%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU787^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 03:30:14 EDT 2024
% Result : Theorem 1.44s 0.78s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 747
% Syntax : Number of formulae : 827 ( 25 unt; 442 typ; 0 def)
% Number of atoms : 4250 ( 640 equ; 0 cnn)
% Maximal formula atoms : 1423 ( 11 avg)
% Number of connectives : 17588 (1207 ~;1308 |; 662 &;11888 @)
% ( 396 <=>;2127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1431 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 651 ( 651 >; 0 *; 0 +; 0 <<)
% Number of symbols : 446 ( 442 usr; 315 con; 0-6 aty)
% Number of variables : 3366 ( 168 ^3075 !; 123 ?;3366 :)
% 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,
epred1_0: $o ).
thf(decl_374,type,
esk1_2: $i > $i > $i ).
thf(decl_375,type,
esk2_2: $i > $i > $i ).
thf(decl_376,type,
esk3_2: $i > $i > $i ).
thf(decl_377,type,
esk4_1: $i > $i ).
thf(decl_378,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_379,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_380,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_381,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_382,type,
esk9_1: $i > $i ).
thf(decl_383,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_384,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_385,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_386,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_387,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_388,type,
esk15_2: $i > $i > $i ).
thf(decl_389,type,
esk16_2: $i > $i > $i ).
thf(decl_390,type,
esk17_1: $i > $i ).
thf(decl_391,type,
esk18_1: $i > $i ).
thf(decl_392,type,
esk19_1: $i > $i ).
thf(decl_393,type,
esk20_2: $i > $i > $i ).
thf(decl_394,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_395,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_396,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_397,type,
esk24_1: $i > $i ).
thf(decl_398,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_399,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_400,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_401,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_402,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_403,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_404,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_405,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_406,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_407,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_408,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_409,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_410,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_411,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_412,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_413,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_414,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_415,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_416,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_417,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_418,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_419,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_420,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_421,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_422,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_423,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_424,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_425,type,
esk52_2: $i > $i > $i ).
thf(decl_426,type,
esk53_2: $i > $i > $i ).
thf(decl_427,type,
esk54_2: $i > $i > $i ).
thf(decl_428,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_429,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_430,type,
esk57_2: $i > $i > $i ).
thf(decl_431,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_432,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_433,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_434,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_435,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_436,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_437,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_438,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_439,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_440,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_441,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_442,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_443,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_444,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_445,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_446,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_447,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_448,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_449,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_450,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_451,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_452,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_453,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_454,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_455,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_456,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_457,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_458,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_459,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_460,type,
esk87_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_461,type,
esk88_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_462,type,
esk89_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_463,type,
esk90_3: $i > $i > ( $i > $o ) > $i ).
thf(decl_464,type,
esk91_3: $i > $i > $i > $i ).
thf(decl_465,type,
esk92_3: $i > $i > $i > $i ).
thf(decl_466,type,
esk93_3: $i > $i > $i > $i ).
thf(decl_467,type,
esk94_3: $i > $i > $i > $i ).
thf(decl_468,type,
esk95_3: $i > $i > $i > $i ).
thf(decl_469,type,
esk96_3: $i > $i > $i > $i ).
thf(decl_470,type,
esk97_5: $i > $i > $i > $i > $i > $i ).
thf(decl_471,type,
esk98_6: $i > $i > $i > $i > $i > $o > $i ).
thf(decl_472,type,
esk99_0: $i ).
thf(decl_473,type,
esk100_0: $i ).
thf(decl_474,type,
esk101_0: $i ).
thf(decl_475,type,
esk102_0: $i ).
thf(decl_476,type,
esk103_0: $i ).
thf(decl_477,type,
epred2_0: $o ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(setOfPairsIsBReln1,axiom,
( setOfPairsIsBReln1
<=> ! [X4: $i,X53: $i > $i > $o] :
( breln1 @ X4
@ ( dpsetconstr @ X4 @ X4
@ ^ [X2: $i,X3: $i] : ( X53 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(breln1unionEcases,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
=> ! [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/sandbox2/benchmark/theBenchmark.p',breln1unionEcases) ).
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/sandbox2/benchmark/theBenchmark.p',demorgan2b2) ).
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/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(intersectInPowersetIntersectUnions,axiom,
( intersectInPowersetIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(inComplementUnionImpNotIn1,axiom,
( inComplementUnionImpNotIn1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inComplementUnionImpInComplement1,axiom,
( inComplementUnionImpInComplement1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(binunionTE,axiom,
( binunionTE
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X50: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ( ( ( in @ X2 @ X21 )
=> X50 )
=> ( ( ( in @ X2 @ X48 )
=> X50 )
=> X50 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).
thf(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/sandbox2/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(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/sandbox2/benchmark/theBenchmark.p',demorgan2a1) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',demorgan1a) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',demorgan1) ).
thf(demorgan2a,axiom,
( demorgan2a
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',demorgan2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',woz13rule1) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',woz13rule3) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(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/sandbox2/benchmark/theBenchmark.p',woz13rule4) ).
thf(woz1_1,axiom,
( woz1_1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',woz1_3) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',woz1_5) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
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/sandbox2/benchmark/theBenchmark.p',breln1all2) ).
thf(breln1SetBreln1,axiom,
( breln1SetBreln1
<=> ! [X4: $i,X33: $i] :
( ( in @ X33 @ ( breln1Set @ X4 ) )
=> ( breln1 @ X4 @ X33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1SetBreln1) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
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/sandbox2/benchmark/theBenchmark.p',breln1all1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eqbreln1) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(breln1invprop,axiom,
( breln1invprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ( breln1 @ X4 @ ( breln1invset @ X4 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',breln1invI) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(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/sandbox2/benchmark/theBenchmark.p',breln1invE) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(breln1compprop,axiom,
( breln1compprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( breln1 @ X4 @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',breln1compE) ).
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/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(breln1unionprop,axiom,
( breln1unionprop
<=> ! [X4: $i,X33: $i] :
( ( breln1 @ X4 @ X33 )
=> ! [X35: $i] :
( ( breln1 @ X4 @ X35 )
=> ( breln1 @ X4 @ ( binunion @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionprop) ).
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/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
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/sandbox2/benchmark/theBenchmark.p',breln1unionIR) ).
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/sandbox2/benchmark/theBenchmark.p',breln1unionI) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_304,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_305,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_306,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_307,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_308,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_309,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_310,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_311,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_312,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_313,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_314,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_315,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_316,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_317,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_318,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_319,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_320,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_321,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_322,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_323,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_324,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_325,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_326,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_327,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_328,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_329,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_330,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_331,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_332,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_333,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_334,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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,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_345,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_346,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_347,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_348,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_349,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_350,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_351,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_352,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X1075: $i] :
( ( X1 @ X1075 )
& ! [X1076: $i] :
( ( X1 @ X1076 )
=> ( X1075 = X1076 ) ) )
=> ( ? [X1077: $i] :
( ( X17 @ X1077 )
& ! [X1078: $i] :
( ( X17 @ X1078 )
=> ( X1077 = X1078 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_304,c_0_305]) ).
thf(c_0_353,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X1073: $i] :
( ( X1 @ X1073 )
& ! [X1074: $i] :
( ( X1 @ X1074 )
=> ( X1073 = X1074 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_306,c_0_305]) ).
thf(c_0_354,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X1069: $i] :
( ( X1 @ X1069 )
& ! [X1070: $i] :
( ( X1 @ X1070 )
=> ( X1069 = X1070 ) ) )
<=> ? [X1071: $i] :
( ( X17 @ X1071 )
& ! [X1072: $i] :
( ( X17 @ X1072 )
=> ( X1071 = X1072 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_307,c_0_305]) ).
thf(c_0_355,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X1067: $i] :
( ( X1 @ X1067 )
& ! [X1068: $i] :
( ( X1 @ X1068 )
=> ( X1067 = X1068 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_308,c_0_305]) ).
thf(c_0_356,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X1065: $i] :
( ( X1 @ X1065 )
& ! [X1066: $i] :
( ( X1 @ X1066 )
=> ( X1065 = X1066 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_309,c_0_305]) ).
thf(c_0_357,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X1063: $i] :
( ( X1 @ X1063 )
& ! [X1064: $i] :
( ( X1 @ X1064 )
=> ( X1063 = X1064 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_310,c_0_305]) ).
thf(c_0_358,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X1061: $i] :
( ( X1 @ X1061 )
& ! [X1062: $i] :
( ( X1 @ X1062 )
=> ( X1061 = X1062 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_311,c_0_305]) ).
thf(c_0_359,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_360,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_312]) ).
thf(c_0_361,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X1059: $i] :
( ( X1 @ X1059 )
& ! [X1060: $i] :
( ( X1 @ X1060 )
=> ( X1059 = X1060 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_313,c_0_305]) ).
thf(c_0_362,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_363,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_312]) ).
thf(c_0_364,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_314,c_0_312]) ).
thf(c_0_365,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_312]) ).
thf(c_0_366,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_367,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X1057: $i] :
( ( X1 @ X1057 )
& ! [X1058: $i] :
( ( X1 @ X1058 )
=> ( X1057 = X1058 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_315,c_0_305]) ).
thf(c_0_368,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X1055: $i] :
( ( X1 @ X1055 )
& ! [X1056: $i] :
( ( X1 @ X1056 )
=> ( X1055 = X1056 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_316,c_0_305]) ).
thf(c_0_369,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_370,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_371,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_372,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X1053: $i] :
( ( X1 @ X1053 )
& ! [X1054: $i] :
( ( X1 @ X1054 )
=> ( X1053 = X1054 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_317,c_0_305]) ).
thf(c_0_373,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X1051: $i] :
( ( X6 @ X2 @ X1051 )
& ! [X1052: $i] :
( ( X6 @ X2 @ X1052 )
=> ( X1051 = X1052 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_318,c_0_305]) ).
thf(c_0_374,plain,
( epred1_0
<=> ! [X1108: $i] :
? [X1109: $i] :
( ! [X1110: $i] :
( ( in @ X1110 @ X1109 )
=> ! [X1111: $i] :
( ( in @ X1111 @ X1110 )
=> ( in @ X1111 @ X1108 ) ) )
& ! [X1112: $i,X1113: $i] :
( ( ( in @ X1112 @ X1108 )
& ( in @ X1113 @ X1108 ) )
=> ( ! [X1114: $i] :
( ( in @ X1114 @ X1109 )
=> ( ( in @ X1112 @ X1114 )
<=> ( in @ X1113 @ X1114 ) ) )
=> ( X1112 = X1113 ) ) )
& ! [X1115: $i,X1116: $i] :
( ( ( in @ X1115 @ X1109 )
& ( in @ X1116 @ X1109 ) )
=> ( ! [X1117: $i] :
( ( in @ X1117 @ X1115 )
=> ( in @ X1117 @ X1116 ) )
| ! [X1118: $i] :
( ( in @ X1118 @ X1116 )
=> ( in @ X1118 @ X1115 ) ) ) )
& ! [X1119: $i] :
( ( ! [X1120: $i] :
( ( in @ X1120 @ X1119 )
=> ( in @ X1120 @ X1108 ) )
& ? [X1121: $i] : ( in @ X1121 @ X1119 ) )
=> ? [X1122: $i,X1123: $i] :
( ( in @ X1122 @ X1109 )
& ( in @ X1123 @ X1119 )
& ~ ? [X1124: $i] :
( ( in @ X1124 @ X1122 )
& ( in @ X1124 @ X1119 ) )
& ! [X1125: $i] :
( ( in @ X1125 @ X1109 )
=> ( ! [X1126: $i] :
( ( in @ X1126 @ X1125 )
=> ( in @ X1126 @ X1122 ) )
| ( in @ X1123 @ X1125 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_375,negated_conjecture,
~ ( ! [X1079: $i,X1080: $i] :
( ! [X1081: $i] :
( ( in @ X1081 @ X1079 )
<=> ( in @ X1081 @ X1080 ) )
=> ( X1079 = X1080 ) )
=> ( ! [X1082: $i] :
~ ( in @ X1082 @ emptyset )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ( in @ X1085 @ ( setadjoin @ X1083 @ X1084 ) )
<=> ( ( X1085 = X1083 )
| ( in @ X1085 @ X1084 ) ) )
=> ( ! [X1086: $i,X1087: $i] :
( ( in @ X1087 @ ( powerset @ X1086 ) )
<=> ! [X1088: $i] :
( ( in @ X1088 @ X1087 )
=> ( in @ X1088 @ X1086 ) ) )
=> ( ! [X1089: $i,X1090: $i] :
( ( in @ X1090 @ ( setunion @ X1089 ) )
<=> ? [X1091: $i] :
( ( in @ X1090 @ X1091 )
& ( in @ X1091 @ X1089 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X1092: $i] :
( ( in @ X1092 @ omega )
=> ( in @ ( setadjoin @ X1092 @ X1092 ) @ omega ) )
=> ( ! [X1093: $i] :
( ( ( in @ emptyset @ X1093 )
& ! [X1094: $i] :
( ( ( in @ X1094 @ omega )
& ( in @ X1094 @ X1093 ) )
=> ( in @ ( setadjoin @ X1094 @ X1094 ) @ X1093 ) ) )
=> ! [X1095: $i] :
( ( in @ X1095 @ omega )
=> ( in @ X1095 @ X1093 ) ) )
=> ( ! [X1096: $i > $i > $o,X1097: $i] :
( ! [X1098: $i] :
( ( in @ X1098 @ X1097 )
=> ? [X1099: $i] :
( ( X1096 @ X1098 @ X1099 )
& ! [X1100: $i] :
( ( X1096 @ X1098 @ X1100 )
=> ( X1099 = X1100 ) ) ) )
=> ? [X1101: $i] :
! [X1102: $i] :
( ( in @ X1102 @ X1101 )
<=> ? [X1103: $i] :
( ( in @ X1103 @ X1097 )
& ( X1096 @ X1103 @ X1102 ) ) ) )
=> ( ! [X1104: $i] :
( ? [X1105: $i] : ( in @ X1105 @ X1104 )
=> ? [X1106: $i] :
( ( in @ X1106 @ X1104 )
& ~ ? [X1107: $i] :
( ( in @ X1107 @ X1106 )
& ( in @ X1107 @ X1104 ) ) ) )
=> ( epred1_0
=> ( ! [X1127: $i > $o] :
( ? [X1128: $i] :
( ( X1127 @ X1128 )
& ! [X1129: $i] :
( ( X1127 @ X1129 )
=> ( X1128 = X1129 ) ) )
=> ( X1127
@ ( descr
@ ^ [Z0: $i] : ( X1127 @ Z0 ) ) ) )
=> ( ! [X1130: $i,X1131: $i > $o,X1132: $i] :
( ( in @ X1132 @ X1130 )
=> ( ( X1131 @ X1132 )
=> ( in @ X1132 @ ( dsetconstr @ X1130 @ X1131 ) ) ) )
=> ( ! [X1133: $i,X1134: $i > $o,X1135: $i] :
( ( in @ X1135 @ ( dsetconstr @ X1133 @ X1134 ) )
=> ( in @ X1135 @ X1133 ) )
=> ( ! [X1136: $i,X1137: $i > $o,X1138: $i] :
( ( in @ X1138 @ ( dsetconstr @ X1136 @ X1137 ) )
=> ( X1137 @ X1138 ) )
=> ( ! [X1139: $i > $o] :
( ? [X1140: $i] :
( ( X1139 @ X1140 )
& ! [X1141: $i] :
( ( X1139 @ X1141 )
=> ( X1140 = X1141 ) ) )
=> ? [X1142: $i] :
( ( X1139 @ X1142 )
& ! [X1143: $i] :
( ( X1139 @ X1143 )
=> ( X1142 = X1143 ) ) ) )
=> ( ! [X1144: $o,X1145: $i] :
( ( in @ X1145 @ ( prop2set @ X1144 ) )
=> X1144 )
=> ( ! [X1146: $i] :
( ( in @ X1146 @ emptyset )
=> ! [X1147: $o] : X1147 )
=> ( ! [X1148: $i] :
( ( in @ X1148 @ emptyset )
=> ~ $true )
=> ( ! [X1149: $i] :
~ ( in @ X1149 @ emptyset )
=> ( ! [X1150: $i > $o] :
( ? [X1151: $i] :
( ( X1150 @ X1151 )
& ! [X1152: $i] :
( ( X1150 @ X1152 )
=> ( X1151 = X1152 ) ) )
=> ? [X1153: $i] : ( X1150 @ X1153 ) )
=> ( ! [X1154: $i,X1155: $i] :
( ! [X1156: $i] :
( ( in @ X1156 @ X1154 )
=> ( in @ X1156 @ X1155 ) )
=> ( ! [X1157: $i] :
( ( in @ X1157 @ X1155 )
=> ( in @ X1157 @ X1154 ) )
=> ( X1154 = X1155 ) ) )
=> ( ! [X1158: $i] :
( ! [X1159: $i] :
~ ( in @ X1159 @ X1158 )
=> ( X1158 = emptyset ) )
=> ( ! [X1160: $i] :
( ! [X1161: $i] :
~ ( in @ X1161 @ X1160 )
=> ( X1160 = emptyset ) )
=> ( ! [X1162: $i,X1163: $i > $o,X1164: $i] :
( ( in @ X1164 @ X1162 )
=> ( ( in @ X1164 @ ( dsetconstr @ X1162 @ X1163 ) )
<=> ( X1163 @ X1164 ) ) )
=> ( ! [X1165: $i] :
( ( X1165 != emptyset )
=> ? [X1166: $i] : ( in @ X1166 @ X1165 ) )
=> ( ! [X1167: $i,X1168: $i > $o,X1169: $i] :
( ( in @ X1169 @ X1167 )
=> ( ( X1168 @ X1169 )
=> ( ( dsetconstr @ X1167 @ X1168 )
!= emptyset ) ) )
=> ( ! [X1170: $i] :
( ? [X1171: $i] : ( in @ X1171 @ X1170 )
=> ( X1170 != emptyset ) )
=> ( ! [X1172: $i,X1173: $i] : ( in @ X1172 @ ( setadjoin @ X1172 @ X1173 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1174: $i,X1175: $i,X1176: $i] :
( ( in @ X1176 @ X1175 )
=> ( in @ X1176 @ ( setadjoin @ X1174 @ X1175 ) ) )
=> ( ! [X1177: $i,X1178: $i,X1179: $i] :
( ( in @ X1179 @ ( setadjoin @ X1177 @ X1178 ) )
=> ! [X1180: $o] :
( ( ( X1179 = X1177 )
=> X1180 )
=> ( ( ( in @ X1179 @ X1178 )
=> X1180 )
=> X1180 ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ ( setadjoin @ X1181 @ X1182 ) )
=> ( ( X1183 = X1181 )
| ( in @ X1183 @ X1182 ) ) )
=> ( ! [X1184: $i] :
( ( dsetconstr @ X1184
@ ^ [Z0: $i] : $true )
= X1184 )
=> ( ! [X1185: $i,X1186: $i] :
( ! [X1187: $i] :
( ( in @ X1187 @ X1186 )
=> ( in @ X1187 @ X1185 ) )
=> ( in @ X1186 @ ( powerset @ X1185 ) ) )
=> ( ! [X1188: $i] : ( in @ emptyset @ ( powerset @ X1188 ) )
=> ( ! [X1189: $i] : ( in @ emptyset @ ( powerset @ X1189 ) )
=> ( ! [X1190: $i,X1191: $i,X1192: $i] :
( ( in @ X1191 @ ( powerset @ X1190 ) )
=> ( ( in @ X1192 @ X1191 )
=> ( in @ X1192 @ X1190 ) ) )
=> ( ! [X1193: $i,X1194: $i,X1195: $i] :
( ( in @ X1194 @ X1195 )
=> ( ( in @ X1195 @ X1193 )
=> ( in @ X1194 @ ( setunion @ X1193 ) ) ) )
=> ( ! [X1196: $i,X1197: $i] :
( ( in @ X1197 @ ( setunion @ X1196 ) )
=> ! [X1198: $o] :
( ! [X1199: $i] :
( ( in @ X1197 @ X1199 )
=> ( ( in @ X1199 @ X1196 )
=> X1198 ) )
=> X1198 ) )
=> ( ! [X1200: $i,X1201: $i] :
( ( in @ X1201 @ X1200 )
=> ( in @ X1201 @ ( powerset @ ( setunion @ X1200 ) ) ) )
=> ( ! [X1202: $i > $o] :
( ? [X1203: $i] :
( ( X1202 @ X1203 )
& ! [X1204: $i] :
( ( X1202 @ X1204 )
=> ( X1203 = X1204 ) ) )
=> ? [X1205: $i] :
! [X1206: $i] :
( ( X1202 @ X1206 )
<=> ( X1206 = X1205 ) ) )
=> ( ! [X1207: $i] :
( ( X1207 != emptyset )
=> ? [X1208: $i] :
( ( in @ X1208 @ X1207 )
& $true ) )
=> ( ! [X1209: $i,X1210: $i] :
( ( in @ X1209 @ ( setadjoin @ X1210 @ emptyset ) )
=> ( X1209 = X1210 ) )
=> ( ! [X1211: $i,X1212: $i] :
( ( X1211 != X1212 )
=> ~ ( in @ X1212 @ ( setadjoin @ X1211 @ emptyset ) ) )
=> ( ! [X1213: $i,X1214: $i] :
( ( X1213 = X1214 )
=> ( in @ X1213 @ ( setadjoin @ X1214 @ emptyset ) ) )
=> ( ! [X1215: $i,X1216: $i] :
( ( in @ X1215 @ ( setadjoin @ X1216 @ emptyset ) )
=> ( in @ X1216 @ ( setadjoin @ X1215 @ emptyset ) ) )
=> ( ! [X1217: $i,X1218: $i,X1219: $i] :
( ( in @ X1219 @ ( setadjoin @ X1217 @ ( setadjoin @ X1218 @ emptyset ) ) )
=> ( ( X1219 = X1217 )
| ( X1219 = X1218 ) ) )
=> ( ! [X1220: $i,X1221: $i] : ( in @ X1220 @ ( setadjoin @ X1220 @ ( setadjoin @ X1221 @ emptyset ) ) )
=> ( ! [X1222: $i,X1223: $i] : ( in @ X1223 @ ( setadjoin @ X1222 @ ( setadjoin @ X1223 @ emptyset ) ) )
=> ( ! [X1224: $i,X1225: $i > $o] :
( ? [X1226: $i] :
( ( in @ X1226 @ X1224 )
& ( X1225 @ X1226 ) )
=> ( ( ( dsetconstr @ X1224 @ X1225 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1227: $i > $o,X1228: $i] :
( ( in @ X1228 @ emptyset )
=> ( X1227 @ X1228 ) )
=> ( ! [X1229: $i,X1230: $i > $o] :
( ~ ! [X1231: $i] :
( ( in @ X1231 @ X1229 )
=> ( X1230 @ X1231 ) )
=> ? [X1232: $i] :
( ( in @ X1232 @ X1229 )
& ~ ( X1230 @ X1232 ) ) )
=> ( ! [X1233: $i,X1234: $i > $o] :
( ! [X1235: $i] :
( ( in @ X1235 @ X1233 )
=> ~ ( X1234 @ X1235 ) )
=> ~ ? [X1236: $i] :
( ( in @ X1236 @ X1233 )
& ( X1234 @ X1236 ) ) )
=> ( ! [X1237: $i,X1238: $i > $o] :
( ~ ? [X1239: $i] :
( ( in @ X1239 @ X1237 )
& ( X1238 @ X1239 ) )
=> ! [X1240: $i] :
( ( in @ X1240 @ X1237 )
=> ~ ( X1238 @ X1240 ) ) )
=> ( ! [X1241: $i,X1242: $i > $o] :
( ? [X1243: $i] :
( ( in @ X1243 @ X1241 )
& ~ ( X1242 @ X1243 ) )
=> ~ ! [X1244: $i] :
( ( in @ X1244 @ X1241 )
=> ( X1242 @ X1244 ) ) )
=> ( ! [X1245: $o] :
( X1245
=> ( in @ emptyset @ ( prop2set @ X1245 ) ) )
=> ( prop2set2propI
=> ( ! [X1246: $i,X1247: $i > $o] :
( ~ ? [X1248: $i] :
( ( in @ X1248 @ X1246 )
& ( X1247 @ X1248 ) )
=> ! [X1249: $i] :
( ( in @ X1249 @ X1246 )
=> ~ ( X1247 @ X1249 ) ) )
=> ( ! [X1250: $i,X1251: $i > $o] :
( ~ ! [X1252: $i] :
( ( in @ X1252 @ X1250 )
=> ( X1251 @ X1252 ) )
=> ? [X1253: $i] :
( ( in @ X1253 @ X1250 )
& ~ ( X1251 @ X1253 ) ) )
=> ( ! [X1254: $i > $o] :
( ? [X1255: $i] :
( ( X1254 @ X1255 )
& ! [X1256: $i] :
( ( X1254 @ X1256 )
=> ( X1255 = X1256 ) ) )
=> ? [X1257: $i] :
( ( X1254 @ X1257 )
& ! [X1258: $i] :
( ( X1254 @ X1258 )
=> ( X1257 = X1258 ) ) ) )
=> ( ! [X1259: $i > $o] :
( ? [X1260: $i] : ( X1259 @ X1260 )
=> ( ! [X1261: $i,X1262: $i] :
( ( X1259 @ X1261 )
=> ( ( X1259 @ X1262 )
=> ( X1261 = X1262 ) ) )
=> ? [X1263: $i] :
( ( X1259 @ X1263 )
& ! [X1264: $i] :
( ( X1259 @ X1264 )
=> ( X1263 = X1264 ) ) ) ) )
=> ( ! [X1265: $i > $o] :
( ? [X1266: $i] :
! [X1267: $i] :
( ( X1265 @ X1267 )
<=> ( X1267 = X1266 ) )
=> ? [X1268: $i] :
( ( X1265 @ X1268 )
& ! [X1269: $i] :
( ( X1265 @ X1269 )
=> ( X1268 = X1269 ) ) ) )
=> ( ! [X1270: $i,X1271: $i] :
( ( X1270 = X1271 )
=> ! [X1272: $i,X1273: $i] :
( ( X1272 = X1273 )
=> ( ( in @ X1272 @ X1270 )
=> ( in @ X1273 @ X1271 ) ) ) )
=> ( ! [X1274: $i,X1275: $i] :
( ( X1274 = X1275 )
=> ! [X1276: $i,X1277: $i] :
( ( X1276 = X1277 )
=> ( ( in @ X1276 @ X1274 )
<=> ( in @ X1277 @ X1275 ) ) ) )
=> ( ! [X1278: $i > $o] :
( ? [X1279: $i] :
( ( X1278 @ X1279 )
& ! [X1280: $i] :
( ( X1278 @ X1280 )
=> ( X1279 = X1280 ) ) )
=> ! [X1281: $i,X1282: $i] :
( ( X1278 @ X1281 )
=> ( ( X1278 @ X1282 )
=> ( X1281 = X1282 ) ) ) )
=> ( ! [X1283: $i > $o,X1284: $i > $o] :
( ! [X1285: $i,X1286: $i] :
( ( X1285 = X1286 )
=> ( ( X1283 @ X1285 )
<=> ( X1284 @ X1286 ) ) )
=> ( ? [X1287: $i] :
( ( X1283 @ X1287 )
& ! [X1288: $i] :
( ( X1283 @ X1288 )
=> ( X1287 = X1288 ) ) )
<=> ? [X1289: $i] :
( ( X1284 @ X1289 )
& ! [X1290: $i] :
( ( X1284 @ X1290 )
=> ( X1289 = X1290 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1291: $i,X1292: $i] :
( ( X1291 = X1292 )
=> ! [X1293: $i,X1294: $i] :
( ( X1293 = X1294 )
=> ( ( setadjoin @ X1291 @ X1293 )
= ( setadjoin @ X1292 @ X1294 ) ) ) )
=> ( ! [X1295: $i,X1296: $i] :
( ( X1295 = X1296 )
=> ( ( powerset @ X1295 )
= ( powerset @ X1296 ) ) )
=> ( ! [X1297: $i,X1298: $i] :
( ( X1297 = X1298 )
=> ( ( setunion @ X1297 )
= ( setunion @ X1298 ) ) )
=> ( ( omega = omega )
=> ( ! [X1299: $i > $o] :
( ? [X1300: $i] :
( ( X1299 @ X1300 )
& ! [X1301: $i] :
( ( X1299 @ X1301 )
=> ( X1300 = X1301 ) ) )
=> ! [X1302: $i,X1303: $i] :
( ( X1299 @ X1302 )
=> ( ( X1299 @ X1303 )
=> ( X1302 = X1303 ) ) ) )
=> ( ! [X1304: $i > $o,X1305: $i > $o] :
( ! [X1306: $i,X1307: $i] :
( ( X1306 = X1307 )
=> ( ( X1304 @ X1306 )
<=> ( X1305 @ X1307 ) ) )
=> ( ? [X1308: $i] :
( ( X1304 @ X1308 )
& ! [X1309: $i] :
( ( X1304 @ X1309 )
=> ( X1308 = X1309 ) ) )
=> ( ? [X1310: $i] :
( ( X1305 @ X1310 )
& ! [X1311: $i] :
( ( X1305 @ X1311 )
=> ( X1310 = X1311 ) ) )
=> ( ( descr @ X1304 )
= ( descr @ X1305 ) ) ) ) )
=> ( ! [X1312: $i,X1313: $i] :
( ( X1312 = X1313 )
=> ! [X1314: $i > $o,X1315: $i > $o] :
( ! [X1316: $i] :
( ( in @ X1316 @ X1312 )
=> ! [X1317: $i] :
( ( in @ X1317 @ X1313 )
=> ( ( X1316 = X1317 )
=> ( ( X1314 @ X1316 )
<=> ( X1315 @ X1317 ) ) ) ) )
=> ( ( dsetconstr @ X1312 @ X1314 )
= ( dsetconstr @ X1313 @ X1315 ) ) ) )
=> ( ! [X1318: $i,X1319: $i] :
( ! [X1320: $i] :
( ( in @ X1320 @ X1318 )
=> ( in @ X1320 @ X1319 ) )
=> ( subset @ X1318 @ X1319 ) )
=> ( ! [X1321: $i,X1322: $i] :
( ( X1321 = X1322 )
=> ( subset @ X1322 @ X1321 ) )
=> ( ! [X1323: $i,X1324: $i] :
( ( X1323 = X1324 )
=> ( subset @ X1323 @ X1324 ) )
=> ( ! [X1325: $i,X1326: $i] :
( ! [X1327: $i] :
( ( in @ X1327 @ X1325 )
=> ( in @ X1327 @ X1326 ) )
=> ( subset @ X1325 @ X1326 ) )
=> ( ! [X1328: $i] : ( subset @ emptyset @ X1328 )
=> ( ! [X1329: $i,X1330: $i,X1331: $i] :
( ( subset @ X1329 @ X1330 )
=> ( ( in @ X1331 @ X1329 )
=> ( in @ X1331 @ X1330 ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( subset @ X1332 @ X1333 )
=> ( ~ ( in @ X1334 @ X1333 )
=> ~ ( in @ X1334 @ X1332 ) ) )
=> ( ! [X1335: $i,X1336: $i,X1337: $i] :
( ( in @ X1337 @ X1335 )
=> ( ~ ( in @ X1337 @ X1336 )
=> ~ ( subset @ X1335 @ X1336 ) ) )
=> ( ! [X1338: $i,X1339: $i] :
( ~ ( subset @ X1338 @ X1339 )
=> ( X1338 != X1339 ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i] :
( ( in @ X1342 @ X1340 )
=> ( ~ ( in @ X1342 @ X1341 )
=> ( X1340 != X1341 ) ) )
=> ( ! [X1343: $i] : ( subset @ X1343 @ X1343 )
=> ( ! [X1344: $i,X1345: $i,X1346: $i] :
( ( subset @ X1344 @ X1345 )
=> ( ( subset @ X1345 @ X1346 )
=> ( subset @ X1344 @ X1346 ) ) )
=> ( ! [X1347: $i,X1348: $i] : ( subset @ X1348 @ ( setadjoin @ X1347 @ X1348 ) )
=> ( ! [X1349: $i,X1350: $i,X1351: $i] :
( ( subset @ X1349 @ X1351 )
=> ( subset @ X1349 @ ( setadjoin @ X1350 @ X1351 ) ) )
=> ( ! [X1352: $i,X1353: $i] :
( ( subset @ X1352 @ X1353 )
=> ( in @ X1352 @ ( powerset @ X1353 ) ) )
=> ( ! [X1354: $i,X1355: $i] :
( ( subset @ X1354 @ X1355 )
=> ( ( subset @ X1355 @ X1354 )
=> ( X1354 = X1355 ) ) )
=> ( ! [X1356: $i] :
( ( subset @ X1356 @ emptyset )
=> ( X1356 = emptyset ) )
=> ( ! [X1357: $i,X1358: $i] :
( ( subset @ X1358 @ X1357 )
=> ( in @ X1358 @ ( powerset @ X1357 ) ) )
=> ( ! [X1359: $i,X1360: $i] :
( ( in @ X1360 @ ( powerset @ X1359 ) )
=> ( subset @ X1360 @ X1359 ) )
=> ( ! [X1361: $i] : ( in @ X1361 @ ( powerset @ X1361 ) )
=> ( ! [X1362: $i,X1363: $i] :
( ( subset @ X1362 @ X1363 )
=> ( subset @ ( powerset @ X1362 ) @ ( powerset @ X1363 ) ) )
=> ( ! [X1364: $i,X1365: $i > $o] : ( in @ ( dsetconstr @ X1364 @ X1365 ) @ ( powerset @ X1364 ) )
=> ( ! [X1366: $i,X1367: $i > $o] : ( subset @ ( dsetconstr @ X1366 @ X1367 ) @ X1366 )
=> ( ! [X1368: $i,X1369: $i,X1370: $i] :
( ( in @ X1370 @ X1368 )
=> ( in @ X1370 @ ( binunion @ X1368 @ X1369 ) ) )
=> ( ! [X1371: $i,X1372: $i] : ( in @ X1372 @ ( setadjoin @ X1371 @ ( setadjoin @ X1372 @ emptyset ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( in @ X1375 @ X1374 )
=> ( in @ X1375 @ ( binunion @ X1373 @ X1374 ) ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i,X1379: $o] :
( ( in @ X1378 @ ( binunion @ X1376 @ X1377 ) )
=> ( ( ( in @ X1378 @ X1376 )
=> X1379 )
=> ( ( ( in @ X1378 @ X1377 )
=> X1379 )
=> X1379 ) ) )
=> ( ! [X1380: $i,X1381: $i,X1382: $i] :
( ( in @ X1382 @ ( binunion @ X1380 @ X1381 ) )
=> ( ( in @ X1382 @ X1380 )
| ( in @ X1382 @ X1381 ) ) )
=> ( ! [X1383: $i,X1384: $i] : ( subset @ X1383 @ ( binunion @ X1383 @ X1384 ) )
=> ( ! [X1385: $i,X1386: $i] : ( subset @ X1386 @ ( binunion @ X1385 @ X1386 ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i] :
( ( in @ X1389 @ X1387 )
=> ( ( in @ X1389 @ X1388 )
=> ( in @ X1389 @ ( binintersect @ X1387 @ X1388 ) ) ) )
=> ( ! [X1390: $i,X1391: $i,X1392: $i] :
( ( subset @ X1392 @ X1390 )
=> ( ( subset @ X1392 @ X1391 )
=> ( subset @ X1392 @ ( binintersect @ X1390 @ X1391 ) ) ) )
=> ( ! [X1393: $i,X1394: $i,X1395: $i] :
( ( in @ X1395 @ ( binintersect @ X1393 @ X1394 ) )
=> ( in @ X1395 @ X1393 ) )
=> ( ! [X1396: $i,X1397: $i] : ( subset @ ( binintersect @ X1396 @ X1397 ) @ X1396 )
=> ( ! [X1398: $i,X1399: $i] :
( ( subset @ X1398 @ X1399 )
=> ( ( binintersect @ X1398 @ X1399 )
= X1398 ) )
=> ( ! [X1400: $i,X1401: $i] :
( ( ( binintersect @ X1400 @ X1401 )
= X1401 )
=> ( subset @ X1401 @ X1400 ) )
=> ( ! [X1402: $i,X1403: $i,X1404: $i] :
( ( in @ X1404 @ ( binintersect @ X1402 @ X1403 ) )
=> ( in @ X1404 @ X1403 ) )
=> ( ! [X1405: $i,X1406: $i] :
( ~ ? [X1407: $i] :
( ( in @ X1407 @ X1405 )
& ( in @ X1407 @ X1406 ) )
=> ( ( binintersect @ X1405 @ X1406 )
= emptyset ) )
=> ( ! [X1408: $i,X1409: $i] : ( subset @ ( binintersect @ X1408 @ X1409 ) @ X1409 )
=> ( ! [X1410: $i,X1411: $i] :
( ( subset @ X1411 @ X1410 )
=> ( ( binintersect @ X1410 @ X1411 )
= X1411 ) )
=> ( ! [X1412: $i,X1413: $i] :
( ( ( binintersect @ X1412 @ X1413 )
= X1412 )
=> ( subset @ X1412 @ X1413 ) )
=> ( ! [X1414: $i,X1415: $i,X1416: $i] :
( ( binintersect @ X1414 @ ( binunion @ X1415 @ X1416 ) )
= ( binunion @ ( binintersect @ X1414 @ X1415 ) @ ( binintersect @ X1414 @ X1416 ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( in @ X1419 @ X1417 )
=> ( ~ ( in @ X1419 @ X1418 )
=> ( in @ X1419 @ ( setminus @ X1417 @ X1418 ) ) ) )
=> ( ! [X1420: $i,X1421: $i,X1422: $i] :
( ( in @ X1422 @ ( setminus @ X1420 @ X1421 ) )
=> ( in @ X1422 @ X1420 ) )
=> ( ! [X1423: $i,X1424: $i,X1425: $i] :
( ( in @ X1425 @ ( setminus @ X1423 @ X1424 ) )
=> ~ ( in @ X1425 @ X1424 ) )
=> ( ! [X1426: $i,X1427: $i] :
( ( subset @ X1426 @ X1427 )
=> ( ( setminus @ X1426 @ X1427 )
= emptyset ) )
=> ( ! [X1428: $i,X1429: $i,X1430: $i] :
( ~ ( in @ X1430 @ ( setminus @ X1428 @ X1429 ) )
=> ( ( in @ X1430 @ X1428 )
=> ( in @ X1430 @ X1429 ) ) )
=> ( ! [X1431: $i,X1432: $i,X1433: $i] :
( ~ ( in @ X1433 @ ( setminus @ X1431 @ X1432 ) )
=> ( ~ ( in @ X1433 @ X1432 )
=> ~ ( in @ X1433 @ X1431 ) ) )
=> ( ! [X1434: $i,X1435: $i,X1436: $i] :
( ~ ( in @ X1436 @ X1434 )
=> ~ ( in @ X1436 @ ( setminus @ X1434 @ X1435 ) ) )
=> ( ! [X1437: $i,X1438: $i,X1439: $i] :
( ( in @ X1439 @ X1438 )
=> ~ ( in @ X1439 @ ( setminus @ X1437 @ X1438 ) ) )
=> ( ! [X1440: $i,X1441: $i] : ( subset @ ( setminus @ X1440 @ X1441 ) @ X1440 )
=> ( ! [X1442: $i,X1443: $i] :
( ( ( setminus @ X1442 @ X1443 )
= emptyset )
=> ( subset @ X1442 @ X1443 ) )
=> ( ! [X1444: $i,X1445: $i,X1446: $i] :
( ( in @ X1446 @ ( symdiff @ X1444 @ X1445 ) )
=> ! [X1447: $o] :
( ( ( in @ X1446 @ X1444 )
=> ( ~ ( in @ X1446 @ X1445 )
=> X1447 ) )
=> ( ( ~ ( in @ X1446 @ X1444 )
=> ( ( in @ X1446 @ X1445 )
=> X1447 ) )
=> X1447 ) ) )
=> ( ! [X1448: $i,X1449: $i,X1450: $i] :
( ( in @ X1450 @ X1448 )
=> ( ~ ( in @ X1450 @ X1449 )
=> ( in @ X1450 @ ( symdiff @ X1448 @ X1449 ) ) ) )
=> ( ! [X1451: $i,X1452: $i,X1453: $i] :
( ~ ( in @ X1453 @ X1451 )
=> ( ( in @ X1453 @ X1452 )
=> ( in @ X1453 @ ( symdiff @ X1451 @ X1452 ) ) ) )
=> ( ! [X1454: $i,X1455: $i,X1456: $i] :
( ( in @ X1456 @ X1454 )
=> ( ( in @ X1456 @ X1455 )
=> ~ ( in @ X1456 @ ( symdiff @ X1454 @ X1455 ) ) ) )
=> ( ! [X1457: $i,X1458: $i,X1459: $i] :
( ~ ( in @ X1459 @ X1457 )
=> ( ~ ( in @ X1459 @ X1458 )
=> ~ ( in @ X1459 @ ( symdiff @ X1457 @ X1458 ) ) ) )
=> ( ! [X1460: $i,X1461: $i] : ( in @ X1461 @ ( setadjoin @ X1460 @ ( setadjoin @ X1461 @ emptyset ) ) )
=> ( ! [X1462: $i,X1463: $i] : ( in @ X1462 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1462 @ ( setadjoin @ X1463 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1464: $i,X1465: $i] : ( in @ X1465 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1464 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1464 @ ( setadjoin @ X1465 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1466: $i,X1467: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1466 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1466 @ ( setadjoin @ X1467 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1468: $i,X1469: $i] : ( iskpair @ ( kpair @ X1468 @ X1469 ) )
=> ( ! [X1470: $i,X1471: $i] :
( ( in @ X1471 @ X1470 )
=> ( subset @ ( setadjoin @ X1471 @ emptyset ) @ X1470 ) )
=> ( ! [X1472: $i,X1473: $i] :
( ( in @ X1473 @ X1472 )
=> ( in @ ( setadjoin @ X1473 @ emptyset ) @ ( powerset @ X1472 ) ) )
=> ( ! [X1474: $i,X1475: $i,X1476: $i] :
( ( in @ X1476 @ X1474 )
=> ( in @ ( setadjoin @ X1476 @ emptyset ) @ ( powerset @ ( binunion @ X1474 @ X1475 ) ) ) )
=> ( ! [X1477: $i,X1478: $i,X1479: $i] :
( ( in @ X1479 @ ( setadjoin @ X1477 @ ( setadjoin @ X1478 @ emptyset ) ) )
=> ( ( X1479 = X1477 )
| ( X1479 = X1478 ) ) )
=> ( ! [X1480: $i,X1481: $i,X1482: $i] :
( ( in @ X1482 @ X1480 )
=> ! [X1483: $i] :
( ( in @ X1483 @ X1481 )
=> ( subset @ ( setadjoin @ X1482 @ ( setadjoin @ X1483 @ emptyset ) ) @ ( binunion @ X1480 @ X1481 ) ) ) )
=> ( ! [X1484: $i,X1485: $i,X1486: $i] :
( ( in @ X1486 @ X1484 )
=> ! [X1487: $i] :
( ( in @ X1487 @ X1485 )
=> ( in @ ( setadjoin @ X1486 @ ( setadjoin @ X1487 @ emptyset ) ) @ ( powerset @ ( binunion @ X1484 @ X1485 ) ) ) ) )
=> ( ! [X1488: $i,X1489: $i,X1490: $i] :
( ( in @ X1490 @ X1488 )
=> ! [X1491: $i] :
( ( in @ X1491 @ X1489 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1490 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1490 @ ( setadjoin @ X1491 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1488 @ X1489 ) ) ) ) )
=> ( ! [X1492: $i,X1493: $i,X1494: $i] :
( ( in @ X1494 @ X1492 )
=> ! [X1495: $i] :
( ( in @ X1495 @ X1493 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1494 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1494 @ ( setadjoin @ X1495 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1492 @ X1493 ) ) ) ) ) )
=> ( ! [X1496: $i,X1497: $i,X1498: $i] :
( ( in @ X1498 @ X1496 )
=> ! [X1499: $i] :
( ( in @ X1499 @ X1497 )
=> ( in @ ( kpair @ X1498 @ X1499 ) @ ( powerset @ ( powerset @ ( binunion @ X1496 @ X1497 ) ) ) ) ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i] :
( ( in @ X1502 @ X1500 )
=> ! [X1503: $i] :
( ( in @ X1503 @ X1501 )
=> ( in @ ( kpair @ X1502 @ X1503 ) @ ( cartprod @ X1500 @ X1501 ) ) ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i] :
( ( in @ X1506 @ ( cartprod @ X1504 @ X1505 ) )
=> ? [X1507: $i] :
( ( in @ X1507 @ X1504 )
& ? [X1508: $i] :
( ( in @ X1508 @ X1505 )
& ( X1506
= ( kpair @ X1507 @ X1508 ) ) ) ) )
=> ( ! [X1509: $i,X1510: $i,X1511: $i] :
( ( in @ X1511 @ ( cartprod @ X1509 @ X1510 ) )
=> ( iskpair @ X1511 ) )
=> ( ! [X1512: $i,X1513: $i] :
( ( in @ X1513 @ ( setunion @ X1512 ) )
=> ? [X1514: $i] :
( ( in @ X1514 @ X1512 )
& ( in @ X1513 @ X1514 ) ) )
=> ( ! [X1515: $i] : ( subset @ ( setunion @ ( setadjoin @ X1515 @ emptyset ) ) @ X1515 )
=> ( ! [X1516: $i] : ( subset @ X1516 @ ( setunion @ ( setadjoin @ X1516 @ emptyset ) ) )
=> ( ! [X1517: $i] :
( ( setunion @ ( setadjoin @ X1517 @ emptyset ) )
= X1517 )
=> ( ! [X1518: $i,X1519: $i > $o] :
( ! [X1520: $i] :
( ( in @ X1520 @ X1518 )
=> ! [X1521: $i] :
( ( in @ X1521 @ X1518 )
=> ( ( X1519 @ X1520 )
=> ( ( X1519 @ X1521 )
=> ( X1520 = X1521 ) ) ) ) )
=> ( ? [X1522: $i] :
( ( in @ X1522 @ X1518 )
& ( X1519 @ X1522 ) )
=> ( singleton @ ( dsetconstr @ X1518 @ X1519 ) ) ) )
=> ( ! [X1523: $i,X1524: $i > $o] :
( ( ex1 @ X1523 @ X1524 )
=> ? [X1525: $i] :
( ( in @ X1525 @ X1523 )
& ( X1524 @ X1525 ) ) )
=> ( ! [X1526: $i,X1527: $i > $o,X1528: $i] :
( ( in @ X1528 @ X1526 )
=> ( ( X1527 @ X1528 )
=> ( ! [X1529: $i] :
( ( in @ X1529 @ X1526 )
=> ( ( X1527 @ X1529 )
=> ( X1529 = X1528 ) ) )
=> ( ex1 @ X1526 @ X1527 ) ) ) )
=> ( ! [X1530: $i,X1531: $i > $o] :
( ! [X1532: $i] :
( ( in @ X1532 @ X1530 )
=> ! [X1533: $i] :
( ( in @ X1533 @ X1530 )
=> ( ( X1531 @ X1532 )
=> ( ( X1531 @ X1533 )
=> ( X1532 = X1533 ) ) ) ) )
=> ( ? [X1534: $i] :
( ( in @ X1534 @ X1530 )
& ( X1531 @ X1534 ) )
=> ( ex1 @ X1530 @ X1531 ) ) )
=> ( ! [X1535: $i,X1536: $i] :
( ( ( setadjoin @ X1535 @ emptyset )
= ( setadjoin @ X1536 @ emptyset ) )
=> ( X1535 = X1536 ) )
=> ( ! [X1537: $i,X1538: $i,X1539: $i] :
( ( in @ ( setadjoin @ X1539 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1537 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1537 @ ( setadjoin @ X1538 @ emptyset ) ) @ emptyset ) ) )
=> ( X1537 = X1539 ) )
=> ( ! [X1540: $i] :
( ( iskpair @ X1540 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1540 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1540 ) ) ) )
=> ( ! [X1541: $i] :
( ( singleton @ X1541 )
=> ( in @ ( setunion @ X1541 ) @ X1541 ) )
=> ( ! [X1542: $i,X1543: $i] :
( ( kfst @ ( kpair @ X1542 @ X1543 ) )
= X1542 )
=> ( ! [X1544: $i,X1545: $i,X1546: $i] :
( ( in @ X1546 @ ( cartprod @ X1544 @ X1545 ) )
=> ( in @ ( kfst @ X1546 ) @ X1544 ) )
=> ( ! [X1547: $i,X1548: $i,X1549: $i,X1550: $i] :
( ( ( setadjoin @ ( setadjoin @ X1547 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1547 @ ( setadjoin @ X1548 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1549 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1549 @ ( setadjoin @ X1550 @ emptyset ) ) @ emptyset ) ) )
=> ( X1547 = X1549 ) )
=> ( ! [X1551: $i,X1552: $i,X1553: $i,X1554: $i] :
( ( ( kpair @ X1551 @ X1552 )
= ( kpair @ X1553 @ X1554 ) )
=> ( X1551 = X1553 ) )
=> ( ! [X1555: $i,X1556: $i] :
( ( X1555 = X1556 )
=> ( ( setadjoin @ X1555 @ ( setadjoin @ X1556 @ emptyset ) )
= ( setadjoin @ X1555 @ emptyset ) ) )
=> ( ! [X1557: $i,X1558: $i] :
( ( X1557 = X1558 )
=> ( ( setadjoin @ ( setadjoin @ X1557 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1557 @ ( setadjoin @ X1558 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1557 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1559: $i,X1560: $i,X1561: $i,X1562: $i] :
( ( ( setadjoin @ ( setadjoin @ X1559 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1559 @ ( setadjoin @ X1560 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1561 @ ( setadjoin @ X1562 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1561 = X1562 )
=> ( X1560 = X1562 ) ) )
=> ( ! [X1563: $i,X1564: $i,X1565: $i] :
( ( ( setadjoin @ X1563 @ ( setadjoin @ X1564 @ emptyset ) )
= ( setadjoin @ X1565 @ emptyset ) )
=> ( X1563 = X1564 ) )
=> ( ! [X1566: $i,X1567: $i,X1568: $i,X1569: $i] :
( ( ( setadjoin @ ( setadjoin @ X1566 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1566 @ ( setadjoin @ X1567 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1568 @ ( setadjoin @ X1569 @ emptyset ) ) @ emptyset ) ) )
=> ( X1567 = X1569 ) )
=> ( ! [X1570: $i,X1571: $i,X1572: $i,X1573: $i] :
( ( ( kpair @ X1570 @ X1571 )
= ( kpair @ X1572 @ X1573 ) )
=> ( X1571 = X1573 ) )
=> ( ! [X1574: $i] :
( ( iskpair @ X1574 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1574 )
@ ^ [Z0: $i] :
( X1574
= ( kpair @ ( kfst @ X1574 ) @ Z0 ) ) ) ) )
=> ( ! [X1575: $i,X1576: $i] :
( ( ksnd @ ( kpair @ X1575 @ X1576 ) )
= X1576 )
=> ( ! [X1577: $i] :
( ( iskpair @ X1577 )
=> ( ( kpair @ ( kfst @ X1577 ) @ ( ksnd @ X1577 ) )
= X1577 ) )
=> ( ! [X1578: $i,X1579: $i,X1580: $i] :
( ( in @ X1580 @ ( cartprod @ X1578 @ X1579 ) )
=> ( in @ ( ksnd @ X1580 ) @ X1579 ) )
=> ( ! [X1581: $i,X1582: $i,X1583: $i,X1584: $i] :
( ( in @ ( kpair @ X1583 @ X1584 ) @ ( cartprod @ X1581 @ X1582 ) )
=> ( in @ X1583 @ X1581 ) )
=> ( ! [X1585: $i,X1586: $i,X1587: $i,X1588: $i] :
( ( in @ ( kpair @ X1587 @ X1588 ) @ ( cartprod @ X1585 @ X1586 ) )
=> ( in @ X1588 @ X1586 ) )
=> ( ! [X1589: $i,X1590: $i,X1591: $i] :
( ( in @ X1591 @ X1589 )
=> ! [X1592: $i] :
( ( in @ X1592 @ X1590 )
=> ( ( kpair @ X1591 @ X1592 )
= ( kpair @ X1591 @ X1592 ) ) ) )
=> ( ! [X1593: $i,X1594: $i,X1595: $i] :
( ( in @ X1595 @ X1593 )
=> ! [X1596: $i] :
( ( in @ X1596 @ X1594 )
=> ( ( kfst @ ( kpair @ X1595 @ X1596 ) )
= X1595 ) ) )
=> ( ! [X1597: $i,X1598: $i,X1599: $i] :
( ( in @ X1599 @ X1597 )
=> ! [X1600: $i] :
( ( in @ X1600 @ X1598 )
=> ( ( ksnd @ ( kpair @ X1599 @ X1600 ) )
= X1600 ) ) )
=> ( ! [X1601: $i,X1602: $i,X1603: $i] :
( ( in @ X1603 @ ( cartprod @ X1601 @ X1602 ) )
=> ( ( kpair @ ( kfst @ X1603 ) @ ( ksnd @ X1603 ) )
= X1603 ) )
=> ( ! [X1604: $i,X1605: $i,X1606: $i > $i > $o,X1607: $i] :
( ( in @ X1607 @ X1604 )
=> ! [X1608: $i] :
( ( in @ X1608 @ X1605 )
=> ( ( X1606 @ X1607 @ X1608 )
=> ( in @ ( kpair @ X1607 @ X1608 ) @ ( dpsetconstr @ X1604 @ X1605 @ X1606 ) ) ) ) )
=> ( ! [X1609: $i,X1610: $i,X1611: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1609 @ X1610 @ X1611 ) @ ( cartprod @ X1609 @ X1610 ) )
=> ( ! [X1612: $i,X1613: $i,X1614: $i > $i > $o] : ( breln @ X1612 @ X1613 @ ( dpsetconstr @ X1612 @ X1613 @ X1614 ) )
=> ( ! [X1615: $i,X1616: $i,X1617: $i > $i > $o,X1618: $i] :
( ( in @ X1618 @ X1615 )
=> ! [X1619: $i] :
( ( in @ X1619 @ X1616 )
=> ( ( in @ ( kpair @ X1618 @ X1619 ) @ ( dpsetconstr @ X1615 @ X1616 @ X1617 ) )
=> ( X1617 @ X1618 @ X1619 ) ) ) )
=> ( ! [X1620: $i,X1621: $i,X1622: $i > $i > $o,X1623: $i,X1624: $i] :
( ( in @ ( kpair @ X1623 @ X1624 ) @ ( dpsetconstr @ X1620 @ X1621 @ X1622 ) )
=> ( in @ X1623 @ X1620 ) )
=> ( ! [X1625: $i,X1626: $i,X1627: $i > $i > $o,X1628: $i,X1629: $i] :
( ( in @ ( kpair @ X1628 @ X1629 ) @ ( dpsetconstr @ X1625 @ X1626 @ X1627 ) )
=> ( in @ X1629 @ X1626 ) )
=> ( ! [X1630: $i,X1631: $i,X1632: $i > $i > $o,X1633: $i,X1634: $i] :
( ( in @ ( kpair @ X1633 @ X1634 ) @ ( dpsetconstr @ X1630 @ X1631 @ X1632 ) )
=> ( X1632 @ X1633 @ X1634 ) )
=> ( ! [X1635: $i,X1636: $i,X1637: $i] :
( ( func @ X1635 @ X1636 @ X1637 )
=> ! [X1638: $i] :
( ( in @ X1638 @ X1635 )
=> ( singleton
@ ( dsetconstr @ X1636
@ ^ [Z0: $i] : ( in @ ( kpair @ X1638 @ Z0 ) @ X1637 ) ) ) ) )
=> ( ! [X1639: $i,X1640: $i,X1641: $i] :
( ( func @ X1639 @ X1640 @ X1641 )
=> ! [X1642: $i] :
( ( in @ X1642 @ X1639 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1640
@ ^ [Z0: $i] : ( in @ ( kpair @ X1642 @ Z0 ) @ X1641 ) ) )
@ X1640 ) ) )
=> ( ! [X1643: $i,X1644: $i,X1645: $i] :
( ( func @ X1643 @ X1644 @ X1645 )
=> ! [X1646: $i] :
( ( in @ X1646 @ X1643 )
=> ( in @ ( ap @ X1643 @ X1644 @ X1645 @ X1646 ) @ X1644 ) ) )
=> ( ! [X1647: $i,X1648: $i,X1649: $i] :
( ( in @ X1649 @ ( funcSet @ X1647 @ X1648 ) )
=> ( func @ X1647 @ X1648 @ X1649 ) )
=> ( ! [X1650: $i,X1651: $i,X1652: $i] :
( ( in @ X1652 @ ( funcSet @ X1650 @ X1651 ) )
=> ! [X1653: $i] :
( ( in @ X1653 @ X1650 )
=> ( in @ ( ap @ X1650 @ X1651 @ X1652 @ X1653 ) @ X1651 ) ) )
=> ( ! [X1654: $i,X1655: $i,X1656: $i] :
( ( func @ X1654 @ X1655 @ X1656 )
=> ( in @ X1656 @ ( funcSet @ X1654 @ X1655 ) ) )
=> ( ! [X1657: $i,X1658: $i,X1659: $i > $i] :
( ! [X1660: $i] :
( ( in @ X1660 @ X1657 )
=> ( in @ ( X1659 @ X1660 ) @ X1658 ) )
=> ( func @ X1657 @ X1658
@ ( dpsetconstr @ X1657 @ X1658
@ ^ [Z0: $i] : ( $eq @ ( X1659 @ Z0 ) ) ) ) )
=> ( ! [X1661: $i,X1662: $i,X1663: $i > $i] :
( ! [X1664: $i] :
( ( in @ X1664 @ X1661 )
=> ( in @ ( X1663 @ X1664 ) @ X1662 ) )
=> ( func @ X1661 @ X1662 @ ( lam @ X1661 @ X1662 @ X1663 ) ) )
=> ( ! [X1665: $i,X1666: $i,X1667: $i > $i] :
( ! [X1668: $i] :
( ( in @ X1668 @ X1665 )
=> ( in @ ( X1667 @ X1668 ) @ X1666 ) )
=> ( in @ ( lam @ X1665 @ X1666 @ X1667 ) @ ( funcSet @ X1665 @ X1666 ) ) )
=> ( ! [X1669: $i,X1670: $i,X1671: $i] :
( ( breln @ X1669 @ X1670 @ X1671 )
=> ! [X1672: $i > $o] :
( ! [X1673: $i] :
( ( in @ X1673 @ X1669 )
=> ! [X1674: $i] :
( ( in @ X1674 @ X1670 )
=> ( ( in @ ( kpair @ X1673 @ X1674 ) @ X1671 )
=> ( X1672 @ ( kpair @ X1673 @ X1674 ) ) ) ) )
=> ! [X1675: $i] :
( ( in @ X1675 @ X1671 )
=> ( X1672 @ X1675 ) ) ) )
=> ( ! [X1676: $i,X1677: $i,X1678: $i] :
( ( breln @ X1676 @ X1677 @ X1678 )
=> ! [X1679: $i > $o] :
( ! [X1680: $i] :
( ( in @ X1680 @ X1676 )
=> ! [X1681: $i] :
( ( in @ X1681 @ X1677 )
=> ( ( in @ ( kpair @ X1680 @ X1681 ) @ X1678 )
=> ( X1679 @ ( kpair @ X1680 @ X1681 ) ) ) ) )
=> ! [X1682: $i] :
( ( in @ X1682 @ X1678 )
=> ( X1679 @ X1682 ) ) ) )
=> ( ! [X1683: $i,X1684: $i > $o] :
( ( ex1 @ X1683 @ X1684 )
=> ! [X1685: $i] :
( ( in @ X1685 @ X1683 )
=> ! [X1686: $i] :
( ( in @ X1686 @ X1683 )
=> ( ( X1684 @ X1685 )
=> ( ( X1684 @ X1686 )
=> ( X1685 = X1686 ) ) ) ) ) )
=> ( ! [X1687: $i,X1688: $i,X1689: $i] :
( ( func @ X1687 @ X1688 @ X1689 )
=> ! [X1690: $i] :
( ( in @ X1690 @ X1687 )
=> ( in @ ( kpair @ X1690 @ ( ap @ X1687 @ X1688 @ X1689 @ X1690 ) ) @ X1689 ) ) )
=> ( ! [X1691: $i,X1692: $i,X1693: $i] :
( ( in @ X1693 @ ( funcSet @ X1691 @ X1692 ) )
=> ! [X1694: $i] :
( ( in @ X1694 @ X1691 )
=> ( in @ ( kpair @ X1694 @ ( ap @ X1691 @ X1692 @ X1693 @ X1694 ) ) @ X1693 ) ) )
=> ( ! [X1695: $i,X1696: $i,X1697: $i] :
( ( func @ X1695 @ X1696 @ X1697 )
=> ! [X1698: $i] :
( ( in @ X1698 @ X1695 )
=> ! [X1699: $i] :
( ( in @ X1699 @ X1696 )
=> ( ( in @ ( kpair @ X1698 @ X1699 ) @ X1697 )
=> ( ( ap @ X1695 @ X1696 @ X1697 @ X1698 )
= X1699 ) ) ) ) )
=> ( ! [X1700: $i,X1701: $i,X1702: $i] :
( ( func @ X1700 @ X1701 @ X1702 )
=> ! [X1703: $i] :
( ( func @ X1700 @ X1701 @ X1703 )
=> ( ! [X1704: $i] :
( ( in @ X1704 @ X1700 )
=> ( ( ap @ X1700 @ X1701 @ X1702 @ X1704 )
= ( ap @ X1700 @ X1701 @ X1703 @ X1704 ) ) )
=> ! [X1705: $i] :
( ( in @ X1705 @ X1700 )
=> ! [X1706: $i] :
( ( in @ X1706 @ X1701 )
=> ( ( in @ ( kpair @ X1705 @ X1706 ) @ X1703 )
=> ( in @ ( kpair @ X1705 @ X1706 ) @ X1702 ) ) ) ) ) ) )
=> ( ! [X1707: $i,X1708: $i,X1709: $i] :
( ( in @ X1709 @ ( funcSet @ X1707 @ X1708 ) )
=> ! [X1710: $i] :
( ( in @ X1710 @ X1707 )
=> ! [X1711: $i] :
( ( in @ X1711 @ X1708 )
=> ( ( in @ ( kpair @ X1710 @ X1711 ) @ X1709 )
=> ( ( ap @ X1707 @ X1708 @ X1709 @ X1710 )
= X1711 ) ) ) ) )
=> ( ! [X1712: $i,X1713: $i,X1714: $i] :
( ( breln @ X1712 @ X1713 @ X1714 )
=> ! [X1715: $i] :
( ( breln @ X1712 @ X1713 @ X1715 )
=> ( ! [X1716: $i] :
( ( in @ X1716 @ X1712 )
=> ! [X1717: $i] :
( ( in @ X1717 @ X1713 )
=> ( ( in @ ( kpair @ X1716 @ X1717 ) @ X1714 )
=> ( in @ ( kpair @ X1716 @ X1717 ) @ X1715 ) ) ) )
=> ( subset @ X1714 @ X1715 ) ) ) )
=> ( ! [X1718: $i,X1719: $i,X1720: $i] :
( ( breln @ X1718 @ X1719 @ X1720 )
=> ! [X1721: $i] :
( ( breln @ X1718 @ X1719 @ X1721 )
=> ( ! [X1722: $i] :
( ( in @ X1722 @ X1718 )
=> ! [X1723: $i] :
( ( in @ X1723 @ X1719 )
=> ( ( in @ ( kpair @ X1722 @ X1723 ) @ X1720 )
=> ( in @ ( kpair @ X1722 @ X1723 ) @ X1721 ) ) ) )
=> ( ! [X1724: $i] :
( ( in @ X1724 @ X1718 )
=> ! [X1725: $i] :
( ( in @ X1725 @ X1719 )
=> ( ( in @ ( kpair @ X1724 @ X1725 ) @ X1721 )
=> ( in @ ( kpair @ X1724 @ X1725 ) @ X1720 ) ) ) )
=> ( X1720 = X1721 ) ) ) ) )
=> ( ! [X1726: $i,X1727: $i,X1728: $i] :
( ( func @ X1726 @ X1727 @ X1728 )
=> ! [X1729: $i] :
( ( func @ X1726 @ X1727 @ X1729 )
=> ( ! [X1730: $i] :
( ( in @ X1730 @ X1726 )
=> ( ( ap @ X1726 @ X1727 @ X1728 @ X1730 )
= ( ap @ X1726 @ X1727 @ X1729 @ X1730 ) ) )
=> ( X1728 = X1729 ) ) ) )
=> ( ! [X1731: $i,X1732: $i,X1733: $i] :
( ( in @ X1733 @ ( funcSet @ X1731 @ X1732 ) )
=> ! [X1734: $i] :
( ( in @ X1734 @ ( funcSet @ X1731 @ X1732 ) )
=> ( ! [X1735: $i] :
( ( in @ X1735 @ X1731 )
=> ( ( ap @ X1731 @ X1732 @ X1733 @ X1735 )
= ( ap @ X1731 @ X1732 @ X1734 @ X1735 ) ) )
=> ( X1733 = X1734 ) ) ) )
=> ( ! [X1736: $i,X1737: $i,X1738: $i] :
( ( in @ X1738 @ ( funcSet @ X1736 @ X1737 ) )
=> ! [X1739: $i] :
( ( in @ X1739 @ X1736 )
=> ( ( ap @ X1736 @ X1737 @ X1738 @ X1739 )
= ( ap @ X1736 @ X1737 @ X1738 @ X1739 ) ) ) )
=> ( ! [X1740: $i,X1741: $i,X1742: $i] :
( ( func @ X1740 @ X1741 @ X1742 )
=> ! [X1743: $i] :
( ( in @ X1743 @ X1740 )
=> ( ( ap @ X1740 @ X1741 @ X1742 @ X1743 )
= ( ap @ X1740 @ X1741 @ X1742 @ X1743 ) ) ) )
=> ( ! [X1744: $i,X1745: $i,X1746: $i > $i] :
( ! [X1747: $i] :
( ( in @ X1747 @ X1744 )
=> ( in @ ( X1746 @ X1747 ) @ X1745 ) )
=> ! [X1748: $i] :
( ( in @ X1748 @ X1744 )
=> ( ( ap @ X1744 @ X1745 @ ( lam @ X1744 @ X1745 @ X1746 ) @ X1748 )
= ( X1746 @ X1748 ) ) ) )
=> ( ! [X1749: $i,X1750: $i,X1751: $i] :
( ( func @ X1749 @ X1750 @ X1751 )
=> ( ( lam @ X1749 @ X1750 @ ( ap @ X1749 @ X1750 @ X1751 ) )
= X1751 ) )
=> ( ! [X1752: $i,X1753: $i,X1754: $i > $i] :
( ! [X1755: $i] :
( ( in @ X1755 @ X1752 )
=> ( in @ ( X1754 @ X1755 ) @ X1753 ) )
=> ( ( lam @ X1752 @ X1753 @ X1754 )
= ( lam @ X1752 @ X1753 @ X1754 ) ) )
=> ( ! [X1756: $i,X1757: $i,X1758: $i > $i] :
( ! [X1759: $i] :
( ( in @ X1759 @ X1756 )
=> ( in @ ( X1758 @ X1759 ) @ X1757 ) )
=> ! [X1760: $i] :
( ( in @ X1760 @ X1756 )
=> ( ( ap @ X1756 @ X1757 @ ( lam @ X1756 @ X1757 @ X1758 ) @ X1760 )
= ( X1758 @ X1760 ) ) ) )
=> ( ! [X1761: $i,X1762: $i,X1763: $i] :
( ( in @ X1763 @ ( funcSet @ X1761 @ X1762 ) )
=> ( ( lam @ X1761 @ X1762 @ ( ap @ X1761 @ X1762 @ X1763 ) )
= X1763 ) )
=> ( ! [X1764: $i,X1765: $o,X1766: $i] :
( ( in @ X1766 @ X1764 )
=> ! [X1767: $i] :
( ( in @ X1767 @ X1764 )
=> ( ~ X1765
=> ( in @ X1767
@ ( dsetconstr @ X1764
@ ^ [Z0: $i] :
( ( X1765
& ( Z0 = X1766 ) )
| ( ~ X1765
& ( Z0 = X1767 ) ) ) ) ) ) ) )
=> ( ! [X1768: $i,X1769: $o,X1770: $i] :
( ( in @ X1770 @ X1768 )
=> ! [X1771: $i] :
( ( in @ X1771 @ X1768 )
=> ( ~ X1769
=> ( ( dsetconstr @ X1768
@ ^ [Z0: $i] :
( ( X1769
& ( Z0 = X1770 ) )
| ( ~ X1769
& ( Z0 = X1771 ) ) ) )
= ( setadjoin @ X1771 @ emptyset ) ) ) ) )
=> ( ! [X1772: $i,X1773: $o,X1774: $i] :
( ( in @ X1774 @ X1772 )
=> ! [X1775: $i] :
( ( in @ X1775 @ X1772 )
=> ( X1773
=> ( in @ X1774
@ ( dsetconstr @ X1772
@ ^ [Z0: $i] :
( ( X1773
& ( Z0 = X1774 ) )
| ( ~ X1773
& ( Z0 = X1775 ) ) ) ) ) ) ) )
=> ( ! [X1776: $i,X1777: $o,X1778: $i] :
( ( in @ X1778 @ X1776 )
=> ! [X1779: $i] :
( ( in @ X1779 @ X1776 )
=> ( X1777
=> ( ( dsetconstr @ X1776
@ ^ [Z0: $i] :
( ( X1777
& ( Z0 = X1778 ) )
| ( ~ X1777
& ( Z0 = X1779 ) ) ) )
= ( setadjoin @ X1778 @ emptyset ) ) ) ) )
=> ( ! [X1780: $i,X1781: $o,X1782: $i] :
( ( in @ X1782 @ X1780 )
=> ! [X1783: $i] :
( ( in @ X1783 @ X1780 )
=> ( singleton
@ ( dsetconstr @ X1780
@ ^ [Z0: $i] :
( ( X1781
& ( Z0 = X1782 ) )
| ( ~ X1781
& ( Z0 = X1783 ) ) ) ) ) ) )
=> ( ! [X1784: $i,X1785: $o,X1786: $i] :
( ( in @ X1786 @ X1784 )
=> ! [X1787: $i] :
( ( in @ X1787 @ X1784 )
=> ( in @ ( if @ X1784 @ X1785 @ X1786 @ X1787 ) @ X1784 ) ) )
=> ( ! [X1788: $i] :
( ( singleton @ X1788 )
=> ! [X1789: $i] :
( ( in @ X1789 @ X1788 )
=> ( ( setunion @ X1788 )
= X1789 ) ) )
=> ( ! [X1790: $i,X1791: $o,X1792: $i] :
( ( in @ X1792 @ X1790 )
=> ! [X1793: $i] :
( ( in @ X1793 @ X1790 )
=> ( X1791
=> ( ( if @ X1790 @ X1791 @ X1792 @ X1793 )
= X1792 ) ) ) )
=> ( ! [X1794: $i,X1795: $o,X1796: $i] :
( ( in @ X1796 @ X1794 )
=> ! [X1797: $i] :
( ( in @ X1797 @ X1794 )
=> ( ~ X1795
=> ( ( if @ X1794 @ X1795 @ X1796 @ X1797 )
= X1797 ) ) ) )
=> ( ! [X1798: $i,X1799: $o,X1800: $i] :
( ( in @ X1800 @ X1798 )
=> ! [X1801: $i] :
( ( in @ X1801 @ X1798 )
=> ( in @ ( if @ X1798 @ X1799 @ X1800 @ X1801 ) @ ( setadjoin @ X1800 @ ( setadjoin @ X1801 @ emptyset ) ) ) ) )
=> ( ! [X1802: $i,X1803: $i] :
( ( in @ X1803 @ ( powerset @ X1802 ) )
=> ! [X1804: $i] :
( ( in @ X1804 @ ( powerset @ X1802 ) )
=> ( in @ ( binintersect @ X1803 @ X1804 ) @ ( powerset @ X1802 ) ) ) )
=> ( ! [X1805: $i,X1806: $i] :
( ( in @ X1806 @ ( powerset @ X1805 ) )
=> ! [X1807: $i] :
( ( in @ X1807 @ ( powerset @ X1805 ) )
=> ( in @ ( binunion @ X1806 @ X1807 ) @ ( powerset @ X1805 ) ) ) )
=> ( ! [X1808: $i,X1809: $i] :
( ( in @ X1809 @ ( powerset @ X1808 ) )
=> ( in @ ( powerset @ X1809 ) @ ( powerset @ ( powerset @ X1808 ) ) ) )
=> ( ! [X1810: $i,X1811: $i] :
( ( in @ X1811 @ ( powerset @ X1810 ) )
=> ! [X1812: $i] :
( ( in @ X1812 @ ( powerset @ X1810 ) )
=> ( in @ ( setminus @ X1811 @ X1812 ) @ ( powerset @ X1810 ) ) ) )
=> ( ! [X1813: $i,X1814: $i] :
( ( in @ X1814 @ ( powerset @ X1813 ) )
=> ( in @ ( setminus @ X1813 @ X1814 ) @ ( powerset @ X1813 ) ) )
=> ( ! [X1815: $i,X1816: $i] :
( ( in @ X1816 @ ( powerset @ X1815 ) )
=> ! [X1817: $i] :
( ( in @ X1817 @ ( powerset @ X1815 ) )
=> ( ! [X1818: $i] :
( ( in @ X1818 @ X1815 )
=> ( ( in @ X1818 @ X1816 )
=> ( in @ X1818 @ X1817 ) ) )
=> ( ! [X1819: $i] :
( ( in @ X1819 @ X1815 )
=> ( ( in @ X1819 @ X1817 )
=> ( in @ X1819 @ X1816 ) ) )
=> ( X1816 = X1817 ) ) ) ) )
=> ( ! [X1820: $i,X1821: $i] :
( ( in @ X1821 @ ( powerset @ X1820 ) )
=> ! [X1822: $i] :
( ( in @ X1822 @ ( powerset @ X1820 ) )
=> ( ! [X1823: $i] :
( ( in @ X1823 @ X1820 )
=> ( ( in @ X1823 @ X1821 )
=> ( in @ X1823 @ X1822 ) ) )
=> ( subset @ X1821 @ X1822 ) ) ) )
=> ( ! [X1824: $i,X1825: $i] :
( ( in @ X1825 @ ( powerset @ X1824 ) )
=> ! [X1826: $i] :
( ( in @ X1826 @ ( powerset @ X1824 ) )
=> ( ! [X1827: $i] :
( ( in @ X1827 @ X1824 )
=> ( ( in @ X1827 @ X1825 )
=> ( in @ X1827 @ X1826 ) ) )
=> ( in @ X1825 @ ( powerset @ X1826 ) ) ) ) )
=> ( ! [X1828: $i,X1829: $i] :
( ( in @ X1829 @ ( powerset @ X1828 ) )
=> ! [X1830: $i] :
( ( in @ X1830 @ ( powerset @ X1828 ) )
=> ! [X1831: $i] :
( ( in @ X1831 @ X1828 )
=> ( ( in @ X1829 @ ( powerset @ X1830 ) )
=> ( ( in @ X1831 @ X1829 )
=> ( in @ X1831 @ X1830 ) ) ) ) ) )
=> ( ! [X1832: $i,X1833: $i] :
( ( in @ X1833 @ ( powerset @ X1832 ) )
=> ! [X1834: $i] :
( ( in @ X1834 @ X1832 )
=> ( ( in @ X1834 @ X1833 )
=> ~ ( in @ X1834 @ ( setminus @ X1832 @ X1833 ) ) ) ) )
=> ( ! [X1835: $i,X1836: $i] :
( ( in @ X1836 @ ( powerset @ X1835 ) )
=> ! [X1837: $i] :
( ( in @ X1837 @ X1835 )
=> ( ~ ( in @ X1837 @ ( setminus @ X1835 @ X1836 ) )
=> ( in @ X1837 @ X1836 ) ) ) )
=> ( ! [X1838: $i,X1839: $i] :
( ( in @ X1839 @ ( powerset @ X1838 ) )
=> ! [X1840: $i] :
( ( in @ X1840 @ ( powerset @ X1838 ) )
=> ! [X1841: $i] :
( ( in @ X1841 @ X1838 )
=> ( ~ ( in @ X1841 @ X1839 )
=> ~ ( in @ X1841 @ ( binintersect @ X1839 @ X1840 ) ) ) ) ) )
=> ( ! [X1842: $i,X1843: $i] :
( ( in @ X1843 @ ( powerset @ X1842 ) )
=> ! [X1844: $i] :
( ( in @ X1844 @ ( powerset @ X1842 ) )
=> ! [X1845: $i] :
( ( in @ X1845 @ X1842 )
=> ( ~ ( in @ X1845 @ X1844 )
=> ~ ( in @ X1845 @ ( binintersect @ X1843 @ X1844 ) ) ) ) ) )
=> ( ! [X1846: $i,X1847: $i] :
( ( in @ X1847 @ ( powerset @ X1846 ) )
=> ! [X1848: $i] :
( ( in @ X1848 @ ( powerset @ X1846 ) )
=> ! [X1849: $i] :
( ( in @ X1849 @ X1846 )
=> ( ( subset @ X1847 @ ( setminus @ X1846 @ X1848 ) )
=> ( ( in @ X1849 @ X1848 )
=> ~ ( in @ X1849 @ X1847 ) ) ) ) ) )
=> ( ! [X1850: $i,X1851: $i] :
( ( in @ X1851 @ ( powerset @ X1850 ) )
=> ! [X1852: $i] :
( ( in @ X1852 @ ( powerset @ X1850 ) )
=> ! [X1853: $i] :
( ( in @ X1853 @ X1850 )
=> ( ( subset @ X1851 @ X1852 )
=> ( ~ ( in @ X1853 @ X1852 )
=> ~ ( in @ X1853 @ X1851 ) ) ) ) ) )
=> ( ! [X1854: $i,X1855: $i] :
( ( in @ X1855 @ ( powerset @ X1854 ) )
=> ! [X1856: $i] :
( ( in @ X1856 @ ( powerset @ X1854 ) )
=> ( ( subset @ X1855 @ X1856 )
=> ( subset @ ( setminus @ X1854 @ X1856 ) @ ( setminus @ X1854 @ X1855 ) ) ) ) )
=> ( ! [X1857: $i,X1858: $i] :
( ( in @ X1858 @ ( powerset @ X1857 ) )
=> ! [X1859: $i] :
( ( in @ X1859 @ ( powerset @ X1857 ) )
=> ( ( subset @ ( setminus @ X1857 @ X1859 ) @ ( setminus @ X1857 @ X1858 ) )
=> ( subset @ X1858 @ X1859 ) ) ) )
=> ( ! [X1860: $i,X1861: $i] :
( ( in @ X1861 @ ( powerset @ X1860 ) )
=> ! [X1862: $i] :
( ( in @ X1862 @ X1860 )
=> ( ( in @ X1862 @ X1861 )
=> ( in @ X1862 @ ( setminus @ X1860 @ ( setminus @ X1860 @ X1861 ) ) ) ) ) )
=> ( ! [X1863: $i,X1864: $i] :
( ( in @ X1864 @ ( powerset @ X1863 ) )
=> ! [X1865: $i] :
( ( in @ X1865 @ X1863 )
=> ( ( in @ X1865 @ ( setminus @ X1863 @ ( setminus @ X1863 @ X1864 ) ) )
=> ( in @ X1865 @ X1864 ) ) ) )
=> ( ! [X1866: $i,X1867: $i] :
( ( in @ X1867 @ ( powerset @ X1866 ) )
=> ( subset @ X1867 @ ( setminus @ X1866 @ ( setminus @ X1866 @ X1867 ) ) ) )
=> ( ! [X1868: $i,X1869: $i] :
( ( in @ X1869 @ ( powerset @ X1868 ) )
=> ( subset @ ( setminus @ X1868 @ ( setminus @ X1868 @ X1869 ) ) @ X1869 ) )
=> ( ! [X1870: $i,X1871: $i] :
( ( in @ X1871 @ ( powerset @ X1870 ) )
=> ( X1871
= ( setminus @ X1870 @ ( setminus @ X1870 @ X1871 ) ) ) )
=> ( ! [X1872: $i,X1873: $i] :
( ( in @ X1873 @ ( powerset @ X1872 ) )
=> ! [X1874: $i] :
( ( in @ X1874 @ ( powerset @ X1872 ) )
=> ! [X1875: $i] :
( ( in @ X1875 @ X1872 )
=> ( ( in @ X1875 @ ( setminus @ X1872 @ X1873 ) )
=> ~ ( in @ X1875 @ ( binintersect @ X1873 @ X1874 ) ) ) ) ) )
=> ( ! [X1876: $i,X1877: $i] :
( ( in @ X1877 @ ( powerset @ X1876 ) )
=> ! [X1878: $i] :
( ( in @ X1878 @ ( powerset @ X1876 ) )
=> ! [X1879: $i] :
( ( in @ X1879 @ X1876 )
=> ( ( in @ X1879 @ ( setminus @ X1876 @ X1877 ) )
=> ( in @ X1879 @ ( setminus @ X1876 @ ( binintersect @ X1877 @ X1878 ) ) ) ) ) ) )
=> ( ! [X1880: $i,X1881: $i] :
( ( in @ X1881 @ ( powerset @ X1880 ) )
=> ! [X1882: $i] :
( ( in @ X1882 @ ( powerset @ X1880 ) )
=> ( subset @ ( setminus @ X1880 @ X1881 ) @ ( setminus @ X1880 @ ( binintersect @ X1881 @ X1882 ) ) ) ) )
=> ( ! [X1883: $i,X1884: $i] :
( ( in @ X1884 @ ( powerset @ X1883 ) )
=> ! [X1885: $i] :
( ( in @ X1885 @ ( powerset @ X1883 ) )
=> ( in @ ( setminus @ X1883 @ X1884 ) @ ( powerset @ ( setminus @ X1883 @ ( binintersect @ X1884 @ X1885 ) ) ) ) ) )
=> ( ! [X1886: $i,X1887: $i] :
( ( in @ X1887 @ ( powerset @ X1886 ) )
=> ! [X1888: $i] :
( ( in @ X1888 @ ( powerset @ X1886 ) )
=> ( ( subset @ X1887 @ ( setminus @ X1886 @ X1888 ) )
=> ! [X1889: $i] :
( ( in @ X1889 @ X1886 )
=> ( ( in @ X1889 @ X1888 )
=> ( in @ X1889 @ ( setminus @ X1886 @ X1887 ) ) ) ) ) ) )
=> ( ! [X1890: $i,X1891: $i] :
( ( in @ X1891 @ ( powerset @ X1890 ) )
=> ! [X1892: $i] :
( ( in @ X1892 @ ( powerset @ X1890 ) )
=> ( ( subset @ X1891 @ ( setminus @ X1890 @ X1892 ) )
=> ( subset @ X1892 @ ( setminus @ X1890 @ X1891 ) ) ) ) )
=> ( ! [X1893: $i,X1894: $i] :
( ( in @ X1894 @ ( powerset @ X1893 ) )
=> ! [X1895: $i] :
( ( in @ X1895 @ ( powerset @ X1893 ) )
=> ! [X1896: $i] :
( ( in @ X1896 @ X1893 )
=> ( ~ ( in @ X1896 @ ( binunion @ X1894 @ X1895 ) )
=> ~ ( in @ X1896 @ X1894 ) ) ) ) )
=> ( ! [X1897: $i,X1898: $i] :
( ( in @ X1898 @ ( powerset @ X1897 ) )
=> ! [X1899: $i] :
( ( in @ X1899 @ ( powerset @ X1897 ) )
=> ! [X1900: $i] :
( ( in @ X1900 @ X1897 )
=> ( ~ ( in @ X1900 @ ( binunion @ X1898 @ X1899 ) )
=> ~ ( in @ X1900 @ X1899 ) ) ) ) )
=> ( ! [X1901: $i,X1902: $i] :
( ( in @ X1902 @ ( powerset @ X1901 ) )
=> ! [X1903: $i] :
( ( in @ X1903 @ ( powerset @ X1901 ) )
=> ! [X1904: $i] :
( ( in @ X1904 @ ( powerset @ X1901 ) )
=> ! [X1905: $i] :
( ( in @ X1905 @ X1901 )
=> ( ( in @ X1905 @ ( binintersect @ X1902 @ X1903 ) )
=> ( in @ X1905 @ ( binunion @ X1902 @ X1904 ) ) ) ) ) ) )
=> ( ! [X1906: $i,X1907: $i] :
( ( in @ X1907 @ ( powerset @ X1906 ) )
=> ! [X1908: $i] :
( ( in @ X1908 @ ( powerset @ X1906 ) )
=> ! [X1909: $i] :
( ( in @ X1909 @ ( powerset @ X1906 ) )
=> ! [X1910: $i] :
( ( in @ X1910 @ X1906 )
=> ( ( in @ X1910 @ ( binintersect @ X1907 @ X1908 ) )
=> ( in @ X1910 @ ( binunion @ X1908 @ X1909 ) ) ) ) ) ) )
=> ( ! [X1911: $i,X1912: $i] :
( ( in @ X1912 @ ( powerset @ X1911 ) )
=> ! [X1913: $i] :
( ( in @ X1913 @ ( powerset @ X1911 ) )
=> ! [X1914: $i] :
( ( in @ X1914 @ ( powerset @ X1911 ) )
=> ! [X1915: $i] :
( ( in @ X1915 @ X1911 )
=> ( ( in @ X1915 @ ( binintersect @ X1912 @ X1913 ) )
=> ( in @ X1915 @ ( binintersect @ ( binunion @ X1912 @ X1914 ) @ ( binunion @ X1913 @ X1914 ) ) ) ) ) ) ) )
=> ( ! [X1916: $i,X1917: $i] :
( ( in @ X1917 @ ( powerset @ X1916 ) )
=> ! [X1918: $i] :
( ( in @ X1918 @ ( powerset @ X1916 ) )
=> ! [X1919: $i] :
( ( in @ X1919 @ ( powerset @ X1916 ) )
=> ( in @ ( binintersect @ X1917 @ X1918 ) @ ( powerset @ ( binintersect @ ( binunion @ X1917 @ X1919 ) @ ( binunion @ X1918 @ X1919 ) ) ) ) ) ) )
=> ( ! [X1920: $i,X1921: $i] :
( ( in @ X1921 @ ( powerset @ X1920 ) )
=> ! [X1922: $i] :
( ( in @ X1922 @ ( powerset @ X1920 ) )
=> ! [X1923: $i] :
( ( in @ X1923 @ X1920 )
=> ( ( in @ X1923 @ ( setminus @ X1920 @ ( binunion @ X1921 @ X1922 ) ) )
=> ~ ( in @ X1923 @ X1921 ) ) ) ) )
=> ( ! [X1924: $i,X1925: $i] :
( ( in @ X1925 @ ( powerset @ X1924 ) )
=> ! [X1926: $i] :
( ( in @ X1926 @ ( powerset @ X1924 ) )
=> ! [X1927: $i] :
( ( in @ X1927 @ X1924 )
=> ( ( in @ X1927 @ ( setminus @ X1924 @ ( binunion @ X1925 @ X1926 ) ) )
=> ( in @ X1927 @ ( setminus @ X1924 @ X1925 ) ) ) ) ) )
=> ( ! [X1928: $i,X1929: $i] :
( ( in @ X1929 @ ( powerset @ X1928 ) )
=> ! [X1930: $i] :
( ( in @ X1930 @ ( powerset @ X1928 ) )
=> ! [X1931: $o,X1932: $i] :
( ( in @ X1932 @ X1928 )
=> ( ( in @ X1932 @ ( binunion @ X1929 @ X1930 ) )
=> ( ( ( in @ X1932 @ X1929 )
=> X1931 )
=> ( ( ( in @ X1932 @ X1930 )
=> X1931 )
=> X1931 ) ) ) ) ) )
=> ( ! [X1933: $i,X1934: $i] :
( ( in @ X1934 @ ( powerset @ X1933 ) )
=> ! [X1935: $i] :
( ( in @ X1935 @ ( powerset @ X1933 ) )
=> ! [X1936: $i] :
( ( in @ X1936 @ X1933 )
=> ( ~ ( in @ X1936 @ X1934 )
=> ( ~ ( in @ X1936 @ X1935 )
=> ~ ( in @ X1936 @ ( binunion @ X1934 @ X1935 ) ) ) ) ) ) )
=> ( ! [X1937: $i,X1938: $i] :
( ( in @ X1938 @ ( powerset @ X1937 ) )
=> ! [X1939: $i] :
( ( in @ X1939 @ ( powerset @ X1937 ) )
=> ! [X1940: $i] :
( ( in @ X1940 @ X1937 )
=> ( ( in @ X1940 @ ( setminus @ X1937 @ ( binunion @ X1938 @ X1939 ) ) )
=> ( in @ X1940 @ ( setminus @ X1937 @ X1938 ) ) ) ) ) )
=> ( ! [X1941: $i,X1942: $i] :
( ( in @ X1942 @ ( powerset @ X1941 ) )
=> ! [X1943: $i] :
( ( in @ X1943 @ ( powerset @ X1941 ) )
=> ( in @ ( setminus @ X1941 @ ( binunion @ X1942 @ X1943 ) ) @ ( powerset @ ( setminus @ X1941 @ X1942 ) ) ) ) )
=> ( ! [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 @ ( setminus @ X1944 @ X1946 ) ) ) ) ) )
=> ( ! [X1948: $i,X1949: $i] :
( ( in @ X1949 @ ( powerset @ X1948 ) )
=> ! [X1950: $i] :
( ( in @ X1950 @ ( powerset @ X1948 ) )
=> ! [X1951: $i] :
( ( in @ X1951 @ X1948 )
=> ( ( in @ X1951 @ ( setminus @ X1948 @ ( binintersect @ X1949 @ X1950 ) ) )
=> ( in @ X1951 @ ( binunion @ ( setminus @ X1948 @ X1949 ) @ ( setminus @ X1948 @ X1950 ) ) ) ) ) ) )
=> ( ! [X1952: $i,X1953: $i] :
( ( in @ X1953 @ ( powerset @ X1952 ) )
=> ! [X1954: $i] :
( ( in @ X1954 @ ( powerset @ X1952 ) )
=> ! [X1955: $i] :
( ( in @ X1955 @ X1952 )
=> ( ( in @ X1955 @ ( binunion @ ( setminus @ X1952 @ X1953 ) @ ( setminus @ X1952 @ X1954 ) ) )
=> ( in @ X1955 @ ( setminus @ X1952 @ ( binintersect @ X1953 @ X1954 ) ) ) ) ) ) )
=> ( ! [X1956: $i,X1957: $i] :
( ( in @ X1957 @ ( powerset @ X1956 ) )
=> ! [X1958: $i] :
( ( in @ X1958 @ ( powerset @ X1956 ) )
=> ( ( setminus @ X1956 @ ( binintersect @ X1957 @ X1958 ) )
= ( binunion @ ( setminus @ X1956 @ X1957 ) @ ( setminus @ X1956 @ X1958 ) ) ) ) )
=> ( ! [X1959: $i,X1960: $i] :
( ( in @ X1960 @ ( powerset @ X1959 ) )
=> ! [X1961: $i] :
( ( in @ X1961 @ ( powerset @ X1959 ) )
=> ! [X1962: $i] :
( ( in @ X1962 @ X1959 )
=> ( ( in @ X1962 @ ( setminus @ X1959 @ ( binunion @ X1960 @ X1961 ) ) )
=> ( in @ X1962 @ ( binintersect @ ( setminus @ X1959 @ X1960 ) @ ( setminus @ X1959 @ X1961 ) ) ) ) ) ) )
=> ( ! [X1963: $i,X1964: $i] :
( ( in @ X1964 @ ( powerset @ X1963 ) )
=> ! [X1965: $i] :
( ( in @ X1965 @ ( powerset @ X1963 ) )
=> ! [X1966: $i] :
( ( in @ X1966 @ X1963 )
=> ( ( in @ X1966 @ ( setminus @ X1963 @ X1964 ) )
=> ( ( in @ X1966 @ ( setminus @ X1963 @ X1965 ) )
=> ( in @ X1966 @ ( setminus @ X1963 @ ( binunion @ X1964 @ X1965 ) ) ) ) ) ) ) )
=> ( ! [X1967: $i,X1968: $i] :
( ( in @ X1968 @ ( powerset @ X1967 ) )
=> ! [X1969: $i] :
( ( in @ X1969 @ ( powerset @ X1967 ) )
=> ! [X1970: $i] :
( ( in @ X1970 @ X1967 )
=> ( ( in @ X1970 @ ( binintersect @ ( setminus @ X1967 @ X1968 ) @ ( setminus @ X1967 @ X1969 ) ) )
=> ( in @ X1970 @ ( setminus @ X1967 @ ( binunion @ X1968 @ X1969 ) ) ) ) ) ) )
=> ( ! [X1971: $i,X1972: $i] :
( ( in @ X1972 @ ( powerset @ X1971 ) )
=> ! [X1973: $i] :
( ( in @ X1973 @ ( powerset @ X1971 ) )
=> ( ( setminus @ X1971 @ ( binunion @ X1972 @ X1973 ) )
= ( binintersect @ ( setminus @ X1971 @ X1972 ) @ ( setminus @ X1971 @ X1973 ) ) ) ) )
=> ( ! [X1974: $i,X1975: $i] :
( ( in @ X1975 @ ( powerset @ X1974 ) )
=> ! [X1976: $i] :
( ( in @ X1976 @ ( powerset @ X1974 ) )
=> ! [X1977: $i] :
( ( in @ X1977 @ ( binintersect @ X1975 @ X1976 ) )
=> ( in @ X1977 @ X1974 ) ) ) )
=> ( ! [X1978: $i,X1979: $i] :
( ( in @ X1979 @ ( powerset @ X1978 ) )
=> ! [X1980: $i] :
( ( in @ X1980 @ ( powerset @ X1978 ) )
=> ! [X1981: $i] :
( ( in @ X1981 @ ( powerset @ X1978 ) )
=> ( ( subset @ X1979 @ X1981 )
=> ( subset @ ( binintersect @ X1979 @ X1980 ) @ X1981 ) ) ) ) )
=> ( ! [X1982: $i,X1983: $i] :
( ( in @ X1983 @ ( powerset @ X1982 ) )
=> ! [X1984: $i] :
( ( in @ X1984 @ ( powerset @ X1982 ) )
=> ! [X1985: $i] :
( ( in @ X1985 @ ( powerset @ X1982 ) )
=> ( ( subset @ X1984 @ X1985 )
=> ( subset @ ( binintersect @ X1983 @ X1984 ) @ X1985 ) ) ) ) )
=> ( ! [X1986: $i,X1987: $i] :
( ( in @ X1987 @ ( powerset @ X1986 ) )
=> ! [X1988: $i] :
( ( in @ X1988 @ ( powerset @ X1986 ) )
=> ! [X1989: $i] :
( ( in @ X1989 @ ( powerset @ X1986 ) )
=> ( ( subset @ X1987 @ X1988 )
=> ( ( subset @ X1987 @ X1989 )
=> ( subset @ X1987 @ ( binintersect @ X1988 @ X1989 ) ) ) ) ) ) )
=> ( ! [X1990: $i,X1991: $i] :
( ( in @ X1991 @ ( powerset @ X1990 ) )
=> ! [X1992: $i] :
( ( in @ X1992 @ ( powerset @ X1990 ) )
=> ! [X1993: $i] :
( ( in @ X1993 @ ( powerset @ X1990 ) )
=> ! [X1994: $i] :
( ( in @ X1994 @ ( powerset @ X1990 ) )
=> ( ( subset @ X1991 @ X1993 )
=> ( ( subset @ X1992 @ X1994 )
=> ( subset @ ( binintersect @ X1991 @ X1992 ) @ ( binintersect @ X1993 @ X1994 ) ) ) ) ) ) ) )
=> ( ! [X1995: $i,X1996: $i] :
( ( in @ X1996 @ ( powerset @ X1995 ) )
=> ! [X1997: $i] :
( ( in @ X1997 @ ( powerset @ X1995 ) )
=> ( in @ ( setminus @ X1995 @ X1996 ) @ ( powerset @ ( setminus @ X1995 @ ( binintersect @ X1996 @ X1997 ) ) ) ) ) )
=> ( ! [X1998: $i,X1999: $i] :
( ( in @ X1999 @ ( powerset @ X1998 ) )
=> ! [X2000: $i] :
( ( in @ X2000 @ ( powerset @ X1998 ) )
=> ! [X2001: $i] :
( ( in @ X2001 @ ( powerset @ X1998 ) )
=> ! [X2002: $i] :
( ( in @ X2002 @ ( powerset @ X1998 ) )
=> ( ( setminus @ X1998 @ ( binintersect @ ( binunion @ X1999 @ X2000 ) @ ( binunion @ X2001 @ X2002 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1998 @ X1999 ) @ ( setminus @ X1998 @ X2000 ) ) @ ( binintersect @ ( setminus @ X1998 @ X2001 ) @ ( setminus @ X1998 @ X2002 ) ) ) ) ) ) ) )
=> ( ! [X2003: $i,X2004: $i] :
( ( in @ X2004 @ ( powerset @ X2003 ) )
=> ! [X2005: $i] :
( ( in @ X2005 @ ( powerset @ X2003 ) )
=> ! [X2006: $i] :
( ( in @ X2006 @ ( powerset @ X2003 ) )
=> ( in @ ( binintersect @ X2004 @ X2005 ) @ ( powerset @ ( binintersect @ ( binunion @ X2004 @ X2006 ) @ ( binunion @ X2005 @ X2006 ) ) ) ) ) ) )
=> ( ! [X2007: $i,X2008: $i] :
( ( in @ X2008 @ ( powerset @ X2007 ) )
=> ! [X2009: $i] :
( ( in @ X2009 @ ( powerset @ X2007 ) )
=> ( ( subset @ X2008 @ ( setminus @ X2007 @ X2009 ) )
=> ( subset @ X2009 @ ( setminus @ X2007 @ X2008 ) ) ) ) )
=> ( ! [X2010: $i,X2011: $i] :
( ( in @ X2011 @ ( powerset @ X2010 ) )
=> ! [X2012: $i] :
( ( in @ X2012 @ ( powerset @ X2010 ) )
=> ( in @ ( setminus @ X2010 @ ( binunion @ X2011 @ X2012 ) ) @ ( powerset @ ( setminus @ X2010 @ X2011 ) ) ) ) )
=> ( ! [X2013: $i,X2014: $i] :
( ( breln1 @ X2013 @ X2014 )
=> ! [X2015: $i > $o] :
( ! [X2016: $i] :
( ( in @ X2016 @ X2013 )
=> ! [X2017: $i] :
( ( in @ X2017 @ X2013 )
=> ( ( in @ ( kpair @ X2016 @ X2017 ) @ X2014 )
=> ( X2015 @ ( kpair @ X2016 @ X2017 ) ) ) ) )
=> ! [X2018: $i] :
( ( in @ X2018 @ X2014 )
=> ( X2015 @ X2018 ) ) ) )
=> ( ! [X2019: $i,X2020: $i] :
( ( in @ X2020 @ ( breln1Set @ X2019 ) )
=> ( breln1 @ X2019 @ X2020 ) )
=> ( choice2fnsingleton
=> ( ! [X2021: $i,X2022: $i > $i > $o] : ( breln1 @ X2021 @ ( dpsetconstr @ X2021 @ X2021 @ X2022 ) )
=> ( ! [X2023: $i,X2024: $i] :
( ( breln1 @ X2023 @ X2024 )
=> ! [X2025: $i > $o] :
( ! [X2026: $i] :
( ( in @ X2026 @ X2023 )
=> ! [X2027: $i] :
( ( in @ X2027 @ X2023 )
=> ( ( in @ ( kpair @ X2026 @ X2027 ) @ X2024 )
=> ( X2025 @ ( kpair @ X2026 @ X2027 ) ) ) ) )
=> ! [X2028: $i] :
( ( in @ X2028 @ X2024 )
=> ( X2025 @ X2028 ) ) ) )
=> ( ! [X2029: $i,X2030: $i] :
( ( breln1 @ X2029 @ X2030 )
=> ! [X2031: $i] :
( ( breln1 @ X2029 @ X2031 )
=> ( ! [X2032: $i] :
( ( in @ X2032 @ X2029 )
=> ! [X2033: $i] :
( ( in @ X2033 @ X2029 )
=> ( ( in @ ( kpair @ X2032 @ X2033 ) @ X2030 )
=> ( in @ ( kpair @ X2032 @ X2033 ) @ X2031 ) ) ) )
=> ( subset @ X2030 @ X2031 ) ) ) )
=> ( ! [X2034: $i,X2035: $i] :
( ( breln1 @ X2034 @ X2035 )
=> ! [X2036: $i] :
( ( breln1 @ X2034 @ X2036 )
=> ( ! [X2037: $i] :
( ( in @ X2037 @ X2034 )
=> ! [X2038: $i] :
( ( in @ X2038 @ X2034 )
=> ( ( in @ ( kpair @ X2037 @ X2038 ) @ X2035 )
=> ( in @ ( kpair @ X2037 @ X2038 ) @ X2036 ) ) ) )
=> ( ! [X2039: $i] :
( ( in @ X2039 @ X2034 )
=> ! [X2040: $i] :
( ( in @ X2040 @ X2034 )
=> ( ( in @ ( kpair @ X2039 @ X2040 ) @ X2036 )
=> ( in @ ( kpair @ X2039 @ X2040 ) @ X2035 ) ) ) )
=> ( X2035 = X2036 ) ) ) ) )
=> ( ! [X2041: $i,X2042: $i] :
( ( breln1 @ X2041 @ X2042 )
=> ( breln1 @ X2041 @ ( breln1invset @ X2041 @ X2042 ) ) )
=> ( ! [X2043: $i,X2044: $i] :
( ( breln1 @ X2043 @ X2044 )
=> ! [X2045: $i] :
( ( in @ X2045 @ X2043 )
=> ! [X2046: $i] :
( ( in @ X2046 @ X2043 )
=> ( ( in @ ( kpair @ X2045 @ X2046 ) @ X2044 )
=> ( in @ ( kpair @ X2046 @ X2045 ) @ ( breln1invset @ X2043 @ X2044 ) ) ) ) ) )
=> ( ! [X2047: $i,X2048: $i] :
( ( breln1 @ X2047 @ X2048 )
=> ! [X2049: $i] :
( ( in @ X2049 @ X2047 )
=> ! [X2050: $i] :
( ( in @ X2050 @ X2047 )
=> ( ( in @ ( kpair @ X2050 @ X2049 ) @ ( breln1invset @ X2047 @ X2048 ) )
=> ( in @ ( kpair @ X2049 @ X2050 ) @ X2048 ) ) ) ) )
=> ( ! [X2051: $i,X2052: $i] :
( ( breln1 @ X2051 @ X2052 )
=> ! [X2053: $i] :
( ( breln1 @ X2051 @ X2053 )
=> ( breln1 @ X2051 @ ( breln1compset @ X2051 @ X2052 @ X2053 ) ) ) )
=> ( ! [X2054: $i,X2055: $i] :
( ( breln1 @ X2054 @ X2055 )
=> ! [X2056: $i] :
( ( breln1 @ X2054 @ X2056 )
=> ! [X2057: $i] :
( ( in @ X2057 @ X2054 )
=> ! [X2058: $i] :
( ( in @ X2058 @ X2054 )
=> ! [X2059: $i] :
( ( in @ X2059 @ X2054 )
=> ( ( in @ ( kpair @ X2057 @ X2059 ) @ X2055 )
=> ( ( in @ ( kpair @ X2059 @ X2058 ) @ X2056 )
=> ( in @ ( kpair @ X2057 @ X2058 ) @ ( breln1compset @ X2054 @ X2055 @ X2056 ) ) ) ) ) ) ) ) )
=> ( ! [X2060: $i,X2061: $i] :
( ( breln1 @ X2060 @ X2061 )
=> ! [X2062: $i] :
( ( breln1 @ X2060 @ X2062 )
=> ! [X2063: $i] :
( ( in @ X2063 @ X2060 )
=> ! [X2064: $i] :
( ( in @ X2064 @ X2060 )
=> ( ( in @ ( kpair @ X2063 @ X2064 ) @ ( breln1compset @ X2060 @ X2061 @ X2062 ) )
=> ? [X2065: $i] :
( ( in @ X2065 @ X2060 )
& ( in @ ( kpair @ X2063 @ X2065 ) @ X2061 )
& ( in @ ( kpair @ X2065 @ X2064 ) @ X2062 ) ) ) ) ) ) )
=> ( ! [X2066: $i,X2067: $i] :
( ( breln1 @ X2066 @ X2067 )
=> ! [X2068: $i] :
( ( breln1 @ X2066 @ X2068 )
=> ! [X2069: $i] :
( ( in @ X2069 @ X2066 )
=> ! [X2070: $i] :
( ( in @ X2070 @ X2066 )
=> ( ( in @ ( kpair @ X2069 @ X2070 ) @ ( breln1compset @ X2066 @ X2067 @ X2068 ) )
=> ! [X2071: $o] :
( ! [X2072: $i] :
( ( in @ X2072 @ X2066 )
=> ( ( in @ ( kpair @ X2069 @ X2072 ) @ X2067 )
=> ( ( in @ ( kpair @ X2072 @ X2070 ) @ X2068 )
=> X2071 ) ) )
=> X2071 ) ) ) ) ) )
=> ( ! [X2073: $i,X2074: $i] :
( ( breln1 @ X2073 @ X2074 )
=> ! [X2075: $i] :
( ( breln1 @ X2073 @ X2075 )
=> ( breln1 @ X2073 @ ( binunion @ X2074 @ X2075 ) ) ) )
=> ( ! [X2076: $i,X2077: $i] :
( ( breln1 @ X2076 @ X2077 )
=> ! [X2078: $i] :
( ( breln1 @ X2076 @ X2078 )
=> ! [X2079: $i] :
( ( in @ X2079 @ X2076 )
=> ! [X2080: $i] :
( ( in @ X2080 @ X2076 )
=> ( ( in @ ( kpair @ X2079 @ X2080 ) @ X2077 )
=> ( in @ ( kpair @ X2079 @ X2080 ) @ ( binunion @ X2077 @ X2078 ) ) ) ) ) ) )
=> ( ! [X2081: $i,X2082: $i] :
( ( breln1 @ X2081 @ X2082 )
=> ! [X2083: $i] :
( ( breln1 @ X2081 @ X2083 )
=> ! [X2084: $i] :
( ( in @ X2084 @ X2081 )
=> ! [X2085: $i] :
( ( in @ X2085 @ X2081 )
=> ( ( in @ ( kpair @ X2084 @ X2085 ) @ X2083 )
=> ( in @ ( kpair @ X2084 @ X2085 ) @ ( binunion @ X2082 @ X2083 ) ) ) ) ) ) )
=> ( ! [X2086: $i,X2087: $i] :
( ( breln1 @ X2086 @ X2087 )
=> ! [X2088: $i] :
( ( breln1 @ X2086 @ X2088 )
=> ! [X2089: $i] :
( ( in @ X2089 @ X2086 )
=> ! [X2090: $i] :
( ( in @ X2090 @ X2086 )
=> ( ( ( in @ ( kpair @ X2089 @ X2090 ) @ X2087 )
| ( in @ ( kpair @ X2089 @ X2090 ) @ X2088 ) )
=> ( in @ ( kpair @ X2089 @ X2090 ) @ ( binunion @ X2087 @ X2088 ) ) ) ) ) ) )
=> ( ! [X2091: $i,X2092: $i] :
( ( breln1 @ X2091 @ X2092 )
=> ! [X2093: $i] :
( ( breln1 @ X2091 @ X2093 )
=> ! [X2094: $i] :
( ( in @ X2094 @ X2091 )
=> ! [X2095: $i] :
( ( in @ X2095 @ X2091 )
=> ( ( in @ ( kpair @ X2094 @ X2095 ) @ ( binunion @ X2092 @ X2093 ) )
=> ( ( in @ ( kpair @ X2094 @ X2095 ) @ X2092 )
| ( in @ ( kpair @ X2094 @ X2095 ) @ X2093 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[breln1unionEcases]),demorgan2b2]),breln1unionE]),complementInPowersetComplementIntersect]),contraSubsetComplement]),complementTcontraSubset]),disjointsetsI1]),binunionTILcontra]),binunionTIRcontra]),binintersectRsub]),inIntersectImpInUnion]),inIntersectImpInUnion2]),binintersectSubset4]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),binintersectSubset1]),inComplementUnionImpNotIn1]),inComplementUnionImpInComplement1]),bs114d]),binunionTE]),binunionTEcontra]),setminusI]),demorgan2a1]),setminusEL]),complementUnionInPowersetComplement]),demorgan2a2]),demorgan1a]),setminusER]),demorgan1b]),demorgan1]),demorgan2a]),setminusSubset2]),singletoninpowerset]),demorgan2b]),demorgan2]),setminusERneg]),woz13rule0]),woz13rule1]),setminusELneg]),woz13rule2]),woz13rule3]),setminusILneg]),woz13rule4]),woz1_1]),woz1_2]),woz1_3]),setminusIRneg]),woz1_4]),woz1_5]),setminusLsub]),breln1all2]),breln1SetBreln1]),setminusSubset1]),c_0_319]),breln1all1]),symdiffE]),subbreln1]),eqbreln1]),symdiffI1]),breln1invprop]),breln1invI]),symdiffI2]),breln1invE]),symdiffIneg1]),breln1compprop]),breln1compI]),breln1compE]),breln1compEex]),symdiffIneg2]),breln1unionprop]),breln1unionIL]),secondinupair]),breln1unionIR]),breln1unionI]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),singletonsuniq]),setukpairinjL1]),c_0_324]),theprop]),upairset2IR]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),binunionIR]),setukpairinjR]),binunionEcases]),binunionE]),c_0_325]),ksndpairEq]),kpairsurjEq]),powersetTI1]),powersetTE1]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_326]),c_0_327]),c_0_328]),c_0_329]),binunionLsub]),c_0_330]),c_0_331]),c_0_332]),c_0_333]),c_0_334]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_335]),c_0_336]),c_0_337]),brelnall1]),brelnall2]),c_0_338]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_339]),c_0_340]),c_0_341]),c_0_342]),c_0_343]),c_0_344]),c_0_345]),c_0_346]),c_0_347]),c_0_348]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),binunionRsub]),setminusT_lem]),complementT_lem]),setextT]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),subsetTI]),binintersectSubset2]),binintersectSubset3]),complementTI1]),complementTE1]),binintersectTELcontra]),binintersectTERcontra]),contrasubsetT]),contrasubsetT1]),contrasubsetT2]),contrasubsetT3]),doubleComplementI1]),doubleComplementE1]),doubleComplementSub1]),doubleComplementSub2]),doubleComplementEq]),complementTnotintersectT]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),binintersectER]),binunionIL]),c_0_349]),c_0_350]),powersetsubset]),inPowerset]),powersetE1]),powersetI1]),subsetemptysetimpeq]),setextsub]),subset2powerset]),setadjoinSub2]),setadjoinSub]),subsetTrans]),subsetRefl]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_351]),c_0_352]),c_0_353]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_354]),c_0_355]),in__Cong]),inCongP]),c_0_356]),c_0_357]),c_0_358]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_359]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_360]),c_0_361]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_362]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_363]),c_0_364]),c_0_365]),c_0_366]),noeltsimpempty]),emptyI]),setext]),c_0_367]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_368]),c_0_369]),c_0_370]),c_0_371]),c_0_372]),wellorderingAx]),foundationAx]),c_0_373]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_374]) ).
thf(c_0_376,negated_conjecture,
! 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$i,X2213: $i,X2214: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i > $o,X2233: $i,X2234: $i > $o,X2235: $i,X2236: $i,X2237: $i > $o,X2238: $i,X2240: $i,X2241: $i > $o,X2243: $i,X2244: $i,X2245: $i > $o,X2247: $i,X2248: $i,X2249: $i > $o,X2250: $i,X2252: $o,X2253: $i,X2254: $i > $o,X2256: $i,X2257: $i,X2258: $i > $o,X2259: $i,X2261: $i > $o,X2262: $i,X2265: $i,X2266: $i > $o,X2267: $i,X2271: $i,X2272: $i > $o,X2273: $i,X2276: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i > $o,X2286: $i,X2288: $i,X2289: $i,X2290: $i > $o,X2291: $i > $o,X2294: $i,X2297: $i,X2298: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i > $o,X2311: $i,X2313: $i,X2314: $i,X2315: $i > $o,X2316: $i > $o,X2319: $i,X2321: $i,X2323: $i,X2324: $i,X2325: $i > $o,X2326: $i > $o,X2329: $i,X2330: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $i,X2339: $i,X2340: $i,X2341: $i,X2342: $i,X2343: $i,X2344: $i,X2345: $i,X2346: $i,X2347: $i,X2348: $i,X2349: $i,X2350: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,X2363: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2368: $i,X2369: $i,X2370: $i,X2371: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2376: $i > $o,X2377: $i,X2378: $i > $o,X2379: $i,X2380: $i,X2381: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2388: $i,X2389: $i,X2390: $o,X2391: $i,X2392: $i,X2393: $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $i,X2412: $i,X2413: $i,X2414: $i,X2415: $i,X2416: $i,X2417: $i,X2419: $i,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i,X2425: $i,X2426: $i,X2427: $i,X2428: $i,X2429: $i,X2430: $i,X2431: $i,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2436: $i,X2437: $i,X2438: $i,X2439: $i,X2440: $i,X2441: $i,X2442: $i,X2443: $i,X2444: $i,X2445: $i,X2446: $i,X2447: $i,X2448: $i,X2449: $i,X2450: $i,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i,X2456: $i,X2457: $i,X2458: $o,X2459: $i,X2460: $i,X2461: $i,X2462: $i,X2463: $i,X2464: $i,X2465: $i,X2466: $i,X2467: $i,X2468: $i,X2469: $i,X2470: $i,X2471: $i,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2490: $i,X2491: $i,X2492: $i,X2493: $i,X2494: $i,X2495: $i,X2496: $i,X2497: $i,X2498: $i,X2499: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i,X2517: $i,X2520: $i,X2521: $i,X2522: $i,X2523: $i,X2524: $i,X2526: $i,X2527: $i,X2528: $i,X2529: $i,X2530: $i > $o,X2533: $i,X2534: $i,X2535: $i > $o,X2537: $i,X2538: $i > $o,X2539: $i,X2541: $i,X2542: $i > $o,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,X2592: $i,X2593: $i,X2594: $i,X2595: $i,X2596: $i,X2597: $i,X2598: $i,X2599: $i,X2600: $i,X2601: $i,X2602: $i,X2603: $i,X2604: $i,X2605: $i,X2606: $i,X2607: $i,X2608: $i,X2609: $i,X2610: $i,X2611: $i,X2612: $i,X2613: $i,X2614: $i,X2615: $i,X2616: $i,X2617: $i > $i > $o,X2618: $i,X2619: $i,X2620: $i,X2621: $i,X2622: $i > $i > $o,X2623: $i,X2624: $i,X2625: $i > $i > $o,X2626: $i,X2627: $i,X2628: $i > $i > $o,X2629: $i,X2630: $i,X2631: $i,X2632: $i,X2633: $i > $i > $o,X2634: $i,X2635: $i,X2636: $i,X2637: $i,X2638: $i > $i > $o,X2639: $i,X2640: $i,X2641: $i,X2642: $i,X2643: $i > $i > $o,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 > $i,X2672: $i,X2673: $i,X2674: $i > $i,X2676: $i,X2677: $i,X2678: $i > $i,X2680: $i,X2681: $i,X2682: $i,X2683: $i > $o,X2686: $i,X2687: $i,X2688: $i,X2689: $i,X2690: $i > $o,X2693: $i,X2694: $i,X2695: $i > $o,X2696: $i,X2697: $i,X2698: $i,X2699: $i,X2700: $i,X2701: $i,X2702: $i,X2703: $i,X2704: $i,X2705: $i,X2706: $i,X2707: $i,X2708: $i,X2709: $i,X2710: $i,X2711: $i,X2712: $i,X2713: $i,X2714: $i,X2716: $i,X2717: $i,X2718: $i,X2719: $i,X2720: $i,X2721: $i,X2722: $i,X2723: $i,X2724: $i,X2725: $i,X2726: $i,X2729: $i,X2730: $i,X2731: $i,X2732: $i,X2737: $i,X2738: $i,X2739: $i,X2740: $i,X2742: $i,X2743: $i,X2744: $i,X2745: $i,X2747: $i,X2748: $i,X2749: $i,X2750: $i,X2751: $i,X2752: $i,X2753: $i,X2754: $i,X2755: $i,X2756: $i,X2757: $i > $i,X2759: $i,X2760: $i,X2761: $i,X2762: $i,X2763: $i,X2764: $i,X2765: $i > $i,X2767: $i,X2768: $i,X2769: $i > $i,X2771: $i,X2772: $i,X2773: $i,X2774: $i,X2775: $i,X2776: $o,X2777: $i,X2778: $i,X2779: $i,X2780: $o,X2781: $i,X2782: $i,X2783: $i,X2784: $o,X2785: $i,X2786: $i,X2787: $i,X2788: $o,X2789: $i,X2790: $i,X2791: $i,X2792: $o,X2793: $i,X2794: $i,X2795: $i,X2796: $o,X2797: $i,X2798: $i,X2799: $i,X2800: $i,X2801: $i,X2802: $o,X2803: $i,X2804: $i,X2805: $i,X2806: $o,X2807: $i,X2808: $i,X2809: $i,X2810: $o,X2811: $i,X2812: $i,X2813: $i,X2814: $i,X2815: $i,X2816: $i,X2817: $i,X2818: $i,X2819: $i,X2820: $i,X2821: $i,X2822: $i,X2823: $i,X2824: $i,X2825: $i,X2826: $i,X2827: $i,X2828: $i,X2831: $i,X2832: $i,X2833: $i,X2835: $i,X2836: $i,X2837: $i,X2839: $i,X2840: $i,X2841: $i,X2842: $i,X2843: $i,X2844: $i,X2845: $i,X2846: $i,X2847: $i,X2848: $i,X2849: $i,X2850: $i,X2851: $i,X2852: $i,X2853: $i,X2854: $i,X2855: $i,X2856: $i,X2857: $i,X2858: $i,X2859: $i,X2860: $i,X2861: $i,X2862: $i,X2863: $i,X2864: $i,X2865: $i,X2866: $i,X2867: $i,X2868: $i,X2869: $i,X2870: $i,X2871: $i,X2872: $i,X2873: $i,X2874: $i,X2875: $i,X2876: $i,X2877: $i,X2878: $i,X2879: $i,X2880: $i,X2881: $i,X2882: $i,X2883: $i,X2884: $i,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,X2903: $i,X2904: $i,X2905: $i,X2906: $i,X2907: $i,X2908: $i,X2909: $i,X2910: $i,X2911: $i,X2912: $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: $o,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: $i,X3017: $i,X3018: $i,X3019: $i,X3020: $i,X3021: $i,X3022: $i,X3023: $i,X3024: $i,X3025: $i,X3026: $i > $o,X3029: $i,X3030: $i,X3031: $i,X3032: $i,X3033: $i > $i > $o,X3034: $i,X3035: $i,X3036: $i > $o,X3039: $i,X3040: $i,X3041: $i,X3042: $i,X3045: $i,X3046: $i,X3047: $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,X3077: $i,X3078: $i,X3079: $i,X3080: $i,X3081: $i,X3082: $o,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,X3101: $i,X3102: $i,X3103: $i,X3104: $i,X3105: $i,X3106: $i] :
( ( ~ ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2096 )
| ~ ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2097 )
| ( X2096 = X2097 ) )
& ( ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2096 )
| ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2097 )
| ( X2096 = X2097 ) )
& ~ ( in @ X2099 @ emptyset )
& ( ~ ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) )
| ( X2102 = X2100 )
| ( in @ X2102 @ X2101 ) )
& ( ( X2102 != X2100 )
| ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) ) )
& ( ~ ( in @ X2102 @ X2101 )
| ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) ) )
& ( ~ ( in @ X2104 @ ( powerset @ X2103 ) )
| ~ ( in @ X2105 @ X2104 )
| ( in @ X2105 @ X2103 ) )
& ( ( in @ ( esk2_2 @ X2106 @ X2107 ) @ X2107 )
| ( in @ X2107 @ ( powerset @ X2106 ) ) )
& ( ~ ( in @ ( esk2_2 @ X2106 @ X2107 ) @ X2106 )
| ( in @ X2107 @ ( powerset @ X2106 ) ) )
& ( ( in @ X2110 @ ( esk3_2 @ X2109 @ X2110 ) )
| ~ ( in @ X2110 @ ( setunion @ X2109 ) ) )
& ( ( in @ ( esk3_2 @ X2109 @ X2110 ) @ X2109 )
| ~ ( in @ X2110 @ ( setunion @ X2109 ) ) )
& ( ~ ( in @ X2113 @ X2114 )
| ~ ( in @ X2114 @ X2112 )
| ( in @ X2113 @ ( setunion @ X2112 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X2115 @ omega )
| ( in @ ( setadjoin @ X2115 @ X2115 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X2116 ) @ omega )
| ~ ( in @ emptyset @ X2116 )
| ~ ( in @ X2118 @ omega )
| ( in @ X2118 @ X2116 ) )
& ( ( in @ ( esk4_1 @ X2116 ) @ X2116 )
| ~ ( in @ emptyset @ X2116 )
| ~ ( in @ X2118 @ omega )
| ( in @ X2118 @ X2116 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X2116 ) @ ( esk4_1 @ X2116 ) ) @ X2116 )
| ~ ( in @ emptyset @ X2116 )
| ~ ( in @ X2118 @ omega )
| ( in @ X2118 @ X2116 ) )
& ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
& ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
& ( ~ ( in @ X2128 @ X2120 )
| ~ ( X2119 @ X2128 @ X2127 )
| ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
& ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ~ ( in @ X2128 @ X2120 )
| ~ ( X2119 @ X2128 @ X2127 )
| ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2122
!= ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
| ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2122
!= ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ~ ( in @ X2128 @ X2120 )
| ~ ( X2119 @ X2128 @ X2127 )
| ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
| ( X2122
!= ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
| ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
& ( ( in @ ( esk9_1 @ X2129 ) @ X2129 )
| ~ ( in @ X2130 @ X2129 ) )
& ( ~ ( in @ X2132 @ ( esk9_1 @ X2129 ) )
| ~ ( in @ X2132 @ X2129 )
| ~ ( in @ X2130 @ X2129 ) )
& epred1_0
& ( ( X2133 @ ( esk10_2 @ X2133 @ X2134 ) )
| ~ ( X2133 @ X2134 )
| ( X2133 @ ( descr @ X2133 ) ) )
& ( ( X2134
!= ( esk10_2 @ X2133 @ X2134 ) )
| ~ ( X2133 @ X2134 )
| ( X2133 @ ( descr @ X2133 ) ) )
& ( ~ ( in @ X2138 @ X2136 )
| ~ ( X2137 @ X2138 )
| ( in @ X2138 @ ( dsetconstr @ X2136 @ X2137 ) ) )
& ( ~ ( in @ X2141 @ ( dsetconstr @ X2139 @ X2140 ) )
| ( in @ X2141 @ X2139 ) )
& ( ~ ( in @ X2144 @ ( dsetconstr @ X2142 @ X2143 ) )
| ( X2143 @ X2144 ) )
& ( ( X2145 @ ( esk12_1 @ X2145 ) )
| ( X2145 @ ( esk11_2 @ X2145 @ X2146 ) )
| ~ ( X2145 @ X2146 ) )
& ( ~ ( X2145 @ X2149 )
| ( ( esk12_1 @ X2145 )
= X2149 )
| ( X2145 @ ( esk11_2 @ X2145 @ X2146 ) )
| ~ ( X2145 @ X2146 ) )
& ( ( X2145 @ ( esk12_1 @ X2145 ) )
| ( X2146
!= ( esk11_2 @ X2145 @ X2146 ) )
| ~ ( X2145 @ X2146 ) )
& ( ~ ( X2145 @ X2149 )
| ( ( esk12_1 @ X2145 )
= X2149 )
| ( X2146
!= ( esk11_2 @ X2145 @ X2146 ) )
| ~ ( X2145 @ X2146 ) )
& ( ~ ( in @ X2151 @ ( prop2set @ X2150 ) )
| X2150 )
& ( ~ ( in @ X2152 @ emptyset )
| X2153 )
& ( ~ ( in @ X2154 @ emptyset )
| ~ $true )
& ~ ( in @ X2155 @ emptyset )
& ( ( X2156 @ ( esk13_2 @ X2156 @ X2157 ) )
| ~ ( X2156 @ X2157 )
| ( X2156 @ ( esk14_1 @ X2156 ) ) )
& ( ( X2157
!= ( esk13_2 @ X2156 @ X2157 ) )
| ~ ( X2156 @ X2157 )
| ( X2156 @ ( esk14_1 @ X2156 ) ) )
& ( ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2161 )
| ( X2160 = X2161 )
| ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2160 ) )
& ( ~ ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2160 )
| ( X2160 = X2161 )
| ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2160 ) )
& ( ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2161 )
| ( X2160 = X2161 )
| ~ ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2161 ) )
& ( ~ ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2160 )
| ( X2160 = X2161 )
| ~ ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2161 ) )
& ( ( in @ ( esk17_1 @ X2164 ) @ X2164 )
| ( X2164 = emptyset ) )
& ( ( in @ ( esk18_1 @ X2166 ) @ X2166 )
| ( X2166 = emptyset ) )
& ( ~ ( in @ X2170 @ ( dsetconstr @ X2168 @ X2169 ) )
| ( X2169 @ X2170 )
| ~ ( in @ X2170 @ X2168 ) )
& ( ~ ( X2169 @ X2170 )
| ( in @ X2170 @ ( dsetconstr @ X2168 @ X2169 ) )
| ~ ( in @ X2170 @ X2168 ) )
& ( ( X2171 = emptyset )
| ( in @ ( esk19_1 @ X2171 ) @ X2171 ) )
& ( ~ ( in @ X2175 @ X2173 )
| ~ ( X2174 @ X2175 )
| ( ( dsetconstr @ X2173 @ X2174 )
!= emptyset ) )
& ( ~ ( in @ X2177 @ X2176 )
| ( X2176 != emptyset ) )
& ( in @ X2178 @ ( setadjoin @ X2178 @ X2179 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X2182 @ X2181 )
| ( in @ X2182 @ ( setadjoin @ X2180 @ X2181 ) ) )
& ( ( in @ X2185 @ X2184 )
| X2186
| ( X2185 = X2183 )
| ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
& ( ~ X2186
| X2186
| ( X2185 = X2183 )
| ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
& ( ( in @ X2185 @ X2184 )
| X2186
| ~ X2186
| ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
& ( ~ X2186
| X2186
| ~ X2186
| ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
& ( ~ ( in @ X2189 @ ( setadjoin @ X2187 @ X2188 ) )
| ( X2189 = X2187 )
| ( in @ X2189 @ X2188 ) )
& ( ( dsetconstr @ X2190
@ ^ [Z0: $i] : $true )
= X2190 )
& ( ( in @ ( esk20_2 @ X2191 @ X2192 ) @ X2192 )
| ( in @ X2192 @ ( powerset @ X2191 ) ) )
& ( ~ ( in @ ( esk20_2 @ X2191 @ X2192 ) @ X2191 )
| ( in @ X2192 @ ( powerset @ X2191 ) ) )
& ( in @ emptyset @ ( powerset @ X2194 ) )
& ( in @ emptyset @ ( powerset @ X2195 ) )
& ( ~ ( in @ X2197 @ ( powerset @ X2196 ) )
| ~ ( in @ X2198 @ X2197 )
| ( in @ X2198 @ X2196 ) )
& ( ~ ( in @ X2200 @ X2201 )
| ~ ( in @ X2201 @ X2199 )
| ( in @ X2200 @ ( setunion @ X2199 ) ) )
& ( ( in @ X2203 @ ( esk21_3 @ X2202 @ X2203 @ X2204 ) )
| X2204
| ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
& ( ( in @ ( esk21_3 @ X2202 @ X2203 @ X2204 ) @ X2202 )
| X2204
| ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
& ( ~ X2204
| X2204
| ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
& ( ~ ( in @ X2207 @ X2206 )
| ( in @ X2207 @ ( powerset @ ( setunion @ X2206 ) ) ) )
& ( ~ ( X2208 @ X2212 )
| ( X2212
= ( esk23_1 @ X2208 ) )
| ( X2208 @ ( esk22_2 @ X2208 @ X2209 ) )
| ~ ( X2208 @ X2209 ) )
& ( ( X2213
!= ( esk23_1 @ X2208 ) )
| ( X2208 @ X2213 )
| ( X2208 @ ( esk22_2 @ X2208 @ X2209 ) )
| ~ ( X2208 @ X2209 ) )
& ( ~ ( X2208 @ X2212 )
| ( X2212
= ( esk23_1 @ X2208 ) )
| ( X2209
!= ( esk22_2 @ X2208 @ X2209 ) )
| ~ ( X2208 @ X2209 ) )
& ( ( X2213
!= ( esk23_1 @ X2208 ) )
| ( X2208 @ X2213 )
| ( X2209
!= ( esk22_2 @ X2208 @ X2209 ) )
| ~ ( X2208 @ X2209 ) )
& ( ( in @ ( esk24_1 @ X2214 ) @ X2214 )
| ( X2214 = emptyset ) )
& ( $true
| ( X2214 = emptyset ) )
& ( ~ ( in @ X2216 @ ( setadjoin @ X2217 @ emptyset ) )
| ( X2216 = X2217 ) )
& ( ( X2218 = X2219 )
| ~ ( in @ X2219 @ ( setadjoin @ X2218 @ emptyset ) ) )
& ( ( X2220 != X2221 )
| ( in @ X2220 @ ( setadjoin @ X2221 @ emptyset ) ) )
& ( ~ ( in @ X2222 @ ( setadjoin @ X2223 @ emptyset ) )
| ( in @ X2223 @ ( setadjoin @ X2222 @ emptyset ) ) )
& ( ~ ( in @ X2226 @ ( setadjoin @ X2224 @ ( setadjoin @ X2225 @ emptyset ) ) )
| ( X2226 = X2224 )
| ( X2226 = X2225 ) )
& ( in @ X2227 @ ( setadjoin @ X2227 @ ( setadjoin @ X2228 @ emptyset ) ) )
& ( in @ X2230 @ ( setadjoin @ X2229 @ ( setadjoin @ X2230 @ emptyset ) ) )
& ( ~ ( in @ X2233 @ X2231 )
| ~ ( X2232 @ X2233 )
| ( ( dsetconstr @ X2231 @ X2232 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X2235 @ emptyset )
| ( X2234 @ X2235 ) )
& ( ( in @ ( esk25_2 @ X2236 @ X2237 ) @ X2236 )
| ~ ( in @ X2238 @ X2236 )
| ( X2237 @ X2238 ) )
& ( ~ ( X2237 @ ( esk25_2 @ X2236 @ X2237 ) )
| ~ ( in @ X2238 @ X2236 )
| ( X2237 @ X2238 ) )
& ( ( in @ ( esk26_2 @ X2240 @ X2241 ) @ X2240 )
| ~ ( in @ X2243 @ X2240 )
| ~ ( X2241 @ X2243 ) )
& ( ( X2241 @ ( esk26_2 @ X2240 @ X2241 ) )
| ~ ( in @ X2243 @ X2240 )
| ~ ( X2241 @ X2243 ) )
& ( ( in @ ( esk27_2 @ X2244 @ X2245 ) @ X2244 )
| ~ ( in @ X2247 @ X2244 )
| ~ ( X2245 @ X2247 ) )
& ( ( X2245 @ ( esk27_2 @ X2244 @ X2245 ) )
| ~ ( in @ X2247 @ X2244 )
| ~ ( X2245 @ X2247 ) )
& ( ( in @ ( esk28_2 @ X2248 @ X2249 ) @ X2248 )
| ~ ( in @ X2250 @ X2248 )
| ( X2249 @ X2250 ) )
& ( ~ ( X2249 @ ( esk28_2 @ X2248 @ X2249 ) )
| ~ ( in @ X2250 @ X2248 )
| ( X2249 @ X2250 ) )
& ( ~ X2252
| ( in @ emptyset @ ( prop2set @ X2252 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X2253 @ X2254 ) @ X2253 )
| ~ ( in @ X2256 @ X2253 )
| ~ ( X2254 @ X2256 ) )
& ( ( X2254 @ ( esk29_2 @ X2253 @ X2254 ) )
| ~ ( in @ X2256 @ X2253 )
| ~ ( X2254 @ X2256 ) )
& ( ( in @ ( esk30_2 @ X2257 @ X2258 ) @ X2257 )
| ~ ( in @ X2259 @ X2257 )
| ( X2258 @ X2259 ) )
& ( ~ ( X2258 @ ( esk30_2 @ X2257 @ X2258 ) )
| ~ ( in @ X2259 @ X2257 )
| ( X2258 @ X2259 ) )
& ( ( X2261 @ ( esk32_1 @ X2261 ) )
| ( X2261 @ ( esk31_2 @ X2261 @ X2262 ) )
| ~ ( X2261 @ X2262 ) )
& ( ~ ( X2261 @ X2265 )
| ( ( esk32_1 @ X2261 )
= X2265 )
| ( X2261 @ ( esk31_2 @ X2261 @ X2262 ) )
| ~ ( X2261 @ X2262 ) )
& ( ( X2261 @ ( esk32_1 @ X2261 ) )
| ( X2262
!= ( esk31_2 @ X2261 @ X2262 ) )
| ~ ( X2261 @ X2262 ) )
& ( ~ ( X2261 @ X2265 )
| ( ( esk32_1 @ X2261 )
= X2265 )
| ( X2262
!= ( esk31_2 @ X2261 @ X2262 ) )
| ~ ( X2261 @ X2262 ) )
& ( ( X2266 @ ( esk35_1 @ X2266 ) )
| ( X2266 @ ( esk33_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ~ ( X2266 @ X2271 )
| ( ( esk35_1 @ X2266 )
= X2271 )
| ( X2266 @ ( esk33_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ( X2266 @ ( esk35_1 @ X2266 ) )
| ( X2266 @ ( esk34_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ~ ( X2266 @ X2271 )
| ( ( esk35_1 @ X2266 )
= X2271 )
| ( X2266 @ ( esk34_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ( X2266 @ ( esk35_1 @ X2266 ) )
| ( ( esk33_1 @ X2266 )
!= ( esk34_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ~ ( X2266 @ X2271 )
| ( ( esk35_1 @ X2266 )
= X2271 )
| ( ( esk33_1 @ X2266 )
!= ( esk34_1 @ X2266 ) )
| ~ ( X2266 @ X2267 ) )
& ( ( X2272 @ ( esk37_1 @ X2272 ) )
| ~ ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
| ( ( esk36_2 @ X2272 @ X2273 )
!= X2273 ) )
& ( ~ ( X2272 @ X2276 )
| ( ( esk37_1 @ X2272 )
= X2276 )
| ~ ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
| ( ( esk36_2 @ X2272 @ X2273 )
!= X2273 ) )
& ( ( X2272 @ ( esk37_1 @ X2272 ) )
| ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
| ( ( esk36_2 @ X2272 @ X2273 )
= X2273 ) )
& ( ~ ( X2272 @ X2276 )
| ( ( esk37_1 @ X2272 )
= X2276 )
| ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
| ( ( esk36_2 @ X2272 @ X2273 )
= X2273 ) )
& ( ( X2277 != X2278 )
| ( X2279 != X2280 )
| ~ ( in @ X2279 @ X2277 )
| ( in @ X2280 @ X2278 ) )
& ( ~ ( in @ X2283 @ X2281 )
| ( in @ X2284 @ X2282 )
| ( X2283 != X2284 )
| ( X2281 != X2282 ) )
& ( ~ ( in @ X2284 @ X2282 )
| ( in @ X2283 @ X2281 )
| ( X2283 != X2284 )
| ( X2281 != X2282 ) )
& ( ( X2285 @ ( esk38_2 @ X2285 @ X2286 ) )
| ~ ( X2285 @ X2286 )
| ~ ( X2285 @ X2288 )
| ~ ( X2285 @ X2289 )
| ( X2288 = X2289 ) )
& ( ( X2286
!= ( esk38_2 @ X2285 @ X2286 ) )
| ~ ( X2285 @ X2286 )
| ~ ( X2285 @ X2288 )
| ~ ( X2285 @ X2289 )
| ( X2288 = X2289 ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( ( esk39_2 @ X2290 @ X2291 )
= ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2291 @ X2297 )
| ( ( esk42_2 @ X2290 @ X2291 )
= X2297 )
| ( X2294
!= ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
| ~ ( X2290 @ X2294 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( ~ ( X2290 @ X2301 )
| ( ( esk44_2 @ X2290 @ X2291 )
= X2301 )
| ( X2298
!= ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
| ~ ( X2291 @ X2298 )
| ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
| ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
& ( emptyset = emptyset )
& ( ( X2302 != X2303 )
| ( X2304 != X2305 )
| ( ( setadjoin @ X2302 @ X2304 )
= ( setadjoin @ X2303 @ X2305 ) ) )
& ( ( X2306 != X2307 )
| ( ( powerset @ X2306 )
= ( powerset @ X2307 ) ) )
& ( ( X2308 != X2309 )
| ( ( setunion @ X2308 )
= ( setunion @ X2309 ) ) )
& ( omega = omega )
& ( ( X2310 @ ( esk45_2 @ X2310 @ X2311 ) )
| ~ ( X2310 @ X2311 )
| ~ ( X2310 @ X2313 )
| ~ ( X2310 @ X2314 )
| ( X2313 = X2314 ) )
& ( ( X2311
!= ( esk45_2 @ X2310 @ X2311 ) )
| ~ ( X2310 @ X2311 )
| ~ ( X2310 @ X2313 )
| ~ ( X2310 @ X2314 )
| ( X2313 = X2314 ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( ( esk46_2 @ X2315 @ X2316 )
= ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( ( esk46_2 @ X2315 @ X2316 )
= ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( ( esk46_2 @ X2315 @ X2316 )
= ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( ( esk46_2 @ X2315 @ X2316 )
= ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( X2321
!= ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
| ~ ( X2316 @ X2321 )
| ( ( descr @ X2315 )
= ( descr @ X2316 ) )
| ( X2319
!= ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
| ~ ( X2315 @ X2319 )
| ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
| ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
& ( ( in @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) @ X2323 )
| ( ( dsetconstr @ X2323 @ X2325 )
= ( dsetconstr @ X2324 @ X2326 ) )
| ( X2323 != X2324 ) )
& ( ( in @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) @ X2324 )
| ( ( dsetconstr @ X2323 @ X2325 )
= ( dsetconstr @ X2324 @ X2326 ) )
| ( X2323 != X2324 ) )
& ( ( ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 )
= ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
| ( ( dsetconstr @ X2323 @ X2325 )
= ( dsetconstr @ X2324 @ X2326 ) )
| ( X2323 != X2324 ) )
& ( ~ ( X2325 @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
| ~ ( X2326 @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
| ( ( dsetconstr @ X2323 @ X2325 )
= ( dsetconstr @ X2324 @ X2326 ) )
| ( X2323 != X2324 ) )
& ( ( X2325 @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
| ( X2326 @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
| ( ( dsetconstr @ X2323 @ X2325 )
= ( dsetconstr @ X2324 @ X2326 ) )
| ( X2323 != X2324 ) )
& ( ( in @ ( esk52_2 @ X2329 @ X2330 ) @ X2329 )
| ( subset @ X2329 @ X2330 ) )
& ( ~ ( in @ ( esk52_2 @ X2329 @ X2330 ) @ X2330 )
| ( subset @ X2329 @ X2330 ) )
& ( ( X2332 != X2333 )
| ( subset @ X2333 @ X2332 ) )
& ( ( X2334 != X2335 )
| ( subset @ X2334 @ X2335 ) )
& ( ( in @ ( esk53_2 @ X2336 @ X2337 ) @ X2336 )
| ( subset @ X2336 @ X2337 ) )
& ( ~ ( in @ ( esk53_2 @ X2336 @ X2337 ) @ X2337 )
| ( subset @ X2336 @ X2337 ) )
& ( subset @ emptyset @ X2339 )
& ( ~ ( subset @ X2340 @ X2341 )
| ~ ( in @ X2342 @ X2340 )
| ( in @ X2342 @ X2341 ) )
& ( ~ ( subset @ X2343 @ X2344 )
| ( in @ X2345 @ X2344 )
| ~ ( in @ X2345 @ X2343 ) )
& ( ~ ( in @ X2348 @ X2346 )
| ( in @ X2348 @ X2347 )
| ~ ( subset @ X2346 @ X2347 ) )
& ( ( subset @ X2349 @ X2350 )
| ( X2349 != X2350 ) )
& ( ~ ( in @ X2353 @ X2351 )
| ( in @ X2353 @ X2352 )
| ( X2351 != X2352 ) )
& ( subset @ X2354 @ X2354 )
& ( ~ ( subset @ X2355 @ X2356 )
| ~ ( subset @ X2356 @ X2357 )
| ( subset @ X2355 @ X2357 ) )
& ( subset @ X2359 @ ( setadjoin @ X2358 @ X2359 ) )
& ( ~ ( subset @ X2360 @ X2362 )
| ( subset @ X2360 @ ( setadjoin @ X2361 @ X2362 ) ) )
& ( ~ ( subset @ X2363 @ X2364 )
| ( in @ X2363 @ ( powerset @ X2364 ) ) )
& ( ~ ( subset @ X2365 @ X2366 )
| ~ ( subset @ X2366 @ X2365 )
| ( X2365 = X2366 ) )
& ( ~ ( subset @ X2367 @ emptyset )
| ( X2367 = emptyset ) )
& ( ~ ( subset @ X2369 @ X2368 )
| ( in @ X2369 @ ( powerset @ X2368 ) ) )
& ( ~ ( in @ X2371 @ ( powerset @ X2370 ) )
| ( subset @ X2371 @ X2370 ) )
& ( in @ X2372 @ ( powerset @ X2372 ) )
& ( ~ ( subset @ X2373 @ X2374 )
| ( subset @ ( powerset @ X2373 ) @ ( powerset @ X2374 ) ) )
& ( in @ ( dsetconstr @ X2375 @ X2376 ) @ ( powerset @ X2375 ) )
& ( subset @ ( dsetconstr @ X2377 @ X2378 ) @ X2377 )
& ( ~ ( in @ X2381 @ X2379 )
| ( in @ X2381 @ ( binunion @ X2379 @ X2380 ) ) )
& ( in @ X2383 @ ( setadjoin @ X2382 @ ( setadjoin @ X2383 @ emptyset ) ) )
& ( ~ ( in @ X2386 @ X2385 )
| ( in @ X2386 @ ( binunion @ X2384 @ X2385 ) ) )
& ( ( in @ X2389 @ X2388 )
| X2390
| ( in @ X2389 @ X2387 )
| ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
& ( ~ X2390
| X2390
| ( in @ X2389 @ X2387 )
| ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
& ( ( in @ X2389 @ X2388 )
| X2390
| ~ X2390
| ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
& ( ~ X2390
| X2390
| ~ X2390
| ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
& ( ~ ( in @ X2393 @ ( binunion @ X2391 @ X2392 ) )
| ( in @ X2393 @ X2391 )
| ( in @ X2393 @ X2392 ) )
& ( subset @ X2394 @ ( binunion @ X2394 @ X2395 ) )
& ( subset @ X2397 @ ( binunion @ X2396 @ X2397 ) )
& ( ~ ( in @ X2400 @ X2398 )
| ~ ( in @ X2400 @ X2399 )
| ( in @ X2400 @ ( binintersect @ X2398 @ X2399 ) ) )
& ( ~ ( subset @ X2403 @ X2401 )
| ~ ( subset @ X2403 @ X2402 )
| ( subset @ X2403 @ ( binintersect @ X2401 @ X2402 ) ) )
& ( ~ ( in @ X2406 @ ( binintersect @ X2404 @ X2405 ) )
| ( in @ X2406 @ X2404 ) )
& ( subset @ ( binintersect @ X2407 @ X2408 ) @ X2407 )
& ( ~ ( subset @ X2409 @ X2410 )
| ( ( binintersect @ X2409 @ X2410 )
= X2409 ) )
& ( ( ( binintersect @ X2411 @ X2412 )
!= X2412 )
| ( subset @ X2412 @ X2411 ) )
& ( ~ ( in @ X2415 @ ( binintersect @ X2413 @ X2414 ) )
| ( in @ X2415 @ X2414 ) )
& ( ( in @ ( esk54_2 @ X2416 @ X2417 ) @ X2416 )
| ( ( binintersect @ X2416 @ X2417 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X2416 @ X2417 ) @ X2417 )
| ( ( binintersect @ X2416 @ X2417 )
= emptyset ) )
& ( subset @ ( binintersect @ X2419 @ X2420 ) @ X2420 )
& ( ~ ( subset @ X2422 @ X2421 )
| ( ( binintersect @ X2421 @ X2422 )
= X2422 ) )
& ( ( ( binintersect @ X2423 @ X2424 )
!= X2423 )
| ( subset @ X2423 @ X2424 ) )
& ( ( binintersect @ X2425 @ ( binunion @ X2426 @ X2427 ) )
= ( binunion @ ( binintersect @ X2425 @ X2426 ) @ ( binintersect @ X2425 @ X2427 ) ) )
& ( ~ ( in @ X2430 @ X2428 )
| ( in @ X2430 @ X2429 )
| ( in @ X2430 @ ( setminus @ X2428 @ X2429 ) ) )
& ( ~ ( in @ X2433 @ ( setminus @ X2431 @ X2432 ) )
| ( in @ X2433 @ X2431 ) )
& ( ~ ( in @ X2436 @ ( setminus @ X2434 @ X2435 ) )
| ~ ( in @ X2436 @ X2435 ) )
& ( ~ ( subset @ X2437 @ X2438 )
| ( ( setminus @ X2437 @ X2438 )
= emptyset ) )
& ( ( in @ X2441 @ ( setminus @ X2439 @ X2440 ) )
| ~ ( in @ X2441 @ X2439 )
| ( in @ X2441 @ X2440 ) )
& ( ( in @ X2444 @ ( setminus @ X2442 @ X2443 ) )
| ( in @ X2444 @ X2443 )
| ~ ( in @ X2444 @ X2442 ) )
& ( ( in @ X2447 @ X2445 )
| ~ ( in @ X2447 @ ( setminus @ X2445 @ X2446 ) ) )
& ( ~ ( in @ X2450 @ X2449 )
| ~ ( in @ X2450 @ ( setminus @ X2448 @ X2449 ) ) )
& ( subset @ ( setminus @ X2451 @ X2452 ) @ X2451 )
& ( ( ( setminus @ X2453 @ X2454 )
!= emptyset )
| ( subset @ X2453 @ X2454 ) )
& ( ~ ( in @ X2457 @ X2455 )
| X2458
| ( in @ X2457 @ X2455 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ( in @ X2457 @ X2456 )
| X2458
| ( in @ X2457 @ X2455 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ X2458
| X2458
| ( in @ X2457 @ X2455 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ ( in @ X2457 @ X2455 )
| X2458
| ~ ( in @ X2457 @ X2456 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ( in @ X2457 @ X2456 )
| X2458
| ~ ( in @ X2457 @ X2456 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ X2458
| X2458
| ~ ( in @ X2457 @ X2456 )
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ ( in @ X2457 @ X2455 )
| X2458
| ~ X2458
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ( in @ X2457 @ X2456 )
| X2458
| ~ X2458
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ X2458
| X2458
| ~ X2458
| ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
& ( ~ ( in @ X2461 @ X2459 )
| ( in @ X2461 @ X2460 )
| ( in @ X2461 @ ( symdiff @ X2459 @ X2460 ) ) )
& ( ( in @ X2464 @ X2462 )
| ~ ( in @ X2464 @ X2463 )
| ( in @ X2464 @ ( symdiff @ X2462 @ X2463 ) ) )
& ( ~ ( in @ X2467 @ X2465 )
| ~ ( in @ X2467 @ X2466 )
| ~ ( in @ X2467 @ ( symdiff @ X2465 @ X2466 ) ) )
& ( ( in @ X2470 @ X2468 )
| ( in @ X2470 @ X2469 )
| ~ ( in @ X2470 @ ( symdiff @ X2468 @ X2469 ) ) )
& ( in @ X2472 @ ( setadjoin @ X2471 @ ( setadjoin @ X2472 @ emptyset ) ) )
& ( in @ X2473 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2473 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2473 @ ( setadjoin @ X2474 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2476 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2475 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2475 @ ( setadjoin @ X2476 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2477 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2477 @ ( setadjoin @ X2478 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2479 @ X2480 ) )
& ( ~ ( in @ X2482 @ X2481 )
| ( subset @ ( setadjoin @ X2482 @ emptyset ) @ X2481 ) )
& ( ~ ( in @ X2484 @ X2483 )
| ( in @ ( setadjoin @ X2484 @ emptyset ) @ ( powerset @ X2483 ) ) )
& ( ~ ( in @ X2487 @ X2485 )
| ( in @ ( setadjoin @ X2487 @ emptyset ) @ ( powerset @ ( binunion @ X2485 @ X2486 ) ) ) )
& ( ~ ( in @ X2490 @ ( setadjoin @ X2488 @ ( setadjoin @ X2489 @ emptyset ) ) )
| ( X2490 = X2488 )
| ( X2490 = X2489 ) )
& ( ~ ( in @ X2493 @ X2491 )
| ~ ( in @ X2494 @ X2492 )
| ( subset @ ( setadjoin @ X2493 @ ( setadjoin @ X2494 @ emptyset ) ) @ ( binunion @ X2491 @ X2492 ) ) )
& ( ~ ( in @ X2497 @ X2495 )
| ~ ( in @ X2498 @ X2496 )
| ( in @ ( setadjoin @ X2497 @ ( setadjoin @ X2498 @ emptyset ) ) @ ( powerset @ ( binunion @ X2495 @ X2496 ) ) ) )
& ( ~ ( in @ X2501 @ X2499 )
| ~ ( in @ X2502 @ X2500 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2501 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2501 @ ( setadjoin @ X2502 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2499 @ X2500 ) ) ) )
& ( ~ ( in @ X2505 @ X2503 )
| ~ ( in @ X2506 @ X2504 )
| ( in @ ( setadjoin @ ( setadjoin @ X2505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2505 @ ( setadjoin @ X2506 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2503 @ X2504 ) ) ) ) )
& ( ~ ( in @ X2509 @ X2507 )
| ~ ( in @ X2510 @ X2508 )
| ( in @ ( kpair @ X2509 @ X2510 ) @ ( powerset @ ( powerset @ ( binunion @ X2507 @ X2508 ) ) ) ) )
& ( ~ ( in @ X2513 @ X2511 )
| ~ ( in @ X2514 @ X2512 )
| ( in @ ( kpair @ X2513 @ X2514 ) @ ( cartprod @ X2511 @ X2512 ) ) )
& ( ( in @ ( esk55_3 @ X2515 @ X2516 @ X2517 ) @ X2515 )
| ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk56_3 @ X2515 @ X2516 @ X2517 ) @ X2516 )
| ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( X2517
= ( kpair @ ( esk55_3 @ X2515 @ X2516 @ X2517 ) @ ( esk56_3 @ X2515 @ X2516 @ X2517 ) ) )
| ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ~ ( in @ X2522 @ ( cartprod @ X2520 @ X2521 ) )
| ( iskpair @ X2522 ) )
& ( ( in @ ( esk57_2 @ X2523 @ X2524 ) @ X2523 )
| ~ ( in @ X2524 @ ( setunion @ X2523 ) ) )
& ( ( in @ X2524 @ ( esk57_2 @ X2523 @ X2524 ) )
| ~ ( in @ X2524 @ ( setunion @ X2523 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2526 @ emptyset ) ) @ X2526 )
& ( subset @ X2527 @ ( setunion @ ( setadjoin @ X2527 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2528 @ emptyset ) )
= X2528 )
& ( ( in @ ( esk58_2 @ X2529 @ X2530 ) @ X2529 )
| ~ ( in @ X2533 @ X2529 )
| ~ ( X2530 @ X2533 )
| ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
& ( ( in @ ( esk59_2 @ X2529 @ X2530 ) @ X2529 )
| ~ ( in @ X2533 @ X2529 )
| ~ ( X2530 @ X2533 )
| ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
& ( ( X2530 @ ( esk58_2 @ X2529 @ X2530 ) )
| ~ ( in @ X2533 @ X2529 )
| ~ ( X2530 @ X2533 )
| ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
& ( ( X2530 @ ( esk59_2 @ X2529 @ X2530 ) )
| ~ ( in @ X2533 @ X2529 )
| ~ ( X2530 @ X2533 )
| ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
& ( ( ( esk58_2 @ X2529 @ X2530 )
!= ( esk59_2 @ X2529 @ X2530 ) )
| ~ ( in @ X2533 @ X2529 )
| ~ ( X2530 @ X2533 )
| ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
& ( ( in @ ( esk60_2 @ X2534 @ X2535 ) @ X2534 )
| ~ ( ex1 @ X2534 @ X2535 ) )
& ( ( X2535 @ ( esk60_2 @ X2534 @ X2535 ) )
| ~ ( ex1 @ X2534 @ X2535 ) )
& ( ( in @ ( esk61_3 @ X2537 @ X2538 @ X2539 ) @ X2537 )
| ( ex1 @ X2537 @ X2538 )
| ~ ( X2538 @ X2539 )
| ~ ( in @ X2539 @ X2537 ) )
& ( ( X2538 @ ( esk61_3 @ X2537 @ X2538 @ X2539 ) )
| ( ex1 @ X2537 @ X2538 )
| ~ ( X2538 @ X2539 )
| ~ ( in @ X2539 @ X2537 ) )
& ( ( ( esk61_3 @ X2537 @ X2538 @ X2539 )
!= X2539 )
| ( ex1 @ X2537 @ X2538 )
| ~ ( X2538 @ X2539 )
| ~ ( in @ X2539 @ X2537 ) )
& ( ( in @ ( esk62_2 @ X2541 @ X2542 ) @ X2541 )
| ~ ( in @ X2545 @ X2541 )
| ~ ( X2542 @ X2545 )
| ( ex1 @ X2541 @ X2542 ) )
& ( ( in @ ( esk63_2 @ X2541 @ X2542 ) @ X2541 )
| ~ ( in @ X2545 @ X2541 )
| ~ ( X2542 @ X2545 )
| ( ex1 @ X2541 @ X2542 ) )
& ( ( X2542 @ ( esk62_2 @ X2541 @ X2542 ) )
| ~ ( in @ X2545 @ X2541 )
| ~ ( X2542 @ X2545 )
| ( ex1 @ X2541 @ X2542 ) )
& ( ( X2542 @ ( esk63_2 @ X2541 @ X2542 ) )
| ~ ( in @ X2545 @ X2541 )
| ~ ( X2542 @ X2545 )
| ( ex1 @ X2541 @ X2542 ) )
& ( ( ( esk62_2 @ X2541 @ X2542 )
!= ( esk63_2 @ X2541 @ X2542 ) )
| ~ ( in @ X2545 @ X2541 )
| ~ ( X2542 @ X2545 )
| ( ex1 @ X2541 @ X2542 ) )
& ( ( ( setadjoin @ X2546 @ emptyset )
!= ( setadjoin @ X2547 @ emptyset ) )
| ( X2546 = X2547 ) )
& ( ~ ( in @ ( setadjoin @ X2550 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2548 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2548 @ ( setadjoin @ X2549 @ emptyset ) ) @ emptyset ) ) )
| ( X2548 = X2550 ) )
& ( ~ ( iskpair @ X2551 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2551 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2551 ) ) ) )
& ( ~ ( singleton @ X2552 )
| ( in @ ( setunion @ X2552 ) @ X2552 ) )
& ( ( kfst @ ( kpair @ X2553 @ X2554 ) )
= X2553 )
& ( ~ ( in @ X2557 @ ( cartprod @ X2555 @ X2556 ) )
| ( in @ ( kfst @ X2557 ) @ X2555 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2558 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2558 @ ( setadjoin @ X2559 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2560 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2560 @ ( setadjoin @ X2561 @ emptyset ) ) @ emptyset ) ) )
| ( X2558 = X2560 ) )
& ( ( ( kpair @ X2562 @ X2563 )
!= ( kpair @ X2564 @ X2565 ) )
| ( X2562 = X2564 ) )
& ( ( X2566 != X2567 )
| ( ( setadjoin @ X2566 @ ( setadjoin @ X2567 @ emptyset ) )
= ( setadjoin @ X2566 @ emptyset ) ) )
& ( ( X2568 != X2569 )
| ( ( setadjoin @ ( setadjoin @ X2568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2568 @ ( setadjoin @ X2569 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2568 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2570 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2570 @ ( setadjoin @ X2571 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2572 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2572 @ ( setadjoin @ X2573 @ emptyset ) ) @ emptyset ) ) )
| ( X2572 != X2573 )
| ( X2571 = X2573 ) )
& ( ( ( setadjoin @ X2574 @ ( setadjoin @ X2575 @ emptyset ) )
!= ( setadjoin @ X2576 @ emptyset ) )
| ( X2574 = X2575 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2577 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2577 @ ( setadjoin @ X2578 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2579 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2579 @ ( setadjoin @ X2580 @ emptyset ) ) @ emptyset ) ) )
| ( X2578 = X2580 ) )
& ( ( ( kpair @ X2581 @ X2582 )
!= ( kpair @ X2583 @ X2584 ) )
| ( X2582 = X2584 ) )
& ( ~ ( iskpair @ X2585 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2585 )
@ ^ [Z0: $i] :
( X2585
= ( kpair @ ( kfst @ X2585 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2586 @ X2587 ) )
= X2587 )
& ( ~ ( iskpair @ X2588 )
| ( ( kpair @ ( kfst @ X2588 ) @ ( ksnd @ X2588 ) )
= X2588 ) )
& ( ~ ( in @ X2591 @ ( cartprod @ X2589 @ X2590 ) )
| ( in @ ( ksnd @ X2591 ) @ X2590 ) )
& ( ~ ( in @ ( kpair @ X2594 @ X2595 ) @ ( cartprod @ X2592 @ X2593 ) )
| ( in @ X2594 @ X2592 ) )
& ( ~ ( in @ ( kpair @ X2598 @ X2599 ) @ ( cartprod @ X2596 @ X2597 ) )
| ( in @ X2599 @ X2597 ) )
& ( ~ ( in @ X2602 @ X2600 )
| ~ ( in @ X2603 @ X2601 )
| ( ( kpair @ X2602 @ X2603 )
= ( kpair @ X2602 @ X2603 ) ) )
& ( ~ ( in @ X2606 @ X2604 )
| ~ ( in @ X2607 @ X2605 )
| ( ( kfst @ ( kpair @ X2606 @ X2607 ) )
= X2606 ) )
& ( ~ ( in @ X2610 @ X2608 )
| ~ ( in @ X2611 @ X2609 )
| ( ( ksnd @ ( kpair @ X2610 @ X2611 ) )
= X2611 ) )
& ( ~ ( in @ X2614 @ ( cartprod @ X2612 @ X2613 ) )
| ( ( kpair @ ( kfst @ X2614 ) @ ( ksnd @ X2614 ) )
= X2614 ) )
& ( ~ ( in @ X2618 @ X2615 )
| ~ ( in @ X2619 @ X2616 )
| ~ ( X2617 @ X2618 @ X2619 )
| ( in @ ( kpair @ X2618 @ X2619 ) @ ( dpsetconstr @ X2615 @ X2616 @ X2617 ) ) )
& ( subset @ ( dpsetconstr @ X2620 @ X2621 @ X2622 ) @ ( cartprod @ X2620 @ X2621 ) )
& ( breln @ X2623 @ X2624 @ ( dpsetconstr @ X2623 @ X2624 @ X2625 ) )
& ( ~ ( in @ X2629 @ X2626 )
| ~ ( in @ X2630 @ X2627 )
| ~ ( in @ ( kpair @ X2629 @ X2630 ) @ ( dpsetconstr @ X2626 @ X2627 @ X2628 ) )
| ( X2628 @ X2629 @ X2630 ) )
& ( ~ ( in @ ( kpair @ X2634 @ X2635 ) @ ( dpsetconstr @ X2631 @ X2632 @ X2633 ) )
| ( in @ X2634 @ X2631 ) )
& ( ~ ( in @ ( kpair @ X2639 @ X2640 ) @ ( dpsetconstr @ X2636 @ X2637 @ X2638 ) )
| ( in @ X2640 @ X2637 ) )
& ( ~ ( in @ ( kpair @ X2644 @ X2645 ) @ ( dpsetconstr @ X2641 @ X2642 @ X2643 ) )
| ( X2643 @ X2644 @ X2645 ) )
& ( ~ ( func @ X2646 @ X2647 @ X2648 )
| ~ ( in @ X2649 @ X2646 )
| ( singleton
@ ( dsetconstr @ X2647
@ ^ [Z0: $i] : ( in @ ( kpair @ X2649 @ Z0 ) @ X2648 ) ) ) )
& ( ~ ( func @ X2650 @ X2651 @ X2652 )
| ~ ( in @ X2653 @ X2650 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2651
@ ^ [Z0: $i] : ( in @ ( kpair @ X2653 @ Z0 ) @ X2652 ) ) )
@ X2651 ) )
& ( ~ ( func @ X2654 @ X2655 @ X2656 )
| ~ ( in @ X2657 @ X2654 )
| ( in @ ( ap @ X2654 @ X2655 @ X2656 @ X2657 ) @ X2655 ) )
& ( ~ ( in @ X2660 @ ( funcSet @ X2658 @ X2659 ) )
| ( func @ X2658 @ X2659 @ X2660 ) )
& ( ~ ( in @ X2663 @ ( funcSet @ X2661 @ X2662 ) )
| ~ ( in @ X2664 @ X2661 )
| ( in @ ( ap @ X2661 @ X2662 @ X2663 @ X2664 ) @ X2662 ) )
& ( ~ ( func @ X2665 @ X2666 @ X2667 )
| ( in @ X2667 @ ( funcSet @ X2665 @ X2666 ) ) )
& ( ( in @ ( esk64_3 @ X2668 @ X2669 @ X2670 ) @ X2668 )
| ( func @ X2668 @ X2669
@ ( dpsetconstr @ X2668 @ X2669
@ ^ [Z0: $i] : ( $eq @ ( X2670 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2670 @ ( esk64_3 @ X2668 @ X2669 @ X2670 ) ) @ X2669 )
| ( func @ X2668 @ X2669
@ ( dpsetconstr @ X2668 @ X2669
@ ^ [Z0: $i] : ( $eq @ ( X2670 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2672 @ X2673 @ X2674 ) @ X2672 )
| ( func @ X2672 @ X2673 @ ( lam @ X2672 @ X2673 @ X2674 ) ) )
& ( ~ ( in @ ( X2674 @ ( esk65_3 @ X2672 @ X2673 @ X2674 ) ) @ X2673 )
| ( func @ X2672 @ X2673 @ ( lam @ X2672 @ X2673 @ X2674 ) ) )
& ( ( in @ ( esk66_3 @ X2676 @ X2677 @ X2678 ) @ X2676 )
| ( in @ ( lam @ X2676 @ X2677 @ X2678 ) @ ( funcSet @ X2676 @ X2677 ) ) )
& ( ~ ( in @ ( X2678 @ ( esk66_3 @ X2676 @ X2677 @ X2678 ) ) @ X2677 )
| ( in @ ( lam @ X2676 @ X2677 @ X2678 ) @ ( funcSet @ X2676 @ X2677 ) ) )
& ( ( in @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ X2680 )
| ~ ( in @ X2686 @ X2682 )
| ( X2683 @ X2686 )
| ~ ( breln @ X2680 @ X2681 @ X2682 ) )
& ( ( in @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ X2681 )
| ~ ( in @ X2686 @ X2682 )
| ( X2683 @ X2686 )
| ~ ( breln @ X2680 @ X2681 @ X2682 ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) ) @ X2682 )
| ~ ( in @ X2686 @ X2682 )
| ( X2683 @ X2686 )
| ~ ( breln @ X2680 @ X2681 @ X2682 ) )
& ( ~ ( X2683 @ ( kpair @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) ) )
| ~ ( in @ X2686 @ X2682 )
| ( X2683 @ X2686 )
| ~ ( breln @ X2680 @ X2681 @ X2682 ) )
& ( ( in @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ X2687 )
| ~ ( in @ X2693 @ X2689 )
| ( X2690 @ X2693 )
| ~ ( breln @ X2687 @ X2688 @ X2689 ) )
& ( ( in @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ X2688 )
| ~ ( in @ X2693 @ X2689 )
| ( X2690 @ X2693 )
| ~ ( breln @ X2687 @ X2688 @ X2689 ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) ) @ X2689 )
| ~ ( in @ X2693 @ X2689 )
| ( X2690 @ X2693 )
| ~ ( breln @ X2687 @ X2688 @ X2689 ) )
& ( ~ ( X2690 @ ( kpair @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) ) )
| ~ ( in @ X2693 @ X2689 )
| ( X2690 @ X2693 )
| ~ ( breln @ X2687 @ X2688 @ X2689 ) )
& ( ~ ( ex1 @ X2694 @ X2695 )
| ~ ( in @ X2696 @ X2694 )
| ~ ( in @ X2697 @ X2694 )
| ~ ( X2695 @ X2696 )
| ~ ( X2695 @ X2697 )
| ( X2696 = X2697 ) )
& ( ~ ( func @ X2698 @ X2699 @ X2700 )
| ~ ( in @ X2701 @ X2698 )
| ( in @ ( kpair @ X2701 @ ( ap @ X2698 @ X2699 @ X2700 @ X2701 ) ) @ X2700 ) )
& ( ~ ( in @ X2704 @ ( funcSet @ X2702 @ X2703 ) )
| ~ ( in @ X2705 @ X2702 )
| ( in @ ( kpair @ X2705 @ ( ap @ X2702 @ X2703 @ X2704 @ X2705 ) ) @ X2704 ) )
& ( ~ ( func @ X2706 @ X2707 @ X2708 )
| ~ ( in @ X2709 @ X2706 )
| ~ ( in @ X2710 @ X2707 )
| ~ ( in @ ( kpair @ X2709 @ X2710 ) @ X2708 )
| ( ( ap @ X2706 @ X2707 @ X2708 @ X2709 )
= X2710 ) )
& ( ( in @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) @ X2711 )
| ~ ( in @ X2716 @ X2711 )
| ~ ( in @ X2717 @ X2712 )
| ~ ( in @ ( kpair @ X2716 @ X2717 ) @ X2714 )
| ( in @ ( kpair @ X2716 @ X2717 ) @ X2713 )
| ~ ( func @ X2711 @ X2712 @ X2714 )
| ~ ( func @ X2711 @ X2712 @ X2713 ) )
& ( ( ( ap @ X2711 @ X2712 @ X2713 @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) )
!= ( ap @ X2711 @ X2712 @ X2714 @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) ) )
| ~ ( in @ X2716 @ X2711 )
| ~ ( in @ X2717 @ X2712 )
| ~ ( in @ ( kpair @ X2716 @ X2717 ) @ X2714 )
| ( in @ ( kpair @ X2716 @ X2717 ) @ X2713 )
| ~ ( func @ X2711 @ X2712 @ X2714 )
| ~ ( func @ X2711 @ X2712 @ X2713 ) )
& ( ~ ( in @ X2720 @ ( funcSet @ X2718 @ X2719 ) )
| ~ ( in @ X2721 @ X2718 )
| ~ ( in @ X2722 @ X2719 )
| ~ ( in @ ( kpair @ X2721 @ X2722 ) @ X2720 )
| ( ( ap @ X2718 @ X2719 @ X2720 @ X2721 )
= X2722 ) )
& ( ( in @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ X2723 )
| ( subset @ X2725 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2725 ) )
& ( ( in @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ X2724 )
| ( subset @ X2725 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2725 ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) ) @ X2725 )
| ( subset @ X2725 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2725 ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) ) @ X2726 )
| ( subset @ X2725 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2726 )
| ~ ( breln @ X2723 @ X2724 @ X2725 ) )
& ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ( X2731 = X2732 )
| ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ( X2731 = X2732 )
| ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ( X2731 = X2732 )
| ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ( X2731 = X2732 )
| ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ( X2731 = X2732 )
| ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ( X2731 = X2732 )
| ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ( X2731 = X2732 )
| ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ( X2731 = X2732 )
| ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ( X2731 = X2732 )
| ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ( X2731 = X2732 )
| ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ( X2731 = X2732 )
| ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ( X2731 = X2732 )
| ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
| ( X2731 = X2732 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
| ( X2731 = X2732 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ( X2731 = X2732 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
| ( X2731 = X2732 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2732 )
| ~ ( breln @ X2729 @ X2730 @ X2731 ) )
& ( ( in @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) @ X2737 )
| ( X2739 = X2740 )
| ~ ( func @ X2737 @ X2738 @ X2740 )
| ~ ( func @ X2737 @ X2738 @ X2739 ) )
& ( ( ( ap @ X2737 @ X2738 @ X2739 @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) )
!= ( ap @ X2737 @ X2738 @ X2740 @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) ) )
| ( X2739 = X2740 )
| ~ ( func @ X2737 @ X2738 @ X2740 )
| ~ ( func @ X2737 @ X2738 @ X2739 ) )
& ( ( in @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) @ X2742 )
| ( X2744 = X2745 )
| ~ ( in @ X2745 @ ( funcSet @ X2742 @ X2743 ) )
| ~ ( in @ X2744 @ ( funcSet @ X2742 @ X2743 ) ) )
& ( ( ( ap @ X2742 @ X2743 @ X2744 @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) )
!= ( ap @ X2742 @ X2743 @ X2745 @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) ) )
| ( X2744 = X2745 )
| ~ ( in @ X2745 @ ( funcSet @ X2742 @ X2743 ) )
| ~ ( in @ X2744 @ ( funcSet @ X2742 @ X2743 ) ) )
& ( ~ ( in @ X2749 @ ( funcSet @ X2747 @ X2748 ) )
| ~ ( in @ X2750 @ X2747 )
| ( ( ap @ X2747 @ X2748 @ X2749 @ X2750 )
= ( ap @ X2747 @ X2748 @ X2749 @ X2750 ) ) )
& ( ~ ( func @ X2751 @ X2752 @ X2753 )
| ~ ( in @ X2754 @ X2751 )
| ( ( ap @ X2751 @ X2752 @ X2753 @ X2754 )
= ( ap @ X2751 @ X2752 @ X2753 @ X2754 ) ) )
& ( ( in @ ( esk80_3 @ X2755 @ X2756 @ X2757 ) @ X2755 )
| ~ ( in @ X2759 @ X2755 )
| ( ( ap @ X2755 @ X2756 @ ( lam @ X2755 @ X2756 @ X2757 ) @ X2759 )
= ( X2757 @ X2759 ) ) )
& ( ~ ( in @ ( X2757 @ ( esk80_3 @ X2755 @ X2756 @ X2757 ) ) @ X2756 )
| ~ ( in @ X2759 @ X2755 )
| ( ( ap @ X2755 @ X2756 @ ( lam @ X2755 @ X2756 @ X2757 ) @ X2759 )
= ( X2757 @ X2759 ) ) )
& ( ~ ( func @ X2760 @ X2761 @ X2762 )
| ( ( lam @ X2760 @ X2761 @ ( ap @ X2760 @ X2761 @ X2762 ) )
= X2762 ) )
& ( ( in @ ( esk81_3 @ X2763 @ X2764 @ X2765 ) @ X2763 )
| ( ( lam @ X2763 @ X2764 @ X2765 )
= ( lam @ X2763 @ X2764 @ X2765 ) ) )
& ( ~ ( in @ ( X2765 @ ( esk81_3 @ X2763 @ X2764 @ X2765 ) ) @ X2764 )
| ( ( lam @ X2763 @ X2764 @ X2765 )
= ( lam @ X2763 @ X2764 @ X2765 ) ) )
& ( ( in @ ( esk82_3 @ X2767 @ X2768 @ X2769 ) @ X2767 )
| ~ ( in @ X2771 @ X2767 )
| ( ( ap @ X2767 @ X2768 @ ( lam @ X2767 @ X2768 @ X2769 ) @ X2771 )
= ( X2769 @ X2771 ) ) )
& ( ~ ( in @ ( X2769 @ ( esk82_3 @ X2767 @ X2768 @ X2769 ) ) @ X2768 )
| ~ ( in @ X2771 @ X2767 )
| ( ( ap @ X2767 @ X2768 @ ( lam @ X2767 @ X2768 @ X2769 ) @ X2771 )
= ( X2769 @ X2771 ) ) )
& ( ~ ( in @ X2774 @ ( funcSet @ X2772 @ X2773 ) )
| ( ( lam @ X2772 @ X2773 @ ( ap @ X2772 @ X2773 @ X2774 ) )
= X2774 ) )
& ( ~ ( in @ X2777 @ X2775 )
| ~ ( in @ X2778 @ X2775 )
| X2776
| ( in @ X2778
@ ( dsetconstr @ X2775
@ ^ [Z0: $i] :
( ( X2776
& ( Z0 = X2777 ) )
| ( ~ X2776
& ( Z0 = X2778 ) ) ) ) ) )
& ( ~ ( in @ X2781 @ X2779 )
| ~ ( in @ X2782 @ X2779 )
| X2780
| ( ( dsetconstr @ X2779
@ ^ [Z0: $i] :
( ( X2780
& ( Z0 = X2781 ) )
| ( ~ X2780
& ( Z0 = X2782 ) ) ) )
= ( setadjoin @ X2782 @ emptyset ) ) )
& ( ~ ( in @ X2785 @ X2783 )
| ~ ( in @ X2786 @ X2783 )
| ~ X2784
| ( in @ X2785
@ ( dsetconstr @ X2783
@ ^ [Z0: $i] :
( ( X2784
& ( Z0 = X2785 ) )
| ( ~ X2784
& ( Z0 = X2786 ) ) ) ) ) )
& ( ~ ( in @ X2789 @ X2787 )
| ~ ( in @ X2790 @ X2787 )
| ~ X2788
| ( ( dsetconstr @ X2787
@ ^ [Z0: $i] :
( ( X2788
& ( Z0 = X2789 ) )
| ( ~ X2788
& ( Z0 = X2790 ) ) ) )
= ( setadjoin @ X2789 @ emptyset ) ) )
& ( ~ ( in @ X2793 @ X2791 )
| ~ ( in @ X2794 @ X2791 )
| ( singleton
@ ( dsetconstr @ X2791
@ ^ [Z0: $i] :
( ( X2792
& ( Z0 = X2793 ) )
| ( ~ X2792
& ( Z0 = X2794 ) ) ) ) ) )
& ( ~ ( in @ X2797 @ X2795 )
| ~ ( in @ X2798 @ X2795 )
| ( in @ ( if @ X2795 @ X2796 @ X2797 @ X2798 ) @ X2795 ) )
& ( ~ ( singleton @ X2799 )
| ~ ( in @ X2800 @ X2799 )
| ( ( setunion @ X2799 )
= X2800 ) )
& ( ~ ( in @ X2803 @ X2801 )
| ~ ( in @ X2804 @ X2801 )
| ~ X2802
| ( ( if @ X2801 @ X2802 @ X2803 @ X2804 )
= X2803 ) )
& ( ~ ( in @ X2807 @ X2805 )
| ~ ( in @ X2808 @ X2805 )
| X2806
| ( ( if @ X2805 @ X2806 @ X2807 @ X2808 )
= X2808 ) )
& ( ~ ( in @ X2811 @ X2809 )
| ~ ( in @ X2812 @ X2809 )
| ( in @ ( if @ X2809 @ X2810 @ X2811 @ X2812 ) @ ( setadjoin @ X2811 @ ( setadjoin @ X2812 @ emptyset ) ) ) )
& ( ~ ( in @ X2814 @ ( powerset @ X2813 ) )
| ~ ( in @ X2815 @ ( powerset @ X2813 ) )
| ( in @ ( binintersect @ X2814 @ X2815 ) @ ( powerset @ X2813 ) ) )
& ( ~ ( in @ X2817 @ ( powerset @ X2816 ) )
| ~ ( in @ X2818 @ ( powerset @ X2816 ) )
| ( in @ ( binunion @ X2817 @ X2818 ) @ ( powerset @ X2816 ) ) )
& ( ~ ( in @ X2820 @ ( powerset @ X2819 ) )
| ( in @ ( powerset @ X2820 ) @ ( powerset @ ( powerset @ X2819 ) ) ) )
& ( ~ ( in @ X2822 @ ( powerset @ X2821 ) )
| ~ ( in @ X2823 @ ( powerset @ X2821 ) )
| ( in @ ( setminus @ X2822 @ X2823 ) @ ( powerset @ X2821 ) ) )
& ( ~ ( in @ X2825 @ ( powerset @ X2824 ) )
| ( in @ ( setminus @ X2824 @ X2825 ) @ ( powerset @ X2824 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ( X2827 = X2828 )
| ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
| ( X2827 = X2828 )
| ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ( X2827 = X2828 )
| ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
| ( X2827 = X2828 )
| ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
| ~ ( in @ X2828 @ ( powerset @ X2826 ) )
| ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
& ( ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2831 )
| ( subset @ X2832 @ X2833 )
| ~ ( in @ X2833 @ ( powerset @ X2831 ) )
| ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
& ( ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2832 )
| ( subset @ X2832 @ X2833 )
| ~ ( in @ X2833 @ ( powerset @ X2831 ) )
| ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2833 )
| ( subset @ X2832 @ X2833 )
| ~ ( in @ X2833 @ ( powerset @ X2831 ) )
| ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
& ( ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2835 )
| ( in @ X2836 @ ( powerset @ X2837 ) )
| ~ ( in @ X2837 @ ( powerset @ X2835 ) )
| ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
& ( ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2836 )
| ( in @ X2836 @ ( powerset @ X2837 ) )
| ~ ( in @ X2837 @ ( powerset @ X2835 ) )
| ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2837 )
| ( in @ X2836 @ ( powerset @ X2837 ) )
| ~ ( in @ X2837 @ ( powerset @ X2835 ) )
| ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
& ( ~ ( in @ X2840 @ ( powerset @ X2839 ) )
| ~ ( in @ X2841 @ ( powerset @ X2839 ) )
| ~ ( in @ X2842 @ X2839 )
| ~ ( in @ X2840 @ ( powerset @ X2841 ) )
| ~ ( in @ X2842 @ X2840 )
| ( in @ X2842 @ X2841 ) )
& ( ~ ( in @ X2844 @ ( powerset @ X2843 ) )
| ~ ( in @ X2845 @ X2843 )
| ~ ( in @ X2845 @ X2844 )
| ~ ( in @ X2845 @ ( setminus @ X2843 @ X2844 ) ) )
& ( ~ ( in @ X2847 @ ( powerset @ X2846 ) )
| ~ ( in @ X2848 @ X2846 )
| ( in @ X2848 @ ( setminus @ X2846 @ X2847 ) )
| ( in @ X2848 @ X2847 ) )
& ( ~ ( in @ X2850 @ ( powerset @ X2849 ) )
| ~ ( in @ X2851 @ ( powerset @ X2849 ) )
| ~ ( in @ X2852 @ X2849 )
| ( in @ X2852 @ X2850 )
| ~ ( in @ X2852 @ ( binintersect @ X2850 @ X2851 ) ) )
& ( ~ ( in @ X2854 @ ( powerset @ X2853 ) )
| ~ ( in @ X2855 @ ( powerset @ X2853 ) )
| ~ ( in @ X2856 @ X2853 )
| ( in @ X2856 @ X2855 )
| ~ ( in @ X2856 @ ( binintersect @ X2854 @ X2855 ) ) )
& ( ~ ( in @ X2858 @ ( powerset @ X2857 ) )
| ~ ( in @ X2859 @ ( powerset @ X2857 ) )
| ~ ( in @ X2860 @ X2857 )
| ~ ( subset @ X2858 @ ( setminus @ X2857 @ X2859 ) )
| ~ ( in @ X2860 @ X2859 )
| ~ ( in @ X2860 @ X2858 ) )
& ( ~ ( in @ X2862 @ ( powerset @ X2861 ) )
| ~ ( in @ X2863 @ ( powerset @ X2861 ) )
| ~ ( in @ X2864 @ X2861 )
| ~ ( subset @ X2862 @ X2863 )
| ( in @ X2864 @ X2863 )
| ~ ( in @ X2864 @ X2862 ) )
& ( ~ ( in @ X2866 @ ( powerset @ X2865 ) )
| ~ ( in @ X2867 @ ( powerset @ X2865 ) )
| ~ ( subset @ X2866 @ X2867 )
| ( subset @ ( setminus @ X2865 @ X2867 ) @ ( setminus @ X2865 @ X2866 ) ) )
& ( ~ ( in @ X2869 @ ( powerset @ X2868 ) )
| ~ ( in @ X2870 @ ( powerset @ X2868 ) )
| ~ ( subset @ ( setminus @ X2868 @ X2870 ) @ ( setminus @ X2868 @ X2869 ) )
| ( subset @ X2869 @ X2870 ) )
& ( ~ ( in @ X2872 @ ( powerset @ X2871 ) )
| ~ ( in @ X2873 @ X2871 )
| ~ ( in @ X2873 @ X2872 )
| ( in @ X2873 @ ( setminus @ X2871 @ ( setminus @ X2871 @ X2872 ) ) ) )
& ( ~ ( in @ X2875 @ ( powerset @ X2874 ) )
| ~ ( in @ X2876 @ X2874 )
| ~ ( in @ X2876 @ ( setminus @ X2874 @ ( setminus @ X2874 @ X2875 ) ) )
| ( in @ X2876 @ X2875 ) )
& ( ~ ( in @ X2878 @ ( powerset @ X2877 ) )
| ( subset @ X2878 @ ( setminus @ X2877 @ ( setminus @ X2877 @ X2878 ) ) ) )
& ( ~ ( in @ X2880 @ ( powerset @ X2879 ) )
| ( subset @ ( setminus @ X2879 @ ( setminus @ X2879 @ X2880 ) ) @ X2880 ) )
& ( ~ ( in @ X2882 @ ( powerset @ X2881 ) )
| ( X2882
= ( setminus @ X2881 @ ( setminus @ X2881 @ X2882 ) ) ) )
& ( ~ ( in @ X2884 @ ( powerset @ X2883 ) )
| ~ ( in @ X2885 @ ( powerset @ X2883 ) )
| ~ ( in @ X2886 @ X2883 )
| ~ ( in @ X2886 @ ( setminus @ X2883 @ X2884 ) )
| ~ ( in @ X2886 @ ( binintersect @ X2884 @ X2885 ) ) )
& ( ~ ( in @ X2888 @ ( powerset @ X2887 ) )
| ~ ( in @ X2889 @ ( powerset @ X2887 ) )
| ~ ( in @ X2890 @ X2887 )
| ~ ( in @ X2890 @ ( setminus @ X2887 @ X2888 ) )
| ( in @ X2890 @ ( setminus @ X2887 @ ( binintersect @ X2888 @ X2889 ) ) ) )
& ( ~ ( in @ X2892 @ ( powerset @ X2891 ) )
| ~ ( in @ X2893 @ ( powerset @ X2891 ) )
| ( subset @ ( setminus @ X2891 @ X2892 ) @ ( setminus @ X2891 @ ( binintersect @ X2892 @ X2893 ) ) ) )
& ( ~ ( in @ X2895 @ ( powerset @ X2894 ) )
| ~ ( in @ X2896 @ ( powerset @ X2894 ) )
| ( in @ ( setminus @ X2894 @ X2895 ) @ ( powerset @ ( setminus @ X2894 @ ( binintersect @ X2895 @ X2896 ) ) ) ) )
& ( ~ ( in @ X2898 @ ( powerset @ X2897 ) )
| ~ ( in @ X2899 @ ( powerset @ X2897 ) )
| ~ ( subset @ X2898 @ ( setminus @ X2897 @ X2899 ) )
| ~ ( in @ X2900 @ X2897 )
| ~ ( in @ X2900 @ X2899 )
| ( in @ X2900 @ ( setminus @ X2897 @ X2898 ) ) )
& ( ~ ( in @ X2902 @ ( powerset @ X2901 ) )
| ~ ( in @ X2903 @ ( powerset @ X2901 ) )
| ~ ( subset @ X2902 @ ( setminus @ X2901 @ X2903 ) )
| ( subset @ X2903 @ ( setminus @ X2901 @ X2902 ) ) )
& ( ~ ( in @ X2905 @ ( powerset @ X2904 ) )
| ~ ( in @ X2906 @ ( powerset @ X2904 ) )
| ~ ( in @ X2907 @ X2904 )
| ( in @ X2907 @ ( binunion @ X2905 @ X2906 ) )
| ~ ( in @ X2907 @ X2905 ) )
& ( ~ ( in @ X2909 @ ( powerset @ X2908 ) )
| ~ ( in @ X2910 @ ( powerset @ X2908 ) )
| ~ ( in @ X2911 @ X2908 )
| ( in @ X2911 @ ( binunion @ X2909 @ X2910 ) )
| ~ ( in @ X2911 @ X2910 ) )
& ( ~ ( in @ X2913 @ ( powerset @ X2912 ) )
| ~ ( in @ X2914 @ ( powerset @ X2912 ) )
| ~ ( in @ X2915 @ ( powerset @ X2912 ) )
| ~ ( in @ X2916 @ X2912 )
| ~ ( in @ X2916 @ ( binintersect @ X2913 @ X2914 ) )
| ( in @ X2916 @ ( binunion @ X2913 @ X2915 ) ) )
& ( ~ ( in @ X2918 @ ( powerset @ X2917 ) )
| ~ ( in @ X2919 @ ( powerset @ X2917 ) )
| ~ ( in @ X2920 @ ( powerset @ X2917 ) )
| ~ ( in @ X2921 @ X2917 )
| ~ ( in @ X2921 @ ( binintersect @ X2918 @ X2919 ) )
| ( in @ X2921 @ ( binunion @ X2919 @ X2920 ) ) )
& ( ~ ( in @ X2923 @ ( powerset @ X2922 ) )
| ~ ( in @ X2924 @ ( powerset @ X2922 ) )
| ~ ( in @ X2925 @ ( powerset @ X2922 ) )
| ~ ( in @ X2926 @ X2922 )
| ~ ( in @ X2926 @ ( binintersect @ X2923 @ X2924 ) )
| ( in @ X2926 @ ( binintersect @ ( binunion @ X2923 @ X2925 ) @ ( binunion @ X2924 @ X2925 ) ) ) )
& ( ~ ( in @ X2928 @ ( powerset @ X2927 ) )
| ~ ( in @ X2929 @ ( powerset @ X2927 ) )
| ~ ( in @ X2930 @ ( powerset @ X2927 ) )
| ( in @ ( binintersect @ X2928 @ X2929 ) @ ( powerset @ ( binintersect @ ( binunion @ X2928 @ X2930 ) @ ( binunion @ X2929 @ X2930 ) ) ) ) )
& ( ~ ( in @ X2932 @ ( powerset @ X2931 ) )
| ~ ( in @ X2933 @ ( powerset @ X2931 ) )
| ~ ( in @ X2934 @ X2931 )
| ~ ( in @ X2934 @ ( setminus @ X2931 @ ( binunion @ X2932 @ X2933 ) ) )
| ~ ( in @ X2934 @ X2932 ) )
& ( ~ ( in @ X2936 @ ( powerset @ X2935 ) )
| ~ ( in @ X2937 @ ( powerset @ X2935 ) )
| ~ ( in @ X2938 @ X2935 )
| ~ ( in @ X2938 @ ( setminus @ X2935 @ ( binunion @ X2936 @ X2937 ) ) )
| ( in @ X2938 @ ( setminus @ X2935 @ X2936 ) ) )
& ( ( in @ X2943 @ X2941 )
| X2942
| ( in @ X2943 @ X2940 )
| ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
| ~ ( in @ X2943 @ X2939 )
| ~ ( in @ X2941 @ ( powerset @ X2939 ) )
| ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
& ( ~ X2942
| X2942
| ( in @ X2943 @ X2940 )
| ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
| ~ ( in @ X2943 @ X2939 )
| ~ ( in @ X2941 @ ( powerset @ X2939 ) )
| ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
& ( ( in @ X2943 @ X2941 )
| X2942
| ~ X2942
| ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
| ~ ( in @ X2943 @ X2939 )
| ~ ( in @ X2941 @ ( powerset @ X2939 ) )
| ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
& ( ~ X2942
| X2942
| ~ X2942
| ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
| ~ ( in @ X2943 @ X2939 )
| ~ ( in @ X2941 @ ( powerset @ X2939 ) )
| ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
& ( ~ ( in @ X2945 @ ( powerset @ X2944 ) )
| ~ ( in @ X2946 @ ( powerset @ X2944 ) )
| ~ ( in @ X2947 @ X2944 )
| ( in @ X2947 @ X2945 )
| ( in @ X2947 @ X2946 )
| ~ ( in @ X2947 @ ( binunion @ X2945 @ X2946 ) ) )
& ( ~ ( in @ X2949 @ ( powerset @ X2948 ) )
| ~ ( in @ X2950 @ ( powerset @ X2948 ) )
| ~ ( in @ X2951 @ X2948 )
| ~ ( in @ X2951 @ ( setminus @ X2948 @ ( binunion @ X2949 @ X2950 ) ) )
| ( in @ X2951 @ ( setminus @ X2948 @ X2949 ) ) )
& ( ~ ( in @ X2953 @ ( powerset @ X2952 ) )
| ~ ( in @ X2954 @ ( powerset @ X2952 ) )
| ( in @ ( setminus @ X2952 @ ( binunion @ X2953 @ X2954 ) ) @ ( powerset @ ( setminus @ X2952 @ X2953 ) ) ) )
& ( ~ ( in @ X2956 @ ( powerset @ X2955 ) )
| ~ ( in @ X2957 @ ( powerset @ X2955 ) )
| ~ ( in @ X2958 @ X2955 )
| ~ ( in @ X2958 @ ( setminus @ X2955 @ ( binunion @ X2956 @ X2957 ) ) )
| ( in @ X2958 @ ( setminus @ X2955 @ X2957 ) ) )
& ( ~ ( in @ X2960 @ ( powerset @ X2959 ) )
| ~ ( in @ X2961 @ ( powerset @ X2959 ) )
| ~ ( in @ X2962 @ X2959 )
| ~ ( in @ X2962 @ ( setminus @ X2959 @ ( binintersect @ X2960 @ X2961 ) ) )
| ( in @ X2962 @ ( binunion @ ( setminus @ X2959 @ X2960 ) @ ( setminus @ X2959 @ X2961 ) ) ) )
& ( ~ ( in @ X2964 @ ( powerset @ X2963 ) )
| ~ ( in @ X2965 @ ( powerset @ X2963 ) )
| ~ ( in @ X2966 @ X2963 )
| ~ ( in @ X2966 @ ( binunion @ ( setminus @ X2963 @ X2964 ) @ ( setminus @ X2963 @ X2965 ) ) )
| ( in @ X2966 @ ( setminus @ X2963 @ ( binintersect @ X2964 @ X2965 ) ) ) )
& ( ~ ( in @ X2968 @ ( powerset @ X2967 ) )
| ~ ( in @ X2969 @ ( powerset @ X2967 ) )
| ( ( setminus @ X2967 @ ( binintersect @ X2968 @ X2969 ) )
= ( binunion @ ( setminus @ X2967 @ X2968 ) @ ( setminus @ X2967 @ X2969 ) ) ) )
& ( ~ ( in @ X2971 @ ( powerset @ X2970 ) )
| ~ ( in @ X2972 @ ( powerset @ X2970 ) )
| ~ ( in @ X2973 @ X2970 )
| ~ ( in @ X2973 @ ( setminus @ X2970 @ ( binunion @ X2971 @ X2972 ) ) )
| ( in @ X2973 @ ( binintersect @ ( setminus @ X2970 @ X2971 ) @ ( setminus @ X2970 @ X2972 ) ) ) )
& ( ~ ( in @ X2975 @ ( powerset @ X2974 ) )
| ~ ( in @ X2976 @ ( powerset @ X2974 ) )
| ~ ( in @ X2977 @ X2974 )
| ~ ( in @ X2977 @ ( setminus @ X2974 @ X2975 ) )
| ~ ( in @ X2977 @ ( setminus @ X2974 @ X2976 ) )
| ( in @ X2977 @ ( setminus @ X2974 @ ( binunion @ X2975 @ X2976 ) ) ) )
& ( ~ ( in @ X2979 @ ( powerset @ X2978 ) )
| ~ ( in @ X2980 @ ( powerset @ X2978 ) )
| ~ ( in @ X2981 @ X2978 )
| ~ ( in @ X2981 @ ( binintersect @ ( setminus @ X2978 @ X2979 ) @ ( setminus @ X2978 @ X2980 ) ) )
| ( in @ X2981 @ ( setminus @ X2978 @ ( binunion @ X2979 @ X2980 ) ) ) )
& ( ~ ( in @ X2983 @ ( powerset @ X2982 ) )
| ~ ( in @ X2984 @ ( powerset @ X2982 ) )
| ( ( setminus @ X2982 @ ( binunion @ X2983 @ X2984 ) )
= ( binintersect @ ( setminus @ X2982 @ X2983 ) @ ( setminus @ X2982 @ X2984 ) ) ) )
& ( ~ ( in @ X2986 @ ( powerset @ X2985 ) )
| ~ ( in @ X2987 @ ( powerset @ X2985 ) )
| ~ ( in @ X2988 @ ( binintersect @ X2986 @ X2987 ) )
| ( in @ X2988 @ X2985 ) )
& ( ~ ( in @ X2990 @ ( powerset @ X2989 ) )
| ~ ( in @ X2991 @ ( powerset @ X2989 ) )
| ~ ( in @ X2992 @ ( powerset @ X2989 ) )
| ~ ( subset @ X2990 @ X2992 )
| ( subset @ ( binintersect @ X2990 @ X2991 ) @ X2992 ) )
& ( ~ ( in @ X2994 @ ( powerset @ X2993 ) )
| ~ ( in @ X2995 @ ( powerset @ X2993 ) )
| ~ ( in @ X2996 @ ( powerset @ X2993 ) )
| ~ ( subset @ X2995 @ X2996 )
| ( subset @ ( binintersect @ X2994 @ X2995 ) @ X2996 ) )
& ( ~ ( in @ X2998 @ ( powerset @ X2997 ) )
| ~ ( in @ X2999 @ ( powerset @ X2997 ) )
| ~ ( in @ X3000 @ ( powerset @ X2997 ) )
| ~ ( subset @ X2998 @ X2999 )
| ~ ( subset @ X2998 @ X3000 )
| ( subset @ X2998 @ ( binintersect @ X2999 @ X3000 ) ) )
& ( ~ ( in @ X3002 @ ( powerset @ X3001 ) )
| ~ ( in @ X3003 @ ( powerset @ X3001 ) )
| ~ ( in @ X3004 @ ( powerset @ X3001 ) )
| ~ ( in @ X3005 @ ( powerset @ X3001 ) )
| ~ ( subset @ X3002 @ X3004 )
| ~ ( subset @ X3003 @ X3005 )
| ( subset @ ( binintersect @ X3002 @ X3003 ) @ ( binintersect @ X3004 @ X3005 ) ) )
& ( ~ ( in @ X3007 @ ( powerset @ X3006 ) )
| ~ ( in @ X3008 @ ( powerset @ X3006 ) )
| ( in @ ( setminus @ X3006 @ X3007 ) @ ( powerset @ ( setminus @ X3006 @ ( binintersect @ X3007 @ X3008 ) ) ) ) )
& ( ~ ( in @ X3010 @ ( powerset @ X3009 ) )
| ~ ( in @ X3011 @ ( powerset @ X3009 ) )
| ~ ( in @ X3012 @ ( powerset @ X3009 ) )
| ~ ( in @ X3013 @ ( powerset @ X3009 ) )
| ( ( setminus @ X3009 @ ( binintersect @ ( binunion @ X3010 @ X3011 ) @ ( binunion @ X3012 @ X3013 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X3009 @ X3010 ) @ ( setminus @ X3009 @ X3011 ) ) @ ( binintersect @ ( setminus @ X3009 @ X3012 ) @ ( setminus @ X3009 @ X3013 ) ) ) ) )
& ( ~ ( in @ X3015 @ ( powerset @ X3014 ) )
| ~ ( in @ X3016 @ ( powerset @ X3014 ) )
| ~ ( in @ X3017 @ ( powerset @ X3014 ) )
| ( in @ ( binintersect @ X3015 @ X3016 ) @ ( powerset @ ( binintersect @ ( binunion @ X3015 @ X3017 ) @ ( binunion @ X3016 @ X3017 ) ) ) ) )
& ( ~ ( in @ X3019 @ ( powerset @ X3018 ) )
| ~ ( in @ X3020 @ ( powerset @ X3018 ) )
| ~ ( subset @ X3019 @ ( setminus @ X3018 @ X3020 ) )
| ( subset @ X3020 @ ( setminus @ X3018 @ X3019 ) ) )
& ( ~ ( in @ X3022 @ ( powerset @ X3021 ) )
| ~ ( in @ X3023 @ ( powerset @ X3021 ) )
| ( in @ ( setminus @ X3021 @ ( binunion @ X3022 @ X3023 ) ) @ ( powerset @ ( setminus @ X3021 @ X3022 ) ) ) )
& ( ( in @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ X3024 )
| ~ ( in @ X3029 @ X3025 )
| ( X3026 @ X3029 )
| ~ ( breln1 @ X3024 @ X3025 ) )
& ( ( in @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) @ X3024 )
| ~ ( in @ X3029 @ X3025 )
| ( X3026 @ X3029 )
| ~ ( breln1 @ X3024 @ X3025 ) )
& ( ( in @ ( kpair @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) ) @ X3025 )
| ~ ( in @ X3029 @ X3025 )
| ( X3026 @ X3029 )
| ~ ( breln1 @ X3024 @ X3025 ) )
& ( ~ ( X3026 @ ( kpair @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) ) )
| ~ ( in @ X3029 @ X3025 )
| ( X3026 @ X3029 )
| ~ ( breln1 @ X3024 @ X3025 ) )
& ( ~ ( in @ X3031 @ ( breln1Set @ X3030 ) )
| ( breln1 @ X3030 @ X3031 ) )
& choice2fnsingleton
& ( breln1 @ X3032 @ ( dpsetconstr @ X3032 @ X3032 @ X3033 ) )
& ( ( in @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ X3034 )
| ~ ( in @ X3039 @ X3035 )
| ( X3036 @ X3039 )
| ~ ( breln1 @ X3034 @ X3035 ) )
& ( ( in @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) @ X3034 )
| ~ ( in @ X3039 @ X3035 )
| ( X3036 @ X3039 )
| ~ ( breln1 @ X3034 @ X3035 ) )
& ( ( in @ ( kpair @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) ) @ X3035 )
| ~ ( in @ X3039 @ X3035 )
| ( X3036 @ X3039 )
| ~ ( breln1 @ X3034 @ X3035 ) )
& ( ~ ( X3036 @ ( kpair @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) ) )
| ~ ( in @ X3039 @ X3035 )
| ( X3036 @ X3039 )
| ~ ( breln1 @ X3034 @ X3035 ) )
& ( ( in @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ X3040 )
| ( subset @ X3041 @ X3042 )
| ~ ( breln1 @ X3040 @ X3042 )
| ~ ( breln1 @ X3040 @ X3041 ) )
& ( ( in @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) @ X3040 )
| ( subset @ X3041 @ X3042 )
| ~ ( breln1 @ X3040 @ X3042 )
| ~ ( breln1 @ X3040 @ X3041 ) )
& ( ( in @ ( kpair @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) ) @ X3041 )
| ( subset @ X3041 @ X3042 )
| ~ ( breln1 @ X3040 @ X3042 )
| ~ ( breln1 @ X3040 @ X3041 ) )
& ( ~ ( in @ ( kpair @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) ) @ X3042 )
| ( subset @ X3041 @ X3042 )
| ~ ( breln1 @ X3040 @ X3042 )
| ~ ( breln1 @ X3040 @ X3041 ) )
& ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ( X3046 = X3047 )
| ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ( X3046 = X3047 )
| ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ( X3046 = X3047 )
| ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ( X3046 = X3047 )
| ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ( X3046 = X3047 )
| ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ( X3046 = X3047 )
| ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
| ( X3046 = X3047 )
| ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ( X3046 = X3047 )
| ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
| ( X3046 = X3047 )
| ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
| ~ ( breln1 @ X3045 @ X3047 )
| ~ ( breln1 @ X3045 @ X3046 ) )
& ( ~ ( breln1 @ X3052 @ X3053 )
| ( breln1 @ X3052 @ ( breln1invset @ X3052 @ X3053 ) ) )
& ( ~ ( breln1 @ X3054 @ X3055 )
| ~ ( in @ X3056 @ X3054 )
| ~ ( in @ X3057 @ X3054 )
| ~ ( in @ ( kpair @ X3056 @ X3057 ) @ X3055 )
| ( in @ ( kpair @ X3057 @ X3056 ) @ ( breln1invset @ X3054 @ X3055 ) ) )
& ( ~ ( breln1 @ X3058 @ X3059 )
| ~ ( in @ X3060 @ X3058 )
| ~ ( in @ X3061 @ X3058 )
| ~ ( in @ ( kpair @ X3061 @ X3060 ) @ ( breln1invset @ X3058 @ X3059 ) )
| ( in @ ( kpair @ X3060 @ X3061 ) @ X3059 ) )
& ( ~ ( breln1 @ X3062 @ X3063 )
| ~ ( breln1 @ X3062 @ X3064 )
| ( breln1 @ X3062 @ ( breln1compset @ X3062 @ X3063 @ X3064 ) ) )
& ( ~ ( breln1 @ X3065 @ X3066 )
| ~ ( breln1 @ X3065 @ X3067 )
| ~ ( in @ X3068 @ X3065 )
| ~ ( in @ X3069 @ X3065 )
| ~ ( in @ X3070 @ X3065 )
| ~ ( in @ ( kpair @ X3068 @ X3070 ) @ X3066 )
| ~ ( in @ ( kpair @ X3070 @ X3069 ) @ X3067 )
| ( in @ ( kpair @ X3068 @ X3069 ) @ ( breln1compset @ X3065 @ X3066 @ X3067 ) ) )
& ( ( in @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) @ X3071 )
| ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
| ~ ( in @ X3075 @ X3071 )
| ~ ( in @ X3074 @ X3071 )
| ~ ( breln1 @ X3071 @ X3073 )
| ~ ( breln1 @ X3071 @ X3072 ) )
& ( ( in @ ( kpair @ X3074 @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) ) @ X3072 )
| ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
| ~ ( in @ X3075 @ X3071 )
| ~ ( in @ X3074 @ X3071 )
| ~ ( breln1 @ X3071 @ X3073 )
| ~ ( breln1 @ X3071 @ X3072 ) )
& ( ( in @ ( kpair @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) @ X3075 ) @ X3073 )
| ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
| ~ ( in @ X3075 @ X3071 )
| ~ ( in @ X3074 @ X3071 )
| ~ ( breln1 @ X3071 @ X3073 )
| ~ ( breln1 @ X3071 @ X3072 ) )
& ( ( in @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) @ X3077 )
| X3082
| ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
| ~ ( in @ X3081 @ X3077 )
| ~ ( in @ X3080 @ X3077 )
| ~ ( breln1 @ X3077 @ X3079 )
| ~ ( breln1 @ X3077 @ X3078 ) )
& ( ( in @ ( kpair @ X3080 @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) ) @ X3078 )
| X3082
| ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
| ~ ( in @ X3081 @ X3077 )
| ~ ( in @ X3080 @ X3077 )
| ~ ( breln1 @ X3077 @ X3079 )
| ~ ( breln1 @ X3077 @ X3078 ) )
& ( ( in @ ( kpair @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) @ X3081 ) @ X3079 )
| X3082
| ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
| ~ ( in @ X3081 @ X3077 )
| ~ ( in @ X3080 @ X3077 )
| ~ ( breln1 @ X3077 @ X3079 )
| ~ ( breln1 @ X3077 @ X3078 ) )
& ( ~ X3082
| X3082
| ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
| ~ ( in @ X3081 @ X3077 )
| ~ ( in @ X3080 @ X3077 )
| ~ ( breln1 @ X3077 @ X3079 )
| ~ ( breln1 @ X3077 @ X3078 ) )
& ( ~ ( breln1 @ X3084 @ X3085 )
| ~ ( breln1 @ X3084 @ X3086 )
| ( breln1 @ X3084 @ ( binunion @ X3085 @ X3086 ) ) )
& ( ~ ( breln1 @ X3087 @ X3088 )
| ~ ( breln1 @ X3087 @ X3089 )
| ~ ( in @ X3090 @ X3087 )
| ~ ( in @ X3091 @ X3087 )
| ~ ( in @ ( kpair @ X3090 @ X3091 ) @ X3088 )
| ( in @ ( kpair @ X3090 @ X3091 ) @ ( binunion @ X3088 @ X3089 ) ) )
& ( ~ ( breln1 @ X3092 @ X3093 )
| ~ ( breln1 @ X3092 @ X3094 )
| ~ ( in @ X3095 @ X3092 )
| ~ ( in @ X3096 @ X3092 )
| ~ ( in @ ( kpair @ X3095 @ X3096 ) @ X3094 )
| ( in @ ( kpair @ X3095 @ X3096 ) @ ( binunion @ X3093 @ X3094 ) ) )
& ( ~ ( in @ ( kpair @ X3100 @ X3101 ) @ X3098 )
| ( in @ ( kpair @ X3100 @ X3101 ) @ ( binunion @ X3098 @ X3099 ) )
| ~ ( in @ X3101 @ X3097 )
| ~ ( in @ X3100 @ X3097 )
| ~ ( breln1 @ X3097 @ X3099 )
| ~ ( breln1 @ X3097 @ X3098 ) )
& ( ~ ( in @ ( kpair @ X3100 @ X3101 ) @ X3099 )
| ( in @ ( kpair @ X3100 @ X3101 ) @ ( binunion @ X3098 @ X3099 ) )
| ~ ( in @ X3101 @ X3097 )
| ~ ( in @ X3100 @ X3097 )
| ~ ( breln1 @ X3097 @ X3099 )
| ~ ( breln1 @ X3097 @ X3098 ) )
& ( ~ ( breln1 @ X3102 @ X3103 )
| ~ ( breln1 @ X3102 @ X3104 )
| ~ ( in @ X3105 @ X3102 )
| ~ ( in @ X3106 @ X3102 )
| ~ ( in @ ( kpair @ X3105 @ X3106 ) @ ( binunion @ X3103 @ X3104 ) )
| ( in @ ( kpair @ X3105 @ X3106 ) @ X3103 )
| ( in @ ( kpair @ X3105 @ X3106 ) @ X3104 ) )
& ( breln1 @ esk99_0 @ esk100_0 )
& ( breln1 @ esk99_0 @ esk101_0 )
& ( in @ esk102_0 @ esk99_0 )
& ( in @ esk103_0 @ esk99_0 )
& ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ ( binunion @ esk100_0 @ esk101_0 ) )
& ( ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 )
| epred2_0 )
& ( ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 )
| epred2_0 )
& ~ epred2_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_375])])])])])])]) ).
thf(c_0_377,negated_conjecture,
( epred2_0
| ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
thf(c_0_378,negated_conjecture,
~ epred2_0,
inference(split_conjunct,[status(thm)],[c_0_376]) ).
thf(c_0_379,negated_conjecture,
( epred2_0
| ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
thf(c_0_380,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ( in @ X2 @ X4 )
| ~ ( in @ X2 @ ( binunion @ X4 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_376])])]) ).
thf(c_0_381,negated_conjecture,
in @ ( kpair @ esk102_0 @ esk103_0 ) @ ( binunion @ esk100_0 @ esk101_0 ),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
thf(c_0_382,negated_conjecture,
~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 ),
inference(sr,[status(thm)],[c_0_377,c_0_378]) ).
thf(c_0_383,negated_conjecture,
~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 ),
inference(sr,[status(thm)],[c_0_379,c_0_378]) ).
thf(c_0_384,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_380,c_0_381]),c_0_382]),c_0_383]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU787^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 17:09:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.44/0.78 # Version: 3.1.0-ho
% 1.44/0.78 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78 # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78 # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78 # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78 # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78 # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78 # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78 # Starting new_ho_5 with 300s (1) cores
% 1.44/0.78 # new_ho_5 with pid 13033 completed with status 8
% 1.44/0.78 # pre_casc_3 with pid 13029 completed with status 8
% 1.44/0.78 # new_bool_3 with pid 13032 completed with status 0
% 1.44/0.78 # Result found by new_bool_3
% 1.44/0.78 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78 # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78 # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78 # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78 # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78 # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78 # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.78 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.44/0.78 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.78 # Starting ho_unfolding_8 with 61s (1) cores
% 1.44/0.78 # ho_unfolding_8 with pid 13049 completed with status 0
% 1.44/0.78 # Result found by ho_unfolding_8
% 1.44/0.78 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78 # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78 # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78 # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78 # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78 # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78 # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.78 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.44/0.78 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.78 # Starting ho_unfolding_8 with 61s (1) cores
% 1.44/0.78 # Preprocessing time : 0.065 s
% 1.44/0.78 # Presaturation interreduction done
% 1.44/0.78
% 1.44/0.78 # Proof found!
% 1.44/0.78 # SZS status Theorem
% 1.44/0.78 # SZS output start CNFRefutation
% See solution above
% 1.44/0.79 # Parsed axioms : 657
% 1.44/0.79 # Removed by relevancy pruning/SinE : 353
% 1.44/0.79 # Initial clauses : 525
% 1.44/0.79 # Removed in clause preprocessing : 33
% 1.44/0.79 # Initial clauses in saturation : 492
% 1.44/0.79 # Processed clauses : 642
% 1.44/0.79 # ...of these trivial : 9
% 1.44/0.79 # ...subsumed : 48
% 1.44/0.79 # ...remaining for further processing : 585
% 1.44/0.79 # Other redundant clauses eliminated : 24
% 1.44/0.79 # Clauses deleted for lack of memory : 0
% 1.44/0.79 # Backward-subsumed : 2
% 1.44/0.79 # Backward-rewritten : 1
% 1.44/0.79 # Generated clauses : 846
% 1.44/0.79 # ...of the previous two non-redundant : 767
% 1.44/0.79 # ...aggressively subsumed : 0
% 1.44/0.79 # Contextual simplify-reflections : 14
% 1.44/0.79 # Paramodulations : 814
% 1.44/0.79 # Factorizations : 0
% 1.44/0.79 # NegExts : 0
% 1.44/0.79 # Equation resolutions : 29
% 1.44/0.79 # Disequality decompositions : 0
% 1.44/0.79 # Total rewrite steps : 92
% 1.44/0.79 # ...of those cached : 64
% 1.44/0.79 # Propositional unsat checks : 0
% 1.44/0.79 # Propositional check models : 0
% 1.44/0.79 # Propositional check unsatisfiable : 0
% 1.44/0.79 # Propositional clauses : 0
% 1.44/0.79 # Propositional clauses after purity: 0
% 1.44/0.79 # Propositional unsat core size : 0
% 1.44/0.79 # Propositional preprocessing time : 0.000
% 1.44/0.79 # Propositional encoding time : 0.000
% 1.44/0.79 # Propositional solver time : 0.000
% 1.44/0.79 # Success case prop preproc time : 0.000
% 1.44/0.79 # Success case prop encoding time : 0.000
% 1.44/0.79 # Success case prop solver time : 0.000
% 1.44/0.79 # Current number of processed clauses : 140
% 1.44/0.79 # Positive orientable unit clauses : 37
% 1.44/0.79 # Positive unorientable unit clauses: 0
% 1.44/0.79 # Negative unit clauses : 5
% 1.44/0.79 # Non-unit-clauses : 98
% 1.44/0.79 # Current number of unprocessed clauses: 1032
% 1.44/0.79 # ...number of literals in the above : 3107
% 1.44/0.79 # Current number of archived formulas : 0
% 1.44/0.79 # Current number of archived clauses : 430
% 1.44/0.79 # Clause-clause subsumption calls (NU) : 43649
% 1.44/0.79 # Rec. Clause-clause subsumption calls : 12146
% 1.44/0.79 # Non-unit clause-clause subsumptions : 59
% 1.44/0.79 # Unit Clause-clause subsumption calls : 163
% 1.44/0.79 # Rewrite failures with RHS unbound : 0
% 1.44/0.79 # BW rewrite match attempts : 22
% 1.44/0.79 # BW rewrite match successes : 1
% 1.44/0.79 # Condensation attempts : 0
% 1.44/0.79 # Condensation successes : 0
% 1.44/0.79 # Termbank termtop insertions : 108656
% 1.44/0.79 # Search garbage collected termcells : 33492
% 1.44/0.79
% 1.44/0.79 # -------------------------------------------------
% 1.44/0.79 # User time : 0.231 s
% 1.44/0.79 # System time : 0.025 s
% 1.44/0.79 # Total time : 0.256 s
% 1.44/0.79 # Maximum resident set size: 10168 pages
% 1.44/0.79
% 1.44/0.79 # -------------------------------------------------
% 1.44/0.79 # User time : 0.471 s
% 1.44/0.79 # System time : 0.091 s
% 1.44/0.79 # Total time : 0.563 s
% 1.44/0.79 # Maximum resident set size: 2884 pages
% 1.44/0.79 % E---3.1 exiting
% 1.44/0.79 % E exiting
%------------------------------------------------------------------------------