%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU762^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 03:30:00 EDT 2024
% Result : Theorem 6.54s 1.34s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 685
% Syntax : Number of formulae : 779 ( 40 unt; 401 typ; 0 def)
% Number of atoms : 3782 ( 636 equ; 0 cnn)
% Maximal formula atoms : 1174 ( 10 avg)
% Number of connectives : 15408 (1041 ~;1100 |; 604 &;10379 @)
% ( 372 <=>;1912 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1281 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 595 ( 595 >; 0 *; 0 +; 0 <<)
% Number of symbols : 405 ( 401 usr; 289 con; 0-4 aty)
% Number of variables : 3129 ( 182 ^2824 !; 123 ?;3129 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
binunionTEcontra: $o ).
thf(decl_324,type,
demorgan2a1: $o ).
thf(decl_325,type,
complementUnionInPowersetComplement: $o ).
thf(decl_326,type,
demorgan2a2: $o ).
thf(decl_327,type,
demorgan1a: $o ).
thf(decl_328,type,
demorgan1b: $o ).
thf(decl_329,type,
demorgan1: $o ).
thf(decl_330,type,
demorgan2a: $o ).
thf(decl_331,type,
demorgan2b2: $o ).
thf(decl_332,type,
demorgan2b: $o ).
thf(decl_333,type,
demorgan2: $o ).
thf(decl_334,type,
woz13rule0: $o ).
thf(decl_335,type,
woz13rule1: $o ).
thf(decl_336,type,
woz13rule2: $o ).
thf(decl_337,type,
woz13rule3: $o ).
thf(decl_338,type,
epred1_0: $o ).
thf(decl_339,type,
esk1_2: $i > $i > $i ).
thf(decl_340,type,
esk2_2: $i > $i > $i ).
thf(decl_341,type,
esk3_2: $i > $i > $i ).
thf(decl_342,type,
esk4_1: $i > $i ).
thf(decl_343,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_344,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_345,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_346,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_347,type,
esk9_1: $i > $i ).
thf(decl_348,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_349,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_350,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_351,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_352,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_353,type,
esk15_2: $i > $i > $i ).
thf(decl_354,type,
esk16_2: $i > $i > $i ).
thf(decl_355,type,
esk17_1: $i > $i ).
thf(decl_356,type,
esk18_1: $i > $i ).
thf(decl_357,type,
esk19_1: $i > $i ).
thf(decl_358,type,
esk20_2: $i > $i > $i ).
thf(decl_359,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_360,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_361,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_362,type,
esk24_1: $i > $i ).
thf(decl_363,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_364,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_366,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_367,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_368,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_369,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_370,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_371,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_372,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_373,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_374,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_375,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_376,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_377,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_378,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_379,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_380,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_381,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_382,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_383,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_384,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_385,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_386,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_387,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_388,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_389,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_390,type,
esk52_2: $i > $i > $i ).
thf(decl_391,type,
esk53_2: $i > $i > $i ).
thf(decl_392,type,
esk54_2: $i > $i > $i ).
thf(decl_393,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_394,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_395,type,
esk57_2: $i > $i > $i ).
thf(decl_396,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_397,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_398,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_399,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_400,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_401,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_402,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_403,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_404,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_405,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_406,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_407,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_408,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_409,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_410,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_411,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_412,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_413,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_414,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_415,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_416,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_417,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_418,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_419,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_420,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_421,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_422,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_423,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_424,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_425,type,
esk87_0: $i ).
thf(decl_426,type,
esk88_0: $i ).
thf(decl_427,type,
esk89_0: $i ).
thf(decl_428,type,
esk90_0: $i ).
thf(decl_429,type,
esk91_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
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(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(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(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/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(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(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
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(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(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(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(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
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(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(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(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(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(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(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(woz13rule4,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
=> ! [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(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(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
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(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(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(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(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__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(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(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
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(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
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(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(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/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(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/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(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(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(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(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(c_0_283,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_284,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_285,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_286,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_287,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_288,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_289,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_290,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_291,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_292,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_293,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_294,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_295,plain,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
<=> ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu__Cong]) ).
thf(c_0_296,plain,
( 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_297,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_298,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_299,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_300,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_301,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_302,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_303,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_304,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_305,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X941: $i] :
( ( X6 @ X2 @ X941 )
& ! [X942: $i] :
( ( X6 @ X2 @ X942 )
=> ( X941 = X942 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_283,c_0_284]) ).
thf(c_0_306,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X943: $i] :
( ( X1 @ X943 )
& ! [X944: $i] :
( ( X1 @ X944 )
=> ( X943 = X944 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_285,c_0_284]) ).
thf(c_0_307,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_308,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_309,plain,
( 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_310,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X945: $i] :
( ( X1 @ X945 )
& ! [X946: $i] :
( ( X1 @ X946 )
=> ( X945 = X946 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_286,c_0_284]) ).
thf(c_0_311,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X947: $i] :
( ( X1 @ X947 )
& ! [X948: $i] :
( ( X1 @ X948 )
=> ( X947 = X948 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_287,c_0_284]) ).
thf(c_0_312,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_313,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_288]) ).
thf(c_0_314,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_289,c_0_288]) ).
thf(c_0_315,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_288]) ).
thf(c_0_316,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_317,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X949: $i] :
( ( X1 @ X949 )
& ! [X950: $i] :
( ( X1 @ X950 )
=> ( X949 = X950 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_290,c_0_284]) ).
thf(c_0_318,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_288]) ).
thf(c_0_319,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_320,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X951: $i] :
( ( X1 @ X951 )
& ! [X952: $i] :
( ( X1 @ X952 )
=> ( X951 = X952 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_291,c_0_284]) ).
thf(c_0_321,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X953: $i] :
( ( X1 @ X953 )
& ! [X954: $i] :
( ( X1 @ X954 )
=> ( X953 = X954 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_292,c_0_284]) ).
thf(c_0_322,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X955: $i] :
( ( X1 @ X955 )
& ! [X956: $i] :
( ( X1 @ X956 )
=> ( X955 = X956 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_293,c_0_284]) ).
thf(c_0_323,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X957: $i] :
( ( X1 @ X957 )
& ! [X958: $i] :
( ( X1 @ X958 )
=> ( X957 = X958 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_294,c_0_284]) ).
thf(c_0_324,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X959: $i] :
( ( X1 @ X959 )
& ! [X960: $i] :
( ( X1 @ X960 )
=> ( X959 = X960 ) ) )
<=> ? [X961: $i] :
( ( X17 @ X961 )
& ! [X962: $i] :
( ( X17 @ X962 )
=> ( X961 = X962 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_295,c_0_284]) ).
thf(c_0_325,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X963: $i] :
( ( X1 @ X963 )
& ! [X964: $i] :
( ( X1 @ X964 )
=> ( X963 = X964 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_296,c_0_284]) ).
thf(c_0_326,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X965: $i] :
( ( X1 @ X965 )
& ! [X966: $i] :
( ( X1 @ X966 )
=> ( X965 = X966 ) ) )
=> ( ? [X967: $i] :
( ( X17 @ X967 )
& ! [X968: $i] :
( ( X17 @ X968 )
=> ( X967 = X968 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_297,c_0_284]) ).
thf(c_0_327,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_328,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_329,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_330,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_331,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_298,c_0_299]) ).
thf(c_0_332,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_300,c_0_299]) ).
thf(c_0_333,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_301,c_0_299]) ).
thf(c_0_334,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_335,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_336,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_337,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_338,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_302,c_0_303]) ).
thf(c_0_339,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_340,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_341,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_342,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_343,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_344,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_345,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_346,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_347,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_348,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_303]) ).
thf(c_0_349,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_303]) ).
thf(c_0_350,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_304,c_0_299]) ).
thf(c_0_351,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_303]) ).
thf(c_0_352,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_303]) ).
thf(c_0_353,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_354,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_355,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_356,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_357,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_358,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_359,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_360,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_361,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_362,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_363,plain,
( epred1_0
<=> ! [X998: $i] :
? [X999: $i] :
( ! [X1000: $i] :
( ( in @ X1000 @ X999 )
=> ! [X1001: $i] :
( ( in @ X1001 @ X1000 )
=> ( in @ X1001 @ X998 ) ) )
& ! [X1002: $i,X1003: $i] :
( ( ( in @ X1002 @ X998 )
& ( in @ X1003 @ X998 ) )
=> ( ! [X1004: $i] :
( ( in @ X1004 @ X999 )
=> ( ( in @ X1002 @ X1004 )
<=> ( in @ X1003 @ X1004 ) ) )
=> ( X1002 = X1003 ) ) )
& ! [X1005: $i,X1006: $i] :
( ( ( in @ X1005 @ X999 )
& ( in @ X1006 @ X999 ) )
=> ( ! [X1007: $i] :
( ( in @ X1007 @ X1005 )
=> ( in @ X1007 @ X1006 ) )
| ! [X1008: $i] :
( ( in @ X1008 @ X1006 )
=> ( in @ X1008 @ X1005 ) ) ) )
& ! [X1009: $i] :
( ( ! [X1010: $i] :
( ( in @ X1010 @ X1009 )
=> ( in @ X1010 @ X998 ) )
& ? [X1011: $i] : ( in @ X1011 @ X1009 ) )
=> ? [X1012: $i,X1013: $i] :
( ( in @ X1012 @ X999 )
& ( in @ X1013 @ X1009 )
& ~ ? [X1014: $i] :
( ( in @ X1014 @ X1012 )
& ( in @ X1014 @ X1009 ) )
& ! [X1015: $i] :
( ( in @ X1015 @ X999 )
=> ( ! [X1016: $i] :
( ( in @ X1016 @ X1015 )
=> ( in @ X1016 @ X1012 ) )
| ( in @ X1013 @ X1015 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_364,negated_conjecture,
~ ( ! [X969: $i,X970: $i] :
( ! [X971: $i] :
( ( in @ X971 @ X969 )
<=> ( in @ X971 @ X970 ) )
=> ( X969 = X970 ) )
=> ( ! [X972: $i] :
~ ( in @ X972 @ emptyset )
=> ( ! [X973: $i,X974: $i,X975: $i] :
( ( in @ X975 @ ( setadjoin @ X973 @ X974 ) )
<=> ( ( X975 = X973 )
| ( in @ X975 @ X974 ) ) )
=> ( ! [X976: $i,X977: $i] :
( ( in @ X977 @ ( powerset @ X976 ) )
<=> ! [X978: $i] :
( ( in @ X978 @ X977 )
=> ( in @ X978 @ X976 ) ) )
=> ( ! [X979: $i,X980: $i] :
( ( in @ X980 @ ( setunion @ X979 ) )
<=> ? [X981: $i] :
( ( in @ X980 @ X981 )
& ( in @ X981 @ X979 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X982: $i] :
( ( in @ X982 @ omega )
=> ( in @ ( setadjoin @ X982 @ X982 ) @ omega ) )
=> ( ! [X983: $i] :
( ( ( in @ emptyset @ X983 )
& ! [X984: $i] :
( ( ( in @ X984 @ omega )
& ( in @ X984 @ X983 ) )
=> ( in @ ( setadjoin @ X984 @ X984 ) @ X983 ) ) )
=> ! [X985: $i] :
( ( in @ X985 @ omega )
=> ( in @ X985 @ X983 ) ) )
=> ( ! [X986: $i > $i > $o,X987: $i] :
( ! [X988: $i] :
( ( in @ X988 @ X987 )
=> ? [X989: $i] :
( ( X986 @ X988 @ X989 )
& ! [X990: $i] :
( ( X986 @ X988 @ X990 )
=> ( X989 = X990 ) ) ) )
=> ? [X991: $i] :
! [X992: $i] :
( ( in @ X992 @ X991 )
<=> ? [X993: $i] :
( ( in @ X993 @ X987 )
& ( X986 @ X993 @ X992 ) ) ) )
=> ( ! [X994: $i] :
( ? [X995: $i] : ( in @ X995 @ X994 )
=> ? [X996: $i] :
( ( in @ X996 @ X994 )
& ~ ? [X997: $i] :
( ( in @ X997 @ X996 )
& ( in @ X997 @ X994 ) ) ) )
=> ( epred1_0
=> ( ! [X1017: $i > $o] :
( ? [X1018: $i] :
( ( X1017 @ X1018 )
& ! [X1019: $i] :
( ( X1017 @ X1019 )
=> ( X1018 = X1019 ) ) )
=> ( X1017
@ ( descr
@ ^ [Z0: $i] : ( X1017 @ Z0 ) ) ) )
=> ( ! [X1020: $i,X1021: $i > $o,X1022: $i] :
( ( in @ X1022 @ X1020 )
=> ( ( X1021 @ X1022 )
=> ( in @ X1022 @ ( dsetconstr @ X1020 @ X1021 ) ) ) )
=> ( ! [X1023: $i,X1024: $i > $o,X1025: $i] :
( ( in @ X1025 @ ( dsetconstr @ X1023 @ X1024 ) )
=> ( in @ X1025 @ X1023 ) )
=> ( ! [X1026: $i,X1027: $i > $o,X1028: $i] :
( ( in @ X1028 @ ( dsetconstr @ X1026 @ X1027 ) )
=> ( X1027 @ X1028 ) )
=> ( ! [X1029: $i > $o] :
( ? [X1030: $i] :
( ( X1029 @ X1030 )
& ! [X1031: $i] :
( ( X1029 @ X1031 )
=> ( X1030 = X1031 ) ) )
=> ? [X1032: $i] :
( ( X1029 @ X1032 )
& ! [X1033: $i] :
( ( X1029 @ X1033 )
=> ( X1032 = X1033 ) ) ) )
=> ( ! [X1034: $o,X1035: $i] :
( ( in @ X1035 @ ( prop2set @ X1034 ) )
=> X1034 )
=> ( ! [X1036: $i] :
( ( in @ X1036 @ emptyset )
=> ! [X1037: $o] : X1037 )
=> ( ! [X1038: $i] :
( ( in @ X1038 @ emptyset )
=> ~ $true )
=> ( ! [X1039: $i] :
~ ( in @ X1039 @ emptyset )
=> ( ! [X1040: $i > $o] :
( ? [X1041: $i] :
( ( X1040 @ X1041 )
& ! [X1042: $i] :
( ( X1040 @ X1042 )
=> ( X1041 = X1042 ) ) )
=> ? [X1043: $i] : ( X1040 @ X1043 ) )
=> ( ! [X1044: $i,X1045: $i] :
( ! [X1046: $i] :
( ( in @ X1046 @ X1044 )
=> ( in @ X1046 @ X1045 ) )
=> ( ! [X1047: $i] :
( ( in @ X1047 @ X1045 )
=> ( in @ X1047 @ X1044 ) )
=> ( X1044 = X1045 ) ) )
=> ( ! [X1048: $i] :
( ! [X1049: $i] :
~ ( in @ X1049 @ X1048 )
=> ( X1048 = emptyset ) )
=> ( ! [X1050: $i] :
( ! [X1051: $i] :
~ ( in @ X1051 @ X1050 )
=> ( X1050 = emptyset ) )
=> ( ! [X1052: $i,X1053: $i > $o,X1054: $i] :
( ( in @ X1054 @ X1052 )
=> ( ( in @ X1054 @ ( dsetconstr @ X1052 @ X1053 ) )
<=> ( X1053 @ X1054 ) ) )
=> ( ! [X1055: $i] :
( ( X1055 != emptyset )
=> ? [X1056: $i] : ( in @ X1056 @ X1055 ) )
=> ( ! [X1057: $i,X1058: $i > $o,X1059: $i] :
( ( in @ X1059 @ X1057 )
=> ( ( X1058 @ X1059 )
=> ( ( dsetconstr @ X1057 @ X1058 )
!= emptyset ) ) )
=> ( ! [X1060: $i] :
( ? [X1061: $i] : ( in @ X1061 @ X1060 )
=> ( X1060 != emptyset ) )
=> ( ! [X1062: $i,X1063: $i] : ( in @ X1062 @ ( setadjoin @ X1062 @ X1063 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1064: $i,X1065: $i,X1066: $i] :
( ( in @ X1066 @ X1065 )
=> ( in @ X1066 @ ( setadjoin @ X1064 @ X1065 ) ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i] :
( ( in @ X1069 @ ( setadjoin @ X1067 @ X1068 ) )
=> ! [X1070: $o] :
( ( ( X1069 = X1067 )
=> X1070 )
=> ( ( ( in @ X1069 @ X1068 )
=> X1070 )
=> X1070 ) ) )
=> ( ! [X1071: $i,X1072: $i,X1073: $i] :
( ( in @ X1073 @ ( setadjoin @ X1071 @ X1072 ) )
=> ( ( X1073 = X1071 )
| ( in @ X1073 @ X1072 ) ) )
=> ( ! [X1074: $i] :
( ( dsetconstr @ X1074
@ ^ [Z0: $i] : $true )
= X1074 )
=> ( ! [X1075: $i,X1076: $i] :
( ! [X1077: $i] :
( ( in @ X1077 @ X1076 )
=> ( in @ X1077 @ X1075 ) )
=> ( in @ X1076 @ ( powerset @ X1075 ) ) )
=> ( ! [X1078: $i] : ( in @ emptyset @ ( powerset @ X1078 ) )
=> ( ! [X1079: $i] : ( in @ emptyset @ ( powerset @ X1079 ) )
=> ( ! [X1080: $i,X1081: $i,X1082: $i] :
( ( in @ X1081 @ ( powerset @ X1080 ) )
=> ( ( in @ X1082 @ X1081 )
=> ( in @ X1082 @ X1080 ) ) )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ( in @ X1084 @ X1085 )
=> ( ( in @ X1085 @ X1083 )
=> ( in @ X1084 @ ( setunion @ X1083 ) ) ) )
=> ( ! [X1086: $i,X1087: $i] :
( ( in @ X1087 @ ( setunion @ X1086 ) )
=> ! [X1088: $o] :
( ! [X1089: $i] :
( ( in @ X1087 @ X1089 )
=> ( ( in @ X1089 @ X1086 )
=> X1088 ) )
=> X1088 ) )
=> ( ! [X1090: $i,X1091: $i] :
( ( in @ X1091 @ X1090 )
=> ( in @ X1091 @ ( powerset @ ( setunion @ X1090 ) ) ) )
=> ( ! [X1092: $i > $o] :
( ? [X1093: $i] :
( ( X1092 @ X1093 )
& ! [X1094: $i] :
( ( X1092 @ X1094 )
=> ( X1093 = X1094 ) ) )
=> ? [X1095: $i] :
! [X1096: $i] :
( ( X1092 @ X1096 )
<=> ( X1096 = X1095 ) ) )
=> ( ! [X1097: $i] :
( ( X1097 != emptyset )
=> ? [X1098: $i] :
( ( in @ X1098 @ X1097 )
& $true ) )
=> ( ! [X1099: $i,X1100: $i] :
( ( in @ X1099 @ ( setadjoin @ X1100 @ emptyset ) )
=> ( X1099 = X1100 ) )
=> ( ! [X1101: $i,X1102: $i] :
( ( X1101 != X1102 )
=> ~ ( in @ X1102 @ ( setadjoin @ X1101 @ emptyset ) ) )
=> ( ! [X1103: $i,X1104: $i] :
( ( X1103 = X1104 )
=> ( in @ X1103 @ ( setadjoin @ X1104 @ emptyset ) ) )
=> ( ! [X1105: $i,X1106: $i] :
( ( in @ X1105 @ ( setadjoin @ X1106 @ emptyset ) )
=> ( in @ X1106 @ ( setadjoin @ X1105 @ emptyset ) ) )
=> ( ! [X1107: $i,X1108: $i,X1109: $i] :
( ( in @ X1109 @ ( setadjoin @ X1107 @ ( setadjoin @ X1108 @ emptyset ) ) )
=> ( ( X1109 = X1107 )
| ( X1109 = X1108 ) ) )
=> ( ! [X1110: $i,X1111: $i] : ( in @ X1110 @ ( setadjoin @ X1110 @ ( setadjoin @ X1111 @ emptyset ) ) )
=> ( ! [X1112: $i,X1113: $i] : ( in @ X1113 @ ( setadjoin @ X1112 @ ( setadjoin @ X1113 @ emptyset ) ) )
=> ( ! [X1114: $i,X1115: $i > $o] :
( ? [X1116: $i] :
( ( in @ X1116 @ X1114 )
& ( X1115 @ X1116 ) )
=> ( ( ( dsetconstr @ X1114 @ X1115 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1117: $i > $o,X1118: $i] :
( ( in @ X1118 @ emptyset )
=> ( X1117 @ X1118 ) )
=> ( ! [X1119: $i,X1120: $i > $o] :
( ~ ! [X1121: $i] :
( ( in @ X1121 @ X1119 )
=> ( X1120 @ X1121 ) )
=> ? [X1122: $i] :
( ( in @ X1122 @ X1119 )
& ~ ( X1120 @ X1122 ) ) )
=> ( ! [X1123: $i,X1124: $i > $o] :
( ! [X1125: $i] :
( ( in @ X1125 @ X1123 )
=> ~ ( X1124 @ X1125 ) )
=> ~ ? [X1126: $i] :
( ( in @ X1126 @ X1123 )
& ( X1124 @ X1126 ) ) )
=> ( ! [X1127: $i,X1128: $i > $o] :
( ~ ? [X1129: $i] :
( ( in @ X1129 @ X1127 )
& ( X1128 @ X1129 ) )
=> ! [X1130: $i] :
( ( in @ X1130 @ X1127 )
=> ~ ( X1128 @ X1130 ) ) )
=> ( ! [X1131: $i,X1132: $i > $o] :
( ? [X1133: $i] :
( ( in @ X1133 @ X1131 )
& ~ ( X1132 @ X1133 ) )
=> ~ ! [X1134: $i] :
( ( in @ X1134 @ X1131 )
=> ( X1132 @ X1134 ) ) )
=> ( ! [X1135: $o] :
( X1135
=> ( in @ emptyset @ ( prop2set @ X1135 ) ) )
=> ( ! [X1136: $o] :
( X1136
=> ( set2prop @ ( prop2set @ X1136 ) ) )
=> ( ! [X1137: $i,X1138: $i > $o] :
( ~ ? [X1139: $i] :
( ( in @ X1139 @ X1137 )
& ( X1138 @ X1139 ) )
=> ! [X1140: $i] :
( ( in @ X1140 @ X1137 )
=> ~ ( X1138 @ X1140 ) ) )
=> ( ! [X1141: $i,X1142: $i > $o] :
( ~ ! [X1143: $i] :
( ( in @ X1143 @ X1141 )
=> ( X1142 @ X1143 ) )
=> ? [X1144: $i] :
( ( in @ X1144 @ X1141 )
& ~ ( X1142 @ X1144 ) ) )
=> ( ! [X1145: $i > $o] :
( ? [X1146: $i] :
( ( X1145 @ X1146 )
& ! [X1147: $i] :
( ( X1145 @ X1147 )
=> ( X1146 = X1147 ) ) )
=> ? [X1148: $i] :
( ( X1145 @ X1148 )
& ! [X1149: $i] :
( ( X1145 @ X1149 )
=> ( X1148 = X1149 ) ) ) )
=> ( ! [X1150: $i > $o] :
( ? [X1151: $i] : ( X1150 @ X1151 )
=> ( ! [X1152: $i,X1153: $i] :
( ( X1150 @ X1152 )
=> ( ( X1150 @ X1153 )
=> ( X1152 = X1153 ) ) )
=> ? [X1154: $i] :
( ( X1150 @ X1154 )
& ! [X1155: $i] :
( ( X1150 @ X1155 )
=> ( X1154 = X1155 ) ) ) ) )
=> ( ! [X1156: $i > $o] :
( ? [X1157: $i] :
! [X1158: $i] :
( ( X1156 @ X1158 )
<=> ( X1158 = X1157 ) )
=> ? [X1159: $i] :
( ( X1156 @ X1159 )
& ! [X1160: $i] :
( ( X1156 @ X1160 )
=> ( X1159 = X1160 ) ) ) )
=> ( ! [X1161: $i,X1162: $i] :
( ( X1161 = X1162 )
=> ! [X1163: $i,X1164: $i] :
( ( X1163 = X1164 )
=> ( ( in @ X1163 @ X1161 )
=> ( in @ X1164 @ X1162 ) ) ) )
=> ( ! [X1165: $i,X1166: $i] :
( ( X1165 = X1166 )
=> ! [X1167: $i,X1168: $i] :
( ( X1167 = X1168 )
=> ( ( in @ X1167 @ X1165 )
<=> ( in @ X1168 @ X1166 ) ) ) )
=> ( ! [X1169: $i > $o] :
( ? [X1170: $i] :
( ( X1169 @ X1170 )
& ! [X1171: $i] :
( ( X1169 @ X1171 )
=> ( X1170 = X1171 ) ) )
=> ! [X1172: $i,X1173: $i] :
( ( X1169 @ X1172 )
=> ( ( X1169 @ X1173 )
=> ( X1172 = X1173 ) ) ) )
=> ( ! [X1174: $i > $o,X1175: $i > $o] :
( ! [X1176: $i,X1177: $i] :
( ( X1176 = X1177 )
=> ( ( X1174 @ X1176 )
<=> ( X1175 @ X1177 ) ) )
=> ( ? [X1178: $i] :
( ( X1174 @ X1178 )
& ! [X1179: $i] :
( ( X1174 @ X1179 )
=> ( X1178 = X1179 ) ) )
<=> ? [X1180: $i] :
( ( X1175 @ X1180 )
& ! [X1181: $i] :
( ( X1175 @ X1181 )
=> ( X1180 = X1181 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1182: $i,X1183: $i] :
( ( X1182 = X1183 )
=> ! [X1184: $i,X1185: $i] :
( ( X1184 = X1185 )
=> ( ( setadjoin @ X1182 @ X1184 )
= ( setadjoin @ X1183 @ X1185 ) ) ) )
=> ( ! [X1186: $i,X1187: $i] :
( ( X1186 = X1187 )
=> ( ( powerset @ X1186 )
= ( powerset @ X1187 ) ) )
=> ( ! [X1188: $i,X1189: $i] :
( ( X1188 = X1189 )
=> ( ( setunion @ X1188 )
= ( setunion @ X1189 ) ) )
=> ( ( omega = omega )
=> ( ! [X1190: $i > $o] :
( ? [X1191: $i] :
( ( X1190 @ X1191 )
& ! [X1192: $i] :
( ( X1190 @ X1192 )
=> ( X1191 = X1192 ) ) )
=> ! [X1193: $i,X1194: $i] :
( ( X1190 @ X1193 )
=> ( ( X1190 @ X1194 )
=> ( X1193 = X1194 ) ) ) )
=> ( ! [X1195: $i > $o,X1196: $i > $o] :
( ! [X1197: $i,X1198: $i] :
( ( X1197 = X1198 )
=> ( ( X1195 @ X1197 )
<=> ( X1196 @ X1198 ) ) )
=> ( ? [X1199: $i] :
( ( X1195 @ X1199 )
& ! [X1200: $i] :
( ( X1195 @ X1200 )
=> ( X1199 = X1200 ) ) )
=> ( ? [X1201: $i] :
( ( X1196 @ X1201 )
& ! [X1202: $i] :
( ( X1196 @ X1202 )
=> ( X1201 = X1202 ) ) )
=> ( ( descr @ X1195 )
= ( descr @ X1196 ) ) ) ) )
=> ( ! [X1203: $i,X1204: $i] :
( ( X1203 = X1204 )
=> ! [X1205: $i > $o,X1206: $i > $o] :
( ! [X1207: $i] :
( ( in @ X1207 @ X1203 )
=> ! [X1208: $i] :
( ( in @ X1208 @ X1204 )
=> ( ( X1207 = X1208 )
=> ( ( X1205 @ X1207 )
<=> ( X1206 @ X1208 ) ) ) ) )
=> ( ( dsetconstr @ X1203 @ X1205 )
= ( dsetconstr @ X1204 @ X1206 ) ) ) )
=> ( ! [X1209: $i,X1210: $i] :
( ! [X1211: $i] :
( ( in @ X1211 @ X1209 )
=> ( in @ X1211 @ X1210 ) )
=> ( subset @ X1209 @ X1210 ) )
=> ( ! [X1212: $i,X1213: $i] :
( ( X1212 = X1213 )
=> ( subset @ X1213 @ X1212 ) )
=> ( ! [X1214: $i,X1215: $i] :
( ( X1214 = X1215 )
=> ( subset @ X1214 @ X1215 ) )
=> ( ! [X1216: $i,X1217: $i] :
( ! [X1218: $i] :
( ( in @ X1218 @ X1216 )
=> ( in @ X1218 @ X1217 ) )
=> ( subset @ X1216 @ X1217 ) )
=> ( ! [X1219: $i] : ( subset @ emptyset @ X1219 )
=> ( ! [X1220: $i,X1221: $i,X1222: $i] :
( ( subset @ X1220 @ X1221 )
=> ( ( in @ X1222 @ X1220 )
=> ( in @ X1222 @ X1221 ) ) )
=> ( ! [X1223: $i,X1224: $i,X1225: $i] :
( ( subset @ X1223 @ X1224 )
=> ( ~ ( in @ X1225 @ X1224 )
=> ~ ( in @ X1225 @ X1223 ) ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i] :
( ( in @ X1228 @ X1226 )
=> ( ~ ( in @ X1228 @ X1227 )
=> ~ ( subset @ X1226 @ X1227 ) ) )
=> ( ! [X1229: $i,X1230: $i] :
( ~ ( subset @ X1229 @ X1230 )
=> ( X1229 != X1230 ) )
=> ( ! [X1231: $i,X1232: $i,X1233: $i] :
( ( in @ X1233 @ X1231 )
=> ( ~ ( in @ X1233 @ X1232 )
=> ( X1231 != X1232 ) ) )
=> ( ! [X1234: $i] : ( subset @ X1234 @ X1234 )
=> ( ! [X1235: $i,X1236: $i,X1237: $i] :
( ( subset @ X1235 @ X1236 )
=> ( ( subset @ X1236 @ X1237 )
=> ( subset @ X1235 @ X1237 ) ) )
=> ( ! [X1238: $i,X1239: $i] : ( subset @ X1239 @ ( setadjoin @ X1238 @ X1239 ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i] :
( ( subset @ X1240 @ X1242 )
=> ( subset @ X1240 @ ( setadjoin @ X1241 @ X1242 ) ) )
=> ( ! [X1243: $i,X1244: $i] :
( ( subset @ X1243 @ X1244 )
=> ( in @ X1243 @ ( powerset @ X1244 ) ) )
=> ( ! [X1245: $i,X1246: $i] :
( ( subset @ X1245 @ X1246 )
=> ( ( subset @ X1246 @ X1245 )
=> ( X1245 = X1246 ) ) )
=> ( ! [X1247: $i] :
( ( subset @ X1247 @ emptyset )
=> ( X1247 = emptyset ) )
=> ( ! [X1248: $i,X1249: $i] :
( ( subset @ X1249 @ X1248 )
=> ( in @ X1249 @ ( powerset @ X1248 ) ) )
=> ( ! [X1250: $i,X1251: $i] :
( ( in @ X1251 @ ( powerset @ X1250 ) )
=> ( subset @ X1251 @ X1250 ) )
=> ( ! [X1252: $i] : ( in @ X1252 @ ( powerset @ X1252 ) )
=> ( ! [X1253: $i,X1254: $i] :
( ( subset @ X1253 @ X1254 )
=> ( subset @ ( powerset @ X1253 ) @ ( powerset @ X1254 ) ) )
=> ( ! [X1255: $i,X1256: $i > $o] : ( in @ ( dsetconstr @ X1255 @ X1256 ) @ ( powerset @ X1255 ) )
=> ( ! [X1257: $i,X1258: $i > $o] : ( subset @ ( dsetconstr @ X1257 @ X1258 ) @ X1257 )
=> ( ! [X1259: $i,X1260: $i,X1261: $i] :
( ( in @ X1261 @ X1259 )
=> ( in @ X1261 @ ( binunion @ X1259 @ X1260 ) ) )
=> ( ! [X1262: $i,X1263: $i] : ( in @ X1263 @ ( setadjoin @ X1262 @ ( setadjoin @ X1263 @ emptyset ) ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i] :
( ( in @ X1266 @ X1265 )
=> ( in @ X1266 @ ( binunion @ X1264 @ X1265 ) ) )
=> ( ! [X1267: $i,X1268: $i,X1269: $i,X1270: $o] :
( ( in @ X1269 @ ( binunion @ X1267 @ X1268 ) )
=> ( ( ( in @ X1269 @ X1267 )
=> X1270 )
=> ( ( ( in @ X1269 @ X1268 )
=> X1270 )
=> X1270 ) ) )
=> ( ! [X1271: $i,X1272: $i,X1273: $i] :
( ( in @ X1273 @ ( binunion @ X1271 @ X1272 ) )
=> ( ( in @ X1273 @ X1271 )
| ( in @ X1273 @ X1272 ) ) )
=> ( ! [X1274: $i,X1275: $i] : ( subset @ X1274 @ ( binunion @ X1274 @ X1275 ) )
=> ( ! [X1276: $i,X1277: $i] : ( subset @ X1277 @ ( binunion @ X1276 @ X1277 ) )
=> ( ! [X1278: $i,X1279: $i,X1280: $i] :
( ( in @ X1280 @ X1278 )
=> ( ( in @ X1280 @ X1279 )
=> ( in @ X1280 @ ( binintersect @ X1278 @ X1279 ) ) ) )
=> ( ! [X1281: $i,X1282: $i,X1283: $i] :
( ( subset @ X1283 @ X1281 )
=> ( ( subset @ X1283 @ X1282 )
=> ( subset @ X1283 @ ( binintersect @ X1281 @ X1282 ) ) ) )
=> ( ! [X1284: $i,X1285: $i,X1286: $i] :
( ( in @ X1286 @ ( binintersect @ X1284 @ X1285 ) )
=> ( in @ X1286 @ X1284 ) )
=> ( ! [X1287: $i,X1288: $i] : ( subset @ ( binintersect @ X1287 @ X1288 ) @ X1287 )
=> ( ! [X1289: $i,X1290: $i] :
( ( subset @ X1289 @ X1290 )
=> ( ( binintersect @ X1289 @ X1290 )
= X1289 ) )
=> ( ! [X1291: $i,X1292: $i] :
( ( ( binintersect @ X1291 @ X1292 )
= X1292 )
=> ( subset @ X1292 @ X1291 ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i] :
( ( in @ X1295 @ ( binintersect @ X1293 @ X1294 ) )
=> ( in @ X1295 @ X1294 ) )
=> ( ! [X1296: $i,X1297: $i] :
( ~ ? [X1298: $i] :
( ( in @ X1298 @ X1296 )
& ( in @ X1298 @ X1297 ) )
=> ( ( binintersect @ X1296 @ X1297 )
= emptyset ) )
=> ( ! [X1299: $i,X1300: $i] : ( subset @ ( binintersect @ X1299 @ X1300 ) @ X1300 )
=> ( ! [X1301: $i,X1302: $i] :
( ( subset @ X1302 @ X1301 )
=> ( ( binintersect @ X1301 @ X1302 )
= X1302 ) )
=> ( ! [X1303: $i,X1304: $i] :
( ( ( binintersect @ X1303 @ X1304 )
= X1303 )
=> ( subset @ X1303 @ X1304 ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( binintersect @ X1305 @ ( binunion @ X1306 @ X1307 ) )
= ( binunion @ ( binintersect @ X1305 @ X1306 ) @ ( binintersect @ X1305 @ X1307 ) ) )
=> ( ! [X1308: $i,X1309: $i,X1310: $i] :
( ( in @ X1310 @ X1308 )
=> ( ~ ( in @ X1310 @ X1309 )
=> ( in @ X1310 @ ( setminus @ X1308 @ X1309 ) ) ) )
=> ( ! [X1311: $i,X1312: $i,X1313: $i] :
( ( in @ X1313 @ ( setminus @ X1311 @ X1312 ) )
=> ( in @ X1313 @ X1311 ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( in @ X1316 @ ( setminus @ X1314 @ X1315 ) )
=> ~ ( in @ X1316 @ X1315 ) )
=> ( ! [X1317: $i,X1318: $i] :
( ( subset @ X1317 @ X1318 )
=> ( ( setminus @ X1317 @ X1318 )
= emptyset ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i] :
( ~ ( in @ X1321 @ ( setminus @ X1319 @ X1320 ) )
=> ( ( in @ X1321 @ X1319 )
=> ( in @ X1321 @ X1320 ) ) )
=> ( ! [X1322: $i,X1323: $i,X1324: $i] :
( ~ ( in @ X1324 @ ( setminus @ X1322 @ X1323 ) )
=> ( ~ ( in @ X1324 @ X1323 )
=> ~ ( in @ X1324 @ X1322 ) ) )
=> ( ! [X1325: $i,X1326: $i,X1327: $i] :
( ~ ( in @ X1327 @ X1325 )
=> ~ ( in @ X1327 @ ( setminus @ X1325 @ X1326 ) ) )
=> ( ! [X1328: $i,X1329: $i,X1330: $i] :
( ( in @ X1330 @ X1329 )
=> ~ ( in @ X1330 @ ( setminus @ X1328 @ X1329 ) ) )
=> ( ! [X1331: $i,X1332: $i] : ( subset @ ( setminus @ X1331 @ X1332 ) @ X1331 )
=> ( ! [X1333: $i,X1334: $i] :
( ( ( setminus @ X1333 @ X1334 )
= emptyset )
=> ( subset @ X1333 @ X1334 ) )
=> ( ! [X1335: $i,X1336: $i,X1337: $i] :
( ( in @ X1337 @ ( symdiff @ X1335 @ X1336 ) )
=> ! [X1338: $o] :
( ( ( in @ X1337 @ X1335 )
=> ( ~ ( in @ X1337 @ X1336 )
=> X1338 ) )
=> ( ( ~ ( in @ X1337 @ X1335 )
=> ( ( in @ X1337 @ X1336 )
=> X1338 ) )
=> X1338 ) ) )
=> ( ! [X1339: $i,X1340: $i,X1341: $i] :
( ( in @ X1341 @ X1339 )
=> ( ~ ( in @ X1341 @ X1340 )
=> ( in @ X1341 @ ( symdiff @ X1339 @ X1340 ) ) ) )
=> ( ! [X1342: $i,X1343: $i,X1344: $i] :
( ~ ( in @ X1344 @ X1342 )
=> ( ( in @ X1344 @ X1343 )
=> ( in @ X1344 @ ( symdiff @ X1342 @ X1343 ) ) ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i] :
( ( in @ X1347 @ X1345 )
=> ( ( in @ X1347 @ X1346 )
=> ~ ( in @ X1347 @ ( symdiff @ X1345 @ X1346 ) ) ) )
=> ( ! [X1348: $i,X1349: $i,X1350: $i] :
( ~ ( in @ X1350 @ X1348 )
=> ( ~ ( in @ X1350 @ X1349 )
=> ~ ( in @ X1350 @ ( symdiff @ X1348 @ X1349 ) ) ) )
=> ( ! [X1351: $i,X1352: $i] : ( in @ X1352 @ ( setadjoin @ X1351 @ ( setadjoin @ X1352 @ emptyset ) ) )
=> ( ! [X1353: $i,X1354: $i] : ( in @ X1353 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1353 @ ( setadjoin @ X1354 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1355: $i,X1356: $i] : ( in @ X1356 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1355 @ ( setadjoin @ X1356 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1357: $i,X1358: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1357 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1357 @ ( setadjoin @ X1358 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1359: $i,X1360: $i] : ( iskpair @ ( kpair @ X1359 @ X1360 ) )
=> ( ! [X1361: $i,X1362: $i] :
( ( in @ X1362 @ X1361 )
=> ( subset @ ( setadjoin @ X1362 @ emptyset ) @ X1361 ) )
=> ( ! [X1363: $i,X1364: $i] :
( ( in @ X1364 @ X1363 )
=> ( in @ ( setadjoin @ X1364 @ emptyset ) @ ( powerset @ X1363 ) ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i] :
( ( in @ X1367 @ X1365 )
=> ( in @ ( setadjoin @ X1367 @ emptyset ) @ ( powerset @ ( binunion @ X1365 @ X1366 ) ) ) )
=> ( ! [X1368: $i,X1369: $i,X1370: $i] :
( ( in @ X1370 @ ( setadjoin @ X1368 @ ( setadjoin @ X1369 @ emptyset ) ) )
=> ( ( X1370 = X1368 )
| ( X1370 = X1369 ) ) )
=> ( ! [X1371: $i,X1372: $i,X1373: $i] :
( ( in @ X1373 @ X1371 )
=> ! [X1374: $i] :
( ( in @ X1374 @ X1372 )
=> ( subset @ ( setadjoin @ X1373 @ ( setadjoin @ X1374 @ emptyset ) ) @ ( binunion @ X1371 @ X1372 ) ) ) )
=> ( ! [X1375: $i,X1376: $i,X1377: $i] :
( ( in @ X1377 @ X1375 )
=> ! [X1378: $i] :
( ( in @ X1378 @ X1376 )
=> ( in @ ( setadjoin @ X1377 @ ( setadjoin @ X1378 @ emptyset ) ) @ ( powerset @ ( binunion @ X1375 @ X1376 ) ) ) ) )
=> ( ! [X1379: $i,X1380: $i,X1381: $i] :
( ( in @ X1381 @ X1379 )
=> ! [X1382: $i] :
( ( in @ X1382 @ X1380 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1381 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1381 @ ( setadjoin @ X1382 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1379 @ X1380 ) ) ) ) )
=> ( ! [X1383: $i,X1384: $i,X1385: $i] :
( ( in @ X1385 @ X1383 )
=> ! [X1386: $i] :
( ( in @ X1386 @ X1384 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1385 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1385 @ ( setadjoin @ X1386 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1383 @ X1384 ) ) ) ) ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i] :
( ( in @ X1389 @ X1387 )
=> ! [X1390: $i] :
( ( in @ X1390 @ X1388 )
=> ( in @ ( kpair @ X1389 @ X1390 ) @ ( powerset @ ( powerset @ ( binunion @ X1387 @ X1388 ) ) ) ) ) )
=> ( ! [X1391: $i,X1392: $i,X1393: $i] :
( ( in @ X1393 @ X1391 )
=> ! [X1394: $i] :
( ( in @ X1394 @ X1392 )
=> ( in @ ( kpair @ X1393 @ X1394 ) @ ( cartprod @ X1391 @ X1392 ) ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i] :
( ( in @ X1397 @ ( cartprod @ X1395 @ X1396 ) )
=> ? [X1398: $i] :
( ( in @ X1398 @ X1395 )
& ? [X1399: $i] :
( ( in @ X1399 @ X1396 )
& ( X1397
= ( kpair @ X1398 @ X1399 ) ) ) ) )
=> ( ! [X1400: $i,X1401: $i,X1402: $i] :
( ( in @ X1402 @ ( cartprod @ X1400 @ X1401 ) )
=> ( iskpair @ X1402 ) )
=> ( ! [X1403: $i,X1404: $i] :
( ( in @ X1404 @ ( setunion @ X1403 ) )
=> ? [X1405: $i] :
( ( in @ X1405 @ X1403 )
& ( in @ X1404 @ X1405 ) ) )
=> ( ! [X1406: $i] : ( subset @ ( setunion @ ( setadjoin @ X1406 @ emptyset ) ) @ X1406 )
=> ( ! [X1407: $i] : ( subset @ X1407 @ ( setunion @ ( setadjoin @ X1407 @ emptyset ) ) )
=> ( ! [X1408: $i] :
( ( setunion @ ( setadjoin @ X1408 @ emptyset ) )
= X1408 )
=> ( ! [X1409: $i,X1410: $i > $o] :
( ! [X1411: $i] :
( ( in @ X1411 @ X1409 )
=> ! [X1412: $i] :
( ( in @ X1412 @ X1409 )
=> ( ( X1410 @ X1411 )
=> ( ( X1410 @ X1412 )
=> ( X1411 = X1412 ) ) ) ) )
=> ( ? [X1413: $i] :
( ( in @ X1413 @ X1409 )
& ( X1410 @ X1413 ) )
=> ( singleton @ ( dsetconstr @ X1409 @ X1410 ) ) ) )
=> ( ! [X1414: $i,X1415: $i > $o] :
( ( singleton @ ( dsetconstr @ X1414 @ X1415 ) )
=> ? [X1416: $i] :
( ( in @ X1416 @ X1414 )
& ( X1415 @ X1416 ) ) )
=> ( ! [X1417: $i,X1418: $i > $o,X1419: $i] :
( ( in @ X1419 @ X1417 )
=> ( ( X1418 @ X1419 )
=> ( ! [X1420: $i] :
( ( in @ X1420 @ X1417 )
=> ( ( X1418 @ X1420 )
=> ( X1420 = X1419 ) ) )
=> ( singleton @ ( dsetconstr @ X1417 @ X1418 ) ) ) ) )
=> ( ! [X1421: $i,X1422: $i > $o] :
( ! [X1423: $i] :
( ( in @ X1423 @ X1421 )
=> ! [X1424: $i] :
( ( in @ X1424 @ X1421 )
=> ( ( X1422 @ X1423 )
=> ( ( X1422 @ X1424 )
=> ( X1423 = X1424 ) ) ) ) )
=> ( ? [X1425: $i] :
( ( in @ X1425 @ X1421 )
& ( X1422 @ X1425 ) )
=> ( singleton @ ( dsetconstr @ X1421 @ X1422 ) ) ) )
=> ( ! [X1426: $i,X1427: $i] :
( ( ( setadjoin @ X1426 @ emptyset )
= ( setadjoin @ X1427 @ emptyset ) )
=> ( X1426 = X1427 ) )
=> ( ! [X1428: $i,X1429: $i,X1430: $i] :
( ( in @ ( setadjoin @ X1430 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1428 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1428 @ ( setadjoin @ X1429 @ emptyset ) ) @ emptyset ) ) )
=> ( X1428 = X1430 ) )
=> ( ! [X1431: $i] :
( ( iskpair @ X1431 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1431 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1431 ) ) ) )
=> ( ! [X1432: $i] :
( ( singleton @ X1432 )
=> ( in @ ( setunion @ X1432 ) @ X1432 ) )
=> ( ! [X1433: $i,X1434: $i] :
( ( kfst @ ( kpair @ X1433 @ X1434 ) )
= X1433 )
=> ( ! [X1435: $i,X1436: $i,X1437: $i] :
( ( in @ X1437 @ ( cartprod @ X1435 @ X1436 ) )
=> ( in @ ( kfst @ X1437 ) @ X1435 ) )
=> ( ! [X1438: $i,X1439: $i,X1440: $i,X1441: $i] :
( ( ( setadjoin @ ( setadjoin @ X1438 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1438 @ ( setadjoin @ X1439 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1440 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1440 @ ( setadjoin @ X1441 @ emptyset ) ) @ emptyset ) ) )
=> ( X1438 = X1440 ) )
=> ( ! [X1442: $i,X1443: $i,X1444: $i,X1445: $i] :
( ( ( kpair @ X1442 @ X1443 )
= ( kpair @ X1444 @ X1445 ) )
=> ( X1442 = X1444 ) )
=> ( ! [X1446: $i,X1447: $i] :
( ( X1446 = X1447 )
=> ( ( setadjoin @ X1446 @ ( setadjoin @ X1447 @ emptyset ) )
= ( setadjoin @ X1446 @ emptyset ) ) )
=> ( ! [X1448: $i,X1449: $i] :
( ( X1448 = X1449 )
=> ( ( setadjoin @ ( setadjoin @ X1448 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1448 @ ( setadjoin @ X1449 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1448 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1450: $i,X1451: $i,X1452: $i,X1453: $i] :
( ( ( setadjoin @ ( setadjoin @ X1450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1450 @ ( setadjoin @ X1451 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1452 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1452 @ ( setadjoin @ X1453 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1452 = X1453 )
=> ( X1451 = X1453 ) ) )
=> ( ! [X1454: $i,X1455: $i,X1456: $i] :
( ( ( setadjoin @ X1454 @ ( setadjoin @ X1455 @ emptyset ) )
= ( setadjoin @ X1456 @ emptyset ) )
=> ( X1454 = X1455 ) )
=> ( ! [X1457: $i,X1458: $i,X1459: $i,X1460: $i] :
( ( ( setadjoin @ ( setadjoin @ X1457 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1457 @ ( setadjoin @ X1458 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1459 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1459 @ ( setadjoin @ X1460 @ emptyset ) ) @ emptyset ) ) )
=> ( X1458 = X1460 ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i,X1464: $i] :
( ( ( kpair @ X1461 @ X1462 )
= ( kpair @ X1463 @ X1464 ) )
=> ( X1462 = X1464 ) )
=> ( ! [X1465: $i] :
( ( iskpair @ X1465 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1465 )
@ ^ [Z0: $i] :
( X1465
= ( kpair @ ( kfst @ X1465 ) @ Z0 ) ) ) ) )
=> ( ! [X1466: $i,X1467: $i] :
( ( ksnd @ ( kpair @ X1466 @ X1467 ) )
= X1467 )
=> ( ! [X1468: $i] :
( ( iskpair @ X1468 )
=> ( ( kpair @ ( kfst @ X1468 ) @ ( ksnd @ X1468 ) )
= X1468 ) )
=> ( ! [X1469: $i,X1470: $i,X1471: $i] :
( ( in @ X1471 @ ( cartprod @ X1469 @ X1470 ) )
=> ( in @ ( ksnd @ X1471 ) @ X1470 ) )
=> ( ! [X1472: $i,X1473: $i,X1474: $i,X1475: $i] :
( ( in @ ( kpair @ X1474 @ X1475 ) @ ( cartprod @ X1472 @ X1473 ) )
=> ( in @ X1474 @ X1472 ) )
=> ( ! [X1476: $i,X1477: $i,X1478: $i,X1479: $i] :
( ( in @ ( kpair @ X1478 @ X1479 ) @ ( cartprod @ X1476 @ X1477 ) )
=> ( in @ X1479 @ X1477 ) )
=> ( ! [X1480: $i,X1481: $i,X1482: $i] :
( ( in @ X1482 @ X1480 )
=> ! [X1483: $i] :
( ( in @ X1483 @ X1481 )
=> ( ( kpair @ X1482 @ X1483 )
= ( kpair @ X1482 @ X1483 ) ) ) )
=> ( ! [X1484: $i,X1485: $i,X1486: $i] :
( ( in @ X1486 @ X1484 )
=> ! [X1487: $i] :
( ( in @ X1487 @ X1485 )
=> ( ( kfst @ ( kpair @ X1486 @ X1487 ) )
= X1486 ) ) )
=> ( ! [X1488: $i,X1489: $i,X1490: $i] :
( ( in @ X1490 @ X1488 )
=> ! [X1491: $i] :
( ( in @ X1491 @ X1489 )
=> ( ( ksnd @ ( kpair @ X1490 @ X1491 ) )
= X1491 ) ) )
=> ( ! [X1492: $i,X1493: $i,X1494: $i] :
( ( in @ X1494 @ ( cartprod @ X1492 @ X1493 ) )
=> ( ( kpair @ ( kfst @ X1494 ) @ ( ksnd @ X1494 ) )
= X1494 ) )
=> ( ! [X1495: $i,X1496: $i,X1497: $i > $i > $o,X1498: $i] :
( ( in @ X1498 @ X1495 )
=> ! [X1499: $i] :
( ( in @ X1499 @ X1496 )
=> ( ( X1497 @ X1498 @ X1499 )
=> ( in @ ( kpair @ X1498 @ X1499 ) @ ( dpsetconstr @ X1495 @ X1496 @ X1497 ) ) ) ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1500 @ X1501 @ X1502 ) @ ( cartprod @ X1500 @ X1501 ) )
=> ( ! [X1503: $i,X1504: $i,X1505: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1503 @ X1504 @ X1505 ) @ ( cartprod @ X1503 @ X1504 ) )
=> ( ! [X1506: $i,X1507: $i,X1508: $i > $i > $o,X1509: $i] :
( ( in @ X1509 @ X1506 )
=> ! [X1510: $i] :
( ( in @ X1510 @ X1507 )
=> ( ( in @ ( kpair @ X1509 @ X1510 ) @ ( dpsetconstr @ X1506 @ X1507 @ X1508 ) )
=> ( X1508 @ X1509 @ X1510 ) ) ) )
=> ( ! [X1511: $i,X1512: $i,X1513: $i > $i > $o,X1514: $i,X1515: $i] :
( ( in @ ( kpair @ X1514 @ X1515 ) @ ( dpsetconstr @ X1511 @ X1512 @ X1513 ) )
=> ( in @ X1514 @ X1511 ) )
=> ( ! [X1516: $i,X1517: $i,X1518: $i > $i > $o,X1519: $i,X1520: $i] :
( ( in @ ( kpair @ X1519 @ X1520 ) @ ( dpsetconstr @ X1516 @ X1517 @ X1518 ) )
=> ( in @ X1520 @ X1517 ) )
=> ( ! [X1521: $i,X1522: $i,X1523: $i > $i > $o,X1524: $i,X1525: $i] :
( ( in @ ( kpair @ X1524 @ X1525 ) @ ( dpsetconstr @ X1521 @ X1522 @ X1523 ) )
=> ( X1523 @ X1524 @ X1525 ) )
=> ( ! [X1526: $i,X1527: $i,X1528: $i] :
( ( func @ X1526 @ X1527 @ X1528 )
=> ! [X1529: $i] :
( ( in @ X1529 @ X1526 )
=> ( singleton
@ ( dsetconstr @ X1527
@ ^ [Z0: $i] : ( in @ ( kpair @ X1529 @ Z0 ) @ X1528 ) ) ) ) )
=> ( ! [X1530: $i,X1531: $i,X1532: $i] :
( ( func @ X1530 @ X1531 @ X1532 )
=> ! [X1533: $i] :
( ( in @ X1533 @ X1530 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1531
@ ^ [Z0: $i] : ( in @ ( kpair @ X1533 @ Z0 ) @ X1532 ) ) )
@ X1531 ) ) )
=> ( ! [X1534: $i,X1535: $i,X1536: $i] :
( ( func @ X1534 @ X1535 @ X1536 )
=> ! [X1537: $i] :
( ( in @ X1537 @ X1534 )
=> ( in @ ( ap @ X1534 @ X1535 @ X1536 @ X1537 ) @ X1535 ) ) )
=> ( ! [X1538: $i,X1539: $i,X1540: $i] :
( ( in @ X1540 @ ( funcSet @ X1538 @ X1539 ) )
=> ( func @ X1538 @ X1539 @ X1540 ) )
=> ( ! [X1541: $i,X1542: $i,X1543: $i] :
( ( in @ X1543 @ ( funcSet @ X1541 @ X1542 ) )
=> ! [X1544: $i] :
( ( in @ X1544 @ X1541 )
=> ( in @ ( ap @ X1541 @ X1542 @ X1543 @ X1544 ) @ X1542 ) ) )
=> ( ! [X1545: $i,X1546: $i,X1547: $i] :
( ( func @ X1545 @ X1546 @ X1547 )
=> ( in @ X1547 @ ( funcSet @ X1545 @ X1546 ) ) )
=> ( ! [X1548: $i,X1549: $i,X1550: $i > $i] :
( ! [X1551: $i] :
( ( in @ X1551 @ X1548 )
=> ( in @ ( X1550 @ X1551 ) @ X1549 ) )
=> ( func @ X1548 @ X1549
@ ( dpsetconstr @ X1548 @ X1549
@ ^ [Z0: $i] : ( $eq @ ( X1550 @ Z0 ) ) ) ) )
=> ( ! [X1552: $i,X1553: $i,X1554: $i > $i] :
( ! [X1555: $i] :
( ( in @ X1555 @ X1552 )
=> ( in @ ( X1554 @ X1555 ) @ X1553 ) )
=> ( func @ X1552 @ X1553 @ ( lam @ X1552 @ X1553 @ X1554 ) ) )
=> ( ! [X1556: $i,X1557: $i,X1558: $i > $i] :
( ! [X1559: $i] :
( ( in @ X1559 @ X1556 )
=> ( in @ ( X1558 @ X1559 ) @ X1557 ) )
=> ( in @ ( lam @ X1556 @ X1557 @ X1558 ) @ ( funcSet @ X1556 @ X1557 ) ) )
=> ( ! [X1560: $i,X1561: $i,X1562: $i] :
( ( subset @ X1562 @ ( cartprod @ X1560 @ X1561 ) )
=> ! [X1563: $i > $o] :
( ! [X1564: $i] :
( ( in @ X1564 @ X1560 )
=> ! [X1565: $i] :
( ( in @ X1565 @ X1561 )
=> ( ( in @ ( kpair @ X1564 @ X1565 ) @ X1562 )
=> ( X1563 @ ( kpair @ X1564 @ X1565 ) ) ) ) )
=> ! [X1566: $i] :
( ( in @ X1566 @ X1562 )
=> ( X1563 @ X1566 ) ) ) )
=> ( ! [X1567: $i,X1568: $i,X1569: $i] :
( ( subset @ X1569 @ ( cartprod @ X1567 @ X1568 ) )
=> ! [X1570: $i > $o] :
( ! [X1571: $i] :
( ( in @ X1571 @ X1567 )
=> ! [X1572: $i] :
( ( in @ X1572 @ X1568 )
=> ( ( in @ ( kpair @ X1571 @ X1572 ) @ X1569 )
=> ( X1570 @ ( kpair @ X1571 @ X1572 ) ) ) ) )
=> ! [X1573: $i] :
( ( in @ X1573 @ X1569 )
=> ( X1570 @ X1573 ) ) ) )
=> ( ! [X1574: $i,X1575: $i > $o] :
( ( singleton @ ( dsetconstr @ X1574 @ X1575 ) )
=> ! [X1576: $i] :
( ( in @ X1576 @ X1574 )
=> ! [X1577: $i] :
( ( in @ X1577 @ X1574 )
=> ( ( X1575 @ X1576 )
=> ( ( X1575 @ X1577 )
=> ( X1576 = X1577 ) ) ) ) ) )
=> ( ! [X1578: $i,X1579: $i,X1580: $i] :
( ( func @ X1578 @ X1579 @ X1580 )
=> ! [X1581: $i] :
( ( in @ X1581 @ X1578 )
=> ( in @ ( kpair @ X1581 @ ( ap @ X1578 @ X1579 @ X1580 @ X1581 ) ) @ X1580 ) ) )
=> ( ! [X1582: $i,X1583: $i,X1584: $i] :
( ( in @ X1584 @ ( funcSet @ X1582 @ X1583 ) )
=> ! [X1585: $i] :
( ( in @ X1585 @ X1582 )
=> ( in @ ( kpair @ X1585 @ ( ap @ X1582 @ X1583 @ X1584 @ X1585 ) ) @ X1584 ) ) )
=> ( ! [X1586: $i,X1587: $i,X1588: $i] :
( ( func @ X1586 @ X1587 @ X1588 )
=> ! [X1589: $i] :
( ( in @ X1589 @ X1586 )
=> ! [X1590: $i] :
( ( in @ X1590 @ X1587 )
=> ( ( in @ ( kpair @ X1589 @ X1590 ) @ X1588 )
=> ( ( ap @ X1586 @ X1587 @ X1588 @ X1589 )
= X1590 ) ) ) ) )
=> ( ! [X1591: $i,X1592: $i,X1593: $i] :
( ( func @ X1591 @ X1592 @ X1593 )
=> ! [X1594: $i] :
( ( func @ X1591 @ X1592 @ X1594 )
=> ( ! [X1595: $i] :
( ( in @ X1595 @ X1591 )
=> ( ( ap @ X1591 @ X1592 @ X1593 @ X1595 )
= ( ap @ X1591 @ X1592 @ X1594 @ X1595 ) ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ X1591 )
=> ! [X1597: $i] :
( ( in @ X1597 @ X1592 )
=> ( ( in @ ( kpair @ X1596 @ X1597 ) @ X1594 )
=> ( in @ ( kpair @ X1596 @ X1597 ) @ X1593 ) ) ) ) ) ) )
=> ( ! [X1598: $i,X1599: $i,X1600: $i] :
( ( in @ X1600 @ ( funcSet @ X1598 @ X1599 ) )
=> ! [X1601: $i] :
( ( in @ X1601 @ X1598 )
=> ! [X1602: $i] :
( ( in @ X1602 @ X1599 )
=> ( ( in @ ( kpair @ X1601 @ X1602 ) @ X1600 )
=> ( ( ap @ X1598 @ X1599 @ X1600 @ X1601 )
= X1602 ) ) ) ) )
=> ( ! [X1603: $i,X1604: $i,X1605: $i] :
( ( subset @ X1605 @ ( cartprod @ X1603 @ X1604 ) )
=> ! [X1606: $i] :
( ( subset @ X1606 @ ( cartprod @ X1603 @ X1604 ) )
=> ( ! [X1607: $i] :
( ( in @ X1607 @ X1603 )
=> ! [X1608: $i] :
( ( in @ X1608 @ X1604 )
=> ( ( in @ ( kpair @ X1607 @ X1608 ) @ X1605 )
=> ( in @ ( kpair @ X1607 @ X1608 ) @ X1606 ) ) ) )
=> ( subset @ X1605 @ X1606 ) ) ) )
=> ( ! [X1609: $i,X1610: $i,X1611: $i] :
( ( subset @ X1611 @ ( cartprod @ X1609 @ X1610 ) )
=> ! [X1612: $i] :
( ( subset @ X1612 @ ( cartprod @ X1609 @ X1610 ) )
=> ( ! [X1613: $i] :
( ( in @ X1613 @ X1609 )
=> ! [X1614: $i] :
( ( in @ X1614 @ X1610 )
=> ( ( in @ ( kpair @ X1613 @ X1614 ) @ X1611 )
=> ( in @ ( kpair @ X1613 @ X1614 ) @ X1612 ) ) ) )
=> ( ! [X1615: $i] :
( ( in @ X1615 @ X1609 )
=> ! [X1616: $i] :
( ( in @ X1616 @ X1610 )
=> ( ( in @ ( kpair @ X1615 @ X1616 ) @ X1612 )
=> ( in @ ( kpair @ X1615 @ X1616 ) @ X1611 ) ) ) )
=> ( X1611 = X1612 ) ) ) ) )
=> ( ! [X1617: $i,X1618: $i,X1619: $i] :
( ( func @ X1617 @ X1618 @ X1619 )
=> ! [X1620: $i] :
( ( func @ X1617 @ X1618 @ X1620 )
=> ( ! [X1621: $i] :
( ( in @ X1621 @ X1617 )
=> ( ( ap @ X1617 @ X1618 @ X1619 @ X1621 )
= ( ap @ X1617 @ X1618 @ X1620 @ X1621 ) ) )
=> ( X1619 = X1620 ) ) ) )
=> ( ! [X1622: $i,X1623: $i,X1624: $i] :
( ( in @ X1624 @ ( funcSet @ X1622 @ X1623 ) )
=> ! [X1625: $i] :
( ( in @ X1625 @ ( funcSet @ X1622 @ X1623 ) )
=> ( ! [X1626: $i] :
( ( in @ X1626 @ X1622 )
=> ( ( ap @ X1622 @ X1623 @ X1624 @ X1626 )
= ( ap @ X1622 @ X1623 @ X1625 @ X1626 ) ) )
=> ( X1624 = X1625 ) ) ) )
=> ( ! [X1627: $i,X1628: $i,X1629: $i] :
( ( in @ X1629 @ ( funcSet @ X1627 @ X1628 ) )
=> ! [X1630: $i] :
( ( in @ X1630 @ X1627 )
=> ( ( ap @ X1627 @ X1628 @ X1629 @ X1630 )
= ( ap @ X1627 @ X1628 @ X1629 @ X1630 ) ) ) )
=> ( ! [X1631: $i,X1632: $i,X1633: $i] :
( ( func @ X1631 @ X1632 @ X1633 )
=> ! [X1634: $i] :
( ( in @ X1634 @ X1631 )
=> ( ( ap @ X1631 @ X1632 @ X1633 @ X1634 )
= ( ap @ X1631 @ X1632 @ X1633 @ X1634 ) ) ) )
=> ( ! [X1635: $i,X1636: $i,X1637: $i > $i] :
( ! [X1638: $i] :
( ( in @ X1638 @ X1635 )
=> ( in @ ( X1637 @ X1638 ) @ X1636 ) )
=> ! [X1639: $i] :
( ( in @ X1639 @ X1635 )
=> ( ( ap @ X1635 @ X1636 @ ( lam @ X1635 @ X1636 @ X1637 ) @ X1639 )
= ( X1637 @ X1639 ) ) ) )
=> ( ! [X1640: $i,X1641: $i,X1642: $i] :
( ( func @ X1640 @ X1641 @ X1642 )
=> ( ( lam @ X1640 @ X1641 @ ( ap @ X1640 @ X1641 @ X1642 ) )
= X1642 ) )
=> ( ! [X1643: $i,X1644: $i,X1645: $i > $i] :
( ! [X1646: $i] :
( ( in @ X1646 @ X1643 )
=> ( in @ ( X1645 @ X1646 ) @ X1644 ) )
=> ( ( lam @ X1643 @ X1644 @ X1645 )
= ( lam @ X1643 @ X1644 @ X1645 ) ) )
=> ( ! [X1647: $i,X1648: $i,X1649: $i > $i] :
( ! [X1650: $i] :
( ( in @ X1650 @ X1647 )
=> ( in @ ( X1649 @ X1650 ) @ X1648 ) )
=> ! [X1651: $i] :
( ( in @ X1651 @ X1647 )
=> ( ( ap @ X1647 @ X1648 @ ( lam @ X1647 @ X1648 @ X1649 ) @ X1651 )
= ( X1649 @ X1651 ) ) ) )
=> ( ! [X1652: $i,X1653: $i,X1654: $i] :
( ( in @ X1654 @ ( funcSet @ X1652 @ X1653 ) )
=> ( ( lam @ X1652 @ X1653 @ ( ap @ X1652 @ X1653 @ X1654 ) )
= X1654 ) )
=> ( ! [X1655: $i,X1656: $o,X1657: $i] :
( ( in @ X1657 @ X1655 )
=> ! [X1658: $i] :
( ( in @ X1658 @ X1655 )
=> ( ~ X1656
=> ( in @ X1658
@ ( dsetconstr @ X1655
@ ^ [Z0: $i] :
( ( X1656
& ( Z0 = X1657 ) )
| ( ~ X1656
& ( Z0 = X1658 ) ) ) ) ) ) ) )
=> ( ! [X1659: $i,X1660: $o,X1661: $i] :
( ( in @ X1661 @ X1659 )
=> ! [X1662: $i] :
( ( in @ X1662 @ X1659 )
=> ( ~ X1660
=> ( ( dsetconstr @ X1659
@ ^ [Z0: $i] :
( ( X1660
& ( Z0 = X1661 ) )
| ( ~ X1660
& ( Z0 = X1662 ) ) ) )
= ( setadjoin @ X1662 @ emptyset ) ) ) ) )
=> ( ! [X1663: $i,X1664: $o,X1665: $i] :
( ( in @ X1665 @ X1663 )
=> ! [X1666: $i] :
( ( in @ X1666 @ X1663 )
=> ( X1664
=> ( in @ X1665
@ ( dsetconstr @ X1663
@ ^ [Z0: $i] :
( ( X1664
& ( Z0 = X1665 ) )
| ( ~ X1664
& ( Z0 = X1666 ) ) ) ) ) ) ) )
=> ( ! [X1667: $i,X1668: $o,X1669: $i] :
( ( in @ X1669 @ X1667 )
=> ! [X1670: $i] :
( ( in @ X1670 @ X1667 )
=> ( X1668
=> ( ( dsetconstr @ X1667
@ ^ [Z0: $i] :
( ( X1668
& ( Z0 = X1669 ) )
| ( ~ X1668
& ( Z0 = X1670 ) ) ) )
= ( setadjoin @ X1669 @ emptyset ) ) ) ) )
=> ( ! [X1671: $i,X1672: $o,X1673: $i] :
( ( in @ X1673 @ X1671 )
=> ! [X1674: $i] :
( ( in @ X1674 @ X1671 )
=> ( singleton
@ ( dsetconstr @ X1671
@ ^ [Z0: $i] :
( ( X1672
& ( Z0 = X1673 ) )
| ( ~ X1672
& ( Z0 = X1674 ) ) ) ) ) ) )
=> ( ! [X1675: $i,X1676: $o,X1677: $i] :
( ( in @ X1677 @ X1675 )
=> ! [X1678: $i] :
( ( in @ X1678 @ X1675 )
=> ( in @ ( if @ X1675 @ X1676 @ X1677 @ X1678 ) @ X1675 ) ) )
=> ( ! [X1679: $i] :
( ( singleton @ X1679 )
=> ! [X1680: $i] :
( ( in @ X1680 @ X1679 )
=> ( ( setunion @ X1679 )
= X1680 ) ) )
=> ( ! [X1681: $i,X1682: $o,X1683: $i] :
( ( in @ X1683 @ X1681 )
=> ! [X1684: $i] :
( ( in @ X1684 @ X1681 )
=> ( X1682
=> ( ( if @ X1681 @ X1682 @ X1683 @ X1684 )
= X1683 ) ) ) )
=> ( ! [X1685: $i,X1686: $o,X1687: $i] :
( ( in @ X1687 @ X1685 )
=> ! [X1688: $i] :
( ( in @ X1688 @ X1685 )
=> ( ~ X1686
=> ( ( if @ X1685 @ X1686 @ X1687 @ X1688 )
= X1688 ) ) ) )
=> ( ! [X1689: $i,X1690: $o,X1691: $i] :
( ( in @ X1691 @ X1689 )
=> ! [X1692: $i] :
( ( in @ X1692 @ X1689 )
=> ( in @ ( if @ X1689 @ X1690 @ X1691 @ X1692 ) @ ( setadjoin @ X1691 @ ( setadjoin @ X1692 @ emptyset ) ) ) ) )
=> ( ! [X1693: $i,X1694: $i] :
( ( in @ X1694 @ ( powerset @ X1693 ) )
=> ! [X1695: $i] :
( ( in @ X1695 @ ( powerset @ X1693 ) )
=> ( in @ ( binintersect @ X1694 @ X1695 ) @ ( powerset @ X1693 ) ) ) )
=> ( ! [X1696: $i,X1697: $i] :
( ( in @ X1697 @ ( powerset @ X1696 ) )
=> ! [X1698: $i] :
( ( in @ X1698 @ ( powerset @ X1696 ) )
=> ( in @ ( binunion @ X1697 @ X1698 ) @ ( powerset @ X1696 ) ) ) )
=> ( ! [X1699: $i,X1700: $i] :
( ( in @ X1700 @ ( powerset @ X1699 ) )
=> ( in @ ( powerset @ X1700 ) @ ( powerset @ ( powerset @ X1699 ) ) ) )
=> ( ! [X1701: $i,X1702: $i] :
( ( in @ X1702 @ ( powerset @ X1701 ) )
=> ! [X1703: $i] :
( ( in @ X1703 @ ( powerset @ X1701 ) )
=> ( in @ ( setminus @ X1702 @ X1703 ) @ ( powerset @ X1701 ) ) ) )
=> ( ! [X1704: $i,X1705: $i] :
( ( in @ X1705 @ ( powerset @ X1704 ) )
=> ( in @ ( setminus @ X1704 @ X1705 ) @ ( powerset @ X1704 ) ) )
=> ( ! [X1706: $i,X1707: $i] :
( ( in @ X1707 @ ( powerset @ X1706 ) )
=> ! [X1708: $i] :
( ( in @ X1708 @ ( powerset @ X1706 ) )
=> ( ! [X1709: $i] :
( ( in @ X1709 @ X1706 )
=> ( ( in @ X1709 @ X1707 )
=> ( in @ X1709 @ X1708 ) ) )
=> ( ! [X1710: $i] :
( ( in @ X1710 @ X1706 )
=> ( ( in @ X1710 @ X1708 )
=> ( in @ X1710 @ X1707 ) ) )
=> ( X1707 = X1708 ) ) ) ) )
=> ( ! [X1711: $i,X1712: $i] :
( ( in @ X1712 @ ( powerset @ X1711 ) )
=> ! [X1713: $i] :
( ( in @ X1713 @ ( powerset @ X1711 ) )
=> ( ! [X1714: $i] :
( ( in @ X1714 @ X1711 )
=> ( ( in @ X1714 @ X1712 )
=> ( in @ X1714 @ X1713 ) ) )
=> ( subset @ X1712 @ X1713 ) ) ) )
=> ( ! [X1715: $i,X1716: $i] :
( ( in @ X1716 @ ( powerset @ X1715 ) )
=> ! [X1717: $i] :
( ( in @ X1717 @ ( powerset @ X1715 ) )
=> ( ! [X1718: $i] :
( ( in @ X1718 @ X1715 )
=> ( ( in @ X1718 @ X1716 )
=> ( in @ X1718 @ X1717 ) ) )
=> ( in @ X1716 @ ( powerset @ X1717 ) ) ) ) )
=> ( ! [X1719: $i,X1720: $i] :
( ( in @ X1720 @ ( powerset @ X1719 ) )
=> ! [X1721: $i] :
( ( in @ X1721 @ ( powerset @ X1719 ) )
=> ! [X1722: $i] :
( ( in @ X1722 @ X1719 )
=> ( ( in @ X1720 @ ( powerset @ X1721 ) )
=> ( ( in @ X1722 @ X1720 )
=> ( in @ X1722 @ X1721 ) ) ) ) ) )
=> ( ! [X1723: $i,X1724: $i] :
( ( in @ X1724 @ ( powerset @ X1723 ) )
=> ! [X1725: $i] :
( ( in @ X1725 @ X1723 )
=> ( ( in @ X1725 @ X1724 )
=> ~ ( in @ X1725 @ ( setminus @ X1723 @ X1724 ) ) ) ) )
=> ( ! [X1726: $i,X1727: $i] :
( ( in @ X1727 @ ( powerset @ X1726 ) )
=> ! [X1728: $i] :
( ( in @ X1728 @ X1726 )
=> ( ~ ( in @ X1728 @ ( setminus @ X1726 @ X1727 ) )
=> ( in @ X1728 @ X1727 ) ) ) )
=> ( ! [X1729: $i,X1730: $i] :
( ( in @ X1730 @ ( powerset @ X1729 ) )
=> ! [X1731: $i] :
( ( in @ X1731 @ ( powerset @ X1729 ) )
=> ! [X1732: $i] :
( ( in @ X1732 @ X1729 )
=> ( ~ ( in @ X1732 @ X1730 )
=> ~ ( in @ X1732 @ ( binintersect @ X1730 @ X1731 ) ) ) ) ) )
=> ( ! [X1733: $i,X1734: $i] :
( ( in @ X1734 @ ( powerset @ X1733 ) )
=> ! [X1735: $i] :
( ( in @ X1735 @ ( powerset @ X1733 ) )
=> ! [X1736: $i] :
( ( in @ X1736 @ X1733 )
=> ( ~ ( in @ X1736 @ X1735 )
=> ~ ( in @ X1736 @ ( binintersect @ X1734 @ X1735 ) ) ) ) ) )
=> ( ! [X1737: $i,X1738: $i] :
( ( in @ X1738 @ ( powerset @ X1737 ) )
=> ! [X1739: $i] :
( ( in @ X1739 @ ( powerset @ X1737 ) )
=> ! [X1740: $i] :
( ( in @ X1740 @ X1737 )
=> ( ( subset @ X1738 @ ( setminus @ X1737 @ X1739 ) )
=> ( ( in @ X1740 @ X1739 )
=> ~ ( in @ X1740 @ X1738 ) ) ) ) ) )
=> ( ! [X1741: $i,X1742: $i] :
( ( in @ X1742 @ ( powerset @ X1741 ) )
=> ! [X1743: $i] :
( ( in @ X1743 @ ( powerset @ X1741 ) )
=> ! [X1744: $i] :
( ( in @ X1744 @ X1741 )
=> ( ( subset @ X1742 @ X1743 )
=> ( ~ ( in @ X1744 @ X1743 )
=> ~ ( in @ X1744 @ X1742 ) ) ) ) ) )
=> ( ! [X1745: $i,X1746: $i] :
( ( in @ X1746 @ ( powerset @ X1745 ) )
=> ! [X1747: $i] :
( ( in @ X1747 @ ( powerset @ X1745 ) )
=> ( ( subset @ X1746 @ X1747 )
=> ( subset @ ( setminus @ X1745 @ X1747 ) @ ( setminus @ X1745 @ X1746 ) ) ) ) )
=> ( ! [X1748: $i,X1749: $i] :
( ( in @ X1749 @ ( powerset @ X1748 ) )
=> ! [X1750: $i] :
( ( in @ X1750 @ ( powerset @ X1748 ) )
=> ( ( subset @ ( setminus @ X1748 @ X1750 ) @ ( setminus @ X1748 @ X1749 ) )
=> ( subset @ X1749 @ X1750 ) ) ) )
=> ( ! [X1751: $i,X1752: $i] :
( ( in @ X1752 @ ( powerset @ X1751 ) )
=> ! [X1753: $i] :
( ( in @ X1753 @ X1751 )
=> ( ( in @ X1753 @ X1752 )
=> ( in @ X1753 @ ( setminus @ X1751 @ ( setminus @ X1751 @ X1752 ) ) ) ) ) )
=> ( ! [X1754: $i,X1755: $i] :
( ( in @ X1755 @ ( powerset @ X1754 ) )
=> ! [X1756: $i] :
( ( in @ X1756 @ X1754 )
=> ( ( in @ X1756 @ ( setminus @ X1754 @ ( setminus @ X1754 @ X1755 ) ) )
=> ( in @ X1756 @ X1755 ) ) ) )
=> ( ! [X1757: $i,X1758: $i] :
( ( in @ X1758 @ ( powerset @ X1757 ) )
=> ( subset @ X1758 @ ( setminus @ X1757 @ ( setminus @ X1757 @ X1758 ) ) ) )
=> ( ! [X1759: $i,X1760: $i] :
( ( in @ X1760 @ ( powerset @ X1759 ) )
=> ( subset @ ( setminus @ X1759 @ ( setminus @ X1759 @ X1760 ) ) @ X1760 ) )
=> ( ! [X1761: $i,X1762: $i] :
( ( in @ X1762 @ ( powerset @ X1761 ) )
=> ( X1762
= ( setminus @ X1761 @ ( setminus @ X1761 @ X1762 ) ) ) )
=> ( ! [X1763: $i,X1764: $i] :
( ( in @ X1764 @ ( powerset @ X1763 ) )
=> ! [X1765: $i] :
( ( in @ X1765 @ ( powerset @ X1763 ) )
=> ! [X1766: $i] :
( ( in @ X1766 @ X1763 )
=> ( ( in @ X1766 @ ( setminus @ X1763 @ X1764 ) )
=> ~ ( in @ X1766 @ ( binintersect @ X1764 @ X1765 ) ) ) ) ) )
=> ( ! [X1767: $i,X1768: $i] :
( ( in @ X1768 @ ( powerset @ X1767 ) )
=> ! [X1769: $i] :
( ( in @ X1769 @ ( powerset @ X1767 ) )
=> ! [X1770: $i] :
( ( in @ X1770 @ X1767 )
=> ( ( in @ X1770 @ ( setminus @ X1767 @ X1768 ) )
=> ( in @ X1770 @ ( setminus @ X1767 @ ( binintersect @ X1768 @ X1769 ) ) ) ) ) ) )
=> ( ! [X1771: $i,X1772: $i] :
( ( in @ X1772 @ ( powerset @ X1771 ) )
=> ! [X1773: $i] :
( ( in @ X1773 @ ( powerset @ X1771 ) )
=> ( subset @ ( setminus @ X1771 @ X1772 ) @ ( setminus @ X1771 @ ( binintersect @ X1772 @ X1773 ) ) ) ) )
=> ( ! [X1774: $i,X1775: $i] :
( ( in @ X1775 @ ( powerset @ X1774 ) )
=> ! [X1776: $i] :
( ( in @ X1776 @ ( powerset @ X1774 ) )
=> ( in @ ( setminus @ X1774 @ X1775 ) @ ( powerset @ ( setminus @ X1774 @ ( binintersect @ X1775 @ X1776 ) ) ) ) ) )
=> ( ! [X1777: $i,X1778: $i] :
( ( in @ X1778 @ ( powerset @ X1777 ) )
=> ! [X1779: $i] :
( ( in @ X1779 @ ( powerset @ X1777 ) )
=> ( ( subset @ X1778 @ ( setminus @ X1777 @ X1779 ) )
=> ! [X1780: $i] :
( ( in @ X1780 @ X1777 )
=> ( ( in @ X1780 @ X1779 )
=> ( in @ X1780 @ ( setminus @ X1777 @ X1778 ) ) ) ) ) ) )
=> ( ! [X1781: $i,X1782: $i] :
( ( in @ X1782 @ ( powerset @ X1781 ) )
=> ! [X1783: $i] :
( ( in @ X1783 @ ( powerset @ X1781 ) )
=> ( ( subset @ X1782 @ ( setminus @ X1781 @ X1783 ) )
=> ( subset @ X1783 @ ( setminus @ X1781 @ X1782 ) ) ) ) )
=> ( ! [X1784: $i,X1785: $i] :
( ( in @ X1785 @ ( powerset @ X1784 ) )
=> ! [X1786: $i] :
( ( in @ X1786 @ ( powerset @ X1784 ) )
=> ! [X1787: $i] :
( ( in @ X1787 @ X1784 )
=> ( ~ ( in @ X1787 @ ( binunion @ X1785 @ X1786 ) )
=> ~ ( in @ X1787 @ X1785 ) ) ) ) )
=> ( ! [X1788: $i,X1789: $i] :
( ( in @ X1789 @ ( powerset @ X1788 ) )
=> ! [X1790: $i] :
( ( in @ X1790 @ ( powerset @ X1788 ) )
=> ! [X1791: $i] :
( ( in @ X1791 @ X1788 )
=> ( ~ ( in @ X1791 @ ( binunion @ X1789 @ X1790 ) )
=> ~ ( in @ X1791 @ X1790 ) ) ) ) )
=> ( ! [X1792: $i,X1793: $i] :
( ( in @ X1793 @ ( powerset @ X1792 ) )
=> ! [X1794: $i] :
( ( in @ X1794 @ ( powerset @ X1792 ) )
=> ! [X1795: $i] :
( ( in @ X1795 @ ( powerset @ X1792 ) )
=> ! [X1796: $i] :
( ( in @ X1796 @ X1792 )
=> ( ( in @ X1796 @ ( binintersect @ X1793 @ X1794 ) )
=> ( in @ X1796 @ ( binunion @ X1793 @ X1795 ) ) ) ) ) ) )
=> ( ! [X1797: $i,X1798: $i] :
( ( in @ X1798 @ ( powerset @ X1797 ) )
=> ! [X1799: $i] :
( ( in @ X1799 @ ( powerset @ X1797 ) )
=> ! [X1800: $i] :
( ( in @ X1800 @ ( powerset @ X1797 ) )
=> ! [X1801: $i] :
( ( in @ X1801 @ X1797 )
=> ( ( in @ X1801 @ ( binintersect @ X1798 @ X1799 ) )
=> ( in @ X1801 @ ( binunion @ X1799 @ X1800 ) ) ) ) ) ) )
=> ( ! [X1802: $i,X1803: $i] :
( ( in @ X1803 @ ( powerset @ X1802 ) )
=> ! [X1804: $i] :
( ( in @ X1804 @ ( powerset @ X1802 ) )
=> ! [X1805: $i] :
( ( in @ X1805 @ ( powerset @ X1802 ) )
=> ! [X1806: $i] :
( ( in @ X1806 @ X1802 )
=> ( ( in @ X1806 @ ( binintersect @ X1803 @ X1804 ) )
=> ( in @ X1806 @ ( binintersect @ ( binunion @ X1803 @ X1805 ) @ ( binunion @ X1804 @ X1805 ) ) ) ) ) ) ) )
=> ( ! [X1807: $i,X1808: $i] :
( ( in @ X1808 @ ( powerset @ X1807 ) )
=> ! [X1809: $i] :
( ( in @ X1809 @ ( powerset @ X1807 ) )
=> ! [X1810: $i] :
( ( in @ X1810 @ ( powerset @ X1807 ) )
=> ( in @ ( binintersect @ X1808 @ X1809 ) @ ( powerset @ ( binintersect @ ( binunion @ X1808 @ X1810 ) @ ( binunion @ X1809 @ X1810 ) ) ) ) ) ) )
=> ( ! [X1811: $i,X1812: $i] :
( ( in @ X1812 @ ( powerset @ X1811 ) )
=> ! [X1813: $i] :
( ( in @ X1813 @ ( powerset @ X1811 ) )
=> ! [X1814: $i] :
( ( in @ X1814 @ X1811 )
=> ( ( in @ X1814 @ ( setminus @ X1811 @ ( binunion @ X1812 @ X1813 ) ) )
=> ~ ( in @ X1814 @ X1812 ) ) ) ) )
=> ( ! [X1815: $i,X1816: $i] :
( ( in @ X1816 @ ( powerset @ X1815 ) )
=> ! [X1817: $i] :
( ( in @ X1817 @ ( powerset @ X1815 ) )
=> ! [X1818: $i] :
( ( in @ X1818 @ X1815 )
=> ( ( in @ X1818 @ ( setminus @ X1815 @ ( binunion @ X1816 @ X1817 ) ) )
=> ( in @ X1818 @ ( setminus @ X1815 @ X1816 ) ) ) ) ) )
=> ( ! [X1819: $i,X1820: $i] :
( ( in @ X1820 @ ( powerset @ X1819 ) )
=> ! [X1821: $i] :
( ( in @ X1821 @ ( powerset @ X1819 ) )
=> ! [X1822: $o,X1823: $i] :
( ( in @ X1823 @ X1819 )
=> ( ( in @ X1823 @ ( binunion @ X1820 @ X1821 ) )
=> ( ( ( in @ X1823 @ X1820 )
=> X1822 )
=> ( ( ( in @ X1823 @ X1821 )
=> X1822 )
=> 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 @ X1827 @ ( binunion @ X1825 @ X1826 ) ) ) ) ) ) )
=> ( ! [X1828: $i,X1829: $i] :
( ( in @ X1829 @ ( powerset @ X1828 ) )
=> ! [X1830: $i] :
( ( in @ X1830 @ ( powerset @ X1828 ) )
=> ! [X1831: $i] :
( ( in @ X1831 @ X1828 )
=> ( ( in @ X1831 @ ( setminus @ X1828 @ ( binunion @ X1829 @ X1830 ) ) )
=> ( in @ X1831 @ ( setminus @ X1828 @ X1829 ) ) ) ) ) )
=> ( ! [X1832: $i,X1833: $i] :
( ( in @ X1833 @ ( powerset @ X1832 ) )
=> ! [X1834: $i] :
( ( in @ X1834 @ ( powerset @ X1832 ) )
=> ( in @ ( setminus @ X1832 @ ( binunion @ X1833 @ X1834 ) ) @ ( powerset @ ( setminus @ X1832 @ X1833 ) ) ) ) )
=> ( ! [X1835: $i,X1836: $i] :
( ( in @ X1836 @ ( powerset @ X1835 ) )
=> ! [X1837: $i] :
( ( in @ X1837 @ ( powerset @ X1835 ) )
=> ! [X1838: $i] :
( ( in @ X1838 @ X1835 )
=> ( ( in @ X1838 @ ( setminus @ X1835 @ ( binunion @ X1836 @ X1837 ) ) )
=> ( in @ X1838 @ ( setminus @ X1835 @ X1837 ) ) ) ) ) )
=> ( ! [X1839: $i,X1840: $i] :
( ( in @ X1840 @ ( powerset @ X1839 ) )
=> ! [X1841: $i] :
( ( in @ X1841 @ ( powerset @ X1839 ) )
=> ! [X1842: $i] :
( ( in @ X1842 @ X1839 )
=> ( ( in @ X1842 @ ( setminus @ X1839 @ ( binintersect @ X1840 @ X1841 ) ) )
=> ( in @ X1842 @ ( binunion @ ( setminus @ X1839 @ X1840 ) @ ( setminus @ X1839 @ X1841 ) ) ) ) ) ) )
=> ( ! [X1843: $i,X1844: $i] :
( ( in @ X1844 @ ( powerset @ X1843 ) )
=> ! [X1845: $i] :
( ( in @ X1845 @ ( powerset @ X1843 ) )
=> ! [X1846: $i] :
( ( in @ X1846 @ X1843 )
=> ( ( in @ X1846 @ ( binunion @ ( setminus @ X1843 @ X1844 ) @ ( setminus @ X1843 @ X1845 ) ) )
=> ( in @ X1846 @ ( setminus @ X1843 @ ( binintersect @ X1844 @ X1845 ) ) ) ) ) ) )
=> ( ! [X1847: $i,X1848: $i] :
( ( in @ X1848 @ ( powerset @ X1847 ) )
=> ! [X1849: $i] :
( ( in @ X1849 @ ( powerset @ X1847 ) )
=> ( ( setminus @ X1847 @ ( binintersect @ X1848 @ X1849 ) )
= ( binunion @ ( setminus @ X1847 @ X1848 ) @ ( setminus @ X1847 @ X1849 ) ) ) ) )
=> ( ! [X1850: $i,X1851: $i] :
( ( in @ X1851 @ ( powerset @ X1850 ) )
=> ! [X1852: $i] :
( ( in @ X1852 @ ( powerset @ X1850 ) )
=> ! [X1853: $i] :
( ( in @ X1853 @ X1850 )
=> ( ( in @ X1853 @ ( setminus @ X1850 @ ( binunion @ X1851 @ X1852 ) ) )
=> ( in @ X1853 @ ( binintersect @ ( setminus @ X1850 @ X1851 ) @ ( setminus @ X1850 @ X1852 ) ) ) ) ) ) )
=> ( ! [X1854: $i,X1855: $i] :
( ( in @ X1855 @ ( powerset @ X1854 ) )
=> ! [X1856: $i] :
( ( in @ X1856 @ ( powerset @ X1854 ) )
=> ! [X1857: $i] :
( ( in @ X1857 @ X1854 )
=> ( ( in @ X1857 @ ( setminus @ X1854 @ X1855 ) )
=> ( ( in @ X1857 @ ( setminus @ X1854 @ X1856 ) )
=> ( in @ X1857 @ ( setminus @ X1854 @ ( binunion @ X1855 @ X1856 ) ) ) ) ) ) ) )
=> ( ! [X1858: $i,X1859: $i] :
( ( in @ X1859 @ ( powerset @ X1858 ) )
=> ! [X1860: $i] :
( ( in @ X1860 @ ( powerset @ X1858 ) )
=> ! [X1861: $i] :
( ( in @ X1861 @ X1858 )
=> ( ( in @ X1861 @ ( binintersect @ ( setminus @ X1858 @ X1859 ) @ ( setminus @ X1858 @ X1860 ) ) )
=> ( in @ X1861 @ ( setminus @ X1858 @ ( binunion @ X1859 @ X1860 ) ) ) ) ) ) )
=> ( ! [X1862: $i,X1863: $i] :
( ( in @ X1863 @ ( powerset @ X1862 ) )
=> ! [X1864: $i] :
( ( in @ X1864 @ ( powerset @ X1862 ) )
=> ( ( setminus @ X1862 @ ( binunion @ X1863 @ X1864 ) )
= ( binintersect @ ( setminus @ X1862 @ X1863 ) @ ( setminus @ X1862 @ X1864 ) ) ) ) )
=> ( ! [X1865: $i,X1866: $i] :
( ( in @ X1866 @ ( powerset @ X1865 ) )
=> ! [X1867: $i] :
( ( in @ X1867 @ ( powerset @ X1865 ) )
=> ! [X1868: $i] :
( ( in @ X1868 @ ( binintersect @ X1866 @ X1867 ) )
=> ( in @ X1868 @ X1865 ) ) ) )
=> ( ! [X1869: $i,X1870: $i] :
( ( in @ X1870 @ ( powerset @ X1869 ) )
=> ! [X1871: $i] :
( ( in @ X1871 @ ( powerset @ X1869 ) )
=> ! [X1872: $i] :
( ( in @ X1872 @ ( powerset @ X1869 ) )
=> ( ( subset @ X1870 @ X1872 )
=> ( subset @ ( binintersect @ X1870 @ X1871 ) @ X1872 ) ) ) ) )
=> ( ! [X1873: $i,X1874: $i] :
( ( in @ X1874 @ ( powerset @ X1873 ) )
=> ! [X1875: $i] :
( ( in @ X1875 @ ( powerset @ X1873 ) )
=> ! [X1876: $i] :
( ( in @ X1876 @ ( powerset @ X1873 ) )
=> ( ( subset @ X1875 @ X1876 )
=> ( subset @ ( binintersect @ X1874 @ X1875 ) @ X1876 ) ) ) ) )
=> ( ! [X1877: $i,X1878: $i] :
( ( in @ X1878 @ ( powerset @ X1877 ) )
=> ! [X1879: $i] :
( ( in @ X1879 @ ( powerset @ X1877 ) )
=> ! [X1880: $i] :
( ( in @ X1880 @ ( powerset @ X1877 ) )
=> ( ( subset @ X1878 @ X1879 )
=> ( ( subset @ X1878 @ X1880 )
=> ( subset @ X1878 @ ( binintersect @ X1879 @ X1880 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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_0_305]),foundationAx]),wellorderingAx]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),c_0_310]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_311]),setext]),emptyI]),noeltsimpempty]),c_0_312]),c_0_313]),c_0_314]),c_0_315]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_316]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_317]),c_0_318]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_319]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_320]),c_0_321]),c_0_322]),inCongP]),in__Cong]),c_0_323]),c_0_324]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_325]),c_0_326]),c_0_327]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_328]),c_0_329]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_330]),c_0_331]),c_0_332]),c_0_333]),singletonsuniq]),setukpairinjL1]),c_0_334]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_335]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_336]),c_0_337]),c_0_338]),c_0_339]),c_0_340]),c_0_341]),c_0_342]),c_0_343]),c_0_344]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_345]),c_0_346]),c_0_347]),c_0_348]),c_0_349]),c_0_350]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_351]),c_0_352]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_353]),c_0_354]),c_0_355]),c_0_356]),c_0_357]),c_0_358]),c_0_359]),c_0_360]),c_0_361]),c_0_362]),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])])]),c_0_363]) ).
thf(c_0_365,negated_conjecture,
! 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$i,X2116: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i > $o,X2163: $i,X2164: $i > $o,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $o,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i,X2205: $i,X2206: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $o,X2245: $i,X2246: $i,X2247: $i,X2248: $i,X2249: $i,X2250: $i,X2251: $i,X2252: $i,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i,X2272: $i,X2273: $i,X2274: $i,X2275: $i,X2276: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2287: $i,X2288: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i,X2293: $i,X2294: $i,X2295: $i,X2296: $i,X2297: $i,X2298: $i,X2299: $i,X2300: $i,X2301: $i,X2302: $i,X2303: $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i,X2312: $i,X2313: $i,X2314: $i,X2315: $i,X2316: $i > $o,X2319: $i,X2320: $i,X2321: $i > $o,X2323: $i,X2324: $i > $o,X2325: $i,X2327: $i,X2328: $i > $o,X2331: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $i,X2338: $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,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2381: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2388: $i,X2389: $i,X2390: $i,X2391: $i,X2392: $i,X2393: $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i > $i > $o,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2408: $i > $i > $o,X2409: $i,X2410: $i,X2411: $i > $i > $o,X2412: $i,X2413: $i,X2414: $i > $i > $o,X2415: $i,X2416: $i,X2417: $i,X2418: $i,X2419: $i > $i > $o,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i > $i > $o,X2425: $i,X2426: $i,X2427: $i,X2428: $i,X2429: $i > $i > $o,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 > $i,X2458: $i,X2459: $i,X2460: $i > $i,X2462: $i,X2463: $i,X2464: $i > $i,X2466: $i,X2467: $i,X2468: $i,X2469: $i > $o,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i > $o,X2479: $i,X2480: $i,X2481: $i > $o,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,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2515: $i,X2516: $i,X2517: $i,X2518: $i,X2523: $i,X2524: $i,X2525: $i,X2526: $i,X2528: $i,X2529: $i,X2530: $i,X2531: $i,X2533: $i,X2534: $i,X2535: $i,X2536: $i,X2537: $i,X2538: $i,X2539: $i,X2540: $i,X2541: $i,X2542: $i,X2543: $i > $i,X2545: $i,X2546: $i,X2547: $i,X2548: $i,X2549: $i,X2550: $i,X2551: $i > $i,X2553: $i,X2554: $i,X2555: $i > $i,X2557: $i,X2558: $i,X2559: $i,X2560: $i,X2561: $i,X2562: $o,X2563: $i,X2564: $i,X2565: $i,X2566: $o,X2567: $i,X2568: $i,X2569: $i,X2570: $o,X2571: $i,X2572: $i,X2573: $i,X2574: $o,X2575: $i,X2576: $i,X2577: $i,X2578: $o,X2579: $i,X2580: $i,X2581: $i,X2582: $o,X2583: $i,X2584: $i,X2585: $i,X2586: $i,X2587: $i,X2588: $o,X2589: $i,X2590: $i,X2591: $i,X2592: $o,X2593: $i,X2594: $i,X2595: $i,X2596: $o,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,X2617: $i,X2618: $i,X2619: $i,X2621: $i,X2622: $i,X2623: $i,X2625: $i,X2626: $i,X2627: $i,X2628: $i,X2629: $i,X2630: $i,X2631: $i,X2632: $i,X2633: $i,X2634: $i,X2635: $i,X2636: $i,X2637: $i,X2638: $i,X2639: $i,X2640: $i,X2641: $i,X2642: $i,X2643: $i,X2644: $i,X2645: $i,X2646: $i,X2647: $i,X2648: $i,X2649: $i,X2650: $i,X2651: $i,X2652: $i,X2653: $i,X2654: $i,X2655: $i,X2656: $i,X2657: $i,X2658: $i,X2659: $i,X2660: $i,X2661: $i,X2662: $i,X2663: $i,X2664: $i,X2665: $i,X2666: $i,X2667: $i,X2668: $i,X2669: $i,X2670: $i,X2671: $i,X2672: $i,X2673: $i,X2674: $i,X2675: $i,X2676: $i,X2677: $i,X2678: $i,X2679: $i,X2680: $i,X2681: $i,X2682: $i,X2683: $i,X2684: $i,X2685: $i,X2686: $i,X2687: $i,X2688: $i,X2689: $i,X2690: $i,X2691: $i,X2692: $i,X2693: $i,X2694: $i,X2695: $i,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,X2715: $i,X2716: $i,X2717: $i,X2718: $i,X2719: $i,X2720: $i,X2721: $i,X2722: $i,X2723: $i,X2724: $i,X2725: $i,X2726: $i,X2727: $i,X2728: $o,X2729: $i,X2730: $i,X2731: $i,X2732: $i,X2733: $i,X2734: $i,X2735: $i,X2736: $i,X2737: $i,X2738: $i,X2739: $i,X2740: $i,X2741: $i,X2742: $i,X2743: $i,X2744: $i,X2745: $i,X2746: $i,X2747: $i,X2748: $i,X2749: $i,X2750: $i,X2751: $i,X2752: $i,X2753: $i,X2754: $i,X2755: $i,X2756: $i,X2757: $i,X2758: $i,X2759: $i,X2760: $i,X2761: $i,X2762: $i,X2763: $i,X2764: $i,X2765: $i,X2766: $i,X2767: $i,X2768: $i,X2769: $i,X2770: $i,X2771: $i,X2772: $i,X2773: $i,X2774: $i,X2775: $i,X2776: $i,X2777: $i,X2778: $i,X2779: $i,X2780: $i,X2781: $i,X2782: $i,X2783: $i,X2784: $i,X2785: $i,X2786: $i] :
( ( ~ ( in @ ( esk1_2 @ X1881 @ X1882 ) @ X1881 )
| ~ ( in @ ( esk1_2 @ X1881 @ X1882 ) @ X1882 )
| ( X1881 = X1882 ) )
& ( ( in @ ( esk1_2 @ X1881 @ X1882 ) @ X1881 )
| ( in @ ( esk1_2 @ X1881 @ X1882 ) @ X1882 )
| ( X1881 = X1882 ) )
& ~ ( in @ X1884 @ emptyset )
& ( ~ ( in @ X1887 @ ( setadjoin @ X1885 @ X1886 ) )
| ( X1887 = X1885 )
| ( in @ X1887 @ X1886 ) )
& ( ( X1887 != X1885 )
| ( in @ X1887 @ ( setadjoin @ X1885 @ X1886 ) ) )
& ( ~ ( in @ X1887 @ X1886 )
| ( in @ X1887 @ ( setadjoin @ X1885 @ X1886 ) ) )
& ( ~ ( in @ X1889 @ ( powerset @ X1888 ) )
| ~ ( in @ X1890 @ X1889 )
| ( in @ X1890 @ X1888 ) )
& ( ( in @ ( esk2_2 @ X1891 @ X1892 ) @ X1892 )
| ( in @ X1892 @ ( powerset @ X1891 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1891 @ X1892 ) @ X1891 )
| ( in @ X1892 @ ( powerset @ X1891 ) ) )
& ( ( in @ X1895 @ ( esk3_2 @ X1894 @ X1895 ) )
| ~ ( in @ X1895 @ ( setunion @ X1894 ) ) )
& ( ( in @ ( esk3_2 @ X1894 @ X1895 ) @ X1894 )
| ~ ( in @ X1895 @ ( setunion @ X1894 ) ) )
& ( ~ ( in @ X1898 @ X1899 )
| ~ ( in @ X1899 @ X1897 )
| ( in @ X1898 @ ( setunion @ X1897 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1900 @ omega )
| ( in @ ( setadjoin @ X1900 @ X1900 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1901 ) @ omega )
| ~ ( in @ emptyset @ X1901 )
| ~ ( in @ X1903 @ omega )
| ( in @ X1903 @ X1901 ) )
& ( ( in @ ( esk4_1 @ X1901 ) @ X1901 )
| ~ ( in @ emptyset @ X1901 )
| ~ ( in @ X1903 @ omega )
| ( in @ X1903 @ X1901 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1901 ) @ ( esk4_1 @ X1901 ) ) @ X1901 )
| ~ ( in @ emptyset @ X1901 )
| ~ ( in @ X1903 @ omega )
| ( in @ X1903 @ X1901 ) )
& ( ( in @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1905 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( in @ ( esk5_2 @ X1904 @ X1905 ) @ X1905 ) )
& ( ( X1904 @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1910 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( in @ ( esk5_2 @ X1904 @ X1905 ) @ X1905 ) )
& ( ~ ( in @ X1913 @ X1905 )
| ~ ( X1904 @ X1913 @ X1912 )
| ( in @ X1912 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( in @ ( esk5_2 @ X1904 @ X1905 ) @ X1905 ) )
& ( ( in @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1905 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ( X1904 @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1910 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ~ ( in @ X1913 @ X1905 )
| ~ ( X1904 @ X1913 @ X1912 )
| ( in @ X1912 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ( in @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1905 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1907
!= ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ( X1904 @ ( esk8_3 @ X1904 @ X1905 @ X1910 ) @ X1910 )
| ~ ( in @ X1910 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1907
!= ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ~ ( in @ X1913 @ X1905 )
| ~ ( X1904 @ X1913 @ X1912 )
| ( in @ X1912 @ ( esk7_2 @ X1904 @ X1905 ) )
| ( X1907
!= ( esk6_3 @ X1904 @ X1905 @ X1907 ) )
| ~ ( X1904 @ ( esk5_2 @ X1904 @ X1905 ) @ X1907 ) )
& ( ( in @ ( esk9_1 @ X1914 ) @ X1914 )
| ~ ( in @ X1915 @ X1914 ) )
& ( ~ ( in @ X1917 @ ( esk9_1 @ X1914 ) )
| ~ ( in @ X1917 @ X1914 )
| ~ ( in @ X1915 @ X1914 ) )
& epred1_0
& ( ( X1918 @ ( esk10_2 @ X1918 @ X1919 ) )
| ~ ( X1918 @ X1919 )
| ( X1918 @ ( descr @ X1918 ) ) )
& ( ( X1919
!= ( esk10_2 @ X1918 @ X1919 ) )
| ~ ( X1918 @ X1919 )
| ( X1918 @ ( descr @ X1918 ) ) )
& ( ~ ( in @ X1923 @ X1921 )
| ~ ( X1922 @ X1923 )
| ( in @ X1923 @ ( dsetconstr @ X1921 @ X1922 ) ) )
& ( ~ ( in @ X1926 @ ( dsetconstr @ X1924 @ X1925 ) )
| ( in @ X1926 @ X1924 ) )
& ( ~ ( in @ X1929 @ ( dsetconstr @ X1927 @ X1928 ) )
| ( X1928 @ X1929 ) )
& ( ( X1930 @ ( esk12_1 @ X1930 ) )
| ( X1930 @ ( esk11_2 @ X1930 @ X1931 ) )
| ~ ( X1930 @ X1931 ) )
& ( ~ ( X1930 @ X1934 )
| ( ( esk12_1 @ X1930 )
= X1934 )
| ( X1930 @ ( esk11_2 @ X1930 @ X1931 ) )
| ~ ( X1930 @ X1931 ) )
& ( ( X1930 @ ( esk12_1 @ X1930 ) )
| ( X1931
!= ( esk11_2 @ X1930 @ X1931 ) )
| ~ ( X1930 @ X1931 ) )
& ( ~ ( X1930 @ X1934 )
| ( ( esk12_1 @ X1930 )
= X1934 )
| ( X1931
!= ( esk11_2 @ X1930 @ X1931 ) )
| ~ ( X1930 @ X1931 ) )
& ( ~ ( in @ X1936 @ ( prop2set @ X1935 ) )
| X1935 )
& ( ~ ( in @ X1937 @ emptyset )
| X1938 )
& ( ~ ( in @ X1939 @ emptyset )
| ~ $true )
& ~ ( in @ X1940 @ emptyset )
& ( ( X1941 @ ( esk13_2 @ X1941 @ X1942 ) )
| ~ ( X1941 @ X1942 )
| ( X1941 @ ( esk14_1 @ X1941 ) ) )
& ( ( X1942
!= ( esk13_2 @ X1941 @ X1942 ) )
| ~ ( X1941 @ X1942 )
| ( X1941 @ ( esk14_1 @ X1941 ) ) )
& ( ( in @ ( esk16_2 @ X1945 @ X1946 ) @ X1946 )
| ( X1945 = X1946 )
| ( in @ ( esk15_2 @ X1945 @ X1946 ) @ X1945 ) )
& ( ~ ( in @ ( esk16_2 @ X1945 @ X1946 ) @ X1945 )
| ( X1945 = X1946 )
| ( in @ ( esk15_2 @ X1945 @ X1946 ) @ X1945 ) )
& ( ( in @ ( esk16_2 @ X1945 @ X1946 ) @ X1946 )
| ( X1945 = X1946 )
| ~ ( in @ ( esk15_2 @ X1945 @ X1946 ) @ X1946 ) )
& ( ~ ( in @ ( esk16_2 @ X1945 @ X1946 ) @ X1945 )
| ( X1945 = X1946 )
| ~ ( in @ ( esk15_2 @ X1945 @ X1946 ) @ X1946 ) )
& ( ( in @ ( esk17_1 @ X1949 ) @ X1949 )
| ( X1949 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1951 ) @ X1951 )
| ( X1951 = emptyset ) )
& ( ~ ( in @ X1955 @ ( dsetconstr @ X1953 @ X1954 ) )
| ( X1954 @ X1955 )
| ~ ( in @ X1955 @ X1953 ) )
& ( ~ ( X1954 @ X1955 )
| ( in @ X1955 @ ( dsetconstr @ X1953 @ X1954 ) )
| ~ ( in @ X1955 @ X1953 ) )
& ( ( X1956 = emptyset )
| ( in @ ( esk19_1 @ X1956 ) @ X1956 ) )
& ( ~ ( in @ X1960 @ X1958 )
| ~ ( X1959 @ X1960 )
| ( ( dsetconstr @ X1958 @ X1959 )
!= emptyset ) )
& ( ~ ( in @ X1962 @ X1961 )
| ( X1961 != emptyset ) )
& ( in @ X1963 @ ( setadjoin @ X1963 @ X1964 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1967 @ X1966 )
| ( in @ X1967 @ ( setadjoin @ X1965 @ X1966 ) ) )
& ( ( in @ X1970 @ X1969 )
| X1971
| ( X1970 = X1968 )
| ~ ( in @ X1970 @ ( setadjoin @ X1968 @ X1969 ) ) )
& ( ~ X1971
| X1971
| ( X1970 = X1968 )
| ~ ( in @ X1970 @ ( setadjoin @ X1968 @ X1969 ) ) )
& ( ( in @ X1970 @ X1969 )
| X1971
| ~ X1971
| ~ ( in @ X1970 @ ( setadjoin @ X1968 @ X1969 ) ) )
& ( ~ X1971
| X1971
| ~ X1971
| ~ ( in @ X1970 @ ( setadjoin @ X1968 @ X1969 ) ) )
& ( ~ ( in @ X1974 @ ( setadjoin @ X1972 @ X1973 ) )
| ( X1974 = X1972 )
| ( in @ X1974 @ X1973 ) )
& ( ( dsetconstr @ X1975
@ ^ [Z0: $i] : $true )
= X1975 )
& ( ( in @ ( esk20_2 @ X1976 @ X1977 ) @ X1977 )
| ( in @ X1977 @ ( powerset @ X1976 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1976 @ X1977 ) @ X1976 )
| ( in @ X1977 @ ( powerset @ X1976 ) ) )
& ( in @ emptyset @ ( powerset @ X1979 ) )
& ( in @ emptyset @ ( powerset @ X1980 ) )
& ( ~ ( in @ X1982 @ ( powerset @ X1981 ) )
| ~ ( in @ X1983 @ X1982 )
| ( in @ X1983 @ X1981 ) )
& ( ~ ( in @ X1985 @ X1986 )
| ~ ( in @ X1986 @ X1984 )
| ( in @ X1985 @ ( setunion @ X1984 ) ) )
& ( ( in @ X1988 @ ( esk21_3 @ X1987 @ X1988 @ X1989 ) )
| X1989
| ~ ( in @ X1988 @ ( setunion @ X1987 ) ) )
& ( ( in @ ( esk21_3 @ X1987 @ X1988 @ X1989 ) @ X1987 )
| X1989
| ~ ( in @ X1988 @ ( setunion @ X1987 ) ) )
& ( ~ X1989
| X1989
| ~ ( in @ X1988 @ ( setunion @ X1987 ) ) )
& ( ~ ( in @ X1992 @ X1991 )
| ( in @ X1992 @ ( powerset @ ( setunion @ X1991 ) ) ) )
& ( ~ ( X1993 @ X1997 )
| ( X1997
= ( esk23_1 @ X1993 ) )
| ( X1993 @ ( esk22_2 @ X1993 @ X1994 ) )
| ~ ( X1993 @ X1994 ) )
& ( ( X1998
!= ( esk23_1 @ X1993 ) )
| ( X1993 @ X1998 )
| ( X1993 @ ( esk22_2 @ X1993 @ X1994 ) )
| ~ ( X1993 @ X1994 ) )
& ( ~ ( X1993 @ X1997 )
| ( X1997
= ( esk23_1 @ X1993 ) )
| ( X1994
!= ( esk22_2 @ X1993 @ X1994 ) )
| ~ ( X1993 @ X1994 ) )
& ( ( X1998
!= ( esk23_1 @ X1993 ) )
| ( X1993 @ X1998 )
| ( X1994
!= ( esk22_2 @ X1993 @ X1994 ) )
| ~ ( X1993 @ X1994 ) )
& ( ( in @ ( esk24_1 @ X1999 ) @ X1999 )
| ( X1999 = emptyset ) )
& ( $true
| ( X1999 = emptyset ) )
& ( ~ ( in @ X2001 @ ( setadjoin @ X2002 @ emptyset ) )
| ( X2001 = X2002 ) )
& ( ( X2003 = X2004 )
| ~ ( in @ X2004 @ ( setadjoin @ X2003 @ emptyset ) ) )
& ( ( X2005 != X2006 )
| ( in @ X2005 @ ( setadjoin @ X2006 @ emptyset ) ) )
& ( ~ ( in @ X2007 @ ( setadjoin @ X2008 @ emptyset ) )
| ( in @ X2008 @ ( setadjoin @ X2007 @ emptyset ) ) )
& ( ~ ( in @ X2011 @ ( setadjoin @ X2009 @ ( setadjoin @ X2010 @ emptyset ) ) )
| ( X2011 = X2009 )
| ( X2011 = X2010 ) )
& ( in @ X2012 @ ( setadjoin @ X2012 @ ( setadjoin @ X2013 @ emptyset ) ) )
& ( in @ X2015 @ ( setadjoin @ X2014 @ ( setadjoin @ X2015 @ emptyset ) ) )
& ( ~ ( in @ X2018 @ X2016 )
| ~ ( X2017 @ X2018 )
| ( ( dsetconstr @ X2016 @ X2017 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X2020 @ emptyset )
| ( X2019 @ X2020 ) )
& ( ( in @ ( esk25_2 @ X2021 @ X2022 ) @ X2021 )
| ~ ( in @ X2023 @ X2021 )
| ( X2022 @ X2023 ) )
& ( ~ ( X2022 @ ( esk25_2 @ X2021 @ X2022 ) )
| ~ ( in @ X2023 @ X2021 )
| ( X2022 @ X2023 ) )
& ( ( in @ ( esk26_2 @ X2025 @ X2026 ) @ X2025 )
| ~ ( in @ X2028 @ X2025 )
| ~ ( X2026 @ X2028 ) )
& ( ( X2026 @ ( esk26_2 @ X2025 @ X2026 ) )
| ~ ( in @ X2028 @ X2025 )
| ~ ( X2026 @ X2028 ) )
& ( ( in @ ( esk27_2 @ X2029 @ X2030 ) @ X2029 )
| ~ ( in @ X2032 @ X2029 )
| ~ ( X2030 @ X2032 ) )
& ( ( X2030 @ ( esk27_2 @ X2029 @ X2030 ) )
| ~ ( in @ X2032 @ X2029 )
| ~ ( X2030 @ X2032 ) )
& ( ( in @ ( esk28_2 @ X2033 @ X2034 ) @ X2033 )
| ~ ( in @ X2035 @ X2033 )
| ( X2034 @ X2035 ) )
& ( ~ ( X2034 @ ( esk28_2 @ X2033 @ X2034 ) )
| ~ ( in @ X2035 @ X2033 )
| ( X2034 @ X2035 ) )
& ( ~ X2037
| ( in @ emptyset @ ( prop2set @ X2037 ) ) )
& ( ~ X2038
| ( set2prop @ ( prop2set @ X2038 ) ) )
& ( ( in @ ( esk29_2 @ X2039 @ X2040 ) @ X2039 )
| ~ ( in @ X2042 @ X2039 )
| ~ ( X2040 @ X2042 ) )
& ( ( X2040 @ ( esk29_2 @ X2039 @ X2040 ) )
| ~ ( in @ X2042 @ X2039 )
| ~ ( X2040 @ X2042 ) )
& ( ( in @ ( esk30_2 @ X2043 @ X2044 ) @ X2043 )
| ~ ( in @ X2045 @ X2043 )
| ( X2044 @ X2045 ) )
& ( ~ ( X2044 @ ( esk30_2 @ X2043 @ X2044 ) )
| ~ ( in @ X2045 @ X2043 )
| ( X2044 @ X2045 ) )
& ( ( X2047 @ ( esk32_1 @ X2047 ) )
| ( X2047 @ ( esk31_2 @ X2047 @ X2048 ) )
| ~ ( X2047 @ X2048 ) )
& ( ~ ( X2047 @ X2051 )
| ( ( esk32_1 @ X2047 )
= X2051 )
| ( X2047 @ ( esk31_2 @ X2047 @ X2048 ) )
| ~ ( X2047 @ X2048 ) )
& ( ( X2047 @ ( esk32_1 @ X2047 ) )
| ( X2048
!= ( esk31_2 @ X2047 @ X2048 ) )
| ~ ( X2047 @ X2048 ) )
& ( ~ ( X2047 @ X2051 )
| ( ( esk32_1 @ X2047 )
= X2051 )
| ( X2048
!= ( esk31_2 @ X2047 @ X2048 ) )
| ~ ( X2047 @ X2048 ) )
& ( ( X2052 @ ( esk35_1 @ X2052 ) )
| ( X2052 @ ( esk33_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ~ ( X2052 @ X2057 )
| ( ( esk35_1 @ X2052 )
= X2057 )
| ( X2052 @ ( esk33_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ( X2052 @ ( esk35_1 @ X2052 ) )
| ( X2052 @ ( esk34_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ~ ( X2052 @ X2057 )
| ( ( esk35_1 @ X2052 )
= X2057 )
| ( X2052 @ ( esk34_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ( X2052 @ ( esk35_1 @ X2052 ) )
| ( ( esk33_1 @ X2052 )
!= ( esk34_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ~ ( X2052 @ X2057 )
| ( ( esk35_1 @ X2052 )
= X2057 )
| ( ( esk33_1 @ X2052 )
!= ( esk34_1 @ X2052 ) )
| ~ ( X2052 @ X2053 ) )
& ( ( X2058 @ ( esk37_1 @ X2058 ) )
| ~ ( X2058 @ ( esk36_2 @ X2058 @ X2059 ) )
| ( ( esk36_2 @ X2058 @ X2059 )
!= X2059 ) )
& ( ~ ( X2058 @ X2062 )
| ( ( esk37_1 @ X2058 )
= X2062 )
| ~ ( X2058 @ ( esk36_2 @ X2058 @ X2059 ) )
| ( ( esk36_2 @ X2058 @ X2059 )
!= X2059 ) )
& ( ( X2058 @ ( esk37_1 @ X2058 ) )
| ( X2058 @ ( esk36_2 @ X2058 @ X2059 ) )
| ( ( esk36_2 @ X2058 @ X2059 )
= X2059 ) )
& ( ~ ( X2058 @ X2062 )
| ( ( esk37_1 @ X2058 )
= X2062 )
| ( X2058 @ ( esk36_2 @ X2058 @ X2059 ) )
| ( ( esk36_2 @ X2058 @ X2059 )
= X2059 ) )
& ( ( X2063 != X2064 )
| ( X2065 != X2066 )
| ~ ( in @ X2065 @ X2063 )
| ( in @ X2066 @ X2064 ) )
& ( ~ ( in @ X2069 @ X2067 )
| ( in @ X2070 @ X2068 )
| ( X2069 != X2070 )
| ( X2067 != X2068 ) )
& ( ~ ( in @ X2070 @ X2068 )
| ( in @ X2069 @ X2067 )
| ( X2069 != X2070 )
| ( X2067 != X2068 ) )
& ( ( X2071 @ ( esk38_2 @ X2071 @ X2072 ) )
| ~ ( X2071 @ X2072 )
| ~ ( X2071 @ X2074 )
| ~ ( X2071 @ X2075 )
| ( X2074 = X2075 ) )
& ( ( X2072
!= ( esk38_2 @ X2071 @ X2072 ) )
| ~ ( X2071 @ X2072 )
| ~ ( X2071 @ X2074 )
| ~ ( X2071 @ X2075 )
| ( X2074 = X2075 ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( ( esk39_2 @ X2076 @ X2077 )
= ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ~ ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ~ ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2076 @ ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2077 @ ( esk42_2 @ X2076 @ X2077 ) )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2077 @ X2083 )
| ( ( esk42_2 @ X2076 @ X2077 )
= X2083 )
| ( X2080
!= ( esk41_3 @ X2076 @ X2077 @ X2080 ) )
| ~ ( X2076 @ X2080 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2077 @ ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ( X2076 @ ( esk44_2 @ X2076 @ X2077 ) )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( ~ ( X2076 @ X2087 )
| ( ( esk44_2 @ X2076 @ X2077 )
= X2087 )
| ( X2084
!= ( esk43_3 @ X2076 @ X2077 @ X2084 ) )
| ~ ( X2077 @ X2084 )
| ( X2076 @ ( esk39_2 @ X2076 @ X2077 ) )
| ( X2077 @ ( esk40_2 @ X2076 @ X2077 ) ) )
& ( emptyset = emptyset )
& ( ( X2088 != X2089 )
| ( X2090 != X2091 )
| ( ( setadjoin @ X2088 @ X2090 )
= ( setadjoin @ X2089 @ X2091 ) ) )
& ( ( X2092 != X2093 )
| ( ( powerset @ X2092 )
= ( powerset @ X2093 ) ) )
& ( ( X2094 != X2095 )
| ( ( setunion @ X2094 )
= ( setunion @ X2095 ) ) )
& ( omega = omega )
& ( ( X2096 @ ( esk45_2 @ X2096 @ X2097 ) )
| ~ ( X2096 @ X2097 )
| ~ ( X2096 @ X2099 )
| ~ ( X2096 @ X2100 )
| ( X2099 = X2100 ) )
& ( ( X2097
!= ( esk45_2 @ X2096 @ X2097 ) )
| ~ ( X2096 @ X2097 )
| ~ ( X2096 @ X2099 )
| ~ ( X2096 @ X2100 )
| ( X2099 = X2100 ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( ( esk46_2 @ X2101 @ X2102 )
= ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( ( esk46_2 @ X2101 @ X2102 )
= ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( ( esk46_2 @ X2101 @ X2102 )
= ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( ( esk46_2 @ X2101 @ X2102 )
= ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ~ ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ~ ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ~ ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ~ ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ~ ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ~ ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ~ ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ~ ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2101 @ ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2102 @ ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( X2107
!= ( esk49_3 @ X2101 @ X2102 @ X2107 ) )
| ~ ( X2102 @ X2107 )
| ( ( descr @ X2101 )
= ( descr @ X2102 ) )
| ( X2105
!= ( esk48_3 @ X2101 @ X2102 @ X2105 ) )
| ~ ( X2101 @ X2105 )
| ( X2101 @ ( esk46_2 @ X2101 @ X2102 ) )
| ( X2102 @ ( esk47_2 @ X2101 @ X2102 ) ) )
& ( ( in @ ( esk50_4 @ X2109 @ X2110 @ X2111 @ X2112 ) @ X2109 )
| ( ( dsetconstr @ X2109 @ X2111 )
= ( dsetconstr @ X2110 @ X2112 ) )
| ( X2109 != X2110 ) )
& ( ( in @ ( esk51_4 @ X2109 @ X2110 @ X2111 @ X2112 ) @ X2110 )
| ( ( dsetconstr @ X2109 @ X2111 )
= ( dsetconstr @ X2110 @ X2112 ) )
| ( X2109 != X2110 ) )
& ( ( ( esk50_4 @ X2109 @ X2110 @ X2111 @ X2112 )
= ( esk51_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
| ( ( dsetconstr @ X2109 @ X2111 )
= ( dsetconstr @ X2110 @ X2112 ) )
| ( X2109 != X2110 ) )
& ( ~ ( X2111 @ ( esk50_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
| ~ ( X2112 @ ( esk51_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
| ( ( dsetconstr @ X2109 @ X2111 )
= ( dsetconstr @ X2110 @ X2112 ) )
| ( X2109 != X2110 ) )
& ( ( X2111 @ ( esk50_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
| ( X2112 @ ( esk51_4 @ X2109 @ X2110 @ X2111 @ X2112 ) )
| ( ( dsetconstr @ X2109 @ X2111 )
= ( dsetconstr @ X2110 @ X2112 ) )
| ( X2109 != X2110 ) )
& ( ( in @ ( esk52_2 @ X2115 @ X2116 ) @ X2115 )
| ( subset @ X2115 @ X2116 ) )
& ( ~ ( in @ ( esk52_2 @ X2115 @ X2116 ) @ X2116 )
| ( subset @ X2115 @ X2116 ) )
& ( ( X2118 != X2119 )
| ( subset @ X2119 @ X2118 ) )
& ( ( X2120 != X2121 )
| ( subset @ X2120 @ X2121 ) )
& ( ( in @ ( esk53_2 @ X2122 @ X2123 ) @ X2122 )
| ( subset @ X2122 @ X2123 ) )
& ( ~ ( in @ ( esk53_2 @ X2122 @ X2123 ) @ X2123 )
| ( subset @ X2122 @ X2123 ) )
& ( subset @ emptyset @ X2125 )
& ( ~ ( subset @ X2126 @ X2127 )
| ~ ( in @ X2128 @ X2126 )
| ( in @ X2128 @ X2127 ) )
& ( ~ ( subset @ X2129 @ X2130 )
| ( in @ X2131 @ X2130 )
| ~ ( in @ X2131 @ X2129 ) )
& ( ~ ( in @ X2134 @ X2132 )
| ( in @ X2134 @ X2133 )
| ~ ( subset @ X2132 @ X2133 ) )
& ( ( subset @ X2135 @ X2136 )
| ( X2135 != X2136 ) )
& ( ~ ( in @ X2139 @ X2137 )
| ( in @ X2139 @ X2138 )
| ( X2137 != X2138 ) )
& ( subset @ X2140 @ X2140 )
& ( ~ ( subset @ X2141 @ X2142 )
| ~ ( subset @ X2142 @ X2143 )
| ( subset @ X2141 @ X2143 ) )
& ( subset @ X2145 @ ( setadjoin @ X2144 @ X2145 ) )
& ( ~ ( subset @ X2146 @ X2148 )
| ( subset @ X2146 @ ( setadjoin @ X2147 @ X2148 ) ) )
& ( ~ ( subset @ X2149 @ X2150 )
| ( in @ X2149 @ ( powerset @ X2150 ) ) )
& ( ~ ( subset @ X2151 @ X2152 )
| ~ ( subset @ X2152 @ X2151 )
| ( X2151 = X2152 ) )
& ( ~ ( subset @ X2153 @ emptyset )
| ( X2153 = emptyset ) )
& ( ~ ( subset @ X2155 @ X2154 )
| ( in @ X2155 @ ( powerset @ X2154 ) ) )
& ( ~ ( in @ X2157 @ ( powerset @ X2156 ) )
| ( subset @ X2157 @ X2156 ) )
& ( in @ X2158 @ ( powerset @ X2158 ) )
& ( ~ ( subset @ X2159 @ X2160 )
| ( subset @ ( powerset @ X2159 ) @ ( powerset @ X2160 ) ) )
& ( in @ ( dsetconstr @ X2161 @ X2162 ) @ ( powerset @ X2161 ) )
& ( subset @ ( dsetconstr @ X2163 @ X2164 ) @ X2163 )
& ( ~ ( in @ X2167 @ X2165 )
| ( in @ X2167 @ ( binunion @ X2165 @ X2166 ) ) )
& ( in @ X2169 @ ( setadjoin @ X2168 @ ( setadjoin @ X2169 @ emptyset ) ) )
& ( ~ ( in @ X2172 @ X2171 )
| ( in @ X2172 @ ( binunion @ X2170 @ X2171 ) ) )
& ( ( in @ X2175 @ X2174 )
| X2176
| ( in @ X2175 @ X2173 )
| ~ ( in @ X2175 @ ( binunion @ X2173 @ X2174 ) ) )
& ( ~ X2176
| X2176
| ( in @ X2175 @ X2173 )
| ~ ( in @ X2175 @ ( binunion @ X2173 @ X2174 ) ) )
& ( ( in @ X2175 @ X2174 )
| X2176
| ~ X2176
| ~ ( in @ X2175 @ ( binunion @ X2173 @ X2174 ) ) )
& ( ~ X2176
| X2176
| ~ X2176
| ~ ( in @ X2175 @ ( binunion @ X2173 @ X2174 ) ) )
& ( ~ ( in @ X2179 @ ( binunion @ X2177 @ X2178 ) )
| ( in @ X2179 @ X2177 )
| ( in @ X2179 @ X2178 ) )
& ( subset @ X2180 @ ( binunion @ X2180 @ X2181 ) )
& ( subset @ X2183 @ ( binunion @ X2182 @ X2183 ) )
& ( ~ ( in @ X2186 @ X2184 )
| ~ ( in @ X2186 @ X2185 )
| ( in @ X2186 @ ( binintersect @ X2184 @ X2185 ) ) )
& ( ~ ( subset @ X2189 @ X2187 )
| ~ ( subset @ X2189 @ X2188 )
| ( subset @ X2189 @ ( binintersect @ X2187 @ X2188 ) ) )
& ( ~ ( in @ X2192 @ ( binintersect @ X2190 @ X2191 ) )
| ( in @ X2192 @ X2190 ) )
& ( subset @ ( binintersect @ X2193 @ X2194 ) @ X2193 )
& ( ~ ( subset @ X2195 @ X2196 )
| ( ( binintersect @ X2195 @ X2196 )
= X2195 ) )
& ( ( ( binintersect @ X2197 @ X2198 )
!= X2198 )
| ( subset @ X2198 @ X2197 ) )
& ( ~ ( in @ X2201 @ ( binintersect @ X2199 @ X2200 ) )
| ( in @ X2201 @ X2200 ) )
& ( ( in @ ( esk54_2 @ X2202 @ X2203 ) @ X2202 )
| ( ( binintersect @ X2202 @ X2203 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X2202 @ X2203 ) @ X2203 )
| ( ( binintersect @ X2202 @ X2203 )
= emptyset ) )
& ( subset @ ( binintersect @ X2205 @ X2206 ) @ X2206 )
& ( ~ ( subset @ X2208 @ X2207 )
| ( ( binintersect @ X2207 @ X2208 )
= X2208 ) )
& ( ( ( binintersect @ X2209 @ X2210 )
!= X2209 )
| ( subset @ X2209 @ X2210 ) )
& ( ( binintersect @ X2211 @ ( binunion @ X2212 @ X2213 ) )
= ( binunion @ ( binintersect @ X2211 @ X2212 ) @ ( binintersect @ X2211 @ X2213 ) ) )
& ( ~ ( in @ X2216 @ X2214 )
| ( in @ X2216 @ X2215 )
| ( in @ X2216 @ ( setminus @ X2214 @ X2215 ) ) )
& ( ~ ( in @ X2219 @ ( setminus @ X2217 @ X2218 ) )
| ( in @ X2219 @ X2217 ) )
& ( ~ ( in @ X2222 @ ( setminus @ X2220 @ X2221 ) )
| ~ ( in @ X2222 @ X2221 ) )
& ( ~ ( subset @ X2223 @ X2224 )
| ( ( setminus @ X2223 @ X2224 )
= emptyset ) )
& ( ( in @ X2227 @ ( setminus @ X2225 @ X2226 ) )
| ~ ( in @ X2227 @ X2225 )
| ( in @ X2227 @ X2226 ) )
& ( ( in @ X2230 @ ( setminus @ X2228 @ X2229 ) )
| ( in @ X2230 @ X2229 )
| ~ ( in @ X2230 @ X2228 ) )
& ( ( in @ X2233 @ X2231 )
| ~ ( in @ X2233 @ ( setminus @ X2231 @ X2232 ) ) )
& ( ~ ( in @ X2236 @ X2235 )
| ~ ( in @ X2236 @ ( setminus @ X2234 @ X2235 ) ) )
& ( subset @ ( setminus @ X2237 @ X2238 ) @ X2237 )
& ( ( ( setminus @ X2239 @ X2240 )
!= emptyset )
| ( subset @ X2239 @ X2240 ) )
& ( ~ ( in @ X2243 @ X2241 )
| X2244
| ( in @ X2243 @ X2241 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ( in @ X2243 @ X2242 )
| X2244
| ( in @ X2243 @ X2241 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ X2244
| X2244
| ( in @ X2243 @ X2241 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ ( in @ X2243 @ X2241 )
| X2244
| ~ ( in @ X2243 @ X2242 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ( in @ X2243 @ X2242 )
| X2244
| ~ ( in @ X2243 @ X2242 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ X2244
| X2244
| ~ ( in @ X2243 @ X2242 )
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ ( in @ X2243 @ X2241 )
| X2244
| ~ X2244
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ( in @ X2243 @ X2242 )
| X2244
| ~ X2244
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ X2244
| X2244
| ~ X2244
| ~ ( in @ X2243 @ ( symdiff @ X2241 @ X2242 ) ) )
& ( ~ ( in @ X2247 @ X2245 )
| ( in @ X2247 @ X2246 )
| ( in @ X2247 @ ( symdiff @ X2245 @ X2246 ) ) )
& ( ( in @ X2250 @ X2248 )
| ~ ( in @ X2250 @ X2249 )
| ( in @ X2250 @ ( symdiff @ X2248 @ X2249 ) ) )
& ( ~ ( in @ X2253 @ X2251 )
| ~ ( in @ X2253 @ X2252 )
| ~ ( in @ X2253 @ ( symdiff @ X2251 @ X2252 ) ) )
& ( ( in @ X2256 @ X2254 )
| ( in @ X2256 @ X2255 )
| ~ ( in @ X2256 @ ( symdiff @ X2254 @ X2255 ) ) )
& ( in @ X2258 @ ( setadjoin @ X2257 @ ( setadjoin @ X2258 @ emptyset ) ) )
& ( in @ X2259 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2259 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2259 @ ( setadjoin @ X2260 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2262 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2261 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2261 @ ( setadjoin @ X2262 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2263 @ ( setadjoin @ X2264 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2265 @ X2266 ) )
& ( ~ ( in @ X2268 @ X2267 )
| ( subset @ ( setadjoin @ X2268 @ emptyset ) @ X2267 ) )
& ( ~ ( in @ X2270 @ X2269 )
| ( in @ ( setadjoin @ X2270 @ emptyset ) @ ( powerset @ X2269 ) ) )
& ( ~ ( in @ X2273 @ X2271 )
| ( in @ ( setadjoin @ X2273 @ emptyset ) @ ( powerset @ ( binunion @ X2271 @ X2272 ) ) ) )
& ( ~ ( in @ X2276 @ ( setadjoin @ X2274 @ ( setadjoin @ X2275 @ emptyset ) ) )
| ( X2276 = X2274 )
| ( X2276 = X2275 ) )
& ( ~ ( in @ X2279 @ X2277 )
| ~ ( in @ X2280 @ X2278 )
| ( subset @ ( setadjoin @ X2279 @ ( setadjoin @ X2280 @ emptyset ) ) @ ( binunion @ X2277 @ X2278 ) ) )
& ( ~ ( in @ X2283 @ X2281 )
| ~ ( in @ X2284 @ X2282 )
| ( in @ ( setadjoin @ X2283 @ ( setadjoin @ X2284 @ emptyset ) ) @ ( powerset @ ( binunion @ X2281 @ X2282 ) ) ) )
& ( ~ ( in @ X2287 @ X2285 )
| ~ ( in @ X2288 @ X2286 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2287 @ ( setadjoin @ X2288 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2285 @ X2286 ) ) ) )
& ( ~ ( in @ X2291 @ X2289 )
| ~ ( in @ X2292 @ X2290 )
| ( in @ ( setadjoin @ ( setadjoin @ X2291 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2291 @ ( setadjoin @ X2292 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2289 @ X2290 ) ) ) ) )
& ( ~ ( in @ X2295 @ X2293 )
| ~ ( in @ X2296 @ X2294 )
| ( in @ ( kpair @ X2295 @ X2296 ) @ ( powerset @ ( powerset @ ( binunion @ X2293 @ X2294 ) ) ) ) )
& ( ~ ( in @ X2299 @ X2297 )
| ~ ( in @ X2300 @ X2298 )
| ( in @ ( kpair @ X2299 @ X2300 ) @ ( cartprod @ X2297 @ X2298 ) ) )
& ( ( in @ ( esk55_3 @ X2301 @ X2302 @ X2303 ) @ X2301 )
| ~ ( in @ X2303 @ ( cartprod @ X2301 @ X2302 ) ) )
& ( ( in @ ( esk56_3 @ X2301 @ X2302 @ X2303 ) @ X2302 )
| ~ ( in @ X2303 @ ( cartprod @ X2301 @ X2302 ) ) )
& ( ( X2303
= ( kpair @ ( esk55_3 @ X2301 @ X2302 @ X2303 ) @ ( esk56_3 @ X2301 @ X2302 @ X2303 ) ) )
| ~ ( in @ X2303 @ ( cartprod @ X2301 @ X2302 ) ) )
& ( ~ ( in @ X2308 @ ( cartprod @ X2306 @ X2307 ) )
| ( iskpair @ X2308 ) )
& ( ( in @ ( esk57_2 @ X2309 @ X2310 ) @ X2309 )
| ~ ( in @ X2310 @ ( setunion @ X2309 ) ) )
& ( ( in @ X2310 @ ( esk57_2 @ X2309 @ X2310 ) )
| ~ ( in @ X2310 @ ( setunion @ X2309 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2312 @ emptyset ) ) @ X2312 )
& ( subset @ X2313 @ ( setunion @ ( setadjoin @ X2313 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2314 @ emptyset ) )
= X2314 )
& ( ( in @ ( esk58_2 @ X2315 @ X2316 ) @ X2315 )
| ~ ( in @ X2319 @ X2315 )
| ~ ( X2316 @ X2319 )
| ( singleton @ ( dsetconstr @ X2315 @ X2316 ) ) )
& ( ( in @ ( esk59_2 @ X2315 @ X2316 ) @ X2315 )
| ~ ( in @ X2319 @ X2315 )
| ~ ( X2316 @ X2319 )
| ( singleton @ ( dsetconstr @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk58_2 @ X2315 @ X2316 ) )
| ~ ( in @ X2319 @ X2315 )
| ~ ( X2316 @ X2319 )
| ( singleton @ ( dsetconstr @ X2315 @ X2316 ) ) )
& ( ( X2316 @ ( esk59_2 @ X2315 @ X2316 ) )
| ~ ( in @ X2319 @ X2315 )
| ~ ( X2316 @ X2319 )
| ( singleton @ ( dsetconstr @ X2315 @ X2316 ) ) )
& ( ( ( esk58_2 @ X2315 @ X2316 )
!= ( esk59_2 @ X2315 @ X2316 ) )
| ~ ( in @ X2319 @ X2315 )
| ~ ( X2316 @ X2319 )
| ( singleton @ ( dsetconstr @ X2315 @ X2316 ) ) )
& ( ( in @ ( esk60_2 @ X2320 @ X2321 ) @ X2320 )
| ~ ( singleton @ ( dsetconstr @ X2320 @ X2321 ) ) )
& ( ( X2321 @ ( esk60_2 @ X2320 @ X2321 ) )
| ~ ( singleton @ ( dsetconstr @ X2320 @ X2321 ) ) )
& ( ( in @ ( esk61_3 @ X2323 @ X2324 @ X2325 ) @ X2323 )
| ( singleton @ ( dsetconstr @ X2323 @ X2324 ) )
| ~ ( X2324 @ X2325 )
| ~ ( in @ X2325 @ X2323 ) )
& ( ( X2324 @ ( esk61_3 @ X2323 @ X2324 @ X2325 ) )
| ( singleton @ ( dsetconstr @ X2323 @ X2324 ) )
| ~ ( X2324 @ X2325 )
| ~ ( in @ X2325 @ X2323 ) )
& ( ( ( esk61_3 @ X2323 @ X2324 @ X2325 )
!= X2325 )
| ( singleton @ ( dsetconstr @ X2323 @ X2324 ) )
| ~ ( X2324 @ X2325 )
| ~ ( in @ X2325 @ X2323 ) )
& ( ( in @ ( esk62_2 @ X2327 @ X2328 ) @ X2327 )
| ~ ( in @ X2331 @ X2327 )
| ~ ( X2328 @ X2331 )
| ( singleton @ ( dsetconstr @ X2327 @ X2328 ) ) )
& ( ( in @ ( esk63_2 @ X2327 @ X2328 ) @ X2327 )
| ~ ( in @ X2331 @ X2327 )
| ~ ( X2328 @ X2331 )
| ( singleton @ ( dsetconstr @ X2327 @ X2328 ) ) )
& ( ( X2328 @ ( esk62_2 @ X2327 @ X2328 ) )
| ~ ( in @ X2331 @ X2327 )
| ~ ( X2328 @ X2331 )
| ( singleton @ ( dsetconstr @ X2327 @ X2328 ) ) )
& ( ( X2328 @ ( esk63_2 @ X2327 @ X2328 ) )
| ~ ( in @ X2331 @ X2327 )
| ~ ( X2328 @ X2331 )
| ( singleton @ ( dsetconstr @ X2327 @ X2328 ) ) )
& ( ( ( esk62_2 @ X2327 @ X2328 )
!= ( esk63_2 @ X2327 @ X2328 ) )
| ~ ( in @ X2331 @ X2327 )
| ~ ( X2328 @ X2331 )
| ( singleton @ ( dsetconstr @ X2327 @ X2328 ) ) )
& ( ( ( setadjoin @ X2332 @ emptyset )
!= ( setadjoin @ X2333 @ emptyset ) )
| ( X2332 = X2333 ) )
& ( ~ ( in @ ( setadjoin @ X2336 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2334 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2334 @ ( setadjoin @ X2335 @ emptyset ) ) @ emptyset ) ) )
| ( X2334 = X2336 ) )
& ( ~ ( iskpair @ X2337 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2337 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2337 ) ) ) )
& ( ~ ( singleton @ X2338 )
| ( in @ ( setunion @ X2338 ) @ X2338 ) )
& ( ( kfst @ ( kpair @ X2339 @ X2340 ) )
= X2339 )
& ( ~ ( in @ X2343 @ ( cartprod @ X2341 @ X2342 ) )
| ( in @ ( kfst @ X2343 ) @ X2341 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2344 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2344 @ ( setadjoin @ X2345 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2346 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2346 @ ( setadjoin @ X2347 @ emptyset ) ) @ emptyset ) ) )
| ( X2344 = X2346 ) )
& ( ( ( kpair @ X2348 @ X2349 )
!= ( kpair @ X2350 @ X2351 ) )
| ( X2348 = X2350 ) )
& ( ( X2352 != X2353 )
| ( ( setadjoin @ X2352 @ ( setadjoin @ X2353 @ emptyset ) )
= ( setadjoin @ X2352 @ emptyset ) ) )
& ( ( X2354 != X2355 )
| ( ( setadjoin @ ( setadjoin @ X2354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2354 @ ( setadjoin @ X2355 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2354 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2356 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2356 @ ( setadjoin @ X2357 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2358 @ ( setadjoin @ X2359 @ emptyset ) ) @ emptyset ) ) )
| ( X2358 != X2359 )
| ( X2357 = X2359 ) )
& ( ( ( setadjoin @ X2360 @ ( setadjoin @ X2361 @ emptyset ) )
!= ( setadjoin @ X2362 @ emptyset ) )
| ( X2360 = X2361 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2363 @ ( setadjoin @ X2364 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2365 @ ( setadjoin @ X2366 @ emptyset ) ) @ emptyset ) ) )
| ( X2364 = X2366 ) )
& ( ( ( kpair @ X2367 @ X2368 )
!= ( kpair @ X2369 @ X2370 ) )
| ( X2368 = X2370 ) )
& ( ~ ( iskpair @ X2371 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2371 )
@ ^ [Z0: $i] :
( X2371
= ( kpair @ ( kfst @ X2371 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2372 @ X2373 ) )
= X2373 )
& ( ~ ( iskpair @ X2374 )
| ( ( kpair @ ( kfst @ X2374 ) @ ( ksnd @ X2374 ) )
= X2374 ) )
& ( ~ ( in @ X2377 @ ( cartprod @ X2375 @ X2376 ) )
| ( in @ ( ksnd @ X2377 ) @ X2376 ) )
& ( ~ ( in @ ( kpair @ X2380 @ X2381 ) @ ( cartprod @ X2378 @ X2379 ) )
| ( in @ X2380 @ X2378 ) )
& ( ~ ( in @ ( kpair @ X2384 @ X2385 ) @ ( cartprod @ X2382 @ X2383 ) )
| ( in @ X2385 @ X2383 ) )
& ( ~ ( in @ X2388 @ X2386 )
| ~ ( in @ X2389 @ X2387 )
| ( ( kpair @ X2388 @ X2389 )
= ( kpair @ X2388 @ X2389 ) ) )
& ( ~ ( in @ X2392 @ X2390 )
| ~ ( in @ X2393 @ X2391 )
| ( ( kfst @ ( kpair @ X2392 @ X2393 ) )
= X2392 ) )
& ( ~ ( in @ X2396 @ X2394 )
| ~ ( in @ X2397 @ X2395 )
| ( ( ksnd @ ( kpair @ X2396 @ X2397 ) )
= X2397 ) )
& ( ~ ( in @ X2400 @ ( cartprod @ X2398 @ X2399 ) )
| ( ( kpair @ ( kfst @ X2400 ) @ ( ksnd @ X2400 ) )
= X2400 ) )
& ( ~ ( in @ X2404 @ X2401 )
| ~ ( in @ X2405 @ X2402 )
| ~ ( X2403 @ X2404 @ X2405 )
| ( in @ ( kpair @ X2404 @ X2405 ) @ ( dpsetconstr @ X2401 @ X2402 @ X2403 ) ) )
& ( subset @ ( dpsetconstr @ X2406 @ X2407 @ X2408 ) @ ( cartprod @ X2406 @ X2407 ) )
& ( subset @ ( dpsetconstr @ X2409 @ X2410 @ X2411 ) @ ( cartprod @ X2409 @ X2410 ) )
& ( ~ ( in @ X2415 @ X2412 )
| ~ ( in @ X2416 @ X2413 )
| ~ ( in @ ( kpair @ X2415 @ X2416 ) @ ( dpsetconstr @ X2412 @ X2413 @ X2414 ) )
| ( X2414 @ X2415 @ X2416 ) )
& ( ~ ( in @ ( kpair @ X2420 @ X2421 ) @ ( dpsetconstr @ X2417 @ X2418 @ X2419 ) )
| ( in @ X2420 @ X2417 ) )
& ( ~ ( in @ ( kpair @ X2425 @ X2426 ) @ ( dpsetconstr @ X2422 @ X2423 @ X2424 ) )
| ( in @ X2426 @ X2423 ) )
& ( ~ ( in @ ( kpair @ X2430 @ X2431 ) @ ( dpsetconstr @ X2427 @ X2428 @ X2429 ) )
| ( X2429 @ X2430 @ X2431 ) )
& ( ~ ( func @ X2432 @ X2433 @ X2434 )
| ~ ( in @ X2435 @ X2432 )
| ( singleton
@ ( dsetconstr @ X2433
@ ^ [Z0: $i] : ( in @ ( kpair @ X2435 @ Z0 ) @ X2434 ) ) ) )
& ( ~ ( func @ X2436 @ X2437 @ X2438 )
| ~ ( in @ X2439 @ X2436 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2437
@ ^ [Z0: $i] : ( in @ ( kpair @ X2439 @ Z0 ) @ X2438 ) ) )
@ X2437 ) )
& ( ~ ( func @ X2440 @ X2441 @ X2442 )
| ~ ( in @ X2443 @ X2440 )
| ( in @ ( ap @ X2440 @ X2441 @ X2442 @ X2443 ) @ X2441 ) )
& ( ~ ( in @ X2446 @ ( funcSet @ X2444 @ X2445 ) )
| ( func @ X2444 @ X2445 @ X2446 ) )
& ( ~ ( in @ X2449 @ ( funcSet @ X2447 @ X2448 ) )
| ~ ( in @ X2450 @ X2447 )
| ( in @ ( ap @ X2447 @ X2448 @ X2449 @ X2450 ) @ X2448 ) )
& ( ~ ( func @ X2451 @ X2452 @ X2453 )
| ( in @ X2453 @ ( funcSet @ X2451 @ X2452 ) ) )
& ( ( in @ ( esk64_3 @ X2454 @ X2455 @ X2456 ) @ X2454 )
| ( func @ X2454 @ X2455
@ ( dpsetconstr @ X2454 @ X2455
@ ^ [Z0: $i] : ( $eq @ ( X2456 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2456 @ ( esk64_3 @ X2454 @ X2455 @ X2456 ) ) @ X2455 )
| ( func @ X2454 @ X2455
@ ( dpsetconstr @ X2454 @ X2455
@ ^ [Z0: $i] : ( $eq @ ( X2456 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2458 @ X2459 @ X2460 ) @ X2458 )
| ( func @ X2458 @ X2459 @ ( lam @ X2458 @ X2459 @ X2460 ) ) )
& ( ~ ( in @ ( X2460 @ ( esk65_3 @ X2458 @ X2459 @ X2460 ) ) @ X2459 )
| ( func @ X2458 @ X2459 @ ( lam @ X2458 @ X2459 @ X2460 ) ) )
& ( ( in @ ( esk66_3 @ X2462 @ X2463 @ X2464 ) @ X2462 )
| ( in @ ( lam @ X2462 @ X2463 @ X2464 ) @ ( funcSet @ X2462 @ X2463 ) ) )
& ( ~ ( in @ ( X2464 @ ( esk66_3 @ X2462 @ X2463 @ X2464 ) ) @ X2463 )
| ( in @ ( lam @ X2462 @ X2463 @ X2464 ) @ ( funcSet @ X2462 @ X2463 ) ) )
& ( ( in @ ( esk67_4 @ X2466 @ X2467 @ X2468 @ X2469 ) @ X2466 )
| ~ ( in @ X2472 @ X2468 )
| ( X2469 @ X2472 )
| ~ ( subset @ X2468 @ ( cartprod @ X2466 @ X2467 ) ) )
& ( ( in @ ( esk68_4 @ X2466 @ X2467 @ X2468 @ X2469 ) @ X2467 )
| ~ ( in @ X2472 @ X2468 )
| ( X2469 @ X2472 )
| ~ ( subset @ X2468 @ ( cartprod @ X2466 @ X2467 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2466 @ X2467 @ X2468 @ X2469 ) @ ( esk68_4 @ X2466 @ X2467 @ X2468 @ X2469 ) ) @ X2468 )
| ~ ( in @ X2472 @ X2468 )
| ( X2469 @ X2472 )
| ~ ( subset @ X2468 @ ( cartprod @ X2466 @ X2467 ) ) )
& ( ~ ( X2469 @ ( kpair @ ( esk67_4 @ X2466 @ X2467 @ X2468 @ X2469 ) @ ( esk68_4 @ X2466 @ X2467 @ X2468 @ X2469 ) ) )
| ~ ( in @ X2472 @ X2468 )
| ( X2469 @ X2472 )
| ~ ( subset @ X2468 @ ( cartprod @ X2466 @ X2467 ) ) )
& ( ( in @ ( esk69_4 @ X2473 @ X2474 @ X2475 @ X2476 ) @ X2473 )
| ~ ( in @ X2479 @ X2475 )
| ( X2476 @ X2479 )
| ~ ( subset @ X2475 @ ( cartprod @ X2473 @ X2474 ) ) )
& ( ( in @ ( esk70_4 @ X2473 @ X2474 @ X2475 @ X2476 ) @ X2474 )
| ~ ( in @ X2479 @ X2475 )
| ( X2476 @ X2479 )
| ~ ( subset @ X2475 @ ( cartprod @ X2473 @ X2474 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2473 @ X2474 @ X2475 @ X2476 ) @ ( esk70_4 @ X2473 @ X2474 @ X2475 @ X2476 ) ) @ X2475 )
| ~ ( in @ X2479 @ X2475 )
| ( X2476 @ X2479 )
| ~ ( subset @ X2475 @ ( cartprod @ X2473 @ X2474 ) ) )
& ( ~ ( X2476 @ ( kpair @ ( esk69_4 @ X2473 @ X2474 @ X2475 @ X2476 ) @ ( esk70_4 @ X2473 @ X2474 @ X2475 @ X2476 ) ) )
| ~ ( in @ X2479 @ X2475 )
| ( X2476 @ X2479 )
| ~ ( subset @ X2475 @ ( cartprod @ X2473 @ X2474 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2480 @ X2481 ) )
| ~ ( in @ X2482 @ X2480 )
| ~ ( in @ X2483 @ X2480 )
| ~ ( X2481 @ X2482 )
| ~ ( X2481 @ X2483 )
| ( X2482 = X2483 ) )
& ( ~ ( func @ X2484 @ X2485 @ X2486 )
| ~ ( in @ X2487 @ X2484 )
| ( in @ ( kpair @ X2487 @ ( ap @ X2484 @ X2485 @ X2486 @ X2487 ) ) @ X2486 ) )
& ( ~ ( in @ X2490 @ ( funcSet @ X2488 @ X2489 ) )
| ~ ( in @ X2491 @ X2488 )
| ( in @ ( kpair @ X2491 @ ( ap @ X2488 @ X2489 @ X2490 @ X2491 ) ) @ X2490 ) )
& ( ~ ( func @ X2492 @ X2493 @ X2494 )
| ~ ( in @ X2495 @ X2492 )
| ~ ( in @ X2496 @ X2493 )
| ~ ( in @ ( kpair @ X2495 @ X2496 ) @ X2494 )
| ( ( ap @ X2492 @ X2493 @ X2494 @ X2495 )
= X2496 ) )
& ( ( in @ ( esk71_4 @ X2497 @ X2498 @ X2499 @ X2500 ) @ X2497 )
| ~ ( in @ X2502 @ X2497 )
| ~ ( in @ X2503 @ X2498 )
| ~ ( in @ ( kpair @ X2502 @ X2503 ) @ X2500 )
| ( in @ ( kpair @ X2502 @ X2503 ) @ X2499 )
| ~ ( func @ X2497 @ X2498 @ X2500 )
| ~ ( func @ X2497 @ X2498 @ X2499 ) )
& ( ( ( ap @ X2497 @ X2498 @ X2499 @ ( esk71_4 @ X2497 @ X2498 @ X2499 @ X2500 ) )
!= ( ap @ X2497 @ X2498 @ X2500 @ ( esk71_4 @ X2497 @ X2498 @ X2499 @ X2500 ) ) )
| ~ ( in @ X2502 @ X2497 )
| ~ ( in @ X2503 @ X2498 )
| ~ ( in @ ( kpair @ X2502 @ X2503 ) @ X2500 )
| ( in @ ( kpair @ X2502 @ X2503 ) @ X2499 )
| ~ ( func @ X2497 @ X2498 @ X2500 )
| ~ ( func @ X2497 @ X2498 @ X2499 ) )
& ( ~ ( in @ X2506 @ ( funcSet @ X2504 @ X2505 ) )
| ~ ( in @ X2507 @ X2504 )
| ~ ( in @ X2508 @ X2505 )
| ~ ( in @ ( kpair @ X2507 @ X2508 ) @ X2506 )
| ( ( ap @ X2504 @ X2505 @ X2506 @ X2507 )
= X2508 ) )
& ( ( in @ ( esk72_4 @ X2509 @ X2510 @ X2511 @ X2512 ) @ X2509 )
| ( subset @ X2511 @ X2512 )
| ~ ( subset @ X2512 @ ( cartprod @ X2509 @ X2510 ) )
| ~ ( subset @ X2511 @ ( cartprod @ X2509 @ X2510 ) ) )
& ( ( in @ ( esk73_4 @ X2509 @ X2510 @ X2511 @ X2512 ) @ X2510 )
| ( subset @ X2511 @ X2512 )
| ~ ( subset @ X2512 @ ( cartprod @ X2509 @ X2510 ) )
| ~ ( subset @ X2511 @ ( cartprod @ X2509 @ X2510 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2509 @ X2510 @ X2511 @ X2512 ) @ ( esk73_4 @ X2509 @ X2510 @ X2511 @ X2512 ) ) @ X2511 )
| ( subset @ X2511 @ X2512 )
| ~ ( subset @ X2512 @ ( cartprod @ X2509 @ X2510 ) )
| ~ ( subset @ X2511 @ ( cartprod @ X2509 @ X2510 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2509 @ X2510 @ X2511 @ X2512 ) @ ( esk73_4 @ X2509 @ X2510 @ X2511 @ X2512 ) ) @ X2512 )
| ( subset @ X2511 @ X2512 )
| ~ ( subset @ X2512 @ ( cartprod @ X2509 @ X2510 ) )
| ~ ( subset @ X2511 @ ( cartprod @ X2509 @ X2510 ) ) )
& ( ( in @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ( X2517 = X2518 )
| ( in @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ( X2517 = X2518 )
| ( in @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ( X2517 = X2518 )
| ( in @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ( X2517 = X2518 )
| ( in @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ( X2517 = X2518 )
| ( in @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ( X2517 = X2518 )
| ( in @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ( X2517 = X2518 )
| ( in @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ( X2517 = X2518 )
| ( in @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ( X2517 = X2518 )
| ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ( X2517 = X2518 )
| ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ( X2517 = X2518 )
| ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ( X2517 = X2518 )
| ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2515 )
| ( X2517 = X2518 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ X2516 )
| ( X2517 = X2518 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ( X2517 = X2518 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk77_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2517 )
| ( X2517 = X2518 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2515 @ X2516 @ X2517 @ X2518 ) @ ( esk75_4 @ X2515 @ X2516 @ X2517 @ X2518 ) ) @ X2518 )
| ~ ( subset @ X2518 @ ( cartprod @ X2515 @ X2516 ) )
| ~ ( subset @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
& ( ( in @ ( esk78_4 @ X2523 @ X2524 @ X2525 @ X2526 ) @ X2523 )
| ( X2525 = X2526 )
| ~ ( func @ X2523 @ X2524 @ X2526 )
| ~ ( func @ X2523 @ X2524 @ X2525 ) )
& ( ( ( ap @ X2523 @ X2524 @ X2525 @ ( esk78_4 @ X2523 @ X2524 @ X2525 @ X2526 ) )
!= ( ap @ X2523 @ X2524 @ X2526 @ ( esk78_4 @ X2523 @ X2524 @ X2525 @ X2526 ) ) )
| ( X2525 = X2526 )
| ~ ( func @ X2523 @ X2524 @ X2526 )
| ~ ( func @ X2523 @ X2524 @ X2525 ) )
& ( ( in @ ( esk79_4 @ X2528 @ X2529 @ X2530 @ X2531 ) @ X2528 )
| ( X2530 = X2531 )
| ~ ( in @ X2531 @ ( funcSet @ X2528 @ X2529 ) )
| ~ ( in @ X2530 @ ( funcSet @ X2528 @ X2529 ) ) )
& ( ( ( ap @ X2528 @ X2529 @ X2530 @ ( esk79_4 @ X2528 @ X2529 @ X2530 @ X2531 ) )
!= ( ap @ X2528 @ X2529 @ X2531 @ ( esk79_4 @ X2528 @ X2529 @ X2530 @ X2531 ) ) )
| ( X2530 = X2531 )
| ~ ( in @ X2531 @ ( funcSet @ X2528 @ X2529 ) )
| ~ ( in @ X2530 @ ( funcSet @ X2528 @ X2529 ) ) )
& ( ~ ( in @ X2535 @ ( funcSet @ X2533 @ X2534 ) )
| ~ ( in @ X2536 @ X2533 )
| ( ( ap @ X2533 @ X2534 @ X2535 @ X2536 )
= ( ap @ X2533 @ X2534 @ X2535 @ X2536 ) ) )
& ( ~ ( func @ X2537 @ X2538 @ X2539 )
| ~ ( in @ X2540 @ X2537 )
| ( ( ap @ X2537 @ X2538 @ X2539 @ X2540 )
= ( ap @ X2537 @ X2538 @ X2539 @ X2540 ) ) )
& ( ( in @ ( esk80_3 @ X2541 @ X2542 @ X2543 ) @ X2541 )
| ~ ( in @ X2545 @ X2541 )
| ( ( ap @ X2541 @ X2542 @ ( lam @ X2541 @ X2542 @ X2543 ) @ X2545 )
= ( X2543 @ X2545 ) ) )
& ( ~ ( in @ ( X2543 @ ( esk80_3 @ X2541 @ X2542 @ X2543 ) ) @ X2542 )
| ~ ( in @ X2545 @ X2541 )
| ( ( ap @ X2541 @ X2542 @ ( lam @ X2541 @ X2542 @ X2543 ) @ X2545 )
= ( X2543 @ X2545 ) ) )
& ( ~ ( func @ X2546 @ X2547 @ X2548 )
| ( ( lam @ X2546 @ X2547 @ ( ap @ X2546 @ X2547 @ X2548 ) )
= X2548 ) )
& ( ( in @ ( esk81_3 @ X2549 @ X2550 @ X2551 ) @ X2549 )
| ( ( lam @ X2549 @ X2550 @ X2551 )
= ( lam @ X2549 @ X2550 @ X2551 ) ) )
& ( ~ ( in @ ( X2551 @ ( esk81_3 @ X2549 @ X2550 @ X2551 ) ) @ X2550 )
| ( ( lam @ X2549 @ X2550 @ X2551 )
= ( lam @ X2549 @ X2550 @ X2551 ) ) )
& ( ( in @ ( esk82_3 @ X2553 @ X2554 @ X2555 ) @ X2553 )
| ~ ( in @ X2557 @ X2553 )
| ( ( ap @ X2553 @ X2554 @ ( lam @ X2553 @ X2554 @ X2555 ) @ X2557 )
= ( X2555 @ X2557 ) ) )
& ( ~ ( in @ ( X2555 @ ( esk82_3 @ X2553 @ X2554 @ X2555 ) ) @ X2554 )
| ~ ( in @ X2557 @ X2553 )
| ( ( ap @ X2553 @ X2554 @ ( lam @ X2553 @ X2554 @ X2555 ) @ X2557 )
= ( X2555 @ X2557 ) ) )
& ( ~ ( in @ X2560 @ ( funcSet @ X2558 @ X2559 ) )
| ( ( lam @ X2558 @ X2559 @ ( ap @ X2558 @ X2559 @ X2560 ) )
= X2560 ) )
& ( ~ ( in @ X2563 @ X2561 )
| ~ ( in @ X2564 @ X2561 )
| X2562
| ( in @ X2564
@ ( dsetconstr @ X2561
@ ^ [Z0: $i] :
( ( X2562
& ( Z0 = X2563 ) )
| ( ~ X2562
& ( Z0 = X2564 ) ) ) ) ) )
& ( ~ ( in @ X2567 @ X2565 )
| ~ ( in @ X2568 @ X2565 )
| X2566
| ( ( dsetconstr @ X2565
@ ^ [Z0: $i] :
( ( X2566
& ( Z0 = X2567 ) )
| ( ~ X2566
& ( Z0 = X2568 ) ) ) )
= ( setadjoin @ X2568 @ emptyset ) ) )
& ( ~ ( in @ X2571 @ X2569 )
| ~ ( in @ X2572 @ X2569 )
| ~ X2570
| ( in @ X2571
@ ( dsetconstr @ X2569
@ ^ [Z0: $i] :
( ( X2570
& ( Z0 = X2571 ) )
| ( ~ X2570
& ( Z0 = X2572 ) ) ) ) ) )
& ( ~ ( in @ X2575 @ X2573 )
| ~ ( in @ X2576 @ X2573 )
| ~ X2574
| ( ( dsetconstr @ X2573
@ ^ [Z0: $i] :
( ( X2574
& ( Z0 = X2575 ) )
| ( ~ X2574
& ( Z0 = X2576 ) ) ) )
= ( setadjoin @ X2575 @ emptyset ) ) )
& ( ~ ( in @ X2579 @ X2577 )
| ~ ( in @ X2580 @ X2577 )
| ( singleton
@ ( dsetconstr @ X2577
@ ^ [Z0: $i] :
( ( X2578
& ( Z0 = X2579 ) )
| ( ~ X2578
& ( Z0 = X2580 ) ) ) ) ) )
& ( ~ ( in @ X2583 @ X2581 )
| ~ ( in @ X2584 @ X2581 )
| ( in @ ( if @ X2581 @ X2582 @ X2583 @ X2584 ) @ X2581 ) )
& ( ~ ( singleton @ X2585 )
| ~ ( in @ X2586 @ X2585 )
| ( ( setunion @ X2585 )
= X2586 ) )
& ( ~ ( in @ X2589 @ X2587 )
| ~ ( in @ X2590 @ X2587 )
| ~ X2588
| ( ( if @ X2587 @ X2588 @ X2589 @ X2590 )
= X2589 ) )
& ( ~ ( in @ X2593 @ X2591 )
| ~ ( in @ X2594 @ X2591 )
| X2592
| ( ( if @ X2591 @ X2592 @ X2593 @ X2594 )
= X2594 ) )
& ( ~ ( in @ X2597 @ X2595 )
| ~ ( in @ X2598 @ X2595 )
| ( in @ ( if @ X2595 @ X2596 @ X2597 @ X2598 ) @ ( setadjoin @ X2597 @ ( setadjoin @ X2598 @ emptyset ) ) ) )
& ( ~ ( in @ X2600 @ ( powerset @ X2599 ) )
| ~ ( in @ X2601 @ ( powerset @ X2599 ) )
| ( in @ ( binintersect @ X2600 @ X2601 ) @ ( powerset @ X2599 ) ) )
& ( ~ ( in @ X2603 @ ( powerset @ X2602 ) )
| ~ ( in @ X2604 @ ( powerset @ X2602 ) )
| ( in @ ( binunion @ X2603 @ X2604 ) @ ( powerset @ X2602 ) ) )
& ( ~ ( in @ X2606 @ ( powerset @ X2605 ) )
| ( in @ ( powerset @ X2606 ) @ ( powerset @ ( powerset @ X2605 ) ) ) )
& ( ~ ( in @ X2608 @ ( powerset @ X2607 ) )
| ~ ( in @ X2609 @ ( powerset @ X2607 ) )
| ( in @ ( setminus @ X2608 @ X2609 ) @ ( powerset @ X2607 ) ) )
& ( ~ ( in @ X2611 @ ( powerset @ X2610 ) )
| ( in @ ( setminus @ X2610 @ X2611 ) @ ( powerset @ X2610 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ( X2613 = X2614 )
| ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2612 )
| ( X2613 = X2614 )
| ~ ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ( X2613 = X2614 )
| ~ ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2612 @ X2613 @ X2614 ) @ X2613 )
| ( X2613 = X2614 )
| ~ ( in @ ( esk83_3 @ X2612 @ X2613 @ X2614 ) @ X2614 )
| ~ ( in @ X2614 @ ( powerset @ X2612 ) )
| ~ ( in @ X2613 @ ( powerset @ X2612 ) ) )
& ( ( in @ ( esk85_3 @ X2617 @ X2618 @ X2619 ) @ X2617 )
| ( subset @ X2618 @ X2619 )
| ~ ( in @ X2619 @ ( powerset @ X2617 ) )
| ~ ( in @ X2618 @ ( powerset @ X2617 ) ) )
& ( ( in @ ( esk85_3 @ X2617 @ X2618 @ X2619 ) @ X2618 )
| ( subset @ X2618 @ X2619 )
| ~ ( in @ X2619 @ ( powerset @ X2617 ) )
| ~ ( in @ X2618 @ ( powerset @ X2617 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2617 @ X2618 @ X2619 ) @ X2619 )
| ( subset @ X2618 @ X2619 )
| ~ ( in @ X2619 @ ( powerset @ X2617 ) )
| ~ ( in @ X2618 @ ( powerset @ X2617 ) ) )
& ( ( in @ ( esk86_3 @ X2621 @ X2622 @ X2623 ) @ X2621 )
| ( in @ X2622 @ ( powerset @ X2623 ) )
| ~ ( in @ X2623 @ ( powerset @ X2621 ) )
| ~ ( in @ X2622 @ ( powerset @ X2621 ) ) )
& ( ( in @ ( esk86_3 @ X2621 @ X2622 @ X2623 ) @ X2622 )
| ( in @ X2622 @ ( powerset @ X2623 ) )
| ~ ( in @ X2623 @ ( powerset @ X2621 ) )
| ~ ( in @ X2622 @ ( powerset @ X2621 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2621 @ X2622 @ X2623 ) @ X2623 )
| ( in @ X2622 @ ( powerset @ X2623 ) )
| ~ ( in @ X2623 @ ( powerset @ X2621 ) )
| ~ ( in @ X2622 @ ( powerset @ X2621 ) ) )
& ( ~ ( in @ X2626 @ ( powerset @ X2625 ) )
| ~ ( in @ X2627 @ ( powerset @ X2625 ) )
| ~ ( in @ X2628 @ X2625 )
| ~ ( in @ X2626 @ ( powerset @ X2627 ) )
| ~ ( in @ X2628 @ X2626 )
| ( in @ X2628 @ X2627 ) )
& ( ~ ( in @ X2630 @ ( powerset @ X2629 ) )
| ~ ( in @ X2631 @ X2629 )
| ~ ( in @ X2631 @ X2630 )
| ~ ( in @ X2631 @ ( setminus @ X2629 @ X2630 ) ) )
& ( ~ ( in @ X2633 @ ( powerset @ X2632 ) )
| ~ ( in @ X2634 @ X2632 )
| ( in @ X2634 @ ( setminus @ X2632 @ X2633 ) )
| ( in @ X2634 @ X2633 ) )
& ( ~ ( in @ X2636 @ ( powerset @ X2635 ) )
| ~ ( in @ X2637 @ ( powerset @ X2635 ) )
| ~ ( in @ X2638 @ X2635 )
| ( in @ X2638 @ X2636 )
| ~ ( in @ X2638 @ ( binintersect @ X2636 @ X2637 ) ) )
& ( ~ ( in @ X2640 @ ( powerset @ X2639 ) )
| ~ ( in @ X2641 @ ( powerset @ X2639 ) )
| ~ ( in @ X2642 @ X2639 )
| ( in @ X2642 @ X2641 )
| ~ ( in @ X2642 @ ( binintersect @ X2640 @ X2641 ) ) )
& ( ~ ( in @ X2644 @ ( powerset @ X2643 ) )
| ~ ( in @ X2645 @ ( powerset @ X2643 ) )
| ~ ( in @ X2646 @ X2643 )
| ~ ( subset @ X2644 @ ( setminus @ X2643 @ X2645 ) )
| ~ ( in @ X2646 @ X2645 )
| ~ ( in @ X2646 @ X2644 ) )
& ( ~ ( in @ X2648 @ ( powerset @ X2647 ) )
| ~ ( in @ X2649 @ ( powerset @ X2647 ) )
| ~ ( in @ X2650 @ X2647 )
| ~ ( subset @ X2648 @ X2649 )
| ( in @ X2650 @ X2649 )
| ~ ( in @ X2650 @ X2648 ) )
& ( ~ ( in @ X2652 @ ( powerset @ X2651 ) )
| ~ ( in @ X2653 @ ( powerset @ X2651 ) )
| ~ ( subset @ X2652 @ X2653 )
| ( subset @ ( setminus @ X2651 @ X2653 ) @ ( setminus @ X2651 @ X2652 ) ) )
& ( ~ ( in @ X2655 @ ( powerset @ X2654 ) )
| ~ ( in @ X2656 @ ( powerset @ X2654 ) )
| ~ ( subset @ ( setminus @ X2654 @ X2656 ) @ ( setminus @ X2654 @ X2655 ) )
| ( subset @ X2655 @ X2656 ) )
& ( ~ ( in @ X2658 @ ( powerset @ X2657 ) )
| ~ ( in @ X2659 @ X2657 )
| ~ ( in @ X2659 @ X2658 )
| ( in @ X2659 @ ( setminus @ X2657 @ ( setminus @ X2657 @ X2658 ) ) ) )
& ( ~ ( in @ X2661 @ ( powerset @ X2660 ) )
| ~ ( in @ X2662 @ X2660 )
| ~ ( in @ X2662 @ ( setminus @ X2660 @ ( setminus @ X2660 @ X2661 ) ) )
| ( in @ X2662 @ X2661 ) )
& ( ~ ( in @ X2664 @ ( powerset @ X2663 ) )
| ( subset @ X2664 @ ( setminus @ X2663 @ ( setminus @ X2663 @ X2664 ) ) ) )
& ( ~ ( in @ X2666 @ ( powerset @ X2665 ) )
| ( subset @ ( setminus @ X2665 @ ( setminus @ X2665 @ X2666 ) ) @ X2666 ) )
& ( ~ ( in @ X2668 @ ( powerset @ X2667 ) )
| ( X2668
= ( setminus @ X2667 @ ( setminus @ X2667 @ X2668 ) ) ) )
& ( ~ ( in @ X2670 @ ( powerset @ X2669 ) )
| ~ ( in @ X2671 @ ( powerset @ X2669 ) )
| ~ ( in @ X2672 @ X2669 )
| ~ ( in @ X2672 @ ( setminus @ X2669 @ X2670 ) )
| ~ ( in @ X2672 @ ( binintersect @ X2670 @ X2671 ) ) )
& ( ~ ( in @ X2674 @ ( powerset @ X2673 ) )
| ~ ( in @ X2675 @ ( powerset @ X2673 ) )
| ~ ( in @ X2676 @ X2673 )
| ~ ( in @ X2676 @ ( setminus @ X2673 @ X2674 ) )
| ( in @ X2676 @ ( setminus @ X2673 @ ( binintersect @ X2674 @ X2675 ) ) ) )
& ( ~ ( in @ X2678 @ ( powerset @ X2677 ) )
| ~ ( in @ X2679 @ ( powerset @ X2677 ) )
| ( subset @ ( setminus @ X2677 @ X2678 ) @ ( setminus @ X2677 @ ( binintersect @ X2678 @ X2679 ) ) ) )
& ( ~ ( in @ X2681 @ ( powerset @ X2680 ) )
| ~ ( in @ X2682 @ ( powerset @ X2680 ) )
| ( in @ ( setminus @ X2680 @ X2681 ) @ ( powerset @ ( setminus @ X2680 @ ( binintersect @ X2681 @ X2682 ) ) ) ) )
& ( ~ ( in @ X2684 @ ( powerset @ X2683 ) )
| ~ ( in @ X2685 @ ( powerset @ X2683 ) )
| ~ ( subset @ X2684 @ ( setminus @ X2683 @ X2685 ) )
| ~ ( in @ X2686 @ X2683 )
| ~ ( in @ X2686 @ X2685 )
| ( in @ X2686 @ ( setminus @ X2683 @ X2684 ) ) )
& ( ~ ( in @ X2688 @ ( powerset @ X2687 ) )
| ~ ( in @ X2689 @ ( powerset @ X2687 ) )
| ~ ( subset @ X2688 @ ( setminus @ X2687 @ X2689 ) )
| ( subset @ X2689 @ ( setminus @ X2687 @ X2688 ) ) )
& ( ~ ( in @ X2691 @ ( powerset @ X2690 ) )
| ~ ( in @ X2692 @ ( powerset @ X2690 ) )
| ~ ( in @ X2693 @ X2690 )
| ( in @ X2693 @ ( binunion @ X2691 @ X2692 ) )
| ~ ( in @ X2693 @ X2691 ) )
& ( ~ ( in @ X2695 @ ( powerset @ X2694 ) )
| ~ ( in @ X2696 @ ( powerset @ X2694 ) )
| ~ ( in @ X2697 @ X2694 )
| ( in @ X2697 @ ( binunion @ X2695 @ X2696 ) )
| ~ ( in @ X2697 @ X2696 ) )
& ( ~ ( in @ X2699 @ ( powerset @ X2698 ) )
| ~ ( in @ X2700 @ ( powerset @ X2698 ) )
| ~ ( in @ X2701 @ ( powerset @ X2698 ) )
| ~ ( in @ X2702 @ X2698 )
| ~ ( in @ X2702 @ ( binintersect @ X2699 @ X2700 ) )
| ( in @ X2702 @ ( binunion @ X2699 @ X2701 ) ) )
& ( ~ ( in @ X2704 @ ( powerset @ X2703 ) )
| ~ ( in @ X2705 @ ( powerset @ X2703 ) )
| ~ ( in @ X2706 @ ( powerset @ X2703 ) )
| ~ ( in @ X2707 @ X2703 )
| ~ ( in @ X2707 @ ( binintersect @ X2704 @ X2705 ) )
| ( in @ X2707 @ ( binunion @ X2705 @ X2706 ) ) )
& ( ~ ( in @ X2709 @ ( powerset @ X2708 ) )
| ~ ( in @ X2710 @ ( powerset @ X2708 ) )
| ~ ( in @ X2711 @ ( powerset @ X2708 ) )
| ~ ( in @ X2712 @ X2708 )
| ~ ( in @ X2712 @ ( binintersect @ X2709 @ X2710 ) )
| ( in @ X2712 @ ( binintersect @ ( binunion @ X2709 @ X2711 ) @ ( binunion @ X2710 @ X2711 ) ) ) )
& ( ~ ( in @ X2714 @ ( powerset @ X2713 ) )
| ~ ( in @ X2715 @ ( powerset @ X2713 ) )
| ~ ( in @ X2716 @ ( powerset @ X2713 ) )
| ( in @ ( binintersect @ X2714 @ X2715 ) @ ( powerset @ ( binintersect @ ( binunion @ X2714 @ X2716 ) @ ( binunion @ X2715 @ X2716 ) ) ) ) )
& ( ~ ( in @ X2718 @ ( powerset @ X2717 ) )
| ~ ( in @ X2719 @ ( powerset @ X2717 ) )
| ~ ( in @ X2720 @ X2717 )
| ~ ( in @ X2720 @ ( setminus @ X2717 @ ( binunion @ X2718 @ X2719 ) ) )
| ~ ( in @ X2720 @ X2718 ) )
& ( ~ ( in @ X2722 @ ( powerset @ X2721 ) )
| ~ ( in @ X2723 @ ( powerset @ X2721 ) )
| ~ ( in @ X2724 @ X2721 )
| ~ ( in @ X2724 @ ( setminus @ X2721 @ ( binunion @ X2722 @ X2723 ) ) )
| ( in @ X2724 @ ( setminus @ X2721 @ X2722 ) ) )
& ( ( in @ X2729 @ X2727 )
| X2728
| ( in @ X2729 @ X2726 )
| ~ ( in @ X2729 @ ( binunion @ X2726 @ X2727 ) )
| ~ ( in @ X2729 @ X2725 )
| ~ ( in @ X2727 @ ( powerset @ X2725 ) )
| ~ ( in @ X2726 @ ( powerset @ X2725 ) ) )
& ( ~ X2728
| X2728
| ( in @ X2729 @ X2726 )
| ~ ( in @ X2729 @ ( binunion @ X2726 @ X2727 ) )
| ~ ( in @ X2729 @ X2725 )
| ~ ( in @ X2727 @ ( powerset @ X2725 ) )
| ~ ( in @ X2726 @ ( powerset @ X2725 ) ) )
& ( ( in @ X2729 @ X2727 )
| X2728
| ~ X2728
| ~ ( in @ X2729 @ ( binunion @ X2726 @ X2727 ) )
| ~ ( in @ X2729 @ X2725 )
| ~ ( in @ X2727 @ ( powerset @ X2725 ) )
| ~ ( in @ X2726 @ ( powerset @ X2725 ) ) )
& ( ~ X2728
| X2728
| ~ X2728
| ~ ( in @ X2729 @ ( binunion @ X2726 @ X2727 ) )
| ~ ( in @ X2729 @ X2725 )
| ~ ( in @ X2727 @ ( powerset @ X2725 ) )
| ~ ( in @ X2726 @ ( powerset @ X2725 ) ) )
& ( ~ ( in @ X2731 @ ( powerset @ X2730 ) )
| ~ ( in @ X2732 @ ( powerset @ X2730 ) )
| ~ ( in @ X2733 @ X2730 )
| ( in @ X2733 @ X2731 )
| ( in @ X2733 @ X2732 )
| ~ ( in @ X2733 @ ( binunion @ X2731 @ X2732 ) ) )
& ( ~ ( in @ X2735 @ ( powerset @ X2734 ) )
| ~ ( in @ X2736 @ ( powerset @ X2734 ) )
| ~ ( in @ X2737 @ X2734 )
| ~ ( in @ X2737 @ ( setminus @ X2734 @ ( binunion @ X2735 @ X2736 ) ) )
| ( in @ X2737 @ ( setminus @ X2734 @ X2735 ) ) )
& ( ~ ( in @ X2739 @ ( powerset @ X2738 ) )
| ~ ( in @ X2740 @ ( powerset @ X2738 ) )
| ( in @ ( setminus @ X2738 @ ( binunion @ X2739 @ X2740 ) ) @ ( powerset @ ( setminus @ X2738 @ X2739 ) ) ) )
& ( ~ ( in @ X2742 @ ( powerset @ X2741 ) )
| ~ ( in @ X2743 @ ( powerset @ X2741 ) )
| ~ ( in @ X2744 @ X2741 )
| ~ ( in @ X2744 @ ( setminus @ X2741 @ ( binunion @ X2742 @ X2743 ) ) )
| ( in @ X2744 @ ( setminus @ X2741 @ X2743 ) ) )
& ( ~ ( in @ X2746 @ ( powerset @ X2745 ) )
| ~ ( in @ X2747 @ ( powerset @ X2745 ) )
| ~ ( in @ X2748 @ X2745 )
| ~ ( in @ X2748 @ ( setminus @ X2745 @ ( binintersect @ X2746 @ X2747 ) ) )
| ( in @ X2748 @ ( binunion @ ( setminus @ X2745 @ X2746 ) @ ( setminus @ X2745 @ X2747 ) ) ) )
& ( ~ ( in @ X2750 @ ( powerset @ X2749 ) )
| ~ ( in @ X2751 @ ( powerset @ X2749 ) )
| ~ ( in @ X2752 @ X2749 )
| ~ ( in @ X2752 @ ( binunion @ ( setminus @ X2749 @ X2750 ) @ ( setminus @ X2749 @ X2751 ) ) )
| ( in @ X2752 @ ( setminus @ X2749 @ ( binintersect @ X2750 @ X2751 ) ) ) )
& ( ~ ( in @ X2754 @ ( powerset @ X2753 ) )
| ~ ( in @ X2755 @ ( powerset @ X2753 ) )
| ( ( setminus @ X2753 @ ( binintersect @ X2754 @ X2755 ) )
= ( binunion @ ( setminus @ X2753 @ X2754 ) @ ( setminus @ X2753 @ X2755 ) ) ) )
& ( ~ ( in @ X2757 @ ( powerset @ X2756 ) )
| ~ ( in @ X2758 @ ( powerset @ X2756 ) )
| ~ ( in @ X2759 @ X2756 )
| ~ ( in @ X2759 @ ( setminus @ X2756 @ ( binunion @ X2757 @ X2758 ) ) )
| ( in @ X2759 @ ( binintersect @ ( setminus @ X2756 @ X2757 ) @ ( setminus @ X2756 @ X2758 ) ) ) )
& ( ~ ( in @ X2761 @ ( powerset @ X2760 ) )
| ~ ( in @ X2762 @ ( powerset @ X2760 ) )
| ~ ( in @ X2763 @ X2760 )
| ~ ( in @ X2763 @ ( setminus @ X2760 @ X2761 ) )
| ~ ( in @ X2763 @ ( setminus @ X2760 @ X2762 ) )
| ( in @ X2763 @ ( setminus @ X2760 @ ( binunion @ X2761 @ X2762 ) ) ) )
& ( ~ ( in @ X2765 @ ( powerset @ X2764 ) )
| ~ ( in @ X2766 @ ( powerset @ X2764 ) )
| ~ ( in @ X2767 @ X2764 )
| ~ ( in @ X2767 @ ( binintersect @ ( setminus @ X2764 @ X2765 ) @ ( setminus @ X2764 @ X2766 ) ) )
| ( in @ X2767 @ ( setminus @ X2764 @ ( binunion @ X2765 @ X2766 ) ) ) )
& ( ~ ( in @ X2769 @ ( powerset @ X2768 ) )
| ~ ( in @ X2770 @ ( powerset @ X2768 ) )
| ( ( setminus @ X2768 @ ( binunion @ X2769 @ X2770 ) )
= ( binintersect @ ( setminus @ X2768 @ X2769 ) @ ( setminus @ X2768 @ X2770 ) ) ) )
& ( ~ ( in @ X2772 @ ( powerset @ X2771 ) )
| ~ ( in @ X2773 @ ( powerset @ X2771 ) )
| ~ ( in @ X2774 @ ( binintersect @ X2772 @ X2773 ) )
| ( in @ X2774 @ X2771 ) )
& ( ~ ( in @ X2776 @ ( powerset @ X2775 ) )
| ~ ( in @ X2777 @ ( powerset @ X2775 ) )
| ~ ( in @ X2778 @ ( powerset @ X2775 ) )
| ~ ( subset @ X2776 @ X2778 )
| ( subset @ ( binintersect @ X2776 @ X2777 ) @ X2778 ) )
& ( ~ ( in @ X2780 @ ( powerset @ X2779 ) )
| ~ ( in @ X2781 @ ( powerset @ X2779 ) )
| ~ ( in @ X2782 @ ( powerset @ X2779 ) )
| ~ ( subset @ X2781 @ X2782 )
| ( subset @ ( binintersect @ X2780 @ X2781 ) @ X2782 ) )
& ( ~ ( in @ X2784 @ ( powerset @ X2783 ) )
| ~ ( in @ X2785 @ ( powerset @ X2783 ) )
| ~ ( in @ X2786 @ ( powerset @ X2783 ) )
| ~ ( subset @ X2784 @ X2785 )
| ~ ( subset @ X2784 @ X2786 )
| ( subset @ X2784 @ ( binintersect @ X2785 @ X2786 ) ) )
& ( in @ esk88_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk89_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk90_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk91_0 @ ( powerset @ esk87_0 ) )
& ( subset @ esk88_0 @ esk90_0 )
& ( subset @ esk89_0 @ esk91_0 )
& ~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( binintersect @ esk90_0 @ esk91_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_364])])])])])])]) ).
thf(c_0_366,negated_conjecture,
~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( binintersect @ esk90_0 @ esk91_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_367,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( binintersect @ X3 @ X4 ) )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_368,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ X4 )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_369,negated_conjecture,
subset @ esk89_0 @ esk91_0,
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_370,negated_conjecture,
( ~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ esk91_0 )
| ~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ esk90_0 ) ),
inference(spm,[status(thm)],[c_0_366,c_0_367]) ).
thf(c_0_371,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk91_0 )
| ~ ( subset @ X2 @ esk89_0 ) ),
inference(spm,[status(thm)],[c_0_368,c_0_369]) ).
thf(c_0_372,negated_conjecture,
! [X2: $i,X3: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_373,negated_conjecture,
subset @ esk88_0 @ esk90_0,
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_374,negated_conjecture,
~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ esk90_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_370,c_0_371]),c_0_372])]) ).
thf(c_0_375,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk90_0 )
| ~ ( subset @ X2 @ esk88_0 ) ),
inference(spm,[status(thm)],[c_0_368,c_0_373]) ).
thf(c_0_376,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
thf(c_0_377,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_374,c_0_375]),c_0_376])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU762^1 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.10 % Command : run_E %s %d THM
% 0.09/0.31 % Computer : n024.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Sun May 19 16:42:08 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.16/0.41 Running higher-order theorem proving
% 0.16/0.41 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
% 6.54/1.34 # Version: 3.1.0-ho
% 6.54/1.34 # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.54/1.34 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.54/1.34 # Starting ehoh_best5 with 300s (1) cores
% 6.54/1.34 # Starting almost_fo_3_lam with 300s (1) cores
% 6.54/1.34 # Starting new_bool_5 with 300s (1) cores
% 6.54/1.34 # Starting pre_casc_3 with 300s (1) cores
% 6.54/1.34 # Starting ho_unfolding_8 with 300s (1) cores
% 6.54/1.34 # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.54/1.34 # Starting new_bool_3 with 300s (1) cores
% 6.54/1.34 # Starting new_ho_5 with 300s (1) cores
% 6.54/1.34 # new_ho_5 with pid 5076 completed with status 8
% 6.54/1.34 # new_ho_10_cnf2 with pid 5074 completed with status 0
% 6.54/1.34 # Result found by new_ho_10_cnf2
% 6.54/1.34 # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.54/1.34 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.54/1.34 # Starting ehoh_best5 with 300s (1) cores
% 6.54/1.34 # Starting almost_fo_3_lam with 300s (1) cores
% 6.54/1.34 # Starting new_bool_5 with 300s (1) cores
% 6.54/1.34 # Starting pre_casc_3 with 300s (1) cores
% 6.54/1.34 # Starting ho_unfolding_8 with 300s (1) cores
% 6.54/1.34 # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.54/1.34 # No SInE strategy applied
% 6.54/1.34 # Search class: HGHSM-FSLM32-MHFMMSBN
% 6.54/1.34 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.54/1.34 # Starting ho_unfolding_8 with 61s (1) cores
% 6.54/1.34 # ho_unfolding_8 with pid 5088 completed with status 0
% 6.54/1.34 # Result found by ho_unfolding_8
% 6.54/1.34 # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.54/1.34 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.54/1.34 # Starting ehoh_best5 with 300s (1) cores
% 6.54/1.34 # Starting almost_fo_3_lam with 300s (1) cores
% 6.54/1.34 # Starting new_bool_5 with 300s (1) cores
% 6.54/1.34 # Starting pre_casc_3 with 300s (1) cores
% 6.54/1.34 # Starting ho_unfolding_8 with 300s (1) cores
% 6.54/1.34 # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.54/1.34 # No SInE strategy applied
% 6.54/1.34 # Search class: HGHSM-FSLM32-MHFMMSBN
% 6.54/1.34 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.54/1.34 # Starting ho_unfolding_8 with 61s (1) cores
% 6.54/1.34 # Preprocessing time : 0.073 s
% 6.54/1.34 # Presaturation interreduction done
% 6.54/1.34
% 6.54/1.34 # Proof found!
% 6.54/1.34 # SZS status Theorem
% 6.54/1.34 # SZS output start CNFRefutation
% See solution above
% 6.54/1.34 # Parsed axioms : 599
% 6.54/1.34 # Removed by relevancy pruning/SinE : 0
% 6.54/1.34 # Initial clauses : 806
% 6.54/1.34 # Removed in clause preprocessing : 353
% 6.54/1.34 # Initial clauses in saturation : 453
% 6.54/1.34 # Processed clauses : 1254
% 6.54/1.34 # ...of these trivial : 11
% 6.54/1.34 # ...subsumed : 156
% 6.54/1.34 # ...remaining for further processing : 1087
% 6.54/1.34 # Other redundant clauses eliminated : 58
% 6.54/1.34 # Clauses deleted for lack of memory : 0
% 6.54/1.34 # Backward-subsumed : 29
% 6.54/1.34 # Backward-rewritten : 4
% 6.54/1.34 # Generated clauses : 18393
% 6.54/1.34 # ...of the previous two non-redundant : 17997
% 6.54/1.34 # ...aggressively subsumed : 0
% 6.54/1.34 # Contextual simplify-reflections : 14
% 6.54/1.34 # Paramodulations : 18292
% 6.54/1.34 # Factorizations : 2
% 6.54/1.34 # NegExts : 8
% 6.54/1.34 # Equation resolutions : 65
% 6.54/1.34 # Disequality decompositions : 0
% 6.54/1.34 # Total rewrite steps : 511
% 6.54/1.34 # ...of those cached : 356
% 6.54/1.34 # Propositional unsat checks : 0
% 6.54/1.34 # Propositional check models : 0
% 6.54/1.34 # Propositional check unsatisfiable : 0
% 6.54/1.34 # Propositional clauses : 0
% 6.54/1.34 # Propositional clauses after purity: 0
% 6.54/1.34 # Propositional unsat core size : 0
% 6.54/1.34 # Propositional preprocessing time : 0.000
% 6.54/1.34 # Propositional encoding time : 0.000
% 6.54/1.34 # Propositional solver time : 0.000
% 6.54/1.34 # Success case prop preproc time : 0.000
% 6.54/1.34 # Success case prop encoding time : 0.000
% 6.54/1.34 # Success case prop solver time : 0.000
% 6.54/1.34 # Current number of processed clauses : 638
% 6.54/1.34 # Positive orientable unit clauses : 50
% 6.54/1.34 # Positive unorientable unit clauses: 0
% 6.54/1.34 # Negative unit clauses : 37
% 6.54/1.34 # Non-unit-clauses : 551
% 6.54/1.34 # Current number of unprocessed clauses: 17521
% 6.54/1.34 # ...number of literals in the above : 77548
% 6.54/1.34 # Current number of archived formulas : 0
% 6.54/1.34 # Current number of archived clauses : 431
% 6.54/1.34 # Clause-clause subsumption calls (NU) : 67009
% 6.54/1.34 # Rec. Clause-clause subsumption calls : 25814
% 6.54/1.34 # Non-unit clause-clause subsumptions : 124
% 6.54/1.34 # Unit Clause-clause subsumption calls : 1196
% 6.54/1.34 # Rewrite failures with RHS unbound : 0
% 6.54/1.34 # BW rewrite match attempts : 47
% 6.54/1.34 # BW rewrite match successes : 4
% 6.54/1.34 # Condensation attempts : 0
% 6.54/1.34 # Condensation successes : 0
% 6.54/1.34 # Termbank termtop insertions : 434442
% 6.54/1.34 # Search garbage collected termcells : 29901
% 6.54/1.34
% 6.54/1.34 # -------------------------------------------------
% 6.54/1.34 # User time : 0.834 s
% 6.54/1.34 # System time : 0.037 s
% 6.54/1.34 # Total time : 0.871 s
% 6.54/1.34 # Maximum resident set size: 9064 pages
% 6.54/1.34
% 6.54/1.34 # -------------------------------------------------
% 6.54/1.34 # User time : 0.954 s
% 6.54/1.34 # System time : 0.087 s
% 6.54/1.34 # Total time : 1.041 s
% 6.54/1.34 # Maximum resident set size: 2748 pages
% 6.54/1.35 % E---3.1 exiting
% 6.54/1.35 % E exiting
%------------------------------------------------------------------------------