3 @ X2300 @ X2301 @ X2302 ) )
| X2302
| ~ ( in @ X2301 @ ( setunion @ X2300 ) ) )
& ( ( in @ ( esk17_3 @ X2300 @ X2301 @ X2302 ) @ X2300 )
| X2302
| ~ ( in @ X2301 @ ( setunion @ X2300 ) ) )
& ( ~ X2302
| X2302
| ~ ( in @ X2301 @ ( setunion @ X2300 ) ) )
& ( ~ ( in @ X2305 @ X2304 )
| ( in @ X2305 @ ( powerset @ ( setunion @ X2304 ) ) ) )
& ( ~ ( X2306 @ X2308 )
| ( X2308
= ( esk18_1 @ X2306 ) )
| ~ ( exu @ X2306 ) )
& ( ( X2309
!= ( esk18_1 @ X2306 ) )
| ( X2306 @ X2309 )
| ~ ( exu @ X2306 ) )
& ( ( in @ ( esk19_1 @ X2310 ) @ X2310 )
| ~ ( nonempty @ X2310 ) )
& ( $true
| ~ ( nonempty @ X2310 ) )
& ( ~ ( in @ X2312 @ ( setadjoin @ X2313 @ emptyset ) )
| ( X2312 = X2313 ) )
& ( ( X2314 = X2315 )
| ~ ( in @ X2315 @ ( setadjoin @ X2314 @ emptyset ) ) )
& ( ( X2316 != X2317 )
| ( in @ X2316 @ ( setadjoin @ X2317 @ emptyset ) ) )
& ( ~ ( in @ X2318 @ ( setadjoin @ X2319 @ emptyset ) )
| ( in @ X2319 @ ( setadjoin @ X2318 @ emptyset ) ) )
& ( ~ ( in @ X2322 @ ( setadjoin @ X2320 @ ( setadjoin @ X2321 @ emptyset ) ) )
| ( X2322 = X2320 )
| ( X2322 = X2321 ) )
& ( in @ X2323 @ ( setadjoin @ X2323 @ ( setadjoin @ X2324 @ emptyset ) ) )
& ( in @ X2326 @ ( setadjoin @ X2325 @ ( setadjoin @ X2326 @ emptyset ) ) )
& ( ~ ( in @ X2329 @ X2327 )
| ~ ( X2328 @ X2329 )
| ( ( dsetconstr @ X2327 @ X2328 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X2331 @ emptyset )
| ( X2330 @ X2331 ) )
& ( ( in @ ( esk20_2 @ X2332 @ X2333 ) @ X2332 )
| ~ ( in @ X2334 @ X2332 )
| ( X2333 @ X2334 ) )
& ( ~ ( X2333 @ ( esk20_2 @ X2332 @ X2333 ) )
| ~ ( in @ X2334 @ X2332 )
| ( X2333 @ X2334 ) )
& ( ( in @ ( esk21_2 @ X2336 @ X2337 ) @ X2336 )
| ~ ( in @ X2339 @ X2336 )
| ~ ( X2337 @ X2339 ) )
& ( ( X2337 @ ( esk21_2 @ X2336 @ X2337 ) )
| ~ ( in @ X2339 @ X2336 )
| ~ ( X2337 @ X2339 ) )
& ( ( in @ ( esk22_2 @ X2340 @ X2341 ) @ X2340 )
| ~ ( in @ X2343 @ X2340 )
| ~ ( X2341 @ X2343 ) )
& ( ( X2341 @ ( esk22_2 @ X2340 @ X2341 ) )
| ~ ( in @ X2343 @ X2340 )
| ~ ( X2341 @ X2343 ) )
& ( ( in @ ( esk23_2 @ X2344 @ X2345 ) @ X2344 )
| ~ ( in @ X2346 @ X2344 )
| ( X2345 @ X2346 ) )
& ( ~ ( X2345 @ ( esk23_2 @ X2344 @ X2345 ) )
| ~ ( in @ X2346 @ X2344 )
| ( X2345 @ X2346 ) )
& ( ~ X2348
| ( in @ emptyset @ ( prop2set @ X2348 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X2349 @ X2350 ) @ X2349 )
| ~ ( in @ X2352 @ X2349 )
| ~ ( X2350 @ X2352 ) )
& ( ( X2350 @ ( esk24_2 @ X2349 @ X2350 ) )
| ~ ( in @ X2352 @ X2349 )
| ~ ( X2350 @ X2352 ) )
& ( ( in @ ( esk25_2 @ X2353 @ X2354 ) @ X2353 )
| ~ ( in @ X2355 @ X2353 )
| ( X2354 @ X2355 ) )
& ( ~ ( X2354 @ ( esk25_2 @ X2353 @ X2354 ) )
| ~ ( in @ X2355 @ X2353 )
| ( X2354 @ X2355 ) )
& ( ( X2357 @ ( esk26_2 @ X2357 @ X2358 ) )
| ~ ( X2357 @ X2358 )
| ( exu @ X2357 ) )
& ( ( X2358
!= ( esk26_2 @ X2357 @ X2358 ) )
| ~ ( X2357 @ X2358 )
| ( exu @ X2357 ) )
& ( ( X2360 @ ( esk27_1 @ X2360 ) )
| ( exu @ X2360 )
| ~ ( X2360 @ X2361 ) )
& ( ( X2360 @ ( esk28_1 @ X2360 ) )
| ( exu @ X2360 )
| ~ ( X2360 @ X2361 ) )
& ( ( ( esk27_1 @ X2360 )
!= ( esk28_1 @ X2360 ) )
| ( exu @ X2360 )
| ~ ( X2360 @ X2361 ) )
& ( ~ ( X2364 @ ( esk29_2 @ X2364 @ X2365 ) )
| ( ( esk29_2 @ X2364 @ X2365 )
!= X2365 )
| ( exu @ X2364 ) )
& ( ( X2364 @ ( esk29_2 @ X2364 @ X2365 ) )
| ( ( esk29_2 @ X2364 @ X2365 )
= X2365 )
| ( exu @ X2364 ) )
& ( ( X2367 != X2368 )
| ( X2369 != X2370 )
| ~ ( in @ X2369 @ X2367 )
| ( in @ X2370 @ X2368 ) )
& ( ~ ( in @ X2373 @ X2371 )
| ( in @ X2374 @ X2372 )
| ( X2373 != X2374 )
| ( X2371 != X2372 ) )
& ( ~ ( in @ X2374 @ X2372 )
| ( in @ X2373 @ X2371 )
| ( X2373 != X2374 )
| ( X2371 != X2372 ) )
& ( ~ ( exu @ X2375 )
| ~ ( X2375 @ X2376 )
| ~ ( X2375 @ X2377 )
| ( X2376 = X2377 ) )
& ( ~ ( exu @ X2378 )
| ( exu @ X2379 )
| ( ( esk30_2 @ X2378 @ X2379 )
= ( esk31_2 @ X2378 @ X2379 ) ) )
& ( ~ ( exu @ X2379 )
| ( exu @ X2378 )
| ( ( esk30_2 @ X2378 @ X2379 )
= ( esk31_2 @ X2378 @ X2379 ) ) )
& ( ~ ( exu @ X2378 )
| ( exu @ X2379 )
| ~ ( X2378 @ ( esk30_2 @ X2378 @ X2379 ) )
| ~ ( X2379 @ ( esk31_2 @ X2378 @ X2379 ) ) )
& ( ~ ( exu @ X2379 )
| ( exu @ X2378 )
| ~ ( X2378 @ ( esk30_2 @ X2378 @ X2379 ) )
| ~ ( X2379 @ ( esk31_2 @ X2378 @ X2379 ) ) )
& ( ~ ( exu @ X2378 )
| ( exu @ X2379 )
| ( X2378 @ ( esk30_2 @ X2378 @ X2379 ) )
| ( X2379 @ ( esk31_2 @ X2378 @ X2379 ) ) )
& ( ~ ( exu @ X2379 )
| ( exu @ X2378 )
| ( X2378 @ ( esk30_2 @ X2378 @ X2379 ) )
| ( X2379 @ ( esk31_2 @ X2378 @ X2379 ) ) )
& ( emptyset = emptyset )
& ( ( X2382 != X2383 )
| ( X2384 != X2385 )
| ( ( setadjoin @ X2382 @ X2384 )
= ( setadjoin @ X2383 @ X2385 ) ) )
& ( ( X2386 != X2387 )
| ( ( powerset @ X2386 )
= ( powerset @ X2387 ) ) )
& ( ( X2388 != X2389 )
| ( ( setunion @ X2388 )
= ( setunion @ X2389 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X2390 )
| ~ ( X2390 @ X2391 )
| ~ ( X2390 @ X2392 )
| ( X2391 = X2392 ) )
& ( ( ( esk32_2 @ X2393 @ X2394 )
= ( esk33_2 @ X2393 @ X2394 ) )
| ~ ( exu @ X2393 )
| ~ ( exu @ X2394 )
| ( ( descr @ X2393 )
= ( descr @ X2394 ) ) )
& ( ~ ( X2393 @ ( esk32_2 @ X2393 @ X2394 ) )
| ~ ( X2394 @ ( esk33_2 @ X2393 @ X2394 ) )
| ~ ( exu @ X2393 )
| ~ ( exu @ X2394 )
| ( ( descr @ X2393 )
= ( descr @ X2394 ) ) )
& ( ( X2393 @ ( esk32_2 @ X2393 @ X2394 ) )
| ( X2394 @ ( esk33_2 @ X2393 @ X2394 ) )
| ~ ( exu @ X2393 )
| ~ ( exu @ X2394 )
| ( ( descr @ X2393 )
= ( descr @ X2394 ) ) )
& ( ( in @ ( esk34_4 @ X2397 @ X2398 @ X2399 @ X2400 ) @ X2397 )
| ( ( dsetconstr @ X2397 @ X2399 )
= ( dsetconstr @ X2398 @ X2400 ) )
| ( X2397 != X2398 ) )
& ( ( in @ ( esk35_4 @ X2397 @ X2398 @ X2399 @ X2400 ) @ X2398 )
| ( ( dsetconstr @ X2397 @ X2399 )
= ( dsetconstr @ X2398 @ X2400 ) )
| ( X2397 != X2398 ) )
& ( ( ( esk34_4 @ X2397 @ X2398 @ X2399 @ X2400 )
= ( esk35_4 @ X2397 @ X2398 @ X2399 @ X2400 ) )
| ( ( dsetconstr @ X2397 @ X2399 )
= ( dsetconstr @ X2398 @ X2400 ) )
| ( X2397 != X2398 ) )
& ( ~ ( X2399 @ ( esk34_4 @ X2397 @ X2398 @ X2399 @ X2400 ) )
| ~ ( X2400 @ ( esk35_4 @ X2397 @ X2398 @ X2399 @ X2400 ) )
| ( ( dsetconstr @ X2397 @ X2399 )
= ( dsetconstr @ X2398 @ X2400 ) )
| ( X2397 != X2398 ) )
& ( ( X2399 @ ( esk34_4 @ X2397 @ X2398 @ X2399 @ X2400 ) )
| ( X2400 @ ( esk35_4 @ X2397 @ X2398 @ X2399 @ X2400 ) )
| ( ( dsetconstr @ X2397 @ X2399 )
= ( dsetconstr @ X2398 @ X2400 ) )
| ( X2397 != X2398 ) )
& ( ( in @ ( esk36_2 @ X2403 @ X2404 ) @ X2403 )
| ( subset @ X2403 @ X2404 ) )
& ( ~ ( in @ ( esk36_2 @ X2403 @ X2404 ) @ X2404 )
| ( subset @ X2403 @ X2404 ) )
& ( ( X2406 != X2407 )
| ( subset @ X2407 @ X2406 ) )
& ( ( X2408 != X2409 )
| ( subset @ X2408 @ X2409 ) )
& ( ( in @ ( esk37_2 @ X2410 @ X2411 ) @ X2410 )
| ( subset @ X2410 @ X2411 ) )
& ( ~ ( in @ ( esk37_2 @ X2410 @ X2411 ) @ X2411 )
| ( subset @ X2410 @ X2411 ) )
& ( subset @ emptyset @ X2413 )
& ( ~ ( subset @ X2414 @ X2415 )
| ~ ( in @ X2416 @ X2414 )
| ( in @ X2416 @ X2415 ) )
& ( ~ ( subset @ X2417 @ X2418 )
| ( in @ X2419 @ X2418 )
| ~ ( in @ X2419 @ X2417 ) )
& ( ~ ( in @ X2422 @ X2420 )
| ( in @ X2422 @ X2421 )
| ~ ( subset @ X2420 @ X2421 ) )
& ( ( subset @ X2423 @ X2424 )
| ( X2423 != X2424 ) )
& ( ~ ( in @ X2427 @ X2425 )
| ( in @ X2427 @ X2426 )
| ( X2425 != X2426 ) )
& ( subset @ X2428 @ X2428 )
& ( ~ ( subset @ X2429 @ X2430 )
| ~ ( subset @ X2430 @ X2431 )
| ( subset @ X2429 @ X2431 ) )
& ( subset @ X2433 @ ( setadjoin @ X2432 @ X2433 ) )
& ( ~ ( subset @ X2434 @ X2436 )
| ( subset @ X2434 @ ( setadjoin @ X2435 @ X2436 ) ) )
& ( ~ ( subset @ X2437 @ X2438 )
| ( in @ X2437 @ ( powerset @ X2438 ) ) )
& ( ~ ( subset @ X2439 @ X2440 )
| ~ ( subset @ X2440 @ X2439 )
| ( X2439 = X2440 ) )
& ( ~ ( subset @ X2441 @ emptyset )
| ( X2441 = emptyset ) )
& ( ~ ( subset @ X2443 @ X2442 )
| ( in @ X2443 @ ( powerset @ X2442 ) ) )
& ( ~ ( in @ X2445 @ ( powerset @ X2444 ) )
| ( subset @ X2445 @ X2444 ) )
& ( in @ X2446 @ ( powerset @ X2446 ) )
& ( ~ ( subset @ X2447 @ X2448 )
| ( subset @ ( powerset @ X2447 ) @ ( powerset @ X2448 ) ) )
& ( in @ ( dsetconstr @ X2449 @ X2450 ) @ ( powerset @ X2449 ) )
& ( subset @ ( dsetconstr @ X2451 @ X2452 ) @ X2451 )
& ( ~ ( in @ X2455 @ X2453 )
| ( in @ X2455 @ ( binunion @ X2453 @ X2454 ) ) )
& ( in @ X2457 @ ( setadjoin @ X2456 @ ( setadjoin @ X2457 @ emptyset ) ) )
& ( ~ ( in @ X2460 @ X2459 )
| ( in @ X2460 @ ( binunion @ X2458 @ X2459 ) ) )
& ( ( in @ X2463 @ X2462 )
| X2464
| ( in @ X2463 @ X2461 )
| ~ ( in @ X2463 @ ( binunion @ X2461 @ X2462 ) ) )
& ( ~ X2464
| X2464
| ( in @ X2463 @ X2461 )
| ~ ( in @ X2463 @ ( binunion @ X2461 @ X2462 ) ) )
& ( ( in @ X2463 @ X2462 )
| X2464
| ~ X2464
| ~ ( in @ X2463 @ ( binunion @ X2461 @ X2462 ) ) )
& ( ~ X2464
| X2464
| ~ X2464
| ~ ( in @ X2463 @ ( binunion @ X2461 @ X2462 ) ) )
& ( ~ ( in @ X2467 @ ( binunion @ X2465 @ X2466 ) )
| ( in @ X2467 @ X2465 )
| ( in @ X2467 @ X2466 ) )
& ( subset @ X2468 @ ( binunion @ X2468 @ X2469 ) )
& ( subset @ X2471 @ ( binunion @ X2470 @ X2471 ) )
& ( ~ ( in @ X2474 @ X2472 )
| ~ ( in @ X2474 @ X2473 )
| ( in @ X2474 @ ( binintersect @ X2472 @ X2473 ) ) )
& ( ~ ( subset @ X2477 @ X2475 )
| ~ ( subset @ X2477 @ X2476 )
| ( subset @ X2477 @ ( binintersect @ X2475 @ X2476 ) ) )
& ( ~ ( in @ X2480 @ ( binintersect @ X2478 @ X2479 ) )
| ( in @ X2480 @ X2478 ) )
& ( subset @ ( binintersect @ X2481 @ X2482 ) @ X2481 )
& ( ~ ( subset @ X2483 @ X2484 )
| ( ( binintersect @ X2483 @ X2484 )
= X2483 ) )
& ( ( ( binintersect @ X2485 @ X2486 )
!= X2486 )
| ( subset @ X2486 @ X2485 ) )
& ( ~ ( in @ X2489 @ ( binintersect @ X2487 @ X2488 ) )
| ( in @ X2489 @ X2488 ) )
& ( ( in @ ( esk38_2 @ X2490 @ X2491 ) @ X2490 )
| ( ( binintersect @ X2490 @ X2491 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X2490 @ X2491 ) @ X2491 )
| ( ( binintersect @ X2490 @ X2491 )
= emptyset ) )
& ( subset @ ( binintersect @ X2493 @ X2494 ) @ X2494 )
& ( ~ ( subset @ X2496 @ X2495 )
| ( ( binintersect @ X2495 @ X2496 )
= X2496 ) )
& ( ( ( binintersect @ X2497 @ X2498 )
!= X2497 )
| ( subset @ X2497 @ X2498 ) )
& ( ( binintersect @ X2499 @ ( binunion @ X2500 @ X2501 ) )
= ( binunion @ ( binintersect @ X2499 @ X2500 ) @ ( binintersect @ X2499 @ X2501 ) ) )
& ( ~ ( in @ X2504 @ X2502 )
| ( in @ X2504 @ X2503 )
| ( in @ X2504 @ ( setminus @ X2502 @ X2503 ) ) )
& ( ~ ( in @ X2507 @ ( setminus @ X2505 @ X2506 ) )
| ( in @ X2507 @ X2505 ) )
& ( ~ ( in @ X2510 @ ( setminus @ X2508 @ X2509 ) )
| ~ ( in @ X2510 @ X2509 ) )
& ( ~ ( subset @ X2511 @ X2512 )
| ( ( setminus @ X2511 @ X2512 )
= emptyset ) )
& ( ( in @ X2515 @ ( setminus @ X2513 @ X2514 ) )
| ~ ( in @ X2515 @ X2513 )
| ( in @ X2515 @ X2514 ) )
& ( ( in @ X2518 @ ( setminus @ X2516 @ X2517 ) )
| ( in @ X2518 @ X2517 )
| ~ ( in @ X2518 @ X2516 ) )
& ( ( in @ X2521 @ X2519 )
| ~ ( in @ X2521 @ ( setminus @ X2519 @ X2520 ) ) )
& ( ~ ( in @ X2524 @ X2523 )
| ~ ( in @ X2524 @ ( setminus @ X2522 @ X2523 ) ) )
& ( subset @ ( setminus @ X2525 @ X2526 ) @ X2525 )
& ( ( ( setminus @ X2527 @ X2528 )
!= emptyset )
| ( subset @ X2527 @ X2528 ) )
& ( ~ ( in @ X2531 @ X2529 )
| X2532
| ( in @ X2531 @ X2529 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ( in @ X2531 @ X2530 )
| X2532
| ( in @ X2531 @ X2529 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ X2532
| X2532
| ( in @ X2531 @ X2529 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ ( in @ X2531 @ X2529 )
| X2532
| ~ ( in @ X2531 @ X2530 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ( in @ X2531 @ X2530 )
| X2532
| ~ ( in @ X2531 @ X2530 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ X2532
| X2532
| ~ ( in @ X2531 @ X2530 )
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ ( in @ X2531 @ X2529 )
| X2532
| ~ X2532
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ( in @ X2531 @ X2530 )
| X2532
| ~ X2532
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ X2532
| X2532
| ~ X2532
| ~ ( in @ X2531 @ ( symdiff @ X2529 @ X2530 ) ) )
& ( ~ ( in @ X2535 @ X2533 )
| ( in @ X2535 @ X2534 )
| ( in @ X2535 @ ( symdiff @ X2533 @ X2534 ) ) )
& ( ( in @ X2538 @ X2536 )
| ~ ( in @ X2538 @ X2537 )
| ( in @ X2538 @ ( symdiff @ X2536 @ X2537 ) ) )
& ( ~ ( in @ X2541 @ X2539 )
| ~ ( in @ X2541 @ X2540 )
| ~ ( in @ X2541 @ ( symdiff @ X2539 @ X2540 ) ) )
& ( ( in @ X2544 @ X2542 )
| ( in @ X2544 @ X2543 )
| ~ ( in @ X2544 @ ( symdiff @ X2542 @ X2543 ) ) )
& ( in @ X2546 @ ( setadjoin @ X2545 @ ( setadjoin @ X2546 @ emptyset ) ) )
& ( in @ X2547 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2547 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2547 @ ( setadjoin @ X2548 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2550 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2549 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2549 @ ( setadjoin @ X2550 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2551 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2551 @ ( setadjoin @ X2552 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2553 @ X2554 ) )
& ( ~ ( in @ X2556 @ X2555 )
| ( subset @ ( setadjoin @ X2556 @ emptyset ) @ X2555 ) )
& ( ~ ( in @ X2558 @ X2557 )
| ( in @ ( setadjoin @ X2558 @ emptyset ) @ ( powerset @ X2557 ) ) )
& ( ~ ( in @ X2561 @ X2559 )
| ( in @ ( setadjoin @ X2561 @ emptyset ) @ ( powerset @ ( binunion @ X2559 @ X2560 ) ) ) )
& ( ~ ( in @ X2564 @ ( setadjoin @ X2562 @ ( setadjoin @ X2563 @ emptyset ) ) )
| ( X2564 = X2562 )
| ( X2564 = X2563 ) )
& ( ~ ( in @ X2567 @ X2565 )
| ~ ( in @ X2568 @ X2566 )
| ( subset @ ( setadjoin @ X2567 @ ( setadjoin @ X2568 @ emptyset ) ) @ ( binunion @ X2565 @ X2566 ) ) )
& ( ~ ( in @ X2571 @ X2569 )
| ~ ( in @ X2572 @ X2570 )
| ( in @ ( setadjoin @ X2571 @ ( setadjoin @ X2572 @ emptyset ) ) @ ( powerset @ ( binunion @ X2569 @ X2570 ) ) ) )
& ( ~ ( in @ X2575 @ X2573 )
| ~ ( in @ X2576 @ X2574 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2575 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2575 @ ( setadjoin @ X2576 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2573 @ X2574 ) ) ) )
& ( ~ ( in @ X2579 @ X2577 )
| ~ ( in @ X2580 @ X2578 )
| ( in @ ( setadjoin @ ( setadjoin @ X2579 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2579 @ ( setadjoin @ X2580 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2577 @ X2578 ) ) ) ) )
& ( ~ ( in @ X2583 @ X2581 )
| ~ ( in @ X2584 @ X2582 )
| ( in @ ( kpair @ X2583 @ X2584 ) @ ( powerset @ ( powerset @ ( binunion @ X2581 @ X2582 ) ) ) ) )
& ( ~ ( in @ X2587 @ X2585 )
| ~ ( in @ X2588 @ X2586 )
| ( in @ ( kpair @ X2587 @ X2588 ) @ ( cartprod @ X2585 @ X2586 ) ) )
& ( ( in @ ( esk39_3 @ X2589 @ X2590 @ X2591 ) @ X2589 )
| ~ ( in @ X2591 @ ( cartprod @ X2589 @ X2590 ) ) )
& ( ( in @ ( esk40_3 @ X2589 @ X2590 @ X2591 ) @ X2590 )
| ~ ( in @ X2591 @ ( cartprod @ X2589 @ X2590 ) ) )
& ( ( X2591
= ( kpair @ ( esk39_3 @ X2589 @ X2590 @ X2591 ) @ ( esk40_3 @ X2589 @ X2590 @ X2591 ) ) )
| ~ ( in @ X2591 @ ( cartprod @ X2589 @ X2590 ) ) )
& ( ~ ( in @ X2596 @ ( cartprod @ X2594 @ X2595 ) )
| ( iskpair @ X2596 ) )
& ( ( in @ ( esk41_2 @ X2597 @ X2598 ) @ X2597 )
| ~ ( in @ X2598 @ ( setunion @ X2597 ) ) )
& ( ( in @ X2598 @ ( esk41_2 @ X2597 @ X2598 ) )
| ~ ( in @ X2598 @ ( setunion @ X2597 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2600 @ emptyset ) ) @ X2600 )
& ( subset @ X2601 @ ( setunion @ ( setadjoin @ X2601 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2602 @ emptyset ) )
= X2602 )
& ( ( in @ ( esk42_2 @ X2603 @ X2604 ) @ X2603 )
| ~ ( in @ X2607 @ X2603 )
| ~ ( X2604 @ X2607 )
| ( singleton @ ( dsetconstr @ X2603 @ X2604 ) ) )
& ( ( in @ ( esk43_2 @ X2603 @ X2604 ) @ X2603 )
| ~ ( in @ X2607 @ X2603 )
| ~ ( X2604 @ X2607 )
| ( singleton @ ( dsetconstr @ X2603 @ X2604 ) ) )
& ( ( X2604 @ ( esk42_2 @ X2603 @ X2604 ) )
| ~ ( in @ X2607 @ X2603 )
| ~ ( X2604 @ X2607 )
| ( singleton @ ( dsetconstr @ X2603 @ X2604 ) ) )
& ( ( X2604 @ ( esk43_2 @ X2603 @ X2604 ) )
| ~ ( in @ X2607 @ X2603 )
| ~ ( X2604 @ X2607 )
| ( singleton @ ( dsetconstr @ X2603 @ X2604 ) ) )
& ( ( ( esk42_2 @ X2603 @ X2604 )
!= ( esk43_2 @ X2603 @ X2604 ) )
| ~ ( in @ X2607 @ X2603 )
| ~ ( X2604 @ X2607 )
| ( singleton @ ( dsetconstr @ X2603 @ X2604 ) ) )
& ( ( in @ ( esk44_2 @ X2608 @ X2609 ) @ X2608 )
| ~ ( ex1 @ X2608 @ X2609 ) )
& ( ( X2609 @ ( esk44_2 @ X2608 @ X2609 ) )
| ~ ( ex1 @ X2608 @ X2609 ) )
& ( ( in @ ( esk45_3 @ X2611 @ X2612 @ X2613 ) @ X2611 )
| ( ex1 @ X2611 @ X2612 )
| ~ ( X2612 @ X2613 )
| ~ ( in @ X2613 @ X2611 ) )
& ( ( X2612 @ ( esk45_3 @ X2611 @ X2612 @ X2613 ) )
| ( ex1 @ X2611 @ X2612 )
| ~ ( X2612 @ X2613 )
| ~ ( in @ X2613 @ X2611 ) )
& ( ( ( esk45_3 @ X2611 @ X2612 @ X2613 )
!= X2613 )
| ( ex1 @ X2611 @ X2612 )
| ~ ( X2612 @ X2613 )
| ~ ( in @ X2613 @ X2611 ) )
& ( ( in @ ( esk46_2 @ X2615 @ X2616 ) @ X2615 )
| ~ ( in @ X2619 @ X2615 )
| ~ ( X2616 @ X2619 )
| ( ex1 @ X2615 @ X2616 ) )
& ( ( in @ ( esk47_2 @ X2615 @ X2616 ) @ X2615 )
| ~ ( in @ X2619 @ X2615 )
| ~ ( X2616 @ X2619 )
| ( ex1 @ X2615 @ X2616 ) )
& ( ( X2616 @ ( esk46_2 @ X2615 @ X2616 ) )
| ~ ( in @ X2619 @ X2615 )
| ~ ( X2616 @ X2619 )
| ( ex1 @ X2615 @ X2616 ) )
& ( ( X2616 @ ( esk47_2 @ X2615 @ X2616 ) )
| ~ ( in @ X2619 @ X2615 )
| ~ ( X2616 @ X2619 )
| ( ex1 @ X2615 @ X2616 ) )
& ( ( ( esk46_2 @ X2615 @ X2616 )
!= ( esk47_2 @ X2615 @ X2616 ) )
| ~ ( in @ X2619 @ X2615 )
| ~ ( X2616 @ X2619 )
| ( ex1 @ X2615 @ X2616 ) )
& ( ( ( setadjoin @ X2620 @ emptyset )
!= ( setadjoin @ X2621 @ emptyset ) )
| ( X2620 = X2621 ) )
& ( ~ ( in @ ( setadjoin @ X2624 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2622 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2622 @ ( setadjoin @ X2623 @ emptyset ) ) @ emptyset ) ) )
| ( X2622 = X2624 ) )
& ( ~ ( iskpair @ X2625 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2625 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2625 ) ) ) )
& ( ~ ( singleton @ X2626 )
| ( in @ ( setunion @ X2626 ) @ X2626 ) )
& ( ( kfst @ ( kpair @ X2627 @ X2628 ) )
= X2627 )
& ( ~ ( in @ X2631 @ ( cartprod @ X2629 @ X2630 ) )
| ( in @ ( kfst @ X2631 ) @ X2629 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2632 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2632 @ ( setadjoin @ X2633 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2634 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2634 @ ( setadjoin @ X2635 @ emptyset ) ) @ emptyset ) ) )
| ( X2632 = X2634 ) )
& ( ( ( kpair @ X2636 @ X2637 )
!= ( kpair @ X2638 @ X2639 ) )
| ( X2636 = X2638 ) )
& ( ( X2640 != X2641 )
| ( ( setadjoin @ X2640 @ ( setadjoin @ X2641 @ emptyset ) )
= ( setadjoin @ X2640 @ emptyset ) ) )
& ( ( X2642 != X2643 )
| ( ( setadjoin @ ( setadjoin @ X2642 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2642 @ ( setadjoin @ X2643 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2642 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2644 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2644 @ ( setadjoin @ X2645 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2646 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2646 @ ( setadjoin @ X2647 @ emptyset ) ) @ emptyset ) ) )
| ( X2646 != X2647 )
| ( X2645 = X2647 ) )
& ( ( ( setadjoin @ X2648 @ ( setadjoin @ X2649 @ emptyset ) )
!= ( setadjoin @ X2650 @ emptyset ) )
| ( X2648 = X2649 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2651 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2651 @ ( setadjoin @ X2652 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2653 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2653 @ ( setadjoin @ X2654 @ emptyset ) ) @ emptyset ) ) )
| ( X2652 = X2654 ) )
& ( ( ( kpair @ X2655 @ X2656 )
!= ( kpair @ X2657 @ X2658 ) )
| ( X2656 = X2658 ) )
& ( ~ ( iskpair @ X2659 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2659 )
@ ^ [Z0: $i] :
( X2659
= ( kpair @ ( kfst @ X2659 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2660 @ X2661 ) )
= X2661 )
& ( ~ ( iskpair @ X2662 )
| ( ( kpair @ ( kfst @ X2662 ) @ ( ksnd @ X2662 ) )
= X2662 ) )
& ( ~ ( in @ X2665 @ ( cartprod @ X2663 @ X2664 ) )
| ( in @ ( ksnd @ X2665 ) @ X2664 ) )
& ( ~ ( in @ ( kpair @ X2668 @ X2669 ) @ ( cartprod @ X2666 @ X2667 ) )
| ( in @ X2668 @ X2666 ) )
& ( ~ ( in @ ( kpair @ X2672 @ X2673 ) @ ( cartprod @ X2670 @ X2671 ) )
| ( in @ X2673 @ X2671 ) )
& ( ~ ( in @ X2676 @ X2674 )
| ~ ( in @ X2677 @ X2675 )
| ( ( kpair @ X2676 @ X2677 )
= ( kpair @ X2676 @ X2677 ) ) )
& ( ~ ( in @ X2680 @ X2678 )
| ~ ( in @ X2681 @ X2679 )
| ( ( kfst @ ( kpair @ X2680 @ X2681 ) )
= X2680 ) )
& ( ~ ( in @ X2684 @ X2682 )
| ~ ( in @ X2685 @ X2683 )
| ( ( ksnd @ ( kpair @ X2684 @ X2685 ) )
= X2685 ) )
& ( ~ ( in @ X2688 @ ( cartprod @ X2686 @ X2687 ) )
| ( ( kpair @ ( kfst @ X2688 ) @ ( ksnd @ X2688 ) )
= X2688 ) )
& ( ~ ( in @ X2692 @ X2689 )
| ~ ( in @ X2693 @ X2690 )
| ~ ( X2691 @ X2692 @ X2693 )
| ( in @ ( kpair @ X2692 @ X2693 ) @ ( dpsetconstr @ X2689 @ X2690 @ X2691 ) ) )
& ( subset @ ( dpsetconstr @ X2694 @ X2695 @ X2696 ) @ ( cartprod @ X2694 @ X2695 ) )
& ( breln @ X2697 @ X2698 @ ( dpsetconstr @ X2697 @ X2698 @ X2699 ) )
& ( ~ ( in @ X2703 @ X2700 )
| ~ ( in @ X2704 @ X2701 )
| ~ ( in @ ( kpair @ X2703 @ X2704 ) @ ( dpsetconstr @ X2700 @ X2701 @ X2702 ) )
| ( X2702 @ X2703 @ X2704 ) )
& ( ~ ( in @ ( kpair @ X2708 @ X2709 ) @ ( dpsetconstr @ X2705 @ X2706 @ X2707 ) )
| ( in @ X2708 @ X2705 ) )
& ( ~ ( in @ ( kpair @ X2713 @ X2714 ) @ ( dpsetconstr @ X2710 @ X2711 @ X2712 ) )
| ( in @ X2714 @ X2711 ) )
& ( ~ ( in @ ( kpair @ X2718 @ X2719 ) @ ( dpsetconstr @ X2715 @ X2716 @ X2717 ) )
| ( X2717 @ X2718 @ X2719 ) )
& ( ~ ( func @ X2720 @ X2721 @ X2722 )
| ~ ( in @ X2723 @ X2720 )
| ( singleton
@ ( dsetconstr @ X2721
@ ^ [Z0: $i] : ( in @ ( kpair @ X2723 @ Z0 ) @ X2722 ) ) ) )
& ( ~ ( func @ X2724 @ X2725 @ X2726 )
| ~ ( in @ X2727 @ X2724 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2725
@ ^ [Z0: $i] : ( in @ ( kpair @ X2727 @ Z0 ) @ X2726 ) ) )
@ X2725 ) )
& ( ~ ( func @ X2728 @ X2729 @ X2730 )
| ~ ( in @ X2731 @ X2728 )
| ( in @ ( ap @ X2728 @ X2729 @ X2730 @ X2731 ) @ X2729 ) )
& ( ~ ( in @ X2734 @ ( funcSet @ X2732 @ X2733 ) )
| ( func @ X2732 @ X2733 @ X2734 ) )
& ( ~ ( in @ X2737 @ ( funcSet @ X2735 @ X2736 ) )
| ~ ( in @ X2738 @ X2735 )
| ( in @ ( ap @ X2735 @ X2736 @ X2737 @ X2738 ) @ X2736 ) )
& ( ~ ( func @ X2739 @ X2740 @ X2741 )
| ( in @ X2741 @ ( funcSet @ X2739 @ X2740 ) ) )
& ( ( in @ ( esk48_3 @ X2742 @ X2743 @ X2744 ) @ X2742 )
| ( func @ X2742 @ X2743
@ ( dpsetconstr @ X2742 @ X2743
@ ^ [Z0: $i] : ( $eq @ ( X2744 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2744 @ ( esk48_3 @ X2742 @ X2743 @ X2744 ) ) @ X2743 )
| ( func @ X2742 @ X2743
@ ( dpsetconstr @ X2742 @ X2743
@ ^ [Z0: $i] : ( $eq @ ( X2744 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2746 @ X2747 @ X2748 ) @ X2746 )
| ( func @ X2746 @ X2747 @ ( lam @ X2746 @ X2747 @ X2748 ) ) )
& ( ~ ( in @ ( X2748 @ ( esk49_3 @ X2746 @ X2747 @ X2748 ) ) @ X2747 )
| ( func @ X2746 @ X2747 @ ( lam @ X2746 @ X2747 @ X2748 ) ) )
& ( ( in @ ( esk50_3 @ X2750 @ X2751 @ X2752 ) @ X2750 )
| ( in @ ( lam @ X2750 @ X2751 @ X2752 ) @ ( funcSet @ X2750 @ X2751 ) ) )
& ( ~ ( in @ ( X2752 @ ( esk50_3 @ X2750 @ X2751 @ X2752 ) ) @ X2751 )
| ( in @ ( lam @ X2750 @ X2751 @ X2752 ) @ ( funcSet @ X2750 @ X2751 ) ) )
& ( ( in @ ( esk51_4 @ X2754 @ X2755 @ X2756 @ X2757 ) @ X2754 )
| ~ ( in @ X2760 @ X2756 )
| ( X2757 @ X2760 )
| ~ ( breln @ X2754 @ X2755 @ X2756 ) )
& ( ( in @ ( esk52_4 @ X2754 @ X2755 @ X2756 @ X2757 ) @ X2755 )
| ~ ( in @ X2760 @ X2756 )
| ( X2757 @ X2760 )
| ~ ( breln @ X2754 @ X2755 @ X2756 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2754 @ X2755 @ X2756 @ X2757 ) @ ( esk52_4 @ X2754 @ X2755 @ X2756 @ X2757 ) ) @ X2756 )
| ~ ( in @ X2760 @ X2756 )
| ( X2757 @ X2760 )
| ~ ( breln @ X2754 @ X2755 @ X2756 ) )
& ( ~ ( X2757 @ ( kpair @ ( esk51_4 @ X2754 @ X2755 @ X2756 @ X2757 ) @ ( esk52_4 @ X2754 @ X2755 @ X2756 @ X2757 ) ) )
| ~ ( in @ X2760 @ X2756 )
| ( X2757 @ X2760 )
| ~ ( breln @ X2754 @ X2755 @ X2756 ) )
& ( ( in @ ( esk53_4 @ X2761 @ X2762 @ X2763 @ X2764 ) @ X2761 )
| ~ ( in @ X2767 @ X2763 )
| ( X2764 @ X2767 )
| ~ ( breln @ X2761 @ X2762 @ X2763 ) )
& ( ( in @ ( esk54_4 @ X2761 @ X2762 @ X2763 @ X2764 ) @ X2762 )
| ~ ( in @ X2767 @ X2763 )
| ( X2764 @ X2767 )
| ~ ( breln @ X2761 @ X2762 @ X2763 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2761 @ X2762 @ X2763 @ X2764 ) @ ( esk54_4 @ X2761 @ X2762 @ X2763 @ X2764 ) ) @ X2763 )
| ~ ( in @ X2767 @ X2763 )
| ( X2764 @ X2767 )
| ~ ( breln @ X2761 @ X2762 @ X2763 ) )
& ( ~ ( X2764 @ ( kpair @ ( esk53_4 @ X2761 @ X2762 @ X2763 @ X2764 ) @ ( esk54_4 @ X2761 @ X2762 @ X2763 @ X2764 ) ) )
| ~ ( in @ X2767 @ X2763 )
| ( X2764 @ X2767 )
| ~ ( breln @ X2761 @ X2762 @ X2763 ) )
& ( ~ ( ex1 @ X2768 @ X2769 )
| ~ ( in @ X2770 @ X2768 )
| ~ ( in @ X2771 @ X2768 )
| ~ ( X2769 @ X2770 )
| ~ ( X2769 @ X2771 )
| ( X2770 = X2771 ) )
& ( ~ ( func @ X2772 @ X2773 @ X2774 )
| ~ ( in @ X2775 @ X2772 )
| ( in @ ( kpair @ X2775 @ ( ap @ X2772 @ X2773 @ X2774 @ X2775 ) ) @ X2774 ) )
& ( ~ ( in @ X2778 @ ( funcSet @ X2776 @ X2777 ) )
| ~ ( in @ X2779 @ X2776 )
| ( in @ ( kpair @ X2779 @ ( ap @ X2776 @ X2777 @ X2778 @ X2779 ) ) @ X2778 ) )
& ( ~ ( func @ X2780 @ X2781 @ X2782 )
| ~ ( in @ X2783 @ X2780 )
| ~ ( in @ X2784 @ X2781 )
| ~ ( in @ ( kpair @ X2783 @ X2784 ) @ X2782 )
| ( ( ap @ X2780 @ X2781 @ X2782 @ X2783 )
= X2784 ) )
& ( ( in @ ( esk55_4 @ X2785 @ X2786 @ X2787 @ X2788 ) @ X2785 )
| ~ ( in @ X2790 @ X2785 )
| ~ ( in @ X2791 @ X2786 )
| ~ ( in @ ( kpair @ X2790 @ X2791 ) @ X2788 )
| ( in @ ( kpair @ X2790 @ X2791 ) @ X2787 )
| ~ ( func @ X2785 @ X2786 @ X2788 )
| ~ ( func @ X2785 @ X2786 @ X2787 ) )
& ( ( ( ap @ X2785 @ X2786 @ X2787 @ ( esk55_4 @ X2785 @ X2786 @ X2787 @ X2788 ) )
!= ( ap @ X2785 @ X2786 @ X2788 @ ( esk55_4 @ X2785 @ X2786 @ X2787 @ X2788 ) ) )
| ~ ( in @ X2790 @ X2785 )
| ~ ( in @ X2791 @ X2786 )
| ~ ( in @ ( kpair @ X2790 @ X2791 ) @ X2788 )
| ( in @ ( kpair @ X2790 @ X2791 ) @ X2787 )
| ~ ( func @ X2785 @ X2786 @ X2788 )
| ~ ( func @ X2785 @ X2786 @ X2787 ) )
& ( ~ ( in @ X2794 @ ( funcSet @ X2792 @ X2793 ) )
| ~ ( in @ X2795 @ X2792 )
| ~ ( in @ X2796 @ X2793 )
| ~ ( in @ ( kpair @ X2795 @ X2796 ) @ X2794 )
| ( ( ap @ X2792 @ X2793 @ X2794 @ X2795 )
= X2796 ) )
& ( ( in @ ( esk56_4 @ X2797 @ X2798 @ X2799 @ X2800 ) @ X2797 )
| ( subset @ X2799 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2799 ) )
& ( ( in @ ( esk57_4 @ X2797 @ X2798 @ X2799 @ X2800 ) @ X2798 )
| ( subset @ X2799 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2799 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2797 @ X2798 @ X2799 @ X2800 ) @ ( esk57_4 @ X2797 @ X2798 @ X2799 @ X2800 ) ) @ X2799 )
| ( subset @ X2799 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2799 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2797 @ X2798 @ X2799 @ X2800 ) @ ( esk57_4 @ X2797 @ X2798 @ X2799 @ X2800 ) ) @ X2800 )
| ( subset @ X2799 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2800 )
| ~ ( breln @ X2797 @ X2798 @ X2799 ) )
& ( ( in @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ( X2805 = X2806 )
| ( in @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ( X2805 = X2806 )
| ( in @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ( X2805 = X2806 )
| ( in @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ( X2805 = X2806 )
| ( in @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ( X2805 = X2806 )
| ( in @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ( X2805 = X2806 )
| ( in @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ( X2805 = X2806 )
| ( in @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ( X2805 = X2806 )
| ( in @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ( X2805 = X2806 )
| ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ( X2805 = X2806 )
| ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ( X2805 = X2806 )
| ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ( X2805 = X2806 )
| ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2803 )
| ( X2805 = X2806 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ X2804 )
| ( X2805 = X2806 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ( X2805 = X2806 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk61_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2805 )
| ( X2805 = X2806 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2803 @ X2804 @ X2805 @ X2806 ) @ ( esk59_4 @ X2803 @ X2804 @ X2805 @ X2806 ) ) @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2806 )
| ~ ( breln @ X2803 @ X2804 @ X2805 ) )
& ( ( in @ ( esk62_4 @ X2811 @ X2812 @ X2813 @ X2814 ) @ X2811 )
| ( X2813 = X2814 )
| ~ ( func @ X2811 @ X2812 @ X2814 )
| ~ ( func @ X2811 @ X2812 @ X2813 ) )
& ( ( ( ap @ X2811 @ X2812 @ X2813 @ ( esk62_4 @ X2811 @ X2812 @ X2813 @ X2814 ) )
!= ( ap @ X2811 @ X2812 @ X2814 @ ( esk62_4 @ X2811 @ X2812 @ X2813 @ X2814 ) ) )
| ( X2813 = X2814 )
| ~ ( func @ X2811 @ X2812 @ X2814 )
| ~ ( func @ X2811 @ X2812 @ X2813 ) )
& ( ( in @ ( esk63_4 @ X2816 @ X2817 @ X2818 @ X2819 ) @ X2816 )
| ( X2818 = X2819 )
| ~ ( in @ X2819 @ ( funcSet @ X2816 @ X2817 ) )
| ~ ( in @ X2818 @ ( funcSet @ X2816 @ X2817 ) ) )
& ( ( ( ap @ X2816 @ X2817 @ X2818 @ ( esk63_4 @ X2816 @ X2817 @ X2818 @ X2819 ) )
!= ( ap @ X2816 @ X2817 @ X2819 @ ( esk63_4 @ X2816 @ X2817 @ X2818 @ X2819 ) ) )
| ( X2818 = X2819 )
| ~ ( in @ X2819 @ ( funcSet @ X2816 @ X2817 ) )
| ~ ( in @ X2818 @ ( funcSet @ X2816 @ X2817 ) ) )
& ( ~ ( in @ X2823 @ ( funcSet @ X2821 @ X2822 ) )
| ~ ( in @ X2824 @ X2821 )
| ( ( ap @ X2821 @ X2822 @ X2823 @ X2824 )
= ( ap @ X2821 @ X2822 @ X2823 @ X2824 ) ) )
& ( ~ ( func @ X2825 @ X2826 @ X2827 )
| ~ ( in @ X2828 @ X2825 )
| ( ( ap @ X2825 @ X2826 @ X2827 @ X2828 )
= ( ap @ X2825 @ X2826 @ X2827 @ X2828 ) ) )
& ( ( in @ ( esk64_3 @ X2829 @ X2830 @ X2831 ) @ X2829 )
| ~ ( in @ X2833 @ X2829 )
| ( ( ap @ X2829 @ X2830 @ ( lam @ X2829 @ X2830 @ X2831 ) @ X2833 )
= ( X2831 @ X2833 ) ) )
& ( ~ ( in @ ( X2831 @ ( esk64_3 @ X2829 @ X2830 @ X2831 ) ) @ X2830 )
| ~ ( in @ X2833 @ X2829 )
| ( ( ap @ X2829 @ X2830 @ ( lam @ X2829 @ X2830 @ X2831 ) @ X2833 )
= ( X2831 @ X2833 ) ) )
& ( ~ ( func @ X2834 @ X2835 @ X2836 )
| ( ( lam @ X2834 @ X2835 @ ( ap @ X2834 @ X2835 @ X2836 ) )
= X2836 ) )
& ( ( in @ ( esk65_3 @ X2837 @ X2838 @ X2839 ) @ X2837 )
| ( ( lam @ X2837 @ X2838 @ X2839 )
= ( lam @ X2837 @ X2838 @ X2839 ) ) )
& ( ~ ( in @ ( X2839 @ ( esk65_3 @ X2837 @ X2838 @ X2839 ) ) @ X2838 )
| ( ( lam @ X2837 @ X2838 @ X2839 )
= ( lam @ X2837 @ X2838 @ X2839 ) ) )
& ( ( in @ ( esk66_3 @ X2841 @ X2842 @ X2843 ) @ X2841 )
| ~ ( in @ X2845 @ X2841 )
| ( ( ap @ X2841 @ X2842 @ ( lam @ X2841 @ X2842 @ X2843 ) @ X2845 )
= ( X2843 @ X2845 ) ) )
& ( ~ ( in @ ( X2843 @ ( esk66_3 @ X2841 @ X2842 @ X2843 ) ) @ X2842 )
| ~ ( in @ X2845 @ X2841 )
| ( ( ap @ X2841 @ X2842 @ ( lam @ X2841 @ X2842 @ X2843 ) @ X2845 )
= ( X2843 @ X2845 ) ) )
& ( ~ ( in @ X2848 @ ( funcSet @ X2846 @ X2847 ) )
| ( ( lam @ X2846 @ X2847 @ ( ap @ X2846 @ X2847 @ X2848 ) )
= X2848 ) )
& ( ~ ( in @ X2851 @ X2849 )
| ~ ( in @ X2852 @ X2849 )
| X2850
| ( in @ X2852
@ ( dsetconstr @ X2849
@ ^ [Z0: $i] :
( ( X2850
& ( Z0 = X2851 ) )
| ( ~ X2850
& ( Z0 = X2852 ) ) ) ) ) )
& ( ~ ( in @ X2855 @ X2853 )
| ~ ( in @ X2856 @ X2853 )
| X2854
| ( ( dsetconstr @ X2853
@ ^ [Z0: $i] :
( ( X2854
& ( Z0 = X2855 ) )
| ( ~ X2854
& ( Z0 = X2856 ) ) ) )
= ( setadjoin @ X2856 @ emptyset ) ) )
& ( ~ ( in @ X2859 @ X2857 )
| ~ ( in @ X2860 @ X2857 )
| ~ X2858
| ( in @ X2859
@ ( dsetconstr @ X2857
@ ^ [Z0: $i] :
( ( X2858
& ( Z0 = X2859 ) )
| ( ~ X2858
& ( Z0 = X2860 ) ) ) ) ) )
& ( ~ ( in @ X2863 @ X2861 )
| ~ ( in @ X2864 @ X2861 )
| ~ X2862
| ( ( dsetconstr @ X2861
@ ^ [Z0: $i] :
( ( X2862
& ( Z0 = X2863 ) )
| ( ~ X2862
& ( Z0 = X2864 ) ) ) )
= ( setadjoin @ X2863 @ emptyset ) ) )
& ( ~ ( in @ X2867 @ X2865 )
| ~ ( in @ X2868 @ X2865 )
| ( singleton
@ ( dsetconstr @ X2865
@ ^ [Z0: $i] :
( ( X2866
& ( Z0 = X2867 ) )
| ( ~ X2866
& ( Z0 = X2868 ) ) ) ) ) )
& ( ~ ( in @ X2871 @ X2869 )
| ~ ( in @ X2872 @ X2869 )
| ( in @ ( if @ X2869 @ X2870 @ X2871 @ X2872 ) @ X2869 ) )
& ( ~ ( singleton @ X2873 )
| ~ ( in @ X2874 @ X2873 )
| ( ( setunion @ X2873 )
= X2874 ) )
& ( ~ ( in @ X2877 @ X2875 )
| ~ ( in @ X2878 @ X2875 )
| ~ X2876
| ( ( if @ X2875 @ X2876 @ X2877 @ X2878 )
= X2877 ) )
& ( ~ ( in @ X2881 @ X2879 )
| ~ ( in @ X2882 @ X2879 )
| X2880
| ( ( if @ X2879 @ X2880 @ X2881 @ X2882 )
= X2882 ) )
& ( ~ ( in @ X2885 @ X2883 )
| ~ ( in @ X2886 @ X2883 )
| ( in @ ( if @ X2883 @ X2884 @ X2885 @ X2886 ) @ ( setadjoin @ X2885 @ ( setadjoin @ X2886 @ emptyset ) ) ) )
& ( ~ ( in @ X2888 @ ( powerset @ X2887 ) )
| ~ ( in @ X2889 @ ( powerset @ X2887 ) )
| ( in @ ( binintersect @ X2888 @ X2889 ) @ ( powerset @ X2887 ) ) )
& ( ~ ( in @ X2891 @ ( powerset @ X2890 ) )
| ~ ( in @ X2892 @ ( powerset @ X2890 ) )
| ( in @ ( binunion @ X2891 @ X2892 ) @ ( powerset @ X2890 ) ) )
& ( ~ ( in @ X2894 @ ( powerset @ X2893 ) )
| ( in @ ( powerset @ X2894 ) @ ( powerset @ ( powerset @ X2893 ) ) ) )
& ( ~ ( in @ X2896 @ ( powerset @ X2895 ) )
| ~ ( in @ X2897 @ ( powerset @ X2895 ) )
| ( in @ ( setminus @ X2896 @ X2897 ) @ ( powerset @ X2895 ) ) )
& ( ~ ( in @ X2899 @ ( powerset @ X2898 ) )
| ( in @ ( setminus @ X2898 @ X2899 ) @ ( powerset @ X2898 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ( X2901 = X2902 )
| ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2900 )
| ( X2901 = X2902 )
| ~ ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ( X2901 = X2902 )
| ~ ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2900 @ X2901 @ X2902 ) @ X2901 )
| ( X2901 = X2902 )
| ~ ( in @ ( esk67_3 @ X2900 @ X2901 @ X2902 ) @ X2902 )
| ~ ( in @ X2902 @ ( powerset @ X2900 ) )
| ~ ( in @ X2901 @ ( powerset @ X2900 ) ) )
& ( ( in @ ( esk69_3 @ X2905 @ X2906 @ X2907 ) @ X2905 )
| ( subset @ X2906 @ X2907 )
| ~ ( in @ X2907 @ ( powerset @ X2905 ) )
| ~ ( in @ X2906 @ ( powerset @ X2905 ) ) )
& ( ( in @ ( esk69_3 @ X2905 @ X2906 @ X2907 ) @ X2906 )
| ( subset @ X2906 @ X2907 )
| ~ ( in @ X2907 @ ( powerset @ X2905 ) )
| ~ ( in @ X2906 @ ( powerset @ X2905 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2905 @ X2906 @ X2907 ) @ X2907 )
| ( subset @ X2906 @ X2907 )
| ~ ( in @ X2907 @ ( powerset @ X2905 ) )
| ~ ( in @ X2906 @ ( powerset @ X2905 ) ) )
& ( ( in @ ( esk70_3 @ X2909 @ X2910 @ X2911 ) @ X2909 )
| ( in @ X2910 @ ( powerset @ X2911 ) )
| ~ ( in @ X2911 @ ( powerset @ X2909 ) )
| ~ ( in @ X2910 @ ( powerset @ X2909 ) ) )
& ( ( in @ ( esk70_3 @ X2909 @ X2910 @ X2911 ) @ X2910 )
| ( in @ X2910 @ ( powerset @ X2911 ) )
| ~ ( in @ X2911 @ ( powerset @ X2909 ) )
| ~ ( in @ X2910 @ ( powerset @ X2909 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2909 @ X2910 @ X2911 ) @ X2911 )
| ( in @ X2910 @ ( powerset @ X2911 ) )
| ~ ( in @ X2911 @ ( powerset @ X2909 ) )
| ~ ( in @ X2910 @ ( powerset @ X2909 ) ) )
& ( ~ ( in @ X2914 @ ( powerset @ X2913 ) )
| ~ ( in @ X2915 @ ( powerset @ X2913 ) )
| ~ ( in @ X2916 @ X2913 )
| ~ ( in @ X2914 @ ( powerset @ X2915 ) )
| ~ ( in @ X2916 @ X2914 )
| ( in @ X2916 @ X2915 ) )
& ( ~ ( in @ X2918 @ ( powerset @ X2917 ) )
| ~ ( in @ X2919 @ X2917 )
| ~ ( in @ X2919 @ X2918 )
| ~ ( in @ X2919 @ ( setminus @ X2917 @ X2918 ) ) )
& ( ~ ( in @ X2921 @ ( powerset @ X2920 ) )
| ~ ( in @ X2922 @ X2920 )
| ( in @ X2922 @ ( setminus @ X2920 @ X2921 ) )
| ( in @ X2922 @ X2921 ) )
& ( ~ ( in @ X2924 @ ( powerset @ X2923 ) )
| ~ ( in @ X2925 @ ( powerset @ X2923 ) )
| ~ ( in @ X2926 @ X2923 )
| ( in @ X2926 @ X2924 )
| ~ ( in @ X2926 @ ( binintersect @ X2924 @ X2925 ) ) )
& ( ~ ( in @ X2928 @ ( powerset @ X2927 ) )
| ~ ( in @ X2929 @ ( powerset @ X2927 ) )
| ~ ( in @ X2930 @ X2927 )
| ( in @ X2930 @ X2929 )
| ~ ( in @ X2930 @ ( binintersect @ X2928 @ X2929 ) ) )
& ( ~ ( in @ X2932 @ ( powerset @ X2931 ) )
| ~ ( in @ X2933 @ ( powerset @ X2931 ) )
| ~ ( in @ X2934 @ X2931 )
| ~ ( subset @ X2932 @ ( setminus @ X2931 @ X2933 ) )
| ~ ( in @ X2934 @ X2933 )
| ~ ( in @ X2934 @ X2932 ) )
& ( ~ ( in @ X2936 @ ( powerset @ X2935 ) )
| ~ ( in @ X2937 @ ( powerset @ X2935 ) )
| ~ ( in @ X2938 @ X2935 )
| ~ ( subset @ X2936 @ X2937 )
| ( in @ X2938 @ X2937 )
| ~ ( in @ X2938 @ X2936 ) )
& ( ~ ( in @ X2940 @ ( powerset @ X2939 ) )
| ~ ( in @ X2941 @ ( powerset @ X2939 ) )
| ~ ( subset @ X2940 @ X2941 )
| ( subset @ ( setminus @ X2939 @ X2941 ) @ ( setminus @ X2939 @ X2940 ) ) )
& ( ~ ( in @ X2943 @ ( powerset @ X2942 ) )
| ~ ( in @ X2944 @ ( powerset @ X2942 ) )
| ~ ( subset @ ( setminus @ X2942 @ X2944 ) @ ( setminus @ X2942 @ X2943 ) )
| ( subset @ X2943 @ X2944 ) )
& ( ~ ( in @ X2946 @ ( powerset @ X2945 ) )
| ~ ( in @ X2947 @ X2945 )
| ~ ( in @ X2947 @ X2946 )
| ( in @ X2947 @ ( setminus @ X2945 @ ( setminus @ X2945 @ X2946 ) ) ) )
& ( ~ ( in @ X2949 @ ( powerset @ X2948 ) )
| ~ ( in @ X2950 @ X2948 )
| ~ ( in @ X2950 @ ( setminus @ X2948 @ ( setminus @ X2948 @ X2949 ) ) )
| ( in @ X2950 @ X2949 ) )
& ( ~ ( in @ X2952 @ ( powerset @ X2951 ) )
| ( subset @ X2952 @ ( setminus @ X2951 @ ( setminus @ X2951 @ X2952 ) ) ) )
& ( ~ ( in @ X2954 @ ( powerset @ X2953 ) )
| ( subset @ ( setminus @ X2953 @ ( setminus @ X2953 @ X2954 ) ) @ X2954 ) )
& ( ~ ( in @ X2956 @ ( powerset @ X2955 ) )
| ( X2956
= ( setminus @ X2955 @ ( setminus @ X2955 @ X2956 ) ) ) )
& ( ~ ( in @ X2958 @ ( powerset @ X2957 ) )
| ~ ( in @ X2959 @ ( powerset @ X2957 ) )
| ~ ( in @ X2960 @ X2957 )
| ~ ( in @ X2960 @ ( setminus @ X2957 @ X2958 ) )
| ~ ( in @ X2960 @ ( binintersect @ X2958 @ X2959 ) ) )
& ( ~ ( in @ X2962 @ ( powerset @ X2961 ) )
| ~ ( in @ X2963 @ ( powerset @ X2961 ) )
| ~ ( in @ X2964 @ X2961 )
| ~ ( in @ X2964 @ ( setminus @ X2961 @ X2962 ) )
| ( in @ X2964 @ ( setminus @ X2961 @ ( binintersect @ X2962 @ X2963 ) ) ) )
& ( ~ ( in @ X2966 @ ( powerset @ X2965 ) )
| ~ ( in @ X2967 @ ( powerset @ X2965 ) )
| ( subset @ ( setminus @ X2965 @ X2966 ) @ ( setminus @ X2965 @ ( binintersect @ X2966 @ X2967 ) ) ) )
& ( ~ ( in @ X2969 @ ( powerset @ X2968 ) )
| ~ ( in @ X2970 @ ( powerset @ X2968 ) )
| ( in @ ( setminus @ X2968 @ X2969 ) @ ( powerset @ ( setminus @ X2968 @ ( binintersect @ X2969 @ X2970 ) ) ) ) )
& ( ~ ( in @ X2972 @ ( powerset @ X2971 ) )
| ~ ( in @ X2973 @ ( powerset @ X2971 ) )
| ~ ( subset @ X2972 @ ( setminus @ X2971 @ X2973 ) )
| ~ ( in @ X2974 @ X2971 )
| ~ ( in @ X2974 @ X2973 )
| ( in @ X2974 @ ( setminus @ X2971 @ X2972 ) ) )
& ( ~ ( in @ X2976 @ ( powerset @ X2975 ) )
| ~ ( in @ X2977 @ ( powerset @ X2975 ) )
| ~ ( subset @ X2976 @ ( setminus @ X2975 @ X2977 ) )
| ( subset @ X2977 @ ( setminus @ X2975 @ X2976 ) ) )
& ( ~ ( in @ X2979 @ ( powerset @ X2978 ) )
| ~ ( in @ X2980 @ ( powerset @ X2978 ) )
| ~ ( in @ X2981 @ X2978 )
| ( in @ X2981 @ ( binunion @ X2979 @ X2980 ) )
| ~ ( in @ X2981 @ X2979 ) )
& ( ~ ( in @ X2983 @ ( powerset @ X2982 ) )
| ~ ( in @ X2984 @ ( powerset @ X2982 ) )
| ~ ( in @ X2985 @ X2982 )
| ( in @ X2985 @ ( binunion @ X2983 @ X2984 ) )
| ~ ( in @ X2985 @ X2984 ) )
& ( ~ ( in @ X2987 @ ( powerset @ X2986 ) )
| ~ ( in @ X2988 @ ( powerset @ X2986 ) )
| ~ ( in @ X2989 @ ( powerset @ X2986 ) )
| ~ ( in @ X2990 @ X2986 )
| ~ ( in @ X2990 @ ( binintersect @ X2987 @ X2988 ) )
| ( in @ X2990 @ ( binunion @ X2987 @ X2989 ) ) )
& ( ~ ( in @ X2992 @ ( powerset @ X2991 ) )
| ~ ( in @ X2993 @ ( powerset @ X2991 ) )
| ~ ( in @ X2994 @ ( powerset @ X2991 ) )
| ~ ( in @ X2995 @ X2991 )
| ~ ( in @ X2995 @ ( binintersect @ X2992 @ X2993 ) )
| ( in @ X2995 @ ( binunion @ X2993 @ X2994 ) ) )
& ( ~ ( in @ X2997 @ ( powerset @ X2996 ) )
| ~ ( in @ X2998 @ ( powerset @ X2996 ) )
| ~ ( in @ X2999 @ ( powerset @ X2996 ) )
| ~ ( in @ X3000 @ X2996 )
| ~ ( in @ X3000 @ ( binintersect @ X2997 @ X2998 ) )
| ( in @ X3000 @ ( binintersect @ ( binunion @ X2997 @ X2999 ) @ ( binunion @ X2998 @ X2999 ) ) ) )
& ( ~ ( in @ X3002 @ ( powerset @ X3001 ) )
| ~ ( in @ X3003 @ ( powerset @ X3001 ) )
| ~ ( in @ X3004 @ ( powerset @ X3001 ) )
| ( in @ ( binintersect @ X3002 @ X3003 ) @ ( powerset @ ( binintersect @ ( binunion @ X3002 @ X3004 ) @ ( binunion @ X3003 @ X3004 ) ) ) ) )
& ( ~ ( in @ X3006 @ ( powerset @ X3005 ) )
| ~ ( in @ X3007 @ ( powerset @ X3005 ) )
| ~ ( in @ X3008 @ X3005 )
| ~ ( in @ X3008 @ ( setminus @ X3005 @ ( binunion @ X3006 @ X3007 ) ) )
| ~ ( in @ X3008 @ X3006 ) )
& ( ~ ( in @ X3010 @ ( powerset @ X3009 ) )
| ~ ( in @ X3011 @ ( powerset @ X3009 ) )
| ~ ( in @ X3012 @ X3009 )
| ~ ( in @ X3012 @ ( setminus @ X3009 @ ( binunion @ X3010 @ X3011 ) ) )
| ( in @ X3012 @ ( setminus @ X3009 @ X3010 ) ) )
& ( ( in @ X3017 @ X3015 )
| X3016
| ( in @ X3017 @ X3014 )
| ~ ( in @ X3017 @ ( binunion @ X3014 @ X3015 ) )
| ~ ( in @ X3017 @ X3013 )
| ~ ( in @ X3015 @ ( powerset @ X3013 ) )
| ~ ( in @ X3014 @ ( powerset @ X3013 ) ) )
& ( ~ X3016
| X3016
| ( in @ X3017 @ X3014 )
| ~ ( in @ X3017 @ ( binunion @ X3014 @ X3015 ) )
| ~ ( in @ X3017 @ X3013 )
| ~ ( in @ X3015 @ ( powerset @ X3013 ) )
| ~ ( in @ X3014 @ ( powerset @ X3013 ) ) )
& ( ( in @ X3017 @ X3015 )
| X3016
| ~ X3016
| ~ ( in @ X3017 @ ( binunion @ X3014 @ X3015 ) )
| ~ ( in @ X3017 @ X3013 )
| ~ ( in @ X3015 @ ( powerset @ X3013 ) )
| ~ ( in @ X3014 @ ( powerset @ X3013 ) ) )
& ( ~ X3016
| X3016
| ~ X3016
| ~ ( in @ X3017 @ ( binunion @ X3014 @ X3015 ) )
| ~ ( in @ X3017 @ X3013 )
| ~ ( in @ X3015 @ ( powerset @ X3013 ) )
| ~ ( in @ X3014 @ ( powerset @ X3013 ) ) )
& ( ~ ( in @ X3019 @ ( powerset @ X3018 ) )
| ~ ( in @ X3020 @ ( powerset @ X3018 ) )
| ~ ( in @ X3021 @ X3018 )
| ( in @ X3021 @ X3019 )
| ( in @ X3021 @ X3020 )
| ~ ( in @ X3021 @ ( binunion @ X3019 @ X3020 ) ) )
& ( ~ ( in @ X3023 @ ( powerset @ X3022 ) )
| ~ ( in @ X3024 @ ( powerset @ X3022 ) )
| ~ ( in @ X3025 @ X3022 )
| ~ ( in @ X3025 @ ( setminus @ X3022 @ ( binunion @ X3023 @ X3024 ) ) )
| ( in @ X3025 @ ( setminus @ X3022 @ X3023 ) ) )
& ( ~ ( in @ X3027 @ ( powerset @ X3026 ) )
| ~ ( in @ X3028 @ ( powerset @ X3026 ) )
| ( in @ ( setminus @ X3026 @ ( binunion @ X3027 @ X3028 ) ) @ ( powerset @ ( setminus @ X3026 @ X3027 ) ) ) )
& ( ~ ( in @ X3030 @ ( powerset @ X3029 ) )
| ~ ( in @ X3031 @ ( powerset @ X3029 ) )
| ~ ( in @ X3032 @ X3029 )
| ~ ( in @ X3032 @ ( setminus @ X3029 @ ( binunion @ X3030 @ X3031 ) ) )
| ( in @ X3032 @ ( setminus @ X3029 @ X3031 ) ) )
& ( ~ ( in @ X3034 @ ( powerset @ X3033 ) )
| ~ ( in @ X3035 @ ( powerset @ X3033 ) )
| ~ ( in @ X3036 @ X3033 )
| ~ ( in @ X3036 @ ( setminus @ X3033 @ ( binintersect @ X3034 @ X3035 ) ) )
| ( in @ X3036 @ ( binunion @ ( setminus @ X3033 @ X3034 ) @ ( setminus @ X3033 @ X3035 ) ) ) )
& ( ~ ( in @ X3038 @ ( powerset @ X3037 ) )
| ~ ( in @ X3039 @ ( powerset @ X3037 ) )
| ~ ( in @ X3040 @ X3037 )
| ~ ( in @ X3040 @ ( binunion @ ( setminus @ X3037 @ X3038 ) @ ( setminus @ X3037 @ X3039 ) ) )
| ( in @ X3040 @ ( setminus @ X3037 @ ( binintersect @ X3038 @ X3039 ) ) ) )
& ( ~ ( in @ X3042 @ ( powerset @ X3041 ) )
| ~ ( in @ X3043 @ ( powerset @ X3041 ) )
| ( ( setminus @ X3041 @ ( binintersect @ X3042 @ X3043 ) )
= ( binunion @ ( setminus @ X3041 @ X3042 ) @ ( setminus @ X3041 @ X3043 ) ) ) )
& ( ~ ( in @ X3045 @ ( powerset @ X3044 ) )
| ~ ( in @ X3046 @ ( powerset @ X3044 ) )
| ~ ( in @ X3047 @ X3044 )
| ~ ( in @ X3047 @ ( setminus @ X3044 @ ( binunion @ X3045 @ X3046 ) ) )
| ( in @ X3047 @ ( binintersect @ ( setminus @ X3044 @ X3045 ) @ ( setminus @ X3044 @ X3046 ) ) ) )
& ( ~ ( in @ X3049 @ ( powerset @ X3048 ) )
| ~ ( in @ X3050 @ ( powerset @ X3048 ) )
| ~ ( in @ X3051 @ X3048 )
| ~ ( in @ X3051 @ ( setminus @ X3048 @ X3049 ) )
| ~ ( in @ X3051 @ ( setminus @ X3048 @ X3050 ) )
| ( in @ X3051 @ ( setminus @ X3048 @ ( binunion @ X3049 @ X3050 ) ) ) )
& ( ~ ( in @ X3053 @ ( powerset @ X3052 ) )
| ~ ( in @ X3054 @ ( powerset @ X3052 ) )
| ~ ( in @ X3055 @ X3052 )
| ~ ( in @ X3055 @ ( binintersect @ ( setminus @ X3052 @ X3053 ) @ ( setminus @ X3052 @ X3054 ) ) )
| ( in @ X3055 @ ( setminus @ X3052 @ ( binunion @ X3053 @ X3054 ) ) ) )
& ( ~ ( in @ X3057 @ ( powerset @ X3056 ) )
| ~ ( in @ X3058 @ ( powerset @ X3056 ) )
| ( ( setminus @ X3056 @ ( binunion @ X3057 @ X3058 ) )
= ( binintersect @ ( setminus @ X3056 @ X3057 ) @ ( setminus @ X3056 @ X3058 ) ) ) )
& ( ~ ( in @ X3060 @ ( powerset @ X3059 ) )
| ~ ( in @ X3061 @ ( powerset @ X3059 ) )
| ~ ( in @ X3062 @ ( binintersect @ X3060 @ X3061 ) )
| ( in @ X3062 @ X3059 ) )
& ( ~ ( in @ X3064 @ ( powerset @ X3063 ) )
| ~ ( in @ X3065 @ ( powerset @ X3063 ) )
| ~ ( in @ X3066 @ ( powerset @ X3063 ) )
| ~ ( subset @ X3064 @ X3066 )
| ( subset @ ( binintersect @ X3064 @ X3065 ) @ X3066 ) )
& ( ~ ( in @ X3068 @ ( powerset @ X3067 ) )
| ~ ( in @ X3069 @ ( powerset @ X3067 ) )
| ~ ( in @ X3070 @ ( powerset @ X3067 ) )
| ~ ( subset @ X3069 @ X3070 )
| ( subset @ ( binintersect @ X3068 @ X3069 ) @ X3070 ) )
& ( ~ ( in @ X3072 @ ( powerset @ X3071 ) )
| ~ ( in @ X3073 @ ( powerset @ X3071 ) )
| ~ ( in @ X3074 @ ( powerset @ X3071 ) )
| ~ ( subset @ X3072 @ X3073 )
| ~ ( subset @ X3072 @ X3074 )
| ( subset @ X3072 @ ( binintersect @ X3073 @ X3074 ) ) )
& ( ~ ( in @ X3076 @ ( powerset @ X3075 ) )
| ~ ( in @ X3077 @ ( powerset @ X3075 ) )
| ~ ( in @ X3078 @ ( powerset @ X3075 ) )
| ~ ( in @ X3079 @ ( powerset @ X3075 ) )
| ~ ( subset @ X3076 @ X3078 )
| ~ ( subset @ X3077 @ X3079 )
| ( subset @ ( binintersect @ X3076 @ X3077 ) @ ( binintersect @ X3078 @ X3079 ) ) )
& ( ~ ( in @ X3081 @ ( powerset @ X3080 ) )
| ~ ( in @ X3082 @ ( powerset @ X3080 ) )
| ( in @ ( setminus @ X3080 @ X3081 ) @ ( powerset @ ( setminus @ X3080 @ ( binintersect @ X3081 @ X3082 ) ) ) ) )
& ( ~ ( in @ X3084 @ ( powerset @ X3083 ) )
| ~ ( in @ X3085 @ ( powerset @ X3083 ) )
| ~ ( in @ X3086 @ ( powerset @ X3083 ) )
| ~ ( in @ X3087 @ ( powerset @ X3083 ) )
| ( ( setminus @ X3083 @ ( binintersect @ ( binunion @ X3084 @ X3085 ) @ ( binunion @ X3086 @ X3087 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X3083 @ X3084 ) @ ( setminus @ X3083 @ X3085 ) ) @ ( binintersect @ ( setminus @ X3083 @ X3086 ) @ ( setminus @ X3083 @ X3087 ) ) ) ) )
& ( ~ ( in @ X3089 @ ( powerset @ X3088 ) )
| ~ ( in @ X3090 @ ( powerset @ X3088 ) )
| ~ ( in @ X3091 @ ( powerset @ X3088 ) )
| ( in @ ( binintersect @ X3089 @ X3090 ) @ ( powerset @ ( binintersect @ ( binunion @ X3089 @ X3091 ) @ ( binunion @ X3090 @ X3091 ) ) ) ) )
& ( ~ ( in @ X3093 @ ( powerset @ X3092 ) )
| ~ ( in @ X3094 @ ( powerset @ X3092 ) )
| ~ ( subset @ X3093 @ ( setminus @ X3092 @ X3094 ) )
| ( subset @ X3094 @ ( setminus @ X3092 @ X3093 ) ) )
& ( ~ ( in @ X3096 @ ( powerset @ X3095 ) )
| ~ ( in @ X3097 @ ( powerset @ X3095 ) )
| ( in @ ( setminus @ X3095 @ ( binunion @ X3096 @ X3097 ) ) @ ( powerset @ ( setminus @ X3095 @ X3096 ) ) ) )
& ( ( in @ ( esk71_3 @ X3098 @ X3099 @ X3100 ) @ X3098 )
| ~ ( in @ X3103 @ X3099 )
| ( X3100 @ X3103 )
| ~ ( breln1 @ X3098 @ X3099 ) )
& ( ( in @ ( esk72_3 @ X3098 @ X3099 @ X3100 ) @ X3098 )
| ~ ( in @ X3103 @ X3099 )
| ( X3100 @ X3103 )
| ~ ( breln1 @ X3098 @ X3099 ) )
& ( ( in @ ( kpair @ ( esk71_3 @ X3098 @ X3099 @ X3100 ) @ ( esk72_3 @ X3098 @ X3099 @ X3100 ) ) @ X3099 )
| ~ ( in @ X3103 @ X3099 )
| ( X3100 @ X3103 )
| ~ ( breln1 @ X3098 @ X3099 ) )
& ( ~ ( X3100 @ ( kpair @ ( esk71_3 @ X3098 @ X3099 @ X3100 ) @ ( esk72_3 @ X3098 @ X3099 @ X3100 ) ) )
| ~ ( in @ X3103 @ X3099 )
| ( X3100 @ X3103 )
| ~ ( breln1 @ X3098 @ X3099 ) )
& ( ~ ( in @ X3105 @ ( breln1Set @ X3104 ) )
| ( breln1 @ X3104 @ X3105 ) )
& choice2fnsingleton
& ( breln1 @ X3106 @ ( dpsetconstr @ X3106 @ X3106 @ X3107 ) )
& ( ( in @ ( esk73_3 @ X3108 @ X3109 @ X3110 ) @ X3108 )
| ~ ( in @ X3113 @ X3109 )
| ( X3110 @ X3113 )
| ~ ( breln1 @ X3108 @ X3109 ) )
& ( ( in @ ( esk74_3 @ X3108 @ X3109 @ X3110 ) @ X3108 )
| ~ ( in @ X3113 @ X3109 )
| ( X3110 @ X3113 )
| ~ ( breln1 @ X3108 @ X3109 ) )
& ( ( in @ ( kpair @ ( esk73_3 @ X3108 @ X3109 @ X3110 ) @ ( esk74_3 @ X3108 @ X3109 @ X3110 ) ) @ X3109 )
| ~ ( in @ X3113 @ X3109 )
| ( X3110 @ X3113 )
| ~ ( breln1 @ X3108 @ X3109 ) )
& ( ~ ( X3110 @ ( kpair @ ( esk73_3 @ X3108 @ X3109 @ X3110 ) @ ( esk74_3 @ X3108 @ X3109 @ X3110 ) ) )
| ~ ( in @ X3113 @ X3109 )
| ( X3110 @ X3113 )
| ~ ( breln1 @ X3108 @ X3109 ) )
& ( ( in @ ( esk75_3 @ X3114 @ X3115 @ X3116 ) @ X3114 )
| ( subset @ X3115 @ X3116 )
| ~ ( breln1 @ X3114 @ X3116 )
| ~ ( breln1 @ X3114 @ X3115 ) )
& ( ( in @ ( esk76_3 @ X3114 @ X3115 @ X3116 ) @ X3114 )
| ( subset @ X3115 @ X3116 )
| ~ ( breln1 @ X3114 @ X3116 )
| ~ ( breln1 @ X3114 @ X3115 ) )
& ( ( in @ ( kpair @ ( esk75_3 @ X3114 @ X3115 @ X3116 ) @ ( esk76_3 @ X3114 @ X3115 @ X3116 ) ) @ X3115 )
| ( subset @ X3115 @ X3116 )
| ~ ( breln1 @ X3114 @ X3116 )
| ~ ( breln1 @ X3114 @ X3115 ) )
& ( ~ ( in @ ( kpair @ ( esk75_3 @ X3114 @ X3115 @ X3116 ) @ ( esk76_3 @ X3114 @ X3115 @ X3116 ) ) @ X3116 )
| ( subset @ X3115 @ X3116 )
| ~ ( breln1 @ X3114 @ X3116 )
| ~ ( breln1 @ X3114 @ X3115 ) )
& ( ( in @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ( X3120 = X3121 )
| ( in @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ~ ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ( X3120 = X3121 )
| ( in @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ( X3120 = X3121 )
| ( in @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ~ ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ( X3120 = X3121 )
| ( in @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ( X3120 = X3121 )
| ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ~ ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ( X3120 = X3121 )
| ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ~ ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) @ X3119 )
| ( X3120 = X3121 )
| ~ ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ( X3120 = X3121 )
| ~ ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ~ ( in @ ( kpair @ ( esk79_3 @ X3119 @ X3120 @ X3121 ) @ ( esk80_3 @ X3119 @ X3120 @ X3121 ) ) @ X3120 )
| ( X3120 = X3121 )
| ~ ( in @ ( kpair @ ( esk77_3 @ X3119 @ X3120 @ X3121 ) @ ( esk78_3 @ X3119 @ X3120 @ X3121 ) ) @ X3121 )
| ~ ( breln1 @ X3119 @ X3121 )
| ~ ( breln1 @ X3119 @ X3120 ) )
& ( ~ ( breln1 @ X3126 @ X3127 )
| ( breln1 @ X3126 @ ( breln1invset @ X3126 @ X3127 ) ) )
& ( ~ ( breln1 @ X3128 @ X3129 )
| ~ ( in @ X3130 @ X3128 )
| ~ ( in @ X3131 @ X3128 )
| ~ ( in @ ( kpair @ X3130 @ X3131 ) @ X3129 )
| ( in @ ( kpair @ X3131 @ X3130 ) @ ( breln1invset @ X3128 @ X3129 ) ) )
& ( ~ ( breln1 @ X3132 @ X3133 )
| ~ ( in @ X3134 @ X3132 )
| ~ ( in @ X3135 @ X3132 )
| ~ ( in @ ( kpair @ X3135 @ X3134 ) @ ( breln1invset @ X3132 @ X3133 ) )
| ( in @ ( kpair @ X3134 @ X3135 ) @ X3133 ) )
& ( ~ ( breln1 @ X3136 @ X3137 )
| ~ ( breln1 @ X3136 @ X3138 )
| ( breln1 @ X3136 @ ( breln1compset @ X3136 @ X3137 @ X3138 ) ) )
& ( ~ ( breln1 @ X3139 @ X3140 )
| ~ ( breln1 @ X3139 @ X3141 )
| ~ ( in @ X3142 @ X3139 )
| ~ ( in @ X3143 @ X3139 )
| ~ ( in @ X3144 @ X3139 )
| ~ ( in @ ( kpair @ X3142 @ X3144 ) @ X3140 )
| ~ ( in @ ( kpair @ X3144 @ X3143 ) @ X3141 )
| ( in @ ( kpair @ X3142 @ X3143 ) @ ( breln1compset @ X3139 @ X3140 @ X3141 ) ) )
& ( ( in @ ( esk81_5 @ X3145 @ X3146 @ X3147 @ X3148 @ X3149 ) @ X3145 )
| ~ ( in @ ( kpair @ X3148 @ X3149 ) @ ( breln1compset @ X3145 @ X3146 @ X3147 ) )
| ~ ( in @ X3149 @ X3145 )
| ~ ( in @ X3148 @ X3145 )
| ~ ( breln1 @ X3145 @ X3147 )
| ~ ( breln1 @ X3145 @ X3146 ) )
& ( ( in @ ( kpair @ X3148 @ ( esk81_5 @ X3145 @ X3146 @ X3147 @ X3148 @ X3149 ) ) @ X3146 )
| ~ ( in @ ( kpair @ X3148 @ X3149 ) @ ( breln1compset @ X3145 @ X3146 @ X3147 ) )
| ~ ( in @ X3149 @ X3145 )
| ~ ( in @ X3148 @ X3145 )
| ~ ( breln1 @ X3145 @ X3147 )
| ~ ( breln1 @ X3145 @ X3146 ) )
& ( ( in @ ( kpair @ ( esk81_5 @ X3145 @ X3146 @ X3147 @ X3148 @ X3149 ) @ X3149 ) @ X3147 )
| ~ ( in @ ( kpair @ X3148 @ X3149 ) @ ( breln1compset @ X3145 @ X3146 @ X3147 ) )
| ~ ( in @ X3149 @ X3145 )
| ~ ( in @ X3148 @ X3145 )
| ~ ( breln1 @ X3145 @ X3147 )
| ~ ( breln1 @ X3145 @ X3146 ) )
& ( ( in @ ( esk82_6 @ X3151 @ X3152 @ X3153 @ X3154 @ X3155 @ X3156 ) @ X3151 )
| X3156
| ~ ( in @ ( kpair @ X3154 @ X3155 ) @ ( breln1compset @ X3151 @ X3152 @ X3153 ) )
| ~ ( in @ X3155 @ X3151 )
| ~ ( in @ X3154 @ X3151 )
| ~ ( breln1 @ X3151 @ X3153 )
| ~ ( breln1 @ X3151 @ X3152 ) )
& ( ( in @ ( kpair @ X3154 @ ( esk82_6 @ X3151 @ X3152 @ X3153 @ X3154 @ X3155 @ X3156 ) ) @ X3152 )
| X3156
| ~ ( in @ ( kpair @ X3154 @ X3155 ) @ ( breln1compset @ X3151 @ X3152 @ X3153 ) )
| ~ ( in @ X3155 @ X3151 )
| ~ ( in @ X3154 @ X3151 )
| ~ ( breln1 @ X3151 @ X3153 )
| ~ ( breln1 @ X3151 @ X3152 ) )
& ( ( in @ ( kpair @ ( esk82_6 @ X3151 @ X3152 @ X3153 @ X3154 @ X3155 @ X3156 ) @ X3155 ) @ X3153 )
| X3156
| ~ ( in @ ( kpair @ X3154 @ X3155 ) @ ( breln1compset @ X3151 @ X3152 @ X3153 ) )
| ~ ( in @ X3155 @ X3151 )
| ~ ( in @ X3154 @ X3151 )
| ~ ( breln1 @ X3151 @ X3153 )
| ~ ( breln1 @ X3151 @ X3152 ) )
& ( ~ X3156
| X3156
| ~ ( in @ ( kpair @ X3154 @ X3155 ) @ ( breln1compset @ X3151 @ X3152 @ X3153 ) )
| ~ ( in @ X3155 @ X3151 )
| ~ ( in @ X3154 @ X3151 )
| ~ ( breln1 @ X3151 @ X3153 )
| ~ ( breln1 @ X3151 @ X3152 ) )
& ( ~ ( breln1 @ X3158 @ X3159 )
| ~ ( breln1 @ X3158 @ X3160 )
| ( breln1 @ X3158 @ ( binunion @ X3159 @ X3160 ) ) )
& ( ~ ( breln1 @ X3161 @ X3162 )
| ~ ( breln1 @ X3161 @ X3163 )
| ~ ( in @ X3164 @ X3161 )
| ~ ( in @ X3165 @ X3161 )
| ~ ( in @ ( kpair @ X3164 @ X3165 ) @ X3162 )
| ( in @ ( kpair @ X3164 @ X3165 ) @ ( binunion @ X3162 @ X3163 ) ) )
& ( ~ ( breln1 @ X3166 @ X3167 )
| ~ ( breln1 @ X3166 @ X3168 )
| ~ ( in @ X3169 @ X3166 )
| ~ ( in @ X3170 @ X3166 )
| ~ ( in @ ( kpair @ X3169 @ X3170 ) @ X3168 )
| ( in @ ( kpair @ X3169 @ X3170 ) @ ( binunion @ X3167 @ X3168 ) ) )
& ( ~ ( in @ ( kpair @ X3174 @ X3175 ) @ X3172 )
| ( in @ ( kpair @ X3174 @ X3175 ) @ ( binunion @ X3172 @ X3173 ) )
| ~ ( in @ X3175 @ X3171 )
| ~ ( in @ X3174 @ X3171 )
| ~ ( breln1 @ X3171 @ X3173 )
| ~ ( breln1 @ X3171 @ X3172 ) )
& ( ~ ( in @ ( kpair @ X3174 @ X3175 ) @ X3173 )
| ( in @ ( kpair @ X3174 @ X3175 ) @ ( binunion @ X3172 @ X3173 ) )
| ~ ( in @ X3175 @ X3171 )
| ~ ( in @ X3174 @ X3171 )
| ~ ( breln1 @ X3171 @ X3173 )
| ~ ( breln1 @ X3171 @ X3172 ) )
& ( ~ ( breln1 @ X3176 @ X3177 )
| ~ ( breln1 @ X3176 @ X3178 )
| ~ ( in @ X3179 @ X3176 )
| ~ ( in @ X3180 @ X3176 )
| ~ ( in @ ( kpair @ X3179 @ X3180 ) @ ( binunion @ X3177 @ X3178 ) )
| ( in @ ( kpair @ X3179 @ X3180 ) @ X3177 )
| ( in @ ( kpair @ X3179 @ X3180 ) @ X3178 ) )
& ( ( in @ ( kpair @ X3184 @ X3185 ) @ X3183 )
| X3186
| ( in @ ( kpair @ X3184 @ X3185 ) @ X3182 )
| ~ ( in @ ( kpair @ X3184 @ X3185 ) @ ( binunion @ X3182 @ X3183 ) )
| ~ ( in @ X3185 @ X3181 )
| ~ ( in @ X3184 @ X3181 )
| ~ ( breln1 @ X3181 @ X3183 )
| ~ ( breln1 @ X3181 @ X3182 ) )
& ( ~ X3186
| X3186
| ( in @ ( kpair @ X3184 @ X3185 ) @ X3182 )
| ~ ( in @ ( kpair @ X3184 @ X3185 ) @ ( binunion @ X3182 @ X3183 ) )
| ~ ( in @ X3185 @ X3181 )
| ~ ( in @ X3184 @ X3181 )
| ~ ( breln1 @ X3181 @ X3183 )
| ~ ( breln1 @ X3181 @ X3182 ) )
& ( ( in @ ( kpair @ X3184 @ X3185 ) @ X3183 )
| X3186
| ~ X3186
| ~ ( in @ ( kpair @ X3184 @ X3185 ) @ ( binunion @ X3182 @ X3183 ) )
| ~ ( in @ X3185 @ X3181 )
| ~ ( in @ X3184 @ X3181 )
| ~ ( breln1 @ X3181 @ X3183 )
| ~ ( breln1 @ X3181 @ X3182 ) )
& ( ~ X3186
| X3186
| ~ X3186
| ~ ( in @ ( kpair @ X3184 @ X3185 ) @ ( binunion @ X3182 @ X3183 ) )
| ~ ( in @ X3185 @ X3181 )
| ~ ( in @ X3184 @ X3181 )
| ~ ( breln1 @ X3181 @ X3183 )
| ~ ( breln1 @ X3181 @ X3182 ) )
& ( ~ ( breln1 @ X3187 @ X3188 )
| ~ ( breln1 @ X3187 @ X3189 )
| ( ( binunion @ X3188 @ X3189 )
= ( binunion @ X3189 @ X3188 ) ) )
& ( ~ ( breln1 @ X3190 @ X3191 )
| ( X3191
= ( breln1invset @ X3190 @ ( breln1invset @ X3190 @ X3191 ) ) ) )
& ( ~ ( breln1 @ X3192 @ X3193 )
| ~ ( breln1 @ X3192 @ X3194 )
| ( ( breln1invset @ X3192 @ ( breln1compset @ X3192 @ X3193 @ X3194 ) )
= ( breln1compset @ X3192 @ ( breln1invset @ X3192 @ X3194 ) @ ( breln1invset @ X3192 @ X3193 ) ) ) )
& ( ~ ( breln1 @ X3195 @ X3196 )
| ~ ( breln1 @ X3195 @ X3197 )
| ~ ( breln1 @ X3195 @ X3198 )
| ( ( breln1compset @ X3195 @ ( binunion @ X3196 @ X3197 ) @ X3198 )
= ( binunion @ ( breln1compset @ X3195 @ X3196 @ X3198 ) @ ( breln1compset @ X3195 @ X3197 @ X3198 ) ) ) )
& ( ~ ( breln1 @ X3199 @ X3200 )
| ~ ( breln1 @ X3199 @ X3201 )
| ~ ( breln1 @ X3199 @ X3202 )
| ( ( breln1compset @ X3199 @ ( binunion @ X3200 @ X3201 ) @ X3202 )
= ( binunion @ ( breln1invset @ X3199 @ ( breln1compset @ X3199 @ ( breln1invset @ X3199 @ X3202 ) @ ( breln1invset @ X3199 @ X3201 ) ) ) @ ( breln1invset @ X3199 @ ( breln1compset @ X3199 @ ( breln1invset @ X3199 @ X3202 ) @ ( breln1invset @ X3199 @ X3200 ) ) ) ) ) )
& ( ( in @ ( esk84_3 @ X3203 @ X3204 @ X3206 ) @ X3203 )
| ~ ( in @ X3206 @ ( esk83_2 @ X3203 @ X3204 ) ) )
& ( ( X3206
= ( X3204 @ ( esk84_3 @ X3203 @ X3204 @ X3206 ) ) )
| ~ ( in @ X3206 @ ( esk83_2 @ X3203 @ X3204 ) ) )
& ( ~ ( in @ X3209 @ X3203 )
| ( X3208
!= ( X3204 @ X3209 ) )
| ( in @ X3208 @ ( esk83_2 @ X3203 @ X3204 ) ) )
& ( exu
@ ^ [Z0: $i] :
! [X2149: $i] :
( ( in @ X2149 @ Z0 )
<=> ? [X2150: $i] :
( ( in @ X2150 @ X3210 )
& ( X2149
= ( X3211 @ X2150 ) ) ) ) )
& ( ( in @ ( esk85_3 @ X3212 @ X3213 @ X3214 ) @ X3212 )
| ~ ( in @ X3214 @ ( image1 @ X3212 @ X3213 ) ) )
& ( ( X3214
= ( X3213 @ ( esk85_3 @ X3212 @ X3213 @ X3214 ) ) )
| ~ ( in @ X3214 @ ( image1 @ X3212 @ X3213 ) ) )
& ( ~ ( in @ X3219 @ X3216 )
| ( X3218
!= ( X3217 @ X3219 ) )
| ( in @ X3218 @ ( image1 @ X3216 @ X3217 ) ) )
& ( ( in @ ( esk86_3 @ X3220 @ X3221 @ X3222 ) @ X3220 )
| ~ ( in @ X3222 @ ( image1 @ X3220 @ X3221 ) ) )
& ( ( X3222
= ( X3221 @ ( esk86_3 @ X3220 @ X3221 @ X3222 ) ) )
| ~ ( in @ X3222 @ ( image1 @ X3220 @ X3221 ) ) )
& ( ~ ( in @ X3227 @ X3224 )
| ( X3226
!= ( X3225 @ X3227 ) )
| ( in @ X3226 @ ( image1 @ X3224 @ X3225 ) ) )
& ( ~ ( in @ X3230 @ ( funcSet @ X3228 @ X3229 ) )
| ~ ( injective @ X3228 @ X3229 @ X3230 )
| ( in @ X3230 @ ( injFuncSet @ X3228 @ X3229 ) ) )
& ( ~ ( in @ X3233 @ ( injFuncSet @ X3231 @ X3232 ) )
| ( in @ X3233 @ ( funcSet @ X3231 @ X3232 ) ) )
& ( ~ ( in @ X3236 @ ( injFuncSet @ X3234 @ X3235 ) )
| ( injective @ X3234 @ X3235 @ X3236 ) )
& ( ~ ( in @ X3239 @ ( surjFuncSet @ X3237 @ X3238 ) )
| ( in @ X3239 @ ( funcSet @ X3237 @ X3238 ) ) )
& ( ~ ( in @ X3242 @ ( surjFuncSet @ X3240 @ X3241 ) )
| ( surjective @ X3240 @ X3241 @ X3242 ) )
& ( ( in @ ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) @ X3243 )
| ( surjective @ X3244 @ X3243 @ X3247 )
| ~ ( in @ X3247 @ ( funcSet @ X3244 @ X3243 ) )
| ( in @ ( esk87_3 @ X3243 @ X3244 @ X3245 ) @ X3243 ) )
& ( ( ( ap @ X3244 @ X3243 @ X3247 @ ( X3245 @ ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) ) )
!= ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) )
| ( surjective @ X3244 @ X3243 @ X3247 )
| ~ ( in @ X3247 @ ( funcSet @ X3244 @ X3243 ) )
| ( in @ ( esk87_3 @ X3243 @ X3244 @ X3245 ) @ X3243 ) )
& ( ( in @ ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) @ X3243 )
| ( surjective @ X3244 @ X3243 @ X3247 )
| ~ ( in @ X3247 @ ( funcSet @ X3244 @ X3243 ) )
| ~ ( in @ ( X3245 @ ( esk87_3 @ X3243 @ X3244 @ X3245 ) ) @ X3244 ) )
& ( ( ( ap @ X3244 @ X3243 @ X3247 @ ( X3245 @ ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) ) )
!= ( esk88_4 @ X3243 @ X3244 @ X3245 @ X3247 ) )
| ( surjective @ X3244 @ X3243 @ X3247 )
| ~ ( in @ X3247 @ ( funcSet @ X3244 @ X3243 ) )
| ~ ( in @ ( X3245 @ ( esk87_3 @ X3243 @ X3244 @ X3245 ) ) @ X3244 ) )
& ( ~ ( in @ X3250 @ ( funcSet @ X3249 @ ( powerset @ X3249 ) ) )
| ~ ( surjective @ X3249 @ ( powerset @ X3249 ) @ X3250 ) )
& ( ( in @ ( esk89_1 @ X3251 ) @ X3251 )
| ~ ( nonempty @ X3251 ) )
& ( ( ( binintersect @ ( esk89_1 @ X3251 ) @ X3251 )
= emptyset )
| ~ ( nonempty @ X3251 ) )
& ~ ( in @ X3253 @ X3253 )
& ( ~ ( in @ X3254 @ X3255 )
| ~ ( in @ X3255 @ X3254 ) )
& ( ~ ( in @ X3256 @ omega )
| ( in @ ( omegaS @ X3256 ) @ omega ) )
& ( ~ ( in @ X3257 @ omega )
| ( in @ ( setadjoin @ X3257 @ X3257 ) @ omega ) )
& ( ~ ( in @ X3258 @ omega )
| ( ( omegaS @ X3258 )
!= emptyset ) )
& ( ~ ( in @ X3259 @ omega )
| ~ ( in @ X3260 @ omega )
| ( ( omegaS @ X3259 )
!= ( omegaS @ X3260 ) )
| ( X3259 = X3260 ) )
& ( ( in @ ( esk90_1 @ X3261 ) @ X3261 )
| ~ ( in @ X3263 @ X3261 )
| ( subset @ X3263 @ X3261 ) )
& ( ~ ( subset @ ( esk90_1 @ X3261 ) @ X3261 )
| ~ ( in @ X3263 @ X3261 )
| ( subset @ X3263 @ X3261 ) )
& ( ~ ( in @ X3265 @ esk91_0 )
| ( subset @ X3265 @ esk91_0 ) )
& ( ~ ( in @ X3267 @ esk92_0 )
| ( subset @ X3267 @ esk92_0 ) )
& ( in @ esk93_0 @ ( binintersect @ esk91_0 @ esk92_0 ) )
& ~ ( subset @ esk93_0 @ ( binintersect @ esk91_0 @ esk92_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_388])])])])])])]) ).
thf(c_0_390,negated_conjecture,
~ ( subset @ esk93_0 @ ( binintersect @ esk91_0 @ esk92_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_391,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( binintersect @ X3 @ X4 ) )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_392,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X4 )
| ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_393,negated_conjecture,
in @ esk93_0 @ ( binintersect @ esk91_0 @ esk92_0 ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_394,negated_conjecture,
( ~ ( subset @ esk93_0 @ esk92_0 )
| ~ ( subset @ esk93_0 @ esk91_0 ) ),
inference(spm,[status(thm)],[c_0_390,c_0_391]) ).
thf(c_0_395,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk92_0 )
| ~ ( in @ X2 @ esk92_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_396,negated_conjecture,
in @ esk93_0 @ esk92_0,
inference(spm,[status(thm)],[c_0_392,c_0_393]) ).
thf(c_0_397,negated_conjecture,
~ ( subset @ esk93_0 @ esk91_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_394,c_0_395]),c_0_396])]) ).
thf(c_0_398,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk91_0 )
| ~ ( in @ X2 @ esk91_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_399,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ X3 )
| ~ ( in @ X2 @ ( binintersect @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
thf(c_0_400,negated_conjecture,
~ ( in @ esk93_0 @ esk91_0 ),
inference(spm,[status(thm)],[c_0_397,c_0_398]) ).
thf(c_0_401,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_399,c_0_393]),c_0_400]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU813^1 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 16:23:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 4.53/1.16 # Version: 3.1.0-ho
% 4.53/1.16 # Preprocessing class: HSLMSLSSLLLCHFA.
% 4.53/1.16 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.53/1.16 # Starting ehoh_best5 with 300s (1) cores
% 4.53/1.16 # Starting almost_fo_3_lam with 300s (1) cores
% 4.53/1.16 # Starting new_bool_5 with 300s (1) cores
% 4.53/1.16 # Starting pre_casc_3 with 300s (1) cores
% 4.53/1.16 # Starting ho_unfolding_8 with 300s (1) cores
% 4.53/1.16 # Starting new_ho_10_cnf2 with 300s (1) cores
% 4.53/1.16 # Starting new_bool_3 with 300s (1) cores
% 4.53/1.16 # Starting new_ho_5 with 300s (1) cores
% 4.53/1.16 # new_ho_5 with pid 11770 completed with status 8
% 4.53/1.16 # pre_casc_3 with pid 11766 completed with status 8
% 4.53/1.16 # new_bool_5 with pid 11765 completed with status 0
% 4.53/1.16 # Result found by new_bool_5
% 4.53/1.16 # Preprocessing class: HSLMSLSSLLLCHFA.
% 4.53/1.16 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.53/1.16 # Starting ehoh_best5 with 300s (1) cores
% 4.53/1.16 # Starting almost_fo_3_lam with 300s (1) cores
% 4.53/1.16 # Starting new_bool_5 with 300s (1) cores
% 4.53/1.16 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 4.53/1.16 # Search class: HGHSM-FSLM32-MHFMMSBN
% 4.53/1.16 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 4.53/1.16 # Starting ho_unfolding_8 with 55s (1) cores
% 4.53/1.16 # ho_unfolding_8 with pid 11859 completed with status 0
% 4.53/1.16 # Result found by ho_unfolding_8
% 4.53/1.16 # Preprocessing class: HSLMSLSSLLLCHFA.
% 4.53/1.16 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 4.53/1.16 # Starting ehoh_best5 with 300s (1) cores
% 4.53/1.16 # Starting almost_fo_3_lam with 300s (1) cores
% 4.53/1.16 # Starting new_bool_5 with 300s (1) cores
% 4.53/1.16 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 4.53/1.16 # Search class: HGHSM-FSLM32-MHFMMSBN
% 4.53/1.16 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 4.53/1.16 # Starting ho_unfolding_8 with 55s (1) cores
% 4.53/1.16 # Preprocessing time : 0.066 s
% 4.53/1.16 # Presaturation interreduction done
% 4.53/1.16
% 4.53/1.16 # Proof found!
% 4.53/1.16 # SZS status Theorem
% 4.53/1.16 # SZS output start CNFRefutation
% See solution above
% 4.53/1.17 # Parsed axioms : 721
% 4.53/1.17 # Removed by relevancy pruning/SinE : 392
% 4.53/1.17 # Initial clauses : 542
% 4.53/1.17 # Removed in clause preprocessing : 41
% 4.53/1.17 # Initial clauses in saturation : 501
% 4.53/1.17 # Processed clauses : 999
% 4.53/1.17 # ...of these trivial : 11
% 4.53/1.17 # ...subsumed : 64
% 4.53/1.17 # ...remaining for further processing : 923
% 4.53/1.17 # Other redundant clauses eliminated : 99
% 4.53/1.17 # Clauses deleted for lack of memory : 0
% 4.53/1.17 # Backward-subsumed : 4
% 4.53/1.17 # Backward-rewritten : 2
% 4.53/1.17 # Generated clauses : 15094
% 4.53/1.17 # ...of the previous two non-redundant : 14761
% 4.53/1.17 # ...aggressively subsumed : 0
% 4.53/1.17 # Contextual simplify-reflections : 14
% 4.53/1.17 # Paramodulations : 14959
% 4.53/1.17 # Factorizations : 2
% 4.53/1.17 # NegExts : 0
% 4.53/1.17 # Equation resolutions : 107
% 4.53/1.17 # Disequality decompositions : 0
% 4.53/1.17 # Total rewrite steps : 273
% 4.53/1.17 # ...of those cached : 176
% 4.53/1.17 # Propositional unsat checks : 0
% 4.53/1.17 # Propositional check models : 0
% 4.53/1.17 # Propositional check unsatisfiable : 0
% 4.53/1.17 # Propositional clauses : 0
% 4.53/1.17 # Propositional clauses after purity: 0
% 4.53/1.17 # Propositional unsat core size : 0
% 4.53/1.17 # Propositional preprocessing time : 0.000
% 4.53/1.17 # Propositional encoding time : 0.000
% 4.53/1.17 # Propositional solver time : 0.000
% 4.53/1.17 # Success case prop preproc time : 0.000
% 4.53/1.17 # Success case prop encoding time : 0.000
% 4.53/1.17 # Success case prop solver time : 0.000
% 4.53/1.17 # Current number of processed clauses : 461
% 4.53/1.17 # Positive orientable unit clauses : 47
% 4.53/1.17 # Positive unorientable unit clauses: 0
% 4.53/1.17 # Negative unit clauses : 16
% 4.53/1.17 # Non-unit-clauses : 398
% 4.53/1.17 # Current number of unprocessed clauses: 14694
% 4.53/1.17 # ...number of literals in the above : 69384
% 4.53/1.17 # Current number of archived formulas : 0
% 4.53/1.17 # Current number of archived clauses : 442
% 4.53/1.17 # Clause-clause subsumption calls (NU) : 119169
% 4.53/1.17 # Rec. Clause-clause subsumption calls : 41878
% 4.53/1.17 # Non-unit clause-clause subsumptions : 65
% 4.53/1.17 # Unit Clause-clause subsumption calls : 1484
% 4.53/1.17 # Rewrite failures with RHS unbound : 0
% 4.53/1.17 # BW rewrite match attempts : 30
% 4.53/1.17 # BW rewrite match successes : 2
% 4.53/1.17 # Condensation attempts : 0
% 4.53/1.17 # Condensation successes : 0
% 4.53/1.17 # Termbank termtop insertions : 374061
% 4.53/1.17 # Search garbage collected termcells : 35389
% 4.53/1.17
% 4.53/1.17 # -------------------------------------------------
% 4.53/1.17 # User time : 0.568 s
% 4.53/1.17 # System time : 0.041 s
% 4.53/1.17 # Total time : 0.609 s
% 4.53/1.17 # Maximum resident set size: 10716 pages
% 4.53/1.17
% 4.53/1.17 # -------------------------------------------------
% 4.53/1.17 # User time : 0.844 s
% 4.53/1.17 # System time : 0.143 s
% 4.53/1.17 # Total time : 0.987 s
% 4.53/1.17 # Maximum resident set size: 2892 pages
% 4.53/1.17 % E---3.1 exiting
% 4.53/1.17 % E exiting
%------------------------------------------------------------------------------