%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU734^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:38 EDT 2024
% Result : Theorem 2.56s 1.05s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 605
% Syntax : Number of formulae : 666 ( 6 unt; 354 typ; 0 def)
% Number of atoms : 3083 ( 457 equ; 0 cnn)
% Maximal formula atoms : 971 ( 9 avg)
% Number of connectives : 11780 ( 751 ~; 765 |; 488 &;7919 @)
% ( 337 <=>;1520 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1075 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 358 ( 354 usr; 259 con; 0-4 aty)
% Number of variables : 2591 ( 156 ^2355 !; 80 ?;2591 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
epred1_0: $o ).
thf(decl_311,type,
esk1_2: $i > $i > $i ).
thf(decl_312,type,
esk2_2: $i > $i > $i ).
thf(decl_313,type,
esk3_2: $i > $i > $i ).
thf(decl_314,type,
esk4_1: $i > $i ).
thf(decl_315,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_316,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_317,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_318,type,
esk8_1: $i > $i ).
thf(decl_319,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_320,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_321,type,
esk11_2: $i > $i > $i ).
thf(decl_322,type,
esk12_2: $i > $i > $i ).
thf(decl_323,type,
esk13_1: $i > $i ).
thf(decl_324,type,
esk14_1: $i > $i ).
thf(decl_325,type,
esk15_1: $i > $i ).
thf(decl_326,type,
esk16_2: $i > $i > $i ).
thf(decl_327,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_328,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_329,type,
esk19_1: $i > $i ).
thf(decl_330,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_331,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_332,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_333,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_334,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_335,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_336,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_337,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_338,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_339,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_340,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_341,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_342,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_343,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_344,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_345,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_346,type,
esk36_2: $i > $i > $i ).
thf(decl_347,type,
esk37_2: $i > $i > $i ).
thf(decl_348,type,
esk38_2: $i > $i > $i ).
thf(decl_349,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_350,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_351,type,
esk41_2: $i > $i > $i ).
thf(decl_352,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_354,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_355,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_356,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_357,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_358,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_359,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_360,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_361,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_364,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_366,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_367,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_368,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_369,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_370,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_371,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_372,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_373,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_374,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_375,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_376,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_377,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_378,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_379,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_380,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_381,type,
esk71_0: $i ).
thf(decl_382,type,
esk72_0: $i ).
thf(decl_383,type,
esk73_0: $i ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(complementSubsetComplementIntersect,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
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_250,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_251,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_252,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_253,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_254,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_255,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_256,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_257,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_258,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_259,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_260,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_261,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_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,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_292,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_293,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_294,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_295,plain,
( 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_296,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_297,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_298,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_299,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_300,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_301,plain,
( epred1_0
<=> ! [X852: $i] :
? [X853: $i] :
( ! [X854: $i] :
( ( in @ X854 @ X853 )
=> ! [X855: $i] :
( ( in @ X855 @ X854 )
=> ( in @ X855 @ X852 ) ) )
& ! [X856: $i,X857: $i] :
( ( ( in @ X856 @ X852 )
& ( in @ X857 @ X852 ) )
=> ( ! [X858: $i] :
( ( in @ X858 @ X853 )
=> ( ( in @ X856 @ X858 )
<=> ( in @ X857 @ X858 ) ) )
=> ( X856 = X857 ) ) )
& ! [X859: $i,X860: $i] :
( ( ( in @ X859 @ X853 )
& ( in @ X860 @ X853 ) )
=> ( ! [X861: $i] :
( ( in @ X861 @ X859 )
=> ( in @ X861 @ X860 ) )
| ! [X862: $i] :
( ( in @ X862 @ X860 )
=> ( in @ X862 @ X859 ) ) ) )
& ! [X863: $i] :
( ( ! [X864: $i] :
( ( in @ X864 @ X863 )
=> ( in @ X864 @ X852 ) )
& ? [X865: $i] : ( in @ X865 @ X863 ) )
=> ? [X866: $i,X867: $i] :
( ( in @ X866 @ X853 )
& ( in @ X867 @ X863 )
& ~ ? [X868: $i] :
( ( in @ X868 @ X866 )
& ( in @ X868 @ X863 ) )
& ! [X869: $i] :
( ( in @ X869 @ X853 )
=> ( ! [X870: $i] :
( ( in @ X870 @ X869 )
=> ( in @ X870 @ X866 ) )
| ( in @ X867 @ X869 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_302,negated_conjecture,
~ ( ! [X825: $i,X826: $i] :
( ! [X827: $i] :
( ( in @ X827 @ X825 )
<=> ( in @ X827 @ X826 ) )
=> ( X825 = X826 ) )
=> ( ! [X828: $i] :
~ ( in @ X828 @ emptyset )
=> ( ! [X829: $i,X830: $i,X831: $i] :
( ( in @ X831 @ ( setadjoin @ X829 @ X830 ) )
<=> ( ( X831 = X829 )
| ( in @ X831 @ X830 ) ) )
=> ( ! [X832: $i,X833: $i] :
( ( in @ X833 @ ( powerset @ X832 ) )
<=> ! [X834: $i] :
( ( in @ X834 @ X833 )
=> ( in @ X834 @ X832 ) ) )
=> ( ! [X835: $i,X836: $i] :
( ( in @ X836 @ ( setunion @ X835 ) )
<=> ? [X837: $i] :
( ( in @ X836 @ X837 )
& ( in @ X837 @ X835 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X838: $i] :
( ( in @ X838 @ omega )
=> ( in @ ( setadjoin @ X838 @ X838 ) @ omega ) )
=> ( ! [X839: $i] :
( ( ( in @ emptyset @ X839 )
& ! [X840: $i] :
( ( ( in @ X840 @ omega )
& ( in @ X840 @ X839 ) )
=> ( in @ ( setadjoin @ X840 @ X840 ) @ X839 ) ) )
=> ! [X841: $i] :
( ( in @ X841 @ omega )
=> ( in @ X841 @ X839 ) ) )
=> ( ! [X842: $i > $i > $o,X843: $i] :
( ! [X844: $i] :
( ( in @ X844 @ X843 )
=> ( exu @ ( X842 @ X844 ) ) )
=> ? [X845: $i] :
! [X846: $i] :
( ( in @ X846 @ X845 )
<=> ? [X847: $i] :
( ( in @ X847 @ X843 )
& ( X842 @ X847 @ X846 ) ) ) )
=> ( ! [X848: $i] :
( ? [X849: $i] : ( in @ X849 @ X848 )
=> ? [X850: $i] :
( ( in @ X850 @ X848 )
& ~ ? [X851: $i] :
( ( in @ X851 @ X850 )
& ( in @ X851 @ X848 ) ) ) )
=> ( epred1_0
=> ( ! [X871: $i > $o] :
( ( exu @ X871 )
=> ( X871
@ ( descr
@ ^ [Z0: $i] : ( X871 @ Z0 ) ) ) )
=> ( ! [X872: $i,X873: $i > $o,X874: $i] :
( ( in @ X874 @ X872 )
=> ( ( X873 @ X874 )
=> ( in @ X874 @ ( dsetconstr @ X872 @ X873 ) ) ) )
=> ( ! [X875: $i,X876: $i > $o,X877: $i] :
( ( in @ X877 @ ( dsetconstr @ X875 @ X876 ) )
=> ( in @ X877 @ X875 ) )
=> ( ! [X878: $i,X879: $i > $o,X880: $i] :
( ( in @ X880 @ ( dsetconstr @ X878 @ X879 ) )
=> ( X879 @ X880 ) )
=> ( ! [X881: $i > $o] :
( ( exu @ X881 )
=> ? [X882: $i] :
( ( X881 @ X882 )
& ! [X883: $i] :
( ( X881 @ X883 )
=> ( X882 = X883 ) ) ) )
=> ( ! [X884: $o,X885: $i] :
( ( in @ X885 @ ( prop2set @ X884 ) )
=> X884 )
=> ( ! [X886: $i] :
( ( in @ X886 @ emptyset )
=> ! [X887: $o] : X887 )
=> ( ! [X888: $i] :
( ( in @ X888 @ emptyset )
=> ~ $true )
=> ( ! [X889: $i] :
~ ( in @ X889 @ emptyset )
=> ( ! [X890: $i > $o] :
( ( exu @ X890 )
=> ? [X891: $i] : ( X890 @ X891 ) )
=> ( ! [X892: $i,X893: $i] :
( ! [X894: $i] :
( ( in @ X894 @ X892 )
=> ( in @ X894 @ X893 ) )
=> ( ! [X895: $i] :
( ( in @ X895 @ X893 )
=> ( in @ X895 @ X892 ) )
=> ( X892 = X893 ) ) )
=> ( ! [X896: $i] :
( ! [X897: $i] :
~ ( in @ X897 @ X896 )
=> ( X896 = emptyset ) )
=> ( ! [X898: $i] :
( ! [X899: $i] :
~ ( in @ X899 @ X898 )
=> ( X898 = emptyset ) )
=> ( ! [X900: $i,X901: $i > $o,X902: $i] :
( ( in @ X902 @ X900 )
=> ( ( in @ X902 @ ( dsetconstr @ X900 @ X901 ) )
<=> ( X901 @ X902 ) ) )
=> ( ! [X903: $i] :
( ( nonempty @ X903 )
=> ? [X904: $i] : ( in @ X904 @ X903 ) )
=> ( ! [X905: $i,X906: $i > $o,X907: $i] :
( ( in @ X907 @ X905 )
=> ( ( X906 @ X907 )
=> ( nonempty @ ( dsetconstr @ X905 @ X906 ) ) ) )
=> ( ! [X908: $i] :
( ? [X909: $i] : ( in @ X909 @ X908 )
=> ( nonempty @ X908 ) )
=> ( ! [X910: $i,X911: $i] : ( in @ X910 @ ( setadjoin @ X910 @ X911 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X912: $i,X913: $i,X914: $i] :
( ( in @ X914 @ X913 )
=> ( in @ X914 @ ( setadjoin @ X912 @ X913 ) ) )
=> ( ! [X915: $i,X916: $i,X917: $i] :
( ( in @ X917 @ ( setadjoin @ X915 @ X916 ) )
=> ! [X918: $o] :
( ( ( X917 = X915 )
=> X918 )
=> ( ( ( in @ X917 @ X916 )
=> X918 )
=> X918 ) ) )
=> ( ! [X919: $i,X920: $i,X921: $i] :
( ( in @ X921 @ ( setadjoin @ X919 @ X920 ) )
=> ( ( X921 = X919 )
| ( in @ X921 @ X920 ) ) )
=> ( ! [X922: $i] :
( ( dsetconstr @ X922
@ ^ [Z0: $i] : $true )
= X922 )
=> ( ! [X923: $i,X924: $i] :
( ! [X925: $i] :
( ( in @ X925 @ X924 )
=> ( in @ X925 @ X923 ) )
=> ( in @ X924 @ ( powerset @ X923 ) ) )
=> ( ! [X926: $i] : ( in @ emptyset @ ( powerset @ X926 ) )
=> ( ! [X927: $i] : ( in @ emptyset @ ( powerset @ X927 ) )
=> ( ! [X928: $i,X929: $i,X930: $i] :
( ( in @ X929 @ ( powerset @ X928 ) )
=> ( ( in @ X930 @ X929 )
=> ( in @ X930 @ X928 ) ) )
=> ( ! [X931: $i,X932: $i,X933: $i] :
( ( in @ X932 @ X933 )
=> ( ( in @ X933 @ X931 )
=> ( in @ X932 @ ( setunion @ X931 ) ) ) )
=> ( ! [X934: $i,X935: $i] :
( ( in @ X935 @ ( setunion @ X934 ) )
=> ! [X936: $o] :
( ! [X937: $i] :
( ( in @ X935 @ X937 )
=> ( ( in @ X937 @ X934 )
=> X936 ) )
=> X936 ) )
=> ( ! [X938: $i,X939: $i] :
( ( in @ X939 @ X938 )
=> ( in @ X939 @ ( powerset @ ( setunion @ X938 ) ) ) )
=> ( ! [X940: $i > $o] :
( ( exu @ X940 )
=> ? [X941: $i] :
! [X942: $i] :
( ( X940 @ X942 )
<=> ( X942 = X941 ) ) )
=> ( ! [X943: $i] :
( ( nonempty @ X943 )
=> ? [X944: $i] :
( ( in @ X944 @ X943 )
& $true ) )
=> ( ! [X945: $i,X946: $i] :
( ( in @ X945 @ ( setadjoin @ X946 @ emptyset ) )
=> ( X945 = X946 ) )
=> ( ! [X947: $i,X948: $i] :
( ( X947 != X948 )
=> ~ ( in @ X948 @ ( setadjoin @ X947 @ emptyset ) ) )
=> ( ! [X949: $i,X950: $i] :
( ( X949 = X950 )
=> ( in @ X949 @ ( setadjoin @ X950 @ emptyset ) ) )
=> ( ! [X951: $i,X952: $i] :
( ( in @ X951 @ ( setadjoin @ X952 @ emptyset ) )
=> ( in @ X952 @ ( setadjoin @ X951 @ emptyset ) ) )
=> ( ! [X953: $i,X954: $i,X955: $i] :
( ( in @ X955 @ ( setadjoin @ X953 @ ( setadjoin @ X954 @ emptyset ) ) )
=> ( ( X955 = X953 )
| ( X955 = X954 ) ) )
=> ( ! [X956: $i,X957: $i] : ( in @ X956 @ ( setadjoin @ X956 @ ( setadjoin @ X957 @ emptyset ) ) )
=> ( ! [X958: $i,X959: $i] : ( in @ X959 @ ( setadjoin @ X958 @ ( setadjoin @ X959 @ emptyset ) ) )
=> ( ! [X960: $i,X961: $i > $o] :
( ? [X962: $i] :
( ( in @ X962 @ X960 )
& ( X961 @ X962 ) )
=> ( ( ( dsetconstr @ X960 @ X961 )
= emptyset )
=> ~ $true ) )
=> ( ! [X963: $i > $o,X964: $i] :
( ( in @ X964 @ emptyset )
=> ( X963 @ X964 ) )
=> ( ! [X965: $i,X966: $i > $o] :
( ~ ! [X967: $i] :
( ( in @ X967 @ X965 )
=> ( X966 @ X967 ) )
=> ? [X968: $i] :
( ( in @ X968 @ X965 )
& ~ ( X966 @ X968 ) ) )
=> ( ! [X969: $i,X970: $i > $o] :
( ! [X971: $i] :
( ( in @ X971 @ X969 )
=> ~ ( X970 @ X971 ) )
=> ~ ? [X972: $i] :
( ( in @ X972 @ X969 )
& ( X970 @ X972 ) ) )
=> ( ! [X973: $i,X974: $i > $o] :
( ~ ? [X975: $i] :
( ( in @ X975 @ X973 )
& ( X974 @ X975 ) )
=> ! [X976: $i] :
( ( in @ X976 @ X973 )
=> ~ ( X974 @ X976 ) ) )
=> ( ! [X977: $i,X978: $i > $o] :
( ? [X979: $i] :
( ( in @ X979 @ X977 )
& ~ ( X978 @ X979 ) )
=> ~ ! [X980: $i] :
( ( in @ X980 @ X977 )
=> ( X978 @ X980 ) ) )
=> ( ! [X981: $o] :
( X981
=> ( in @ emptyset @ ( prop2set @ X981 ) ) )
=> ( prop2set2propI
=> ( ! [X982: $i,X983: $i > $o] :
( ~ ? [X984: $i] :
( ( in @ X984 @ X982 )
& ( X983 @ X984 ) )
=> ! [X985: $i] :
( ( in @ X985 @ X982 )
=> ~ ( X983 @ X985 ) ) )
=> ( ! [X986: $i,X987: $i > $o] :
( ~ ! [X988: $i] :
( ( in @ X988 @ X986 )
=> ( X987 @ X988 ) )
=> ? [X989: $i] :
( ( in @ X989 @ X986 )
& ~ ( X987 @ X989 ) ) )
=> ( ! [X990: $i > $o] :
( ? [X991: $i] :
( ( X990 @ X991 )
& ! [X992: $i] :
( ( X990 @ X992 )
=> ( X991 = X992 ) ) )
=> ( exu @ X990 ) )
=> ( ! [X993: $i > $o] :
( ? [X994: $i] : ( X993 @ X994 )
=> ( ! [X995: $i,X996: $i] :
( ( X993 @ X995 )
=> ( ( X993 @ X996 )
=> ( X995 = X996 ) ) )
=> ( exu @ X993 ) ) )
=> ( ! [X997: $i > $o] :
( ? [X998: $i] :
! [X999: $i] :
( ( X997 @ X999 )
<=> ( X999 = X998 ) )
=> ( exu @ X997 ) )
=> ( ! [X1000: $i,X1001: $i] :
( ( X1000 = X1001 )
=> ! [X1002: $i,X1003: $i] :
( ( X1002 = X1003 )
=> ( ( in @ X1002 @ X1000 )
=> ( in @ X1003 @ X1001 ) ) ) )
=> ( ! [X1004: $i,X1005: $i] :
( ( X1004 = X1005 )
=> ! [X1006: $i,X1007: $i] :
( ( X1006 = X1007 )
=> ( ( in @ X1006 @ X1004 )
<=> ( in @ X1007 @ X1005 ) ) ) )
=> ( ! [X1008: $i > $o] :
( ( exu @ X1008 )
=> ! [X1009: $i,X1010: $i] :
( ( X1008 @ X1009 )
=> ( ( X1008 @ X1010 )
=> ( X1009 = X1010 ) ) ) )
=> ( ! [X1011: $i > $o,X1012: $i > $o] :
( ! [X1013: $i,X1014: $i] :
( ( X1013 = X1014 )
=> ( ( X1011 @ X1013 )
<=> ( X1012 @ X1014 ) ) )
=> ( ( exu @ X1011 )
<=> ( exu @ X1012 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1015: $i,X1016: $i] :
( ( X1015 = X1016 )
=> ! [X1017: $i,X1018: $i] :
( ( X1017 = X1018 )
=> ( ( setadjoin @ X1015 @ X1017 )
= ( setadjoin @ X1016 @ X1018 ) ) ) )
=> ( ! [X1019: $i,X1020: $i] :
( ( X1019 = X1020 )
=> ( ( powerset @ X1019 )
= ( powerset @ X1020 ) ) )
=> ( ! [X1021: $i,X1022: $i] :
( ( X1021 = X1022 )
=> ( ( setunion @ X1021 )
= ( setunion @ X1022 ) ) )
=> ( ( omega = omega )
=> ( ! [X1023: $i > $o] :
( ( exu @ X1023 )
=> ! [X1024: $i,X1025: $i] :
( ( X1023 @ X1024 )
=> ( ( X1023 @ X1025 )
=> ( X1024 = X1025 ) ) ) )
=> ( ! [X1026: $i > $o,X1027: $i > $o] :
( ! [X1028: $i,X1029: $i] :
( ( X1028 = X1029 )
=> ( ( X1026 @ X1028 )
<=> ( X1027 @ X1029 ) ) )
=> ( ( exu @ X1026 )
=> ( ( exu @ X1027 )
=> ( ( descr @ X1026 )
= ( descr @ X1027 ) ) ) ) )
=> ( ! [X1030: $i,X1031: $i] :
( ( X1030 = X1031 )
=> ! [X1032: $i > $o,X1033: $i > $o] :
( ! [X1034: $i] :
( ( in @ X1034 @ X1030 )
=> ! [X1035: $i] :
( ( in @ X1035 @ X1031 )
=> ( ( X1034 = X1035 )
=> ( ( X1032 @ X1034 )
<=> ( X1033 @ X1035 ) ) ) ) )
=> ( ( dsetconstr @ X1030 @ X1032 )
= ( dsetconstr @ X1031 @ X1033 ) ) ) )
=> ( ! [X1036: $i,X1037: $i] :
( ! [X1038: $i] :
( ( in @ X1038 @ X1036 )
=> ( in @ X1038 @ X1037 ) )
=> ( subset @ X1036 @ X1037 ) )
=> ( ! [X1039: $i,X1040: $i] :
( ( X1039 = X1040 )
=> ( subset @ X1040 @ X1039 ) )
=> ( ! [X1041: $i,X1042: $i] :
( ( X1041 = X1042 )
=> ( subset @ X1041 @ X1042 ) )
=> ( ! [X1043: $i,X1044: $i] :
( ! [X1045: $i] :
( ( in @ X1045 @ X1043 )
=> ( in @ X1045 @ X1044 ) )
=> ( subset @ X1043 @ X1044 ) )
=> ( ! [X1046: $i] : ( subset @ emptyset @ X1046 )
=> ( ! [X1047: $i,X1048: $i,X1049: $i] :
( ( subset @ X1047 @ X1048 )
=> ( ( in @ X1049 @ X1047 )
=> ( in @ X1049 @ X1048 ) ) )
=> ( ! [X1050: $i,X1051: $i,X1052: $i] :
( ( subset @ X1050 @ X1051 )
=> ( ~ ( in @ X1052 @ X1051 )
=> ~ ( in @ X1052 @ X1050 ) ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i] :
( ( in @ X1055 @ X1053 )
=> ( ~ ( in @ X1055 @ X1054 )
=> ~ ( subset @ X1053 @ X1054 ) ) )
=> ( ! [X1056: $i,X1057: $i] :
( ~ ( subset @ X1056 @ X1057 )
=> ( X1056 != X1057 ) )
=> ( ! [X1058: $i,X1059: $i,X1060: $i] :
( ( in @ X1060 @ X1058 )
=> ( ~ ( in @ X1060 @ X1059 )
=> ( X1058 != X1059 ) ) )
=> ( ! [X1061: $i] : ( subset @ X1061 @ X1061 )
=> ( ! [X1062: $i,X1063: $i,X1064: $i] :
( ( subset @ X1062 @ X1063 )
=> ( ( subset @ X1063 @ X1064 )
=> ( subset @ X1062 @ X1064 ) ) )
=> ( ! [X1065: $i,X1066: $i] : ( subset @ X1066 @ ( setadjoin @ X1065 @ X1066 ) )
=> ( ! [X1067: $i,X1068: $i,X1069: $i] :
( ( subset @ X1067 @ X1069 )
=> ( subset @ X1067 @ ( setadjoin @ X1068 @ X1069 ) ) )
=> ( ! [X1070: $i,X1071: $i] :
( ( subset @ X1070 @ X1071 )
=> ( in @ X1070 @ ( powerset @ X1071 ) ) )
=> ( ! [X1072: $i,X1073: $i] :
( ( subset @ X1072 @ X1073 )
=> ( ( subset @ X1073 @ X1072 )
=> ( X1072 = X1073 ) ) )
=> ( ! [X1074: $i] :
( ( subset @ X1074 @ emptyset )
=> ( X1074 = emptyset ) )
=> ( ! [X1075: $i,X1076: $i] :
( ( subset @ X1076 @ X1075 )
=> ( in @ X1076 @ ( powerset @ X1075 ) ) )
=> ( ! [X1077: $i,X1078: $i] :
( ( in @ X1078 @ ( powerset @ X1077 ) )
=> ( subset @ X1078 @ X1077 ) )
=> ( ! [X1079: $i] : ( in @ X1079 @ ( powerset @ X1079 ) )
=> ( ! [X1080: $i,X1081: $i] :
( ( subset @ X1080 @ X1081 )
=> ( subset @ ( powerset @ X1080 ) @ ( powerset @ X1081 ) ) )
=> ( ! [X1082: $i,X1083: $i > $o] : ( in @ ( dsetconstr @ X1082 @ X1083 ) @ ( powerset @ X1082 ) )
=> ( ! [X1084: $i,X1085: $i > $o] : ( subset @ ( dsetconstr @ X1084 @ X1085 ) @ X1084 )
=> ( ! [X1086: $i,X1087: $i,X1088: $i] :
( ( in @ X1088 @ X1086 )
=> ( in @ X1088 @ ( binunion @ X1086 @ X1087 ) ) )
=> ( ! [X1089: $i,X1090: $i] : ( in @ X1090 @ ( setadjoin @ X1089 @ ( setadjoin @ X1090 @ emptyset ) ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( in @ X1093 @ X1092 )
=> ( in @ X1093 @ ( binunion @ X1091 @ X1092 ) ) )
=> ( ! [X1094: $i,X1095: $i,X1096: $i,X1097: $o] :
( ( in @ X1096 @ ( binunion @ X1094 @ X1095 ) )
=> ( ( ( in @ X1096 @ X1094 )
=> X1097 )
=> ( ( ( in @ X1096 @ X1095 )
=> X1097 )
=> X1097 ) ) )
=> ( ! [X1098: $i,X1099: $i,X1100: $i] :
( ( in @ X1100 @ ( binunion @ X1098 @ X1099 ) )
=> ( ( in @ X1100 @ X1098 )
| ( in @ X1100 @ X1099 ) ) )
=> ( ! [X1101: $i,X1102: $i] : ( subset @ X1101 @ ( binunion @ X1101 @ X1102 ) )
=> ( ! [X1103: $i,X1104: $i] : ( subset @ X1104 @ ( binunion @ X1103 @ X1104 ) )
=> ( ! [X1105: $i,X1106: $i,X1107: $i] :
( ( in @ X1107 @ X1105 )
=> ( ( in @ X1107 @ X1106 )
=> ( in @ X1107 @ ( binintersect @ X1105 @ X1106 ) ) ) )
=> ( ! [X1108: $i,X1109: $i,X1110: $i] :
( ( subset @ X1110 @ X1108 )
=> ( ( subset @ X1110 @ X1109 )
=> ( subset @ X1110 @ ( binintersect @ X1108 @ X1109 ) ) ) )
=> ( ! [X1111: $i,X1112: $i,X1113: $i] :
( ( in @ X1113 @ ( binintersect @ X1111 @ X1112 ) )
=> ( in @ X1113 @ X1111 ) )
=> ( ! [X1114: $i,X1115: $i] : ( subset @ ( binintersect @ X1114 @ X1115 ) @ X1114 )
=> ( ! [X1116: $i,X1117: $i] :
( ( subset @ X1116 @ X1117 )
=> ( ( binintersect @ X1116 @ X1117 )
= X1116 ) )
=> ( ! [X1118: $i,X1119: $i] :
( ( ( binintersect @ X1118 @ X1119 )
= X1119 )
=> ( subset @ X1119 @ X1118 ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ( in @ X1122 @ ( binintersect @ X1120 @ X1121 ) )
=> ( in @ X1122 @ X1121 ) )
=> ( ! [X1123: $i,X1124: $i] :
( ~ ? [X1125: $i] :
( ( in @ X1125 @ X1123 )
& ( in @ X1125 @ X1124 ) )
=> ( ( binintersect @ X1123 @ X1124 )
= emptyset ) )
=> ( ! [X1126: $i,X1127: $i] : ( subset @ ( binintersect @ X1126 @ X1127 ) @ X1127 )
=> ( ! [X1128: $i,X1129: $i] :
( ( subset @ X1129 @ X1128 )
=> ( ( binintersect @ X1128 @ X1129 )
= X1129 ) )
=> ( ! [X1130: $i,X1131: $i] :
( ( ( binintersect @ X1130 @ X1131 )
= X1130 )
=> ( subset @ X1130 @ X1131 ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ( binintersect @ X1132 @ ( binunion @ X1133 @ X1134 ) )
= ( binunion @ ( binintersect @ X1132 @ X1133 ) @ ( binintersect @ X1132 @ X1134 ) ) )
=> ( ! [X1135: $i,X1136: $i,X1137: $i] :
( ( in @ X1137 @ X1135 )
=> ( ~ ( in @ X1137 @ X1136 )
=> ( in @ X1137 @ ( setminus @ X1135 @ X1136 ) ) ) )
=> ( ! [X1138: $i,X1139: $i,X1140: $i] :
( ( in @ X1140 @ ( setminus @ X1138 @ X1139 ) )
=> ( in @ X1140 @ X1138 ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i] :
( ( in @ X1143 @ ( setminus @ X1141 @ X1142 ) )
=> ~ ( in @ X1143 @ X1142 ) )
=> ( ! [X1144: $i,X1145: $i] :
( ( subset @ X1144 @ X1145 )
=> ( ( setminus @ X1144 @ X1145 )
= emptyset ) )
=> ( ! [X1146: $i,X1147: $i,X1148: $i] :
( ~ ( in @ X1148 @ ( setminus @ X1146 @ X1147 ) )
=> ( ( in @ X1148 @ X1146 )
=> ( in @ X1148 @ X1147 ) ) )
=> ( ! [X1149: $i,X1150: $i,X1151: $i] :
( ~ ( in @ X1151 @ ( setminus @ X1149 @ X1150 ) )
=> ( ~ ( in @ X1151 @ X1150 )
=> ~ ( in @ X1151 @ X1149 ) ) )
=> ( ! [X1152: $i,X1153: $i,X1154: $i] :
( ~ ( in @ X1154 @ X1152 )
=> ~ ( in @ X1154 @ ( setminus @ X1152 @ X1153 ) ) )
=> ( ! [X1155: $i,X1156: $i,X1157: $i] :
( ( in @ X1157 @ X1156 )
=> ~ ( in @ X1157 @ ( setminus @ X1155 @ X1156 ) ) )
=> ( ! [X1158: $i,X1159: $i] : ( subset @ ( setminus @ X1158 @ X1159 ) @ X1158 )
=> ( ! [X1160: $i,X1161: $i] :
( ( ( setminus @ X1160 @ X1161 )
= emptyset )
=> ( subset @ X1160 @ X1161 ) )
=> ( ! [X1162: $i,X1163: $i,X1164: $i] :
( ( in @ X1164 @ ( symdiff @ X1162 @ X1163 ) )
=> ! [X1165: $o] :
( ( ( in @ X1164 @ X1162 )
=> ( ~ ( in @ X1164 @ X1163 )
=> X1165 ) )
=> ( ( ~ ( in @ X1164 @ X1162 )
=> ( ( in @ X1164 @ X1163 )
=> X1165 ) )
=> X1165 ) ) )
=> ( ! [X1166: $i,X1167: $i,X1168: $i] :
( ( in @ X1168 @ X1166 )
=> ( ~ ( in @ X1168 @ X1167 )
=> ( in @ X1168 @ ( symdiff @ X1166 @ X1167 ) ) ) )
=> ( ! [X1169: $i,X1170: $i,X1171: $i] :
( ~ ( in @ X1171 @ X1169 )
=> ( ( in @ X1171 @ X1170 )
=> ( in @ X1171 @ ( symdiff @ X1169 @ X1170 ) ) ) )
=> ( ! [X1172: $i,X1173: $i,X1174: $i] :
( ( in @ X1174 @ X1172 )
=> ( ( in @ X1174 @ X1173 )
=> ~ ( in @ X1174 @ ( symdiff @ X1172 @ X1173 ) ) ) )
=> ( ! [X1175: $i,X1176: $i,X1177: $i] :
( ~ ( in @ X1177 @ X1175 )
=> ( ~ ( in @ X1177 @ X1176 )
=> ~ ( in @ X1177 @ ( symdiff @ X1175 @ X1176 ) ) ) )
=> ( ! [X1178: $i,X1179: $i] : ( in @ X1179 @ ( setadjoin @ X1178 @ ( setadjoin @ X1179 @ emptyset ) ) )
=> ( ! [X1180: $i,X1181: $i] : ( in @ X1180 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1180 @ ( setadjoin @ X1181 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1182: $i,X1183: $i] : ( in @ X1183 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1182 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1182 @ ( setadjoin @ X1183 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1184: $i,X1185: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1184 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1184 @ ( setadjoin @ X1185 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1186: $i,X1187: $i] : ( iskpair @ ( kpair @ X1186 @ X1187 ) )
=> ( ! [X1188: $i,X1189: $i] :
( ( in @ X1189 @ X1188 )
=> ( subset @ ( setadjoin @ X1189 @ emptyset ) @ X1188 ) )
=> ( ! [X1190: $i,X1191: $i] :
( ( in @ X1191 @ X1190 )
=> ( in @ ( setadjoin @ X1191 @ emptyset ) @ ( powerset @ X1190 ) ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i] :
( ( in @ X1194 @ X1192 )
=> ( in @ ( setadjoin @ X1194 @ emptyset ) @ ( powerset @ ( binunion @ X1192 @ X1193 ) ) ) )
=> ( ! [X1195: $i,X1196: $i,X1197: $i] :
( ( in @ X1197 @ ( setadjoin @ X1195 @ ( setadjoin @ X1196 @ emptyset ) ) )
=> ( ( X1197 = X1195 )
| ( X1197 = X1196 ) ) )
=> ( ! [X1198: $i,X1199: $i,X1200: $i] :
( ( in @ X1200 @ X1198 )
=> ! [X1201: $i] :
( ( in @ X1201 @ X1199 )
=> ( subset @ ( setadjoin @ X1200 @ ( setadjoin @ X1201 @ emptyset ) ) @ ( binunion @ X1198 @ X1199 ) ) ) )
=> ( ! [X1202: $i,X1203: $i,X1204: $i] :
( ( in @ X1204 @ X1202 )
=> ! [X1205: $i] :
( ( in @ X1205 @ X1203 )
=> ( in @ ( setadjoin @ X1204 @ ( setadjoin @ X1205 @ emptyset ) ) @ ( powerset @ ( binunion @ X1202 @ X1203 ) ) ) ) )
=> ( ! [X1206: $i,X1207: $i,X1208: $i] :
( ( in @ X1208 @ X1206 )
=> ! [X1209: $i] :
( ( in @ X1209 @ X1207 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1208 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1208 @ ( setadjoin @ X1209 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1206 @ X1207 ) ) ) ) )
=> ( ! [X1210: $i,X1211: $i,X1212: $i] :
( ( in @ X1212 @ X1210 )
=> ! [X1213: $i] :
( ( in @ X1213 @ X1211 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1212 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1212 @ ( setadjoin @ X1213 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1210 @ X1211 ) ) ) ) ) )
=> ( ! [X1214: $i,X1215: $i,X1216: $i] :
( ( in @ X1216 @ X1214 )
=> ! [X1217: $i] :
( ( in @ X1217 @ X1215 )
=> ( in @ ( kpair @ X1216 @ X1217 ) @ ( powerset @ ( powerset @ ( binunion @ X1214 @ X1215 ) ) ) ) ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( in @ X1220 @ X1218 )
=> ! [X1221: $i] :
( ( in @ X1221 @ X1219 )
=> ( in @ ( kpair @ X1220 @ X1221 ) @ ( cartprod @ X1218 @ X1219 ) ) ) )
=> ( ! [X1222: $i,X1223: $i,X1224: $i] :
( ( in @ X1224 @ ( cartprod @ X1222 @ X1223 ) )
=> ? [X1225: $i] :
( ( in @ X1225 @ X1222 )
& ? [X1226: $i] :
( ( in @ X1226 @ X1223 )
& ( X1224
= ( kpair @ X1225 @ X1226 ) ) ) ) )
=> ( ! [X1227: $i,X1228: $i,X1229: $i] :
( ( in @ X1229 @ ( cartprod @ X1227 @ X1228 ) )
=> ( iskpair @ X1229 ) )
=> ( ! [X1230: $i,X1231: $i] :
( ( in @ X1231 @ ( setunion @ X1230 ) )
=> ? [X1232: $i] :
( ( in @ X1232 @ X1230 )
& ( in @ X1231 @ X1232 ) ) )
=> ( ! [X1233: $i] : ( subset @ ( setunion @ ( setadjoin @ X1233 @ emptyset ) ) @ X1233 )
=> ( ! [X1234: $i] : ( subset @ X1234 @ ( setunion @ ( setadjoin @ X1234 @ emptyset ) ) )
=> ( ! [X1235: $i] :
( ( setunion @ ( setadjoin @ X1235 @ emptyset ) )
= X1235 )
=> ( ! [X1236: $i,X1237: $i > $o] :
( ! [X1238: $i] :
( ( in @ X1238 @ X1236 )
=> ! [X1239: $i] :
( ( in @ X1239 @ X1236 )
=> ( ( X1237 @ X1238 )
=> ( ( X1237 @ X1239 )
=> ( X1238 = X1239 ) ) ) ) )
=> ( ? [X1240: $i] :
( ( in @ X1240 @ X1236 )
& ( X1237 @ X1240 ) )
=> ( singleton @ ( dsetconstr @ X1236 @ X1237 ) ) ) )
=> ( ! [X1241: $i,X1242: $i > $o] :
( ( ex1 @ X1241 @ X1242 )
=> ? [X1243: $i] :
( ( in @ X1243 @ X1241 )
& ( X1242 @ X1243 ) ) )
=> ( ! [X1244: $i,X1245: $i > $o,X1246: $i] :
( ( in @ X1246 @ X1244 )
=> ( ( X1245 @ X1246 )
=> ( ! [X1247: $i] :
( ( in @ X1247 @ X1244 )
=> ( ( X1245 @ X1247 )
=> ( X1247 = X1246 ) ) )
=> ( ex1 @ X1244 @ X1245 ) ) ) )
=> ( ! [X1248: $i,X1249: $i > $o] :
( ! [X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ! [X1251: $i] :
( ( in @ X1251 @ X1248 )
=> ( ( X1249 @ X1250 )
=> ( ( X1249 @ X1251 )
=> ( X1250 = X1251 ) ) ) ) )
=> ( ? [X1252: $i] :
( ( in @ X1252 @ X1248 )
& ( X1249 @ X1252 ) )
=> ( ex1 @ X1248 @ X1249 ) ) )
=> ( ! [X1253: $i,X1254: $i] :
( ( ( setadjoin @ X1253 @ emptyset )
= ( setadjoin @ X1254 @ emptyset ) )
=> ( X1253 = X1254 ) )
=> ( ! [X1255: $i,X1256: $i,X1257: $i] :
( ( in @ ( setadjoin @ X1257 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1255 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1255 @ ( setadjoin @ X1256 @ emptyset ) ) @ emptyset ) ) )
=> ( X1255 = X1257 ) )
=> ( ! [X1258: $i] :
( ( iskpair @ X1258 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1258 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1258 ) ) ) )
=> ( ! [X1259: $i] :
( ( singleton @ X1259 )
=> ( in @ ( setunion @ X1259 ) @ X1259 ) )
=> ( ! [X1260: $i,X1261: $i] :
( ( kfst @ ( kpair @ X1260 @ X1261 ) )
= X1260 )
=> ( ! [X1262: $i,X1263: $i,X1264: $i] :
( ( in @ X1264 @ ( cartprod @ X1262 @ X1263 ) )
=> ( in @ ( kfst @ X1264 ) @ X1262 ) )
=> ( ! [X1265: $i,X1266: $i,X1267: $i,X1268: $i] :
( ( ( setadjoin @ ( setadjoin @ X1265 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1265 @ ( setadjoin @ X1266 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1267 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1267 @ ( setadjoin @ X1268 @ emptyset ) ) @ emptyset ) ) )
=> ( X1265 = X1267 ) )
=> ( ! [X1269: $i,X1270: $i,X1271: $i,X1272: $i] :
( ( ( kpair @ X1269 @ X1270 )
= ( kpair @ X1271 @ X1272 ) )
=> ( X1269 = X1271 ) )
=> ( ! [X1273: $i,X1274: $i] :
( ( X1273 = X1274 )
=> ( ( setadjoin @ X1273 @ ( setadjoin @ X1274 @ emptyset ) )
= ( setadjoin @ X1273 @ emptyset ) ) )
=> ( ! [X1275: $i,X1276: $i] :
( ( X1275 = X1276 )
=> ( ( setadjoin @ ( setadjoin @ X1275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1275 @ ( setadjoin @ X1276 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1275 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1277: $i,X1278: $i,X1279: $i,X1280: $i] :
( ( ( setadjoin @ ( setadjoin @ X1277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1277 @ ( setadjoin @ X1278 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1279 @ ( setadjoin @ X1280 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1279 = X1280 )
=> ( X1278 = X1280 ) ) )
=> ( ! [X1281: $i,X1282: $i,X1283: $i] :
( ( ( setadjoin @ X1281 @ ( setadjoin @ X1282 @ emptyset ) )
= ( setadjoin @ X1283 @ emptyset ) )
=> ( X1281 = X1282 ) )
=> ( ! [X1284: $i,X1285: $i,X1286: $i,X1287: $i] :
( ( ( setadjoin @ ( setadjoin @ X1284 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1284 @ ( setadjoin @ X1285 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1286 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1286 @ ( setadjoin @ X1287 @ emptyset ) ) @ emptyset ) ) )
=> ( X1285 = X1287 ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i,X1291: $i] :
( ( ( kpair @ X1288 @ X1289 )
= ( kpair @ X1290 @ X1291 ) )
=> ( X1289 = X1291 ) )
=> ( ! [X1292: $i] :
( ( iskpair @ X1292 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1292 )
@ ^ [Z0: $i] :
( X1292
= ( kpair @ ( kfst @ X1292 ) @ Z0 ) ) ) ) )
=> ( ! [X1293: $i,X1294: $i] :
( ( ksnd @ ( kpair @ X1293 @ X1294 ) )
= X1294 )
=> ( ! [X1295: $i] :
( ( iskpair @ X1295 )
=> ( ( kpair @ ( kfst @ X1295 ) @ ( ksnd @ X1295 ) )
= X1295 ) )
=> ( ! [X1296: $i,X1297: $i,X1298: $i] :
( ( in @ X1298 @ ( cartprod @ X1296 @ X1297 ) )
=> ( in @ ( ksnd @ X1298 ) @ X1297 ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i,X1302: $i] :
( ( in @ ( kpair @ X1301 @ X1302 ) @ ( cartprod @ X1299 @ X1300 ) )
=> ( in @ X1301 @ X1299 ) )
=> ( ! [X1303: $i,X1304: $i,X1305: $i,X1306: $i] :
( ( in @ ( kpair @ X1305 @ X1306 ) @ ( cartprod @ X1303 @ X1304 ) )
=> ( in @ X1306 @ X1304 ) )
=> ( ! [X1307: $i,X1308: $i,X1309: $i] :
( ( in @ X1309 @ X1307 )
=> ! [X1310: $i] :
( ( in @ X1310 @ X1308 )
=> ( ( kpair @ X1309 @ X1310 )
= ( kpair @ X1309 @ X1310 ) ) ) )
=> ( ! [X1311: $i,X1312: $i,X1313: $i] :
( ( in @ X1313 @ X1311 )
=> ! [X1314: $i] :
( ( in @ X1314 @ X1312 )
=> ( ( kfst @ ( kpair @ X1313 @ X1314 ) )
= X1313 ) ) )
=> ( ! [X1315: $i,X1316: $i,X1317: $i] :
( ( in @ X1317 @ X1315 )
=> ! [X1318: $i] :
( ( in @ X1318 @ X1316 )
=> ( ( ksnd @ ( kpair @ X1317 @ X1318 ) )
= X1318 ) ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i] :
( ( in @ X1321 @ ( cartprod @ X1319 @ X1320 ) )
=> ( ( kpair @ ( kfst @ X1321 ) @ ( ksnd @ X1321 ) )
= X1321 ) )
=> ( ! [X1322: $i,X1323: $i,X1324: $i > $i > $o,X1325: $i] :
( ( in @ X1325 @ X1322 )
=> ! [X1326: $i] :
( ( in @ X1326 @ X1323 )
=> ( ( X1324 @ X1325 @ X1326 )
=> ( in @ ( kpair @ X1325 @ X1326 ) @ ( dpsetconstr @ X1322 @ X1323 @ X1324 ) ) ) ) )
=> ( ! [X1327: $i,X1328: $i,X1329: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1327 @ X1328 @ X1329 ) @ ( cartprod @ X1327 @ X1328 ) )
=> ( ! [X1330: $i,X1331: $i,X1332: $i > $i > $o] : ( breln @ X1330 @ X1331 @ ( dpsetconstr @ X1330 @ X1331 @ X1332 ) )
=> ( ! [X1333: $i,X1334: $i,X1335: $i > $i > $o,X1336: $i] :
( ( in @ X1336 @ X1333 )
=> ! [X1337: $i] :
( ( in @ X1337 @ X1334 )
=> ( ( in @ ( kpair @ X1336 @ X1337 ) @ ( dpsetconstr @ X1333 @ X1334 @ X1335 ) )
=> ( X1335 @ X1336 @ X1337 ) ) ) )
=> ( ! [X1338: $i,X1339: $i,X1340: $i > $i > $o,X1341: $i,X1342: $i] :
( ( in @ ( kpair @ X1341 @ X1342 ) @ ( dpsetconstr @ X1338 @ X1339 @ X1340 ) )
=> ( in @ X1341 @ X1338 ) )
=> ( ! [X1343: $i,X1344: $i,X1345: $i > $i > $o,X1346: $i,X1347: $i] :
( ( in @ ( kpair @ X1346 @ X1347 ) @ ( dpsetconstr @ X1343 @ X1344 @ X1345 ) )
=> ( in @ X1347 @ X1344 ) )
=> ( ! [X1348: $i,X1349: $i,X1350: $i > $i > $o,X1351: $i,X1352: $i] :
( ( in @ ( kpair @ X1351 @ X1352 ) @ ( dpsetconstr @ X1348 @ X1349 @ X1350 ) )
=> ( X1350 @ X1351 @ X1352 ) )
=> ( ! [X1353: $i,X1354: $i,X1355: $i] :
( ( func @ X1353 @ X1354 @ X1355 )
=> ! [X1356: $i] :
( ( in @ X1356 @ X1353 )
=> ( singleton
@ ( dsetconstr @ X1354
@ ^ [Z0: $i] : ( in @ ( kpair @ X1356 @ Z0 ) @ X1355 ) ) ) ) )
=> ( ! [X1357: $i,X1358: $i,X1359: $i] :
( ( func @ X1357 @ X1358 @ X1359 )
=> ! [X1360: $i] :
( ( in @ X1360 @ X1357 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1358
@ ^ [Z0: $i] : ( in @ ( kpair @ X1360 @ Z0 ) @ X1359 ) ) )
@ X1358 ) ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i] :
( ( func @ X1361 @ X1362 @ X1363 )
=> ! [X1364: $i] :
( ( in @ X1364 @ X1361 )
=> ( in @ ( ap @ X1361 @ X1362 @ X1363 @ X1364 ) @ X1362 ) ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i] :
( ( in @ X1367 @ ( funcSet @ X1365 @ X1366 ) )
=> ( func @ X1365 @ X1366 @ X1367 ) )
=> ( ! [X1368: $i,X1369: $i,X1370: $i] :
( ( in @ X1370 @ ( funcSet @ X1368 @ X1369 ) )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1368 )
=> ( in @ ( ap @ X1368 @ X1369 @ X1370 @ X1371 ) @ X1369 ) ) )
=> ( ! [X1372: $i,X1373: $i,X1374: $i] :
( ( func @ X1372 @ X1373 @ X1374 )
=> ( in @ X1374 @ ( funcSet @ X1372 @ X1373 ) ) )
=> ( ! [X1375: $i,X1376: $i,X1377: $i > $i] :
( ! [X1378: $i] :
( ( in @ X1378 @ X1375 )
=> ( in @ ( X1377 @ X1378 ) @ X1376 ) )
=> ( func @ X1375 @ X1376
@ ( dpsetconstr @ X1375 @ X1376
@ ^ [Z0: $i] : ( $eq @ ( X1377 @ Z0 ) ) ) ) )
=> ( ! [X1379: $i,X1380: $i,X1381: $i > $i] :
( ! [X1382: $i] :
( ( in @ X1382 @ X1379 )
=> ( in @ ( X1381 @ X1382 ) @ X1380 ) )
=> ( func @ X1379 @ X1380 @ ( lam @ X1379 @ X1380 @ X1381 ) ) )
=> ( ! [X1383: $i,X1384: $i,X1385: $i > $i] :
( ! [X1386: $i] :
( ( in @ X1386 @ X1383 )
=> ( in @ ( X1385 @ X1386 ) @ X1384 ) )
=> ( in @ ( lam @ X1383 @ X1384 @ X1385 ) @ ( funcSet @ X1383 @ X1384 ) ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i] :
( ( breln @ X1387 @ X1388 @ X1389 )
=> ! [X1390: $i > $o] :
( ! [X1391: $i] :
( ( in @ X1391 @ X1387 )
=> ! [X1392: $i] :
( ( in @ X1392 @ X1388 )
=> ( ( in @ ( kpair @ X1391 @ X1392 ) @ X1389 )
=> ( X1390 @ ( kpair @ X1391 @ X1392 ) ) ) ) )
=> ! [X1393: $i] :
( ( in @ X1393 @ X1389 )
=> ( X1390 @ X1393 ) ) ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i] :
( ( breln @ X1394 @ X1395 @ X1396 )
=> ! [X1397: $i > $o] :
( ! [X1398: $i] :
( ( in @ X1398 @ X1394 )
=> ! [X1399: $i] :
( ( in @ X1399 @ X1395 )
=> ( ( in @ ( kpair @ X1398 @ X1399 ) @ X1396 )
=> ( X1397 @ ( kpair @ X1398 @ X1399 ) ) ) ) )
=> ! [X1400: $i] :
( ( in @ X1400 @ X1396 )
=> ( X1397 @ X1400 ) ) ) )
=> ( ! [X1401: $i,X1402: $i > $o] :
( ( ex1 @ X1401 @ X1402 )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1401 )
=> ! [X1404: $i] :
( ( in @ X1404 @ X1401 )
=> ( ( X1402 @ X1403 )
=> ( ( X1402 @ X1404 )
=> ( X1403 = X1404 ) ) ) ) ) )
=> ( ! [X1405: $i,X1406: $i,X1407: $i] :
( ( func @ X1405 @ X1406 @ X1407 )
=> ! [X1408: $i] :
( ( in @ X1408 @ X1405 )
=> ( in @ ( kpair @ X1408 @ ( ap @ X1405 @ X1406 @ X1407 @ X1408 ) ) @ X1407 ) ) )
=> ( ! [X1409: $i,X1410: $i,X1411: $i] :
( ( in @ X1411 @ ( funcSet @ X1409 @ X1410 ) )
=> ! [X1412: $i] :
( ( in @ X1412 @ X1409 )
=> ( in @ ( kpair @ X1412 @ ( ap @ X1409 @ X1410 @ X1411 @ X1412 ) ) @ X1411 ) ) )
=> ( ! [X1413: $i,X1414: $i,X1415: $i] :
( ( func @ X1413 @ X1414 @ X1415 )
=> ! [X1416: $i] :
( ( in @ X1416 @ X1413 )
=> ! [X1417: $i] :
( ( in @ X1417 @ X1414 )
=> ( ( in @ ( kpair @ X1416 @ X1417 ) @ X1415 )
=> ( ( ap @ X1413 @ X1414 @ X1415 @ X1416 )
= X1417 ) ) ) ) )
=> ( ! [X1418: $i,X1419: $i,X1420: $i] :
( ( func @ X1418 @ X1419 @ X1420 )
=> ! [X1421: $i] :
( ( func @ X1418 @ X1419 @ X1421 )
=> ( ! [X1422: $i] :
( ( in @ X1422 @ X1418 )
=> ( ( ap @ X1418 @ X1419 @ X1420 @ X1422 )
= ( ap @ X1418 @ X1419 @ X1421 @ X1422 ) ) )
=> ! [X1423: $i] :
( ( in @ X1423 @ X1418 )
=> ! [X1424: $i] :
( ( in @ X1424 @ X1419 )
=> ( ( in @ ( kpair @ X1423 @ X1424 ) @ X1421 )
=> ( in @ ( kpair @ X1423 @ X1424 ) @ X1420 ) ) ) ) ) ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i] :
( ( in @ X1427 @ ( funcSet @ X1425 @ X1426 ) )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1426 )
=> ( ( in @ ( kpair @ X1428 @ X1429 ) @ X1427 )
=> ( ( ap @ X1425 @ X1426 @ X1427 @ X1428 )
= X1429 ) ) ) ) )
=> ( ! [X1430: $i,X1431: $i,X1432: $i] :
( ( breln @ X1430 @ X1431 @ X1432 )
=> ! [X1433: $i] :
( ( breln @ X1430 @ X1431 @ X1433 )
=> ( ! [X1434: $i] :
( ( in @ X1434 @ X1430 )
=> ! [X1435: $i] :
( ( in @ X1435 @ X1431 )
=> ( ( in @ ( kpair @ X1434 @ X1435 ) @ X1432 )
=> ( in @ ( kpair @ X1434 @ X1435 ) @ X1433 ) ) ) )
=> ( subset @ X1432 @ X1433 ) ) ) )
=> ( ! [X1436: $i,X1437: $i,X1438: $i] :
( ( breln @ X1436 @ X1437 @ X1438 )
=> ! [X1439: $i] :
( ( breln @ X1436 @ X1437 @ X1439 )
=> ( ! [X1440: $i] :
( ( in @ X1440 @ X1436 )
=> ! [X1441: $i] :
( ( in @ X1441 @ X1437 )
=> ( ( in @ ( kpair @ X1440 @ X1441 ) @ X1438 )
=> ( in @ ( kpair @ X1440 @ X1441 ) @ X1439 ) ) ) )
=> ( ! [X1442: $i] :
( ( in @ X1442 @ X1436 )
=> ! [X1443: $i] :
( ( in @ X1443 @ X1437 )
=> ( ( in @ ( kpair @ X1442 @ X1443 ) @ X1439 )
=> ( in @ ( kpair @ X1442 @ X1443 ) @ X1438 ) ) ) )
=> ( X1438 = X1439 ) ) ) ) )
=> ( ! [X1444: $i,X1445: $i,X1446: $i] :
( ( func @ X1444 @ X1445 @ X1446 )
=> ! [X1447: $i] :
( ( func @ X1444 @ X1445 @ X1447 )
=> ( ! [X1448: $i] :
( ( in @ X1448 @ X1444 )
=> ( ( ap @ X1444 @ X1445 @ X1446 @ X1448 )
= ( ap @ X1444 @ X1445 @ X1447 @ X1448 ) ) )
=> ( X1446 = X1447 ) ) ) )
=> ( ! [X1449: $i,X1450: $i,X1451: $i] :
( ( in @ X1451 @ ( funcSet @ X1449 @ X1450 ) )
=> ! [X1452: $i] :
( ( in @ X1452 @ ( funcSet @ X1449 @ X1450 ) )
=> ( ! [X1453: $i] :
( ( in @ X1453 @ X1449 )
=> ( ( ap @ X1449 @ X1450 @ X1451 @ X1453 )
= ( ap @ X1449 @ X1450 @ X1452 @ X1453 ) ) )
=> ( X1451 = X1452 ) ) ) )
=> ( ! [X1454: $i,X1455: $i,X1456: $i] :
( ( in @ X1456 @ ( funcSet @ X1454 @ X1455 ) )
=> ! [X1457: $i] :
( ( in @ X1457 @ X1454 )
=> ( ( ap @ X1454 @ X1455 @ X1456 @ X1457 )
= ( ap @ X1454 @ X1455 @ X1456 @ X1457 ) ) ) )
=> ( ! [X1458: $i,X1459: $i,X1460: $i] :
( ( func @ X1458 @ X1459 @ X1460 )
=> ! [X1461: $i] :
( ( in @ X1461 @ X1458 )
=> ( ( ap @ X1458 @ X1459 @ X1460 @ X1461 )
= ( ap @ X1458 @ X1459 @ X1460 @ X1461 ) ) ) )
=> ( ! [X1462: $i,X1463: $i,X1464: $i > $i] :
( ! [X1465: $i] :
( ( in @ X1465 @ X1462 )
=> ( in @ ( X1464 @ X1465 ) @ X1463 ) )
=> ! [X1466: $i] :
( ( in @ X1466 @ X1462 )
=> ( ( ap @ X1462 @ X1463 @ ( lam @ X1462 @ X1463 @ X1464 ) @ X1466 )
= ( X1464 @ X1466 ) ) ) )
=> ( ! [X1467: $i,X1468: $i,X1469: $i] :
( ( func @ X1467 @ X1468 @ X1469 )
=> ( ( lam @ X1467 @ X1468 @ ( ap @ X1467 @ X1468 @ X1469 ) )
= X1469 ) )
=> ( ! [X1470: $i,X1471: $i,X1472: $i > $i] :
( ! [X1473: $i] :
( ( in @ X1473 @ X1470 )
=> ( in @ ( X1472 @ X1473 ) @ X1471 ) )
=> ( ( lam @ X1470 @ X1471 @ X1472 )
= ( lam @ X1470 @ X1471 @ X1472 ) ) )
=> ( ! [X1474: $i,X1475: $i,X1476: $i > $i] :
( ! [X1477: $i] :
( ( in @ X1477 @ X1474 )
=> ( in @ ( X1476 @ X1477 ) @ X1475 ) )
=> ! [X1478: $i] :
( ( in @ X1478 @ X1474 )
=> ( ( ap @ X1474 @ X1475 @ ( lam @ X1474 @ X1475 @ X1476 ) @ X1478 )
= ( X1476 @ X1478 ) ) ) )
=> ( ! [X1479: $i,X1480: $i,X1481: $i] :
( ( in @ X1481 @ ( funcSet @ X1479 @ X1480 ) )
=> ( ( lam @ X1479 @ X1480 @ ( ap @ X1479 @ X1480 @ X1481 ) )
= X1481 ) )
=> ( ! [X1482: $i,X1483: $o,X1484: $i] :
( ( in @ X1484 @ X1482 )
=> ! [X1485: $i] :
( ( in @ X1485 @ X1482 )
=> ( ~ X1483
=> ( in @ X1485
@ ( dsetconstr @ X1482
@ ^ [Z0: $i] :
( ( X1483
& ( Z0 = X1484 ) )
| ( ~ X1483
& ( Z0 = X1485 ) ) ) ) ) ) ) )
=> ( ! [X1486: $i,X1487: $o,X1488: $i] :
( ( in @ X1488 @ X1486 )
=> ! [X1489: $i] :
( ( in @ X1489 @ X1486 )
=> ( ~ X1487
=> ( ( dsetconstr @ X1486
@ ^ [Z0: $i] :
( ( X1487
& ( Z0 = X1488 ) )
| ( ~ X1487
& ( Z0 = X1489 ) ) ) )
= ( setadjoin @ X1489 @ emptyset ) ) ) ) )
=> ( ! [X1490: $i,X1491: $o,X1492: $i] :
( ( in @ X1492 @ X1490 )
=> ! [X1493: $i] :
( ( in @ X1493 @ X1490 )
=> ( X1491
=> ( in @ X1492
@ ( dsetconstr @ X1490
@ ^ [Z0: $i] :
( ( X1491
& ( Z0 = X1492 ) )
| ( ~ X1491
& ( Z0 = X1493 ) ) ) ) ) ) ) )
=> ( ! [X1494: $i,X1495: $o,X1496: $i] :
( ( in @ X1496 @ X1494 )
=> ! [X1497: $i] :
( ( in @ X1497 @ X1494 )
=> ( X1495
=> ( ( dsetconstr @ X1494
@ ^ [Z0: $i] :
( ( X1495
& ( Z0 = X1496 ) )
| ( ~ X1495
& ( Z0 = X1497 ) ) ) )
= ( setadjoin @ X1496 @ emptyset ) ) ) ) )
=> ( ! [X1498: $i,X1499: $o,X1500: $i] :
( ( in @ X1500 @ X1498 )
=> ! [X1501: $i] :
( ( in @ X1501 @ X1498 )
=> ( singleton
@ ( dsetconstr @ X1498
@ ^ [Z0: $i] :
( ( X1499
& ( Z0 = X1500 ) )
| ( ~ X1499
& ( Z0 = X1501 ) ) ) ) ) ) )
=> ( ! [X1502: $i,X1503: $o,X1504: $i] :
( ( in @ X1504 @ X1502 )
=> ! [X1505: $i] :
( ( in @ X1505 @ X1502 )
=> ( in @ ( if @ X1502 @ X1503 @ X1504 @ X1505 ) @ X1502 ) ) )
=> ( ! [X1506: $i] :
( ( singleton @ X1506 )
=> ! [X1507: $i] :
( ( in @ X1507 @ X1506 )
=> ( ( setunion @ X1506 )
= X1507 ) ) )
=> ( ! [X1508: $i,X1509: $o,X1510: $i] :
( ( in @ X1510 @ X1508 )
=> ! [X1511: $i] :
( ( in @ X1511 @ X1508 )
=> ( X1509
=> ( ( if @ X1508 @ X1509 @ X1510 @ X1511 )
= X1510 ) ) ) )
=> ( ! [X1512: $i,X1513: $o,X1514: $i] :
( ( in @ X1514 @ X1512 )
=> ! [X1515: $i] :
( ( in @ X1515 @ X1512 )
=> ( ~ X1513
=> ( ( if @ X1512 @ X1513 @ X1514 @ X1515 )
= X1515 ) ) ) )
=> ( ! [X1516: $i,X1517: $o,X1518: $i] :
( ( in @ X1518 @ X1516 )
=> ! [X1519: $i] :
( ( in @ X1519 @ X1516 )
=> ( in @ ( if @ X1516 @ X1517 @ X1518 @ X1519 ) @ ( setadjoin @ X1518 @ ( setadjoin @ X1519 @ emptyset ) ) ) ) )
=> ( ! [X1520: $i,X1521: $i] :
( ( in @ X1521 @ ( powerset @ X1520 ) )
=> ! [X1522: $i] :
( ( in @ X1522 @ ( powerset @ X1520 ) )
=> ( in @ ( binintersect @ X1521 @ X1522 ) @ ( powerset @ X1520 ) ) ) )
=> ( ! [X1523: $i,X1524: $i] :
( ( in @ X1524 @ ( powerset @ X1523 ) )
=> ! [X1525: $i] :
( ( in @ X1525 @ ( powerset @ X1523 ) )
=> ( in @ ( binunion @ X1524 @ X1525 ) @ ( powerset @ X1523 ) ) ) )
=> ( ! [X1526: $i,X1527: $i] :
( ( in @ X1527 @ ( powerset @ X1526 ) )
=> ( in @ ( powerset @ X1527 ) @ ( powerset @ ( powerset @ X1526 ) ) ) )
=> ( ! [X1528: $i,X1529: $i] :
( ( in @ X1529 @ ( powerset @ X1528 ) )
=> ! [X1530: $i] :
( ( in @ X1530 @ ( powerset @ X1528 ) )
=> ( in @ ( setminus @ X1529 @ X1530 ) @ ( powerset @ X1528 ) ) ) )
=> ( ! [X1531: $i,X1532: $i] :
( ( in @ X1532 @ ( powerset @ X1531 ) )
=> ( in @ ( setminus @ X1531 @ X1532 ) @ ( powerset @ X1531 ) ) )
=> ( ! [X1533: $i,X1534: $i] :
( ( in @ X1534 @ ( powerset @ X1533 ) )
=> ! [X1535: $i] :
( ( in @ X1535 @ ( powerset @ X1533 ) )
=> ( ! [X1536: $i] :
( ( in @ X1536 @ X1533 )
=> ( ( in @ X1536 @ X1534 )
=> ( in @ X1536 @ X1535 ) ) )
=> ( ! [X1537: $i] :
( ( in @ X1537 @ X1533 )
=> ( ( in @ X1537 @ X1535 )
=> ( in @ X1537 @ X1534 ) ) )
=> ( X1534 = X1535 ) ) ) ) )
=> ( ! [X1538: $i,X1539: $i] :
( ( in @ X1539 @ ( powerset @ X1538 ) )
=> ! [X1540: $i] :
( ( in @ X1540 @ ( powerset @ X1538 ) )
=> ( ! [X1541: $i] :
( ( in @ X1541 @ X1538 )
=> ( ( in @ X1541 @ X1539 )
=> ( in @ X1541 @ X1540 ) ) )
=> ( subset @ X1539 @ X1540 ) ) ) )
=> ( ! [X1542: $i,X1543: $i] :
( ( in @ X1543 @ ( powerset @ X1542 ) )
=> ! [X1544: $i] :
( ( in @ X1544 @ ( powerset @ X1542 ) )
=> ( ! [X1545: $i] :
( ( in @ X1545 @ X1542 )
=> ( ( in @ X1545 @ X1543 )
=> ( in @ X1545 @ X1544 ) ) )
=> ( in @ X1543 @ ( powerset @ X1544 ) ) ) ) )
=> ( ! [X1546: $i,X1547: $i] :
( ( in @ X1547 @ ( powerset @ X1546 ) )
=> ! [X1548: $i] :
( ( in @ X1548 @ ( powerset @ X1546 ) )
=> ! [X1549: $i] :
( ( in @ X1549 @ X1546 )
=> ( ( in @ X1547 @ ( powerset @ X1548 ) )
=> ( ( in @ X1549 @ X1547 )
=> ( in @ X1549 @ X1548 ) ) ) ) ) )
=> ( ! [X1550: $i,X1551: $i] :
( ( in @ X1551 @ ( powerset @ X1550 ) )
=> ! [X1552: $i] :
( ( in @ X1552 @ X1550 )
=> ( ( in @ X1552 @ X1551 )
=> ~ ( in @ X1552 @ ( setminus @ X1550 @ X1551 ) ) ) ) )
=> ( ! [X1553: $i,X1554: $i] :
( ( in @ X1554 @ ( powerset @ X1553 ) )
=> ! [X1555: $i] :
( ( in @ X1555 @ X1553 )
=> ( ~ ( in @ X1555 @ ( setminus @ X1553 @ X1554 ) )
=> ( in @ X1555 @ X1554 ) ) ) )
=> ( ! [X1556: $i,X1557: $i] :
( ( in @ X1557 @ ( powerset @ X1556 ) )
=> ! [X1558: $i] :
( ( in @ X1558 @ ( powerset @ X1556 ) )
=> ! [X1559: $i] :
( ( in @ X1559 @ X1556 )
=> ( ~ ( in @ X1559 @ X1557 )
=> ~ ( in @ X1559 @ ( binintersect @ X1557 @ X1558 ) ) ) ) ) )
=> ( ! [X1560: $i,X1561: $i] :
( ( in @ X1561 @ ( powerset @ X1560 ) )
=> ! [X1562: $i] :
( ( in @ X1562 @ ( powerset @ X1560 ) )
=> ! [X1563: $i] :
( ( in @ X1563 @ X1560 )
=> ( ~ ( in @ X1563 @ X1562 )
=> ~ ( in @ X1563 @ ( binintersect @ X1561 @ X1562 ) ) ) ) ) )
=> ( ! [X1564: $i,X1565: $i] :
( ( in @ X1565 @ ( powerset @ X1564 ) )
=> ! [X1566: $i] :
( ( in @ X1566 @ ( powerset @ X1564 ) )
=> ! [X1567: $i] :
( ( in @ X1567 @ X1564 )
=> ( ( subset @ X1565 @ ( setminus @ X1564 @ X1566 ) )
=> ( ( in @ X1567 @ X1566 )
=> ~ ( in @ X1567 @ X1565 ) ) ) ) ) )
=> ( ! [X1568: $i,X1569: $i] :
( ( in @ X1569 @ ( powerset @ X1568 ) )
=> ! [X1570: $i] :
( ( in @ X1570 @ ( powerset @ X1568 ) )
=> ! [X1571: $i] :
( ( in @ X1571 @ X1568 )
=> ( ( subset @ X1569 @ X1570 )
=> ( ~ ( in @ X1571 @ X1570 )
=> ~ ( in @ X1571 @ X1569 ) ) ) ) ) )
=> ( ! [X1572: $i,X1573: $i] :
( ( in @ X1573 @ ( powerset @ X1572 ) )
=> ! [X1574: $i] :
( ( in @ X1574 @ ( powerset @ X1572 ) )
=> ( ( subset @ X1573 @ X1574 )
=> ( subset @ ( setminus @ X1572 @ X1574 ) @ ( setminus @ X1572 @ X1573 ) ) ) ) )
=> ( ! [X1575: $i,X1576: $i] :
( ( in @ X1576 @ ( powerset @ X1575 ) )
=> ! [X1577: $i] :
( ( in @ X1577 @ ( powerset @ X1575 ) )
=> ( ( subset @ ( setminus @ X1575 @ X1577 ) @ ( setminus @ X1575 @ X1576 ) )
=> ( subset @ X1576 @ X1577 ) ) ) )
=> ( ! [X1578: $i,X1579: $i] :
( ( in @ X1579 @ ( powerset @ X1578 ) )
=> ! [X1580: $i] :
( ( in @ X1580 @ X1578 )
=> ( ( in @ X1580 @ X1579 )
=> ( in @ X1580 @ ( setminus @ X1578 @ ( setminus @ X1578 @ X1579 ) ) ) ) ) )
=> ( ! [X1581: $i,X1582: $i] :
( ( in @ X1582 @ ( powerset @ X1581 ) )
=> ! [X1583: $i] :
( ( in @ X1583 @ X1581 )
=> ( ( in @ X1583 @ ( setminus @ X1581 @ ( setminus @ X1581 @ X1582 ) ) )
=> ( in @ X1583 @ X1582 ) ) ) )
=> ( ! [X1584: $i,X1585: $i] :
( ( in @ X1585 @ ( powerset @ X1584 ) )
=> ( subset @ X1585 @ ( setminus @ X1584 @ ( setminus @ X1584 @ X1585 ) ) ) )
=> ( ! [X1586: $i,X1587: $i] :
( ( in @ X1587 @ ( powerset @ X1586 ) )
=> ( subset @ ( setminus @ X1586 @ ( setminus @ X1586 @ X1587 ) ) @ X1587 ) )
=> ( ! [X1588: $i,X1589: $i] :
( ( in @ X1589 @ ( powerset @ X1588 ) )
=> ( X1589
= ( setminus @ X1588 @ ( setminus @ X1588 @ X1589 ) ) ) )
=> ( ! [X1590: $i,X1591: $i] :
( ( in @ X1591 @ ( powerset @ X1590 ) )
=> ! [X1592: $i] :
( ( in @ X1592 @ ( powerset @ X1590 ) )
=> ! [X1593: $i] :
( ( in @ X1593 @ X1590 )
=> ( ( in @ X1593 @ ( setminus @ X1590 @ X1591 ) )
=> ~ ( in @ X1593 @ ( binintersect @ X1591 @ X1592 ) ) ) ) ) )
=> ( ! [X1594: $i,X1595: $i] :
( ( in @ X1595 @ ( powerset @ X1594 ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ ( powerset @ X1594 ) )
=> ! [X1597: $i] :
( ( in @ X1597 @ X1594 )
=> ( ( in @ X1597 @ ( setminus @ X1594 @ X1595 ) )
=> ( in @ X1597 @ ( setminus @ X1594 @ ( binintersect @ X1595 @ X1596 ) ) ) ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[complementSubsetComplementIntersect]),c_0_250]),binintersectT_lem]),complementImpComplementIntersect]),subbreln]),eqbreln]),funcext]),setadjoinSub]),funcext2]),ap2apEq1]),setadjoinSub2]),ap2apEq2]),c_0_251]),subset2powerset]),c_0_252]),c_0_253]),setextsub]),c_0_254]),c_0_255]),subsetemptysetimpeq]),c_0_256]),c_0_257]),powersetI1]),c_0_258]),c_0_259]),powersetE1]),c_0_260]),ifp]),inPowerset]),theeq]),iftrue]),iffalse]),powersetsubset]),iftrueorfalse]),binintersectSubset4]),binunionT_lem]),powersetT_lem]),setminusT_lem]),c_0_261]),complementT_lem]),setextT]),binunionIL]),subsetTI]),powersetTI1]),upairset2IR]),powersetTE1]),complementTI1]),complementTE1]),binintersectTELcontra]),binunionIR]),binintersectTERcontra]),contrasubsetT]),binunionEcases]),contrasubsetT1]),contrasubsetT2]),binunionE]),contrasubsetT3]),doubleComplementI1]),binunionLsub]),doubleComplementE1]),doubleComplementSub1]),binunionRsub]),doubleComplementSub2]),doubleComplementEq]),binintersectI]),complementTnotintersectT]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),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]),subsetE]),ubforcartprodlem3]),subsetE2]),cartprodpairin]),notsubsetI]),cartprodmempair1]),cartprodmempair]),setunionE2]),c_0_262]),c_0_263]),c_0_264]),c_0_265]),singletonsuniq]),setukpairinjL1]),c_0_266]),theprop]),notequalI1]),notequalI2]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_267]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_268]),c_0_269]),c_0_270]),c_0_271]),c_0_272]),c_0_273]),c_0_274]),c_0_275]),c_0_276]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_277]),c_0_278]),c_0_279]),brelnall1]),brelnall2]),c_0_280]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subsetRefl]),subsetTrans]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_281]),c_0_282]),c_0_283]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_284]),c_0_285]),in__Cong]),inCongP]),c_0_286]),c_0_287]),c_0_288]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_289]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_290]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_291]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_292]),nonemptyE1]),c_0_293]),noeltsimpempty]),emptyI]),setext]),c_0_294]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_295]),c_0_296]),c_0_297]),c_0_298]),c_0_299]),wellorderingAx]),foundationAx]),c_0_300]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_301]) ).
thf(c_0_303,negated_conjecture,
! [X1598: $i,X1599: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $i,X1605: $i,X1606: $i,X1607: $i,X1608: $i,X1609: $i,X1611: $i,X1612: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1620: $i,X1621: $i > $i > $o,X1622: $i,X1625: $i,X1627: $i,X1628: $i,X1629: $i,X1630: $i,X1632: $i,X1633: $i > $o,X1634: $i,X1635: $i > $o,X1636: $i,X1637: $i,X1638: $i > $o,X1639: $i,X1640: $i,X1641: $i > $o,X1642: $i,X1643: $i > $o,X1645: $i,X1646: $o,X1647: $i,X1648: $i,X1649: $o,X1650: $i,X1651: $i,X1652: $i > $o,X1654: $i,X1655: $i,X1658: $i,X1660: $i,X1662: $i,X1663: $i > $o,X1664: $i,X1665: $i,X1667: $i,X1668: $i > $o,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $o,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $o,X1700: $i,X1701: $i,X1702: $i > $o,X1704: $i,X1705: $i,X1706: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $i,X1716: $i,X1717: $i,X1718: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1724: $i > $o,X1725: $i,X1726: $i > $o,X1727: $i,X1728: $i,X1729: $i > $o,X1730: $i,X1732: $i,X1733: $i > $o,X1735: $i,X1736: $i,X1737: $i > $o,X1739: $i,X1740: $i,X1741: $i > $o,X1742: $i,X1744: $o,X1745: $i,X1746: $i > $o,X1748: $i,X1749: $i,X1750: $i > $o,X1751: $i,X1753: $i > $o,X1754: $i,X1756: $i > $o,X1757: $i,X1760: $i > $o,X1761: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i > $o,X1772: $i,X1773: $i,X1774: $i > $o,X1775: $i > $o,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i > $o,X1787: $i,X1788: $i,X1789: $i > $o,X1790: $i > $o,X1793: $i,X1794: $i,X1795: $i > $o,X1796: $i > $o,X1799: $i,X1800: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1845: $i,X1846: $i > $o,X1847: $i,X1848: $i > $o,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $o,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $o,X1929: $i,X1930: $i,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $i,X1943: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i,X1950: $i,X1951: $i,X1952: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i > $o,X2003: $i,X2004: $i,X2005: $i > $o,X2007: $i,X2008: $i > $o,X2009: $i,X2011: $i,X2012: $i > $o,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i > $i > $o,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i > $i > $o,X2093: $i,X2094: $i,X2095: $i > $i > $o,X2096: $i,X2097: $i,X2098: $i > $i > $o,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i > $i > $o,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i > $i > $o,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i > $i > $o,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i > $i,X2142: $i,X2143: $i,X2144: $i > $i,X2146: $i,X2147: $i,X2148: $i > $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i > $o,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i > $o,X2163: $i,X2164: $i,X2165: $i > $o,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i > $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i > $i,X2237: $i,X2238: $i,X2239: $i > $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2245: $i,X2246: $o,X2247: $i,X2248: $i,X2249: $i,X2250: $o,X2251: $i,X2252: $i,X2253: $i,X2254: $o,X2255: $i,X2256: $i,X2257: $i,X2258: $o,X2259: $i,X2260: $i,X2261: $i,X2262: $o,X2263: $i,X2264: $i,X2265: $i,X2266: $o,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i,X2272: $o,X2273: $i,X2274: $i,X2275: $i,X2276: $o,X2277: $i,X2278: $i,X2279: $i,X2280: $o,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,X2301: $i,X2302: $i,X2303: $i,X2305: $i,X2306: $i,X2307: $i,X2309: $i,X2310: $i,X2311: $i,X2312: $i,X2313: $i,X2314: $i,X2315: $i,X2316: $i,X2317: $i,X2318: $i,X2319: $i,X2320: $i,X2321: $i,X2322: $i,X2323: $i,X2324: $i,X2325: $i,X2326: $i,X2327: $i,X2328: $i,X2329: $i,X2330: $i,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] :
( ( ~ ( in @ ( esk1_2 @ X1598 @ X1599 ) @ X1598 )
| ~ ( in @ ( esk1_2 @ X1598 @ X1599 ) @ X1599 )
| ( X1598 = X1599 ) )
& ( ( in @ ( esk1_2 @ X1598 @ X1599 ) @ X1598 )
| ( in @ ( esk1_2 @ X1598 @ X1599 ) @ X1599 )
| ( X1598 = X1599 ) )
& ~ ( in @ X1601 @ emptyset )
& ( ~ ( in @ X1604 @ ( setadjoin @ X1602 @ X1603 ) )
| ( X1604 = X1602 )
| ( in @ X1604 @ X1603 ) )
& ( ( X1604 != X1602 )
| ( in @ X1604 @ ( setadjoin @ X1602 @ X1603 ) ) )
& ( ~ ( in @ X1604 @ X1603 )
| ( in @ X1604 @ ( setadjoin @ X1602 @ X1603 ) ) )
& ( ~ ( in @ X1606 @ ( powerset @ X1605 ) )
| ~ ( in @ X1607 @ X1606 )
| ( in @ X1607 @ X1605 ) )
& ( ( in @ ( esk2_2 @ X1608 @ X1609 ) @ X1609 )
| ( in @ X1609 @ ( powerset @ X1608 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1608 @ X1609 ) @ X1608 )
| ( in @ X1609 @ ( powerset @ X1608 ) ) )
& ( ( in @ X1612 @ ( esk3_2 @ X1611 @ X1612 ) )
| ~ ( in @ X1612 @ ( setunion @ X1611 ) ) )
& ( ( in @ ( esk3_2 @ X1611 @ X1612 ) @ X1611 )
| ~ ( in @ X1612 @ ( setunion @ X1611 ) ) )
& ( ~ ( in @ X1615 @ X1616 )
| ~ ( in @ X1616 @ X1614 )
| ( in @ X1615 @ ( setunion @ X1614 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1617 @ omega )
| ( in @ ( setadjoin @ X1617 @ X1617 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1618 ) @ omega )
| ~ ( in @ emptyset @ X1618 )
| ~ ( in @ X1620 @ omega )
| ( in @ X1620 @ X1618 ) )
& ( ( in @ ( esk4_1 @ X1618 ) @ X1618 )
| ~ ( in @ emptyset @ X1618 )
| ~ ( in @ X1620 @ omega )
| ( in @ X1620 @ X1618 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1618 ) @ ( esk4_1 @ X1618 ) ) @ X1618 )
| ~ ( in @ emptyset @ X1618 )
| ~ ( in @ X1620 @ omega )
| ( in @ X1620 @ X1618 ) )
& ( ( in @ ( esk7_3 @ X1621 @ X1622 @ X1625 ) @ X1622 )
| ~ ( in @ X1625 @ ( esk6_2 @ X1621 @ X1622 ) )
| ( in @ ( esk5_2 @ X1621 @ X1622 ) @ X1622 ) )
& ( ( X1621 @ ( esk7_3 @ X1621 @ X1622 @ X1625 ) @ X1625 )
| ~ ( in @ X1625 @ ( esk6_2 @ X1621 @ X1622 ) )
| ( in @ ( esk5_2 @ X1621 @ X1622 ) @ X1622 ) )
& ( ~ ( in @ X1628 @ X1622 )
| ~ ( X1621 @ X1628 @ X1627 )
| ( in @ X1627 @ ( esk6_2 @ X1621 @ X1622 ) )
| ( in @ ( esk5_2 @ X1621 @ X1622 ) @ X1622 ) )
& ( ( in @ ( esk7_3 @ X1621 @ X1622 @ X1625 ) @ X1622 )
| ~ ( in @ X1625 @ ( esk6_2 @ X1621 @ X1622 ) )
| ~ ( exu @ ( X1621 @ ( esk5_2 @ X1621 @ X1622 ) ) ) )
& ( ( X1621 @ ( esk7_3 @ X1621 @ X1622 @ X1625 ) @ X1625 )
| ~ ( in @ X1625 @ ( esk6_2 @ X1621 @ X1622 ) )
| ~ ( exu @ ( X1621 @ ( esk5_2 @ X1621 @ X1622 ) ) ) )
& ( ~ ( in @ X1628 @ X1622 )
| ~ ( X1621 @ X1628 @ X1627 )
| ( in @ X1627 @ ( esk6_2 @ X1621 @ X1622 ) )
| ~ ( exu @ ( X1621 @ ( esk5_2 @ X1621 @ X1622 ) ) ) )
& ( ( in @ ( esk8_1 @ X1629 ) @ X1629 )
| ~ ( in @ X1630 @ X1629 ) )
& ( ~ ( in @ X1632 @ ( esk8_1 @ X1629 ) )
| ~ ( in @ X1632 @ X1629 )
| ~ ( in @ X1630 @ X1629 ) )
& epred1_0
& ( ~ ( exu @ X1633 )
| ( X1633 @ ( descr @ X1633 ) ) )
& ( ~ ( in @ X1636 @ X1634 )
| ~ ( X1635 @ X1636 )
| ( in @ X1636 @ ( dsetconstr @ X1634 @ X1635 ) ) )
& ( ~ ( in @ X1639 @ ( dsetconstr @ X1637 @ X1638 ) )
| ( in @ X1639 @ X1637 ) )
& ( ~ ( in @ X1642 @ ( dsetconstr @ X1640 @ X1641 ) )
| ( X1641 @ X1642 ) )
& ( ( X1643 @ ( esk9_1 @ X1643 ) )
| ~ ( exu @ X1643 ) )
& ( ~ ( X1643 @ X1645 )
| ( ( esk9_1 @ X1643 )
= X1645 )
| ~ ( exu @ X1643 ) )
& ( ~ ( in @ X1647 @ ( prop2set @ X1646 ) )
| X1646 )
& ( ~ ( in @ X1648 @ emptyset )
| X1649 )
& ( ~ ( in @ X1650 @ emptyset )
| ~ $true )
& ~ ( in @ X1651 @ emptyset )
& ( ~ ( exu @ X1652 )
| ( X1652 @ ( esk10_1 @ X1652 ) ) )
& ( ( in @ ( esk12_2 @ X1654 @ X1655 ) @ X1655 )
| ( X1654 = X1655 )
| ( in @ ( esk11_2 @ X1654 @ X1655 ) @ X1654 ) )
& ( ~ ( in @ ( esk12_2 @ X1654 @ X1655 ) @ X1654 )
| ( X1654 = X1655 )
| ( in @ ( esk11_2 @ X1654 @ X1655 ) @ X1654 ) )
& ( ( in @ ( esk12_2 @ X1654 @ X1655 ) @ X1655 )
| ( X1654 = X1655 )
| ~ ( in @ ( esk11_2 @ X1654 @ X1655 ) @ X1655 ) )
& ( ~ ( in @ ( esk12_2 @ X1654 @ X1655 ) @ X1654 )
| ( X1654 = X1655 )
| ~ ( in @ ( esk11_2 @ X1654 @ X1655 ) @ X1655 ) )
& ( ( in @ ( esk13_1 @ X1658 ) @ X1658 )
| ( X1658 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1660 ) @ X1660 )
| ( X1660 = emptyset ) )
& ( ~ ( in @ X1664 @ ( dsetconstr @ X1662 @ X1663 ) )
| ( X1663 @ X1664 )
| ~ ( in @ X1664 @ X1662 ) )
& ( ~ ( X1663 @ X1664 )
| ( in @ X1664 @ ( dsetconstr @ X1662 @ X1663 ) )
| ~ ( in @ X1664 @ X1662 ) )
& ( ~ ( nonempty @ X1665 )
| ( in @ ( esk15_1 @ X1665 ) @ X1665 ) )
& ( ~ ( in @ X1669 @ X1667 )
| ~ ( X1668 @ X1669 )
| ( nonempty @ ( dsetconstr @ X1667 @ X1668 ) ) )
& ( ~ ( in @ X1671 @ X1670 )
| ( nonempty @ X1670 ) )
& ( in @ X1672 @ ( setadjoin @ X1672 @ X1673 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1676 @ X1675 )
| ( in @ X1676 @ ( setadjoin @ X1674 @ X1675 ) ) )
& ( ( in @ X1679 @ X1678 )
| X1680
| ( X1679 = X1677 )
| ~ ( in @ X1679 @ ( setadjoin @ X1677 @ X1678 ) ) )
& ( ~ X1680
| X1680
| ( X1679 = X1677 )
| ~ ( in @ X1679 @ ( setadjoin @ X1677 @ X1678 ) ) )
& ( ( in @ X1679 @ X1678 )
| X1680
| ~ X1680
| ~ ( in @ X1679 @ ( setadjoin @ X1677 @ X1678 ) ) )
& ( ~ X1680
| X1680
| ~ X1680
| ~ ( in @ X1679 @ ( setadjoin @ X1677 @ X1678 ) ) )
& ( ~ ( in @ X1683 @ ( setadjoin @ X1681 @ X1682 ) )
| ( X1683 = X1681 )
| ( in @ X1683 @ X1682 ) )
& ( ( dsetconstr @ X1684
@ ^ [Z0: $i] : $true )
= X1684 )
& ( ( in @ ( esk16_2 @ X1685 @ X1686 ) @ X1686 )
| ( in @ X1686 @ ( powerset @ X1685 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1685 @ X1686 ) @ X1685 )
| ( in @ X1686 @ ( powerset @ X1685 ) ) )
& ( in @ emptyset @ ( powerset @ X1688 ) )
& ( in @ emptyset @ ( powerset @ X1689 ) )
& ( ~ ( in @ X1691 @ ( powerset @ X1690 ) )
| ~ ( in @ X1692 @ X1691 )
| ( in @ X1692 @ X1690 ) )
& ( ~ ( in @ X1694 @ X1695 )
| ~ ( in @ X1695 @ X1693 )
| ( in @ X1694 @ ( setunion @ X1693 ) ) )
& ( ( in @ X1697 @ ( esk17_3 @ X1696 @ X1697 @ X1698 ) )
| X1698
| ~ ( in @ X1697 @ ( setunion @ X1696 ) ) )
& ( ( in @ ( esk17_3 @ X1696 @ X1697 @ X1698 ) @ X1696 )
| X1698
| ~ ( in @ X1697 @ ( setunion @ X1696 ) ) )
& ( ~ X1698
| X1698
| ~ ( in @ X1697 @ ( setunion @ X1696 ) ) )
& ( ~ ( in @ X1701 @ X1700 )
| ( in @ X1701 @ ( powerset @ ( setunion @ X1700 ) ) ) )
& ( ~ ( X1702 @ X1704 )
| ( X1704
= ( esk18_1 @ X1702 ) )
| ~ ( exu @ X1702 ) )
& ( ( X1705
!= ( esk18_1 @ X1702 ) )
| ( X1702 @ X1705 )
| ~ ( exu @ X1702 ) )
& ( ( in @ ( esk19_1 @ X1706 ) @ X1706 )
| ~ ( nonempty @ X1706 ) )
& ( $true
| ~ ( nonempty @ X1706 ) )
& ( ~ ( in @ X1708 @ ( setadjoin @ X1709 @ emptyset ) )
| ( X1708 = X1709 ) )
& ( ( X1710 = X1711 )
| ~ ( in @ X1711 @ ( setadjoin @ X1710 @ emptyset ) ) )
& ( ( X1712 != X1713 )
| ( in @ X1712 @ ( setadjoin @ X1713 @ emptyset ) ) )
& ( ~ ( in @ X1714 @ ( setadjoin @ X1715 @ emptyset ) )
| ( in @ X1715 @ ( setadjoin @ X1714 @ emptyset ) ) )
& ( ~ ( in @ X1718 @ ( setadjoin @ X1716 @ ( setadjoin @ X1717 @ emptyset ) ) )
| ( X1718 = X1716 )
| ( X1718 = X1717 ) )
& ( in @ X1719 @ ( setadjoin @ X1719 @ ( setadjoin @ X1720 @ emptyset ) ) )
& ( in @ X1722 @ ( setadjoin @ X1721 @ ( setadjoin @ X1722 @ emptyset ) ) )
& ( ~ ( in @ X1725 @ X1723 )
| ~ ( X1724 @ X1725 )
| ( ( dsetconstr @ X1723 @ X1724 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1727 @ emptyset )
| ( X1726 @ X1727 ) )
& ( ( in @ ( esk20_2 @ X1728 @ X1729 ) @ X1728 )
| ~ ( in @ X1730 @ X1728 )
| ( X1729 @ X1730 ) )
& ( ~ ( X1729 @ ( esk20_2 @ X1728 @ X1729 ) )
| ~ ( in @ X1730 @ X1728 )
| ( X1729 @ X1730 ) )
& ( ( in @ ( esk21_2 @ X1732 @ X1733 ) @ X1732 )
| ~ ( in @ X1735 @ X1732 )
| ~ ( X1733 @ X1735 ) )
& ( ( X1733 @ ( esk21_2 @ X1732 @ X1733 ) )
| ~ ( in @ X1735 @ X1732 )
| ~ ( X1733 @ X1735 ) )
& ( ( in @ ( esk22_2 @ X1736 @ X1737 ) @ X1736 )
| ~ ( in @ X1739 @ X1736 )
| ~ ( X1737 @ X1739 ) )
& ( ( X1737 @ ( esk22_2 @ X1736 @ X1737 ) )
| ~ ( in @ X1739 @ X1736 )
| ~ ( X1737 @ X1739 ) )
& ( ( in @ ( esk23_2 @ X1740 @ X1741 ) @ X1740 )
| ~ ( in @ X1742 @ X1740 )
| ( X1741 @ X1742 ) )
& ( ~ ( X1741 @ ( esk23_2 @ X1740 @ X1741 ) )
| ~ ( in @ X1742 @ X1740 )
| ( X1741 @ X1742 ) )
& ( ~ X1744
| ( in @ emptyset @ ( prop2set @ X1744 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1745 @ X1746 ) @ X1745 )
| ~ ( in @ X1748 @ X1745 )
| ~ ( X1746 @ X1748 ) )
& ( ( X1746 @ ( esk24_2 @ X1745 @ X1746 ) )
| ~ ( in @ X1748 @ X1745 )
| ~ ( X1746 @ X1748 ) )
& ( ( in @ ( esk25_2 @ X1749 @ X1750 ) @ X1749 )
| ~ ( in @ X1751 @ X1749 )
| ( X1750 @ X1751 ) )
& ( ~ ( X1750 @ ( esk25_2 @ X1749 @ X1750 ) )
| ~ ( in @ X1751 @ X1749 )
| ( X1750 @ X1751 ) )
& ( ( X1753 @ ( esk26_2 @ X1753 @ X1754 ) )
| ~ ( X1753 @ X1754 )
| ( exu @ X1753 ) )
& ( ( X1754
!= ( esk26_2 @ X1753 @ X1754 ) )
| ~ ( X1753 @ X1754 )
| ( exu @ X1753 ) )
& ( ( X1756 @ ( esk27_1 @ X1756 ) )
| ( exu @ X1756 )
| ~ ( X1756 @ X1757 ) )
& ( ( X1756 @ ( esk28_1 @ X1756 ) )
| ( exu @ X1756 )
| ~ ( X1756 @ X1757 ) )
& ( ( ( esk27_1 @ X1756 )
!= ( esk28_1 @ X1756 ) )
| ( exu @ X1756 )
| ~ ( X1756 @ X1757 ) )
& ( ~ ( X1760 @ ( esk29_2 @ X1760 @ X1761 ) )
| ( ( esk29_2 @ X1760 @ X1761 )
!= X1761 )
| ( exu @ X1760 ) )
& ( ( X1760 @ ( esk29_2 @ X1760 @ X1761 ) )
| ( ( esk29_2 @ X1760 @ X1761 )
= X1761 )
| ( exu @ X1760 ) )
& ( ( X1763 != X1764 )
| ( X1765 != X1766 )
| ~ ( in @ X1765 @ X1763 )
| ( in @ X1766 @ X1764 ) )
& ( ~ ( in @ X1769 @ X1767 )
| ( in @ X1770 @ X1768 )
| ( X1769 != X1770 )
| ( X1767 != X1768 ) )
& ( ~ ( in @ X1770 @ X1768 )
| ( in @ X1769 @ X1767 )
| ( X1769 != X1770 )
| ( X1767 != X1768 ) )
& ( ~ ( exu @ X1771 )
| ~ ( X1771 @ X1772 )
| ~ ( X1771 @ X1773 )
| ( X1772 = X1773 ) )
& ( ~ ( exu @ X1774 )
| ( exu @ X1775 )
| ( ( esk30_2 @ X1774 @ X1775 )
= ( esk31_2 @ X1774 @ X1775 ) ) )
& ( ~ ( exu @ X1775 )
| ( exu @ X1774 )
| ( ( esk30_2 @ X1774 @ X1775 )
= ( esk31_2 @ X1774 @ X1775 ) ) )
& ( ~ ( exu @ X1774 )
| ( exu @ X1775 )
| ~ ( X1774 @ ( esk30_2 @ X1774 @ X1775 ) )
| ~ ( X1775 @ ( esk31_2 @ X1774 @ X1775 ) ) )
& ( ~ ( exu @ X1775 )
| ( exu @ X1774 )
| ~ ( X1774 @ ( esk30_2 @ X1774 @ X1775 ) )
| ~ ( X1775 @ ( esk31_2 @ X1774 @ X1775 ) ) )
& ( ~ ( exu @ X1774 )
| ( exu @ X1775 )
| ( X1774 @ ( esk30_2 @ X1774 @ X1775 ) )
| ( X1775 @ ( esk31_2 @ X1774 @ X1775 ) ) )
& ( ~ ( exu @ X1775 )
| ( exu @ X1774 )
| ( X1774 @ ( esk30_2 @ X1774 @ X1775 ) )
| ( X1775 @ ( esk31_2 @ X1774 @ X1775 ) ) )
& ( emptyset = emptyset )
& ( ( X1778 != X1779 )
| ( X1780 != X1781 )
| ( ( setadjoin @ X1778 @ X1780 )
= ( setadjoin @ X1779 @ X1781 ) ) )
& ( ( X1782 != X1783 )
| ( ( powerset @ X1782 )
= ( powerset @ X1783 ) ) )
& ( ( X1784 != X1785 )
| ( ( setunion @ X1784 )
= ( setunion @ X1785 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1786 )
| ~ ( X1786 @ X1787 )
| ~ ( X1786 @ X1788 )
| ( X1787 = X1788 ) )
& ( ( ( esk32_2 @ X1789 @ X1790 )
= ( esk33_2 @ X1789 @ X1790 ) )
| ~ ( exu @ X1789 )
| ~ ( exu @ X1790 )
| ( ( descr @ X1789 )
= ( descr @ X1790 ) ) )
& ( ~ ( X1789 @ ( esk32_2 @ X1789 @ X1790 ) )
| ~ ( X1790 @ ( esk33_2 @ X1789 @ X1790 ) )
| ~ ( exu @ X1789 )
| ~ ( exu @ X1790 )
| ( ( descr @ X1789 )
= ( descr @ X1790 ) ) )
& ( ( X1789 @ ( esk32_2 @ X1789 @ X1790 ) )
| ( X1790 @ ( esk33_2 @ X1789 @ X1790 ) )
| ~ ( exu @ X1789 )
| ~ ( exu @ X1790 )
| ( ( descr @ X1789 )
= ( descr @ X1790 ) ) )
& ( ( in @ ( esk34_4 @ X1793 @ X1794 @ X1795 @ X1796 ) @ X1793 )
| ( ( dsetconstr @ X1793 @ X1795 )
= ( dsetconstr @ X1794 @ X1796 ) )
| ( X1793 != X1794 ) )
& ( ( in @ ( esk35_4 @ X1793 @ X1794 @ X1795 @ X1796 ) @ X1794 )
| ( ( dsetconstr @ X1793 @ X1795 )
= ( dsetconstr @ X1794 @ X1796 ) )
| ( X1793 != X1794 ) )
& ( ( ( esk34_4 @ X1793 @ X1794 @ X1795 @ X1796 )
= ( esk35_4 @ X1793 @ X1794 @ X1795 @ X1796 ) )
| ( ( dsetconstr @ X1793 @ X1795 )
= ( dsetconstr @ X1794 @ X1796 ) )
| ( X1793 != X1794 ) )
& ( ~ ( X1795 @ ( esk34_4 @ X1793 @ X1794 @ X1795 @ X1796 ) )
| ~ ( X1796 @ ( esk35_4 @ X1793 @ X1794 @ X1795 @ X1796 ) )
| ( ( dsetconstr @ X1793 @ X1795 )
= ( dsetconstr @ X1794 @ X1796 ) )
| ( X1793 != X1794 ) )
& ( ( X1795 @ ( esk34_4 @ X1793 @ X1794 @ X1795 @ X1796 ) )
| ( X1796 @ ( esk35_4 @ X1793 @ X1794 @ X1795 @ X1796 ) )
| ( ( dsetconstr @ X1793 @ X1795 )
= ( dsetconstr @ X1794 @ X1796 ) )
| ( X1793 != X1794 ) )
& ( ( in @ ( esk36_2 @ X1799 @ X1800 ) @ X1799 )
| ( subset @ X1799 @ X1800 ) )
& ( ~ ( in @ ( esk36_2 @ X1799 @ X1800 ) @ X1800 )
| ( subset @ X1799 @ X1800 ) )
& ( ( X1802 != X1803 )
| ( subset @ X1803 @ X1802 ) )
& ( ( X1804 != X1805 )
| ( subset @ X1804 @ X1805 ) )
& ( ( in @ ( esk37_2 @ X1806 @ X1807 ) @ X1806 )
| ( subset @ X1806 @ X1807 ) )
& ( ~ ( in @ ( esk37_2 @ X1806 @ X1807 ) @ X1807 )
| ( subset @ X1806 @ X1807 ) )
& ( subset @ emptyset @ X1809 )
& ( ~ ( subset @ X1810 @ X1811 )
| ~ ( in @ X1812 @ X1810 )
| ( in @ X1812 @ X1811 ) )
& ( ~ ( subset @ X1813 @ X1814 )
| ( in @ X1815 @ X1814 )
| ~ ( in @ X1815 @ X1813 ) )
& ( ~ ( in @ X1818 @ X1816 )
| ( in @ X1818 @ X1817 )
| ~ ( subset @ X1816 @ X1817 ) )
& ( ( subset @ X1819 @ X1820 )
| ( X1819 != X1820 ) )
& ( ~ ( in @ X1823 @ X1821 )
| ( in @ X1823 @ X1822 )
| ( X1821 != X1822 ) )
& ( subset @ X1824 @ X1824 )
& ( ~ ( subset @ X1825 @ X1826 )
| ~ ( subset @ X1826 @ X1827 )
| ( subset @ X1825 @ X1827 ) )
& ( subset @ X1829 @ ( setadjoin @ X1828 @ X1829 ) )
& ( ~ ( subset @ X1830 @ X1832 )
| ( subset @ X1830 @ ( setadjoin @ X1831 @ X1832 ) ) )
& ( ~ ( subset @ X1833 @ X1834 )
| ( in @ X1833 @ ( powerset @ X1834 ) ) )
& ( ~ ( subset @ X1835 @ X1836 )
| ~ ( subset @ X1836 @ X1835 )
| ( X1835 = X1836 ) )
& ( ~ ( subset @ X1837 @ emptyset )
| ( X1837 = emptyset ) )
& ( ~ ( subset @ X1839 @ X1838 )
| ( in @ X1839 @ ( powerset @ X1838 ) ) )
& ( ~ ( in @ X1841 @ ( powerset @ X1840 ) )
| ( subset @ X1841 @ X1840 ) )
& ( in @ X1842 @ ( powerset @ X1842 ) )
& ( ~ ( subset @ X1843 @ X1844 )
| ( subset @ ( powerset @ X1843 ) @ ( powerset @ X1844 ) ) )
& ( in @ ( dsetconstr @ X1845 @ X1846 ) @ ( powerset @ X1845 ) )
& ( subset @ ( dsetconstr @ X1847 @ X1848 ) @ X1847 )
& ( ~ ( in @ X1851 @ X1849 )
| ( in @ X1851 @ ( binunion @ X1849 @ X1850 ) ) )
& ( in @ X1853 @ ( setadjoin @ X1852 @ ( setadjoin @ X1853 @ emptyset ) ) )
& ( ~ ( in @ X1856 @ X1855 )
| ( in @ X1856 @ ( binunion @ X1854 @ X1855 ) ) )
& ( ( in @ X1859 @ X1858 )
| X1860
| ( in @ X1859 @ X1857 )
| ~ ( in @ X1859 @ ( binunion @ X1857 @ X1858 ) ) )
& ( ~ X1860
| X1860
| ( in @ X1859 @ X1857 )
| ~ ( in @ X1859 @ ( binunion @ X1857 @ X1858 ) ) )
& ( ( in @ X1859 @ X1858 )
| X1860
| ~ X1860
| ~ ( in @ X1859 @ ( binunion @ X1857 @ X1858 ) ) )
& ( ~ X1860
| X1860
| ~ X1860
| ~ ( in @ X1859 @ ( binunion @ X1857 @ X1858 ) ) )
& ( ~ ( in @ X1863 @ ( binunion @ X1861 @ X1862 ) )
| ( in @ X1863 @ X1861 )
| ( in @ X1863 @ X1862 ) )
& ( subset @ X1864 @ ( binunion @ X1864 @ X1865 ) )
& ( subset @ X1867 @ ( binunion @ X1866 @ X1867 ) )
& ( ~ ( in @ X1870 @ X1868 )
| ~ ( in @ X1870 @ X1869 )
| ( in @ X1870 @ ( binintersect @ X1868 @ X1869 ) ) )
& ( ~ ( subset @ X1873 @ X1871 )
| ~ ( subset @ X1873 @ X1872 )
| ( subset @ X1873 @ ( binintersect @ X1871 @ X1872 ) ) )
& ( ~ ( in @ X1876 @ ( binintersect @ X1874 @ X1875 ) )
| ( in @ X1876 @ X1874 ) )
& ( subset @ ( binintersect @ X1877 @ X1878 ) @ X1877 )
& ( ~ ( subset @ X1879 @ X1880 )
| ( ( binintersect @ X1879 @ X1880 )
= X1879 ) )
& ( ( ( binintersect @ X1881 @ X1882 )
!= X1882 )
| ( subset @ X1882 @ X1881 ) )
& ( ~ ( in @ X1885 @ ( binintersect @ X1883 @ X1884 ) )
| ( in @ X1885 @ X1884 ) )
& ( ( in @ ( esk38_2 @ X1886 @ X1887 ) @ X1886 )
| ( ( binintersect @ X1886 @ X1887 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1886 @ X1887 ) @ X1887 )
| ( ( binintersect @ X1886 @ X1887 )
= emptyset ) )
& ( subset @ ( binintersect @ X1889 @ X1890 ) @ X1890 )
& ( ~ ( subset @ X1892 @ X1891 )
| ( ( binintersect @ X1891 @ X1892 )
= X1892 ) )
& ( ( ( binintersect @ X1893 @ X1894 )
!= X1893 )
| ( subset @ X1893 @ X1894 ) )
& ( ( binintersect @ X1895 @ ( binunion @ X1896 @ X1897 ) )
= ( binunion @ ( binintersect @ X1895 @ X1896 ) @ ( binintersect @ X1895 @ X1897 ) ) )
& ( ~ ( in @ X1900 @ X1898 )
| ( in @ X1900 @ X1899 )
| ( in @ X1900 @ ( setminus @ X1898 @ X1899 ) ) )
& ( ~ ( in @ X1903 @ ( setminus @ X1901 @ X1902 ) )
| ( in @ X1903 @ X1901 ) )
& ( ~ ( in @ X1906 @ ( setminus @ X1904 @ X1905 ) )
| ~ ( in @ X1906 @ X1905 ) )
& ( ~ ( subset @ X1907 @ X1908 )
| ( ( setminus @ X1907 @ X1908 )
= emptyset ) )
& ( ( in @ X1911 @ ( setminus @ X1909 @ X1910 ) )
| ~ ( in @ X1911 @ X1909 )
| ( in @ X1911 @ X1910 ) )
& ( ( in @ X1914 @ ( setminus @ X1912 @ X1913 ) )
| ( in @ X1914 @ X1913 )
| ~ ( in @ X1914 @ X1912 ) )
& ( ( in @ X1917 @ X1915 )
| ~ ( in @ X1917 @ ( setminus @ X1915 @ X1916 ) ) )
& ( ~ ( in @ X1920 @ X1919 )
| ~ ( in @ X1920 @ ( setminus @ X1918 @ X1919 ) ) )
& ( subset @ ( setminus @ X1921 @ X1922 ) @ X1921 )
& ( ( ( setminus @ X1923 @ X1924 )
!= emptyset )
| ( subset @ X1923 @ X1924 ) )
& ( ~ ( in @ X1927 @ X1925 )
| X1928
| ( in @ X1927 @ X1925 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ( in @ X1927 @ X1926 )
| X1928
| ( in @ X1927 @ X1925 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ X1928
| X1928
| ( in @ X1927 @ X1925 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ ( in @ X1927 @ X1925 )
| X1928
| ~ ( in @ X1927 @ X1926 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ( in @ X1927 @ X1926 )
| X1928
| ~ ( in @ X1927 @ X1926 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ X1928
| X1928
| ~ ( in @ X1927 @ X1926 )
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ ( in @ X1927 @ X1925 )
| X1928
| ~ X1928
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ( in @ X1927 @ X1926 )
| X1928
| ~ X1928
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ X1928
| X1928
| ~ X1928
| ~ ( in @ X1927 @ ( symdiff @ X1925 @ X1926 ) ) )
& ( ~ ( in @ X1931 @ X1929 )
| ( in @ X1931 @ X1930 )
| ( in @ X1931 @ ( symdiff @ X1929 @ X1930 ) ) )
& ( ( in @ X1934 @ X1932 )
| ~ ( in @ X1934 @ X1933 )
| ( in @ X1934 @ ( symdiff @ X1932 @ X1933 ) ) )
& ( ~ ( in @ X1937 @ X1935 )
| ~ ( in @ X1937 @ X1936 )
| ~ ( in @ X1937 @ ( symdiff @ X1935 @ X1936 ) ) )
& ( ( in @ X1940 @ X1938 )
| ( in @ X1940 @ X1939 )
| ~ ( in @ X1940 @ ( symdiff @ X1938 @ X1939 ) ) )
& ( in @ X1942 @ ( setadjoin @ X1941 @ ( setadjoin @ X1942 @ emptyset ) ) )
& ( in @ X1943 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1943 @ ( setadjoin @ X1944 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1946 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1945 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1945 @ ( setadjoin @ X1946 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1947 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1947 @ ( setadjoin @ X1948 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1949 @ X1950 ) )
& ( ~ ( in @ X1952 @ X1951 )
| ( subset @ ( setadjoin @ X1952 @ emptyset ) @ X1951 ) )
& ( ~ ( in @ X1954 @ X1953 )
| ( in @ ( setadjoin @ X1954 @ emptyset ) @ ( powerset @ X1953 ) ) )
& ( ~ ( in @ X1957 @ X1955 )
| ( in @ ( setadjoin @ X1957 @ emptyset ) @ ( powerset @ ( binunion @ X1955 @ X1956 ) ) ) )
& ( ~ ( in @ X1960 @ ( setadjoin @ X1958 @ ( setadjoin @ X1959 @ emptyset ) ) )
| ( X1960 = X1958 )
| ( X1960 = X1959 ) )
& ( ~ ( in @ X1963 @ X1961 )
| ~ ( in @ X1964 @ X1962 )
| ( subset @ ( setadjoin @ X1963 @ ( setadjoin @ X1964 @ emptyset ) ) @ ( binunion @ X1961 @ X1962 ) ) )
& ( ~ ( in @ X1967 @ X1965 )
| ~ ( in @ X1968 @ X1966 )
| ( in @ ( setadjoin @ X1967 @ ( setadjoin @ X1968 @ emptyset ) ) @ ( powerset @ ( binunion @ X1965 @ X1966 ) ) ) )
& ( ~ ( in @ X1971 @ X1969 )
| ~ ( in @ X1972 @ X1970 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1971 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1971 @ ( setadjoin @ X1972 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1969 @ X1970 ) ) ) )
& ( ~ ( in @ X1975 @ X1973 )
| ~ ( in @ X1976 @ X1974 )
| ( in @ ( setadjoin @ ( setadjoin @ X1975 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1975 @ ( setadjoin @ X1976 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1973 @ X1974 ) ) ) ) )
& ( ~ ( in @ X1979 @ X1977 )
| ~ ( in @ X1980 @ X1978 )
| ( in @ ( kpair @ X1979 @ X1980 ) @ ( powerset @ ( powerset @ ( binunion @ X1977 @ X1978 ) ) ) ) )
& ( ~ ( in @ X1983 @ X1981 )
| ~ ( in @ X1984 @ X1982 )
| ( in @ ( kpair @ X1983 @ X1984 ) @ ( cartprod @ X1981 @ X1982 ) ) )
& ( ( in @ ( esk39_3 @ X1985 @ X1986 @ X1987 ) @ X1985 )
| ~ ( in @ X1987 @ ( cartprod @ X1985 @ X1986 ) ) )
& ( ( in @ ( esk40_3 @ X1985 @ X1986 @ X1987 ) @ X1986 )
| ~ ( in @ X1987 @ ( cartprod @ X1985 @ X1986 ) ) )
& ( ( X1987
= ( kpair @ ( esk39_3 @ X1985 @ X1986 @ X1987 ) @ ( esk40_3 @ X1985 @ X1986 @ X1987 ) ) )
| ~ ( in @ X1987 @ ( cartprod @ X1985 @ X1986 ) ) )
& ( ~ ( in @ X1992 @ ( cartprod @ X1990 @ X1991 ) )
| ( iskpair @ X1992 ) )
& ( ( in @ ( esk41_2 @ X1993 @ X1994 ) @ X1993 )
| ~ ( in @ X1994 @ ( setunion @ X1993 ) ) )
& ( ( in @ X1994 @ ( esk41_2 @ X1993 @ X1994 ) )
| ~ ( in @ X1994 @ ( setunion @ X1993 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1996 @ emptyset ) ) @ X1996 )
& ( subset @ X1997 @ ( setunion @ ( setadjoin @ X1997 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1998 @ emptyset ) )
= X1998 )
& ( ( in @ ( esk42_2 @ X1999 @ X2000 ) @ X1999 )
| ~ ( in @ X2003 @ X1999 )
| ~ ( X2000 @ X2003 )
| ( singleton @ ( dsetconstr @ X1999 @ X2000 ) ) )
& ( ( in @ ( esk43_2 @ X1999 @ X2000 ) @ X1999 )
| ~ ( in @ X2003 @ X1999 )
| ~ ( X2000 @ X2003 )
| ( singleton @ ( dsetconstr @ X1999 @ X2000 ) ) )
& ( ( X2000 @ ( esk42_2 @ X1999 @ X2000 ) )
| ~ ( in @ X2003 @ X1999 )
| ~ ( X2000 @ X2003 )
| ( singleton @ ( dsetconstr @ X1999 @ X2000 ) ) )
& ( ( X2000 @ ( esk43_2 @ X1999 @ X2000 ) )
| ~ ( in @ X2003 @ X1999 )
| ~ ( X2000 @ X2003 )
| ( singleton @ ( dsetconstr @ X1999 @ X2000 ) ) )
& ( ( ( esk42_2 @ X1999 @ X2000 )
!= ( esk43_2 @ X1999 @ X2000 ) )
| ~ ( in @ X2003 @ X1999 )
| ~ ( X2000 @ X2003 )
| ( singleton @ ( dsetconstr @ X1999 @ X2000 ) ) )
& ( ( in @ ( esk44_2 @ X2004 @ X2005 ) @ X2004 )
| ~ ( ex1 @ X2004 @ X2005 ) )
& ( ( X2005 @ ( esk44_2 @ X2004 @ X2005 ) )
| ~ ( ex1 @ X2004 @ X2005 ) )
& ( ( in @ ( esk45_3 @ X2007 @ X2008 @ X2009 ) @ X2007 )
| ( ex1 @ X2007 @ X2008 )
| ~ ( X2008 @ X2009 )
| ~ ( in @ X2009 @ X2007 ) )
& ( ( X2008 @ ( esk45_3 @ X2007 @ X2008 @ X2009 ) )
| ( ex1 @ X2007 @ X2008 )
| ~ ( X2008 @ X2009 )
| ~ ( in @ X2009 @ X2007 ) )
& ( ( ( esk45_3 @ X2007 @ X2008 @ X2009 )
!= X2009 )
| ( ex1 @ X2007 @ X2008 )
| ~ ( X2008 @ X2009 )
| ~ ( in @ X2009 @ X2007 ) )
& ( ( in @ ( esk46_2 @ X2011 @ X2012 ) @ X2011 )
| ~ ( in @ X2015 @ X2011 )
| ~ ( X2012 @ X2015 )
| ( ex1 @ X2011 @ X2012 ) )
& ( ( in @ ( esk47_2 @ X2011 @ X2012 ) @ X2011 )
| ~ ( in @ X2015 @ X2011 )
| ~ ( X2012 @ X2015 )
| ( ex1 @ X2011 @ X2012 ) )
& ( ( X2012 @ ( esk46_2 @ X2011 @ X2012 ) )
| ~ ( in @ X2015 @ X2011 )
| ~ ( X2012 @ X2015 )
| ( ex1 @ X2011 @ X2012 ) )
& ( ( X2012 @ ( esk47_2 @ X2011 @ X2012 ) )
| ~ ( in @ X2015 @ X2011 )
| ~ ( X2012 @ X2015 )
| ( ex1 @ X2011 @ X2012 ) )
& ( ( ( esk46_2 @ X2011 @ X2012 )
!= ( esk47_2 @ X2011 @ X2012 ) )
| ~ ( in @ X2015 @ X2011 )
| ~ ( X2012 @ X2015 )
| ( ex1 @ X2011 @ X2012 ) )
& ( ( ( setadjoin @ X2016 @ emptyset )
!= ( setadjoin @ X2017 @ emptyset ) )
| ( X2016 = X2017 ) )
& ( ~ ( in @ ( setadjoin @ X2020 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2018 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2018 @ ( setadjoin @ X2019 @ emptyset ) ) @ emptyset ) ) )
| ( X2018 = X2020 ) )
& ( ~ ( iskpair @ X2021 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2021 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2021 ) ) ) )
& ( ~ ( singleton @ X2022 )
| ( in @ ( setunion @ X2022 ) @ X2022 ) )
& ( ( kfst @ ( kpair @ X2023 @ X2024 ) )
= X2023 )
& ( ~ ( in @ X2027 @ ( cartprod @ X2025 @ X2026 ) )
| ( in @ ( kfst @ X2027 ) @ X2025 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2028 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2028 @ ( setadjoin @ X2029 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2030 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2030 @ ( setadjoin @ X2031 @ emptyset ) ) @ emptyset ) ) )
| ( X2028 = X2030 ) )
& ( ( ( kpair @ X2032 @ X2033 )
!= ( kpair @ X2034 @ X2035 ) )
| ( X2032 = X2034 ) )
& ( ( X2036 != X2037 )
| ( ( setadjoin @ X2036 @ ( setadjoin @ X2037 @ emptyset ) )
= ( setadjoin @ X2036 @ emptyset ) ) )
& ( ( X2038 != X2039 )
| ( ( setadjoin @ ( setadjoin @ X2038 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2038 @ ( setadjoin @ X2039 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2038 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2040 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2040 @ ( setadjoin @ X2041 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2042 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2042 @ ( setadjoin @ X2043 @ emptyset ) ) @ emptyset ) ) )
| ( X2042 != X2043 )
| ( X2041 = X2043 ) )
& ( ( ( setadjoin @ X2044 @ ( setadjoin @ X2045 @ emptyset ) )
!= ( setadjoin @ X2046 @ emptyset ) )
| ( X2044 = X2045 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2047 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2047 @ ( setadjoin @ X2048 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2049 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2049 @ ( setadjoin @ X2050 @ emptyset ) ) @ emptyset ) ) )
| ( X2048 = X2050 ) )
& ( ( ( kpair @ X2051 @ X2052 )
!= ( kpair @ X2053 @ X2054 ) )
| ( X2052 = X2054 ) )
& ( ~ ( iskpair @ X2055 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2055 )
@ ^ [Z0: $i] :
( X2055
= ( kpair @ ( kfst @ X2055 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2056 @ X2057 ) )
= X2057 )
& ( ~ ( iskpair @ X2058 )
| ( ( kpair @ ( kfst @ X2058 ) @ ( ksnd @ X2058 ) )
= X2058 ) )
& ( ~ ( in @ X2061 @ ( cartprod @ X2059 @ X2060 ) )
| ( in @ ( ksnd @ X2061 ) @ X2060 ) )
& ( ~ ( in @ ( kpair @ X2064 @ X2065 ) @ ( cartprod @ X2062 @ X2063 ) )
| ( in @ X2064 @ X2062 ) )
& ( ~ ( in @ ( kpair @ X2068 @ X2069 ) @ ( cartprod @ X2066 @ X2067 ) )
| ( in @ X2069 @ X2067 ) )
& ( ~ ( in @ X2072 @ X2070 )
| ~ ( in @ X2073 @ X2071 )
| ( ( kpair @ X2072 @ X2073 )
= ( kpair @ X2072 @ X2073 ) ) )
& ( ~ ( in @ X2076 @ X2074 )
| ~ ( in @ X2077 @ X2075 )
| ( ( kfst @ ( kpair @ X2076 @ X2077 ) )
= X2076 ) )
& ( ~ ( in @ X2080 @ X2078 )
| ~ ( in @ X2081 @ X2079 )
| ( ( ksnd @ ( kpair @ X2080 @ X2081 ) )
= X2081 ) )
& ( ~ ( in @ X2084 @ ( cartprod @ X2082 @ X2083 ) )
| ( ( kpair @ ( kfst @ X2084 ) @ ( ksnd @ X2084 ) )
= X2084 ) )
& ( ~ ( in @ X2088 @ X2085 )
| ~ ( in @ X2089 @ X2086 )
| ~ ( X2087 @ X2088 @ X2089 )
| ( in @ ( kpair @ X2088 @ X2089 ) @ ( dpsetconstr @ X2085 @ X2086 @ X2087 ) ) )
& ( subset @ ( dpsetconstr @ X2090 @ X2091 @ X2092 ) @ ( cartprod @ X2090 @ X2091 ) )
& ( breln @ X2093 @ X2094 @ ( dpsetconstr @ X2093 @ X2094 @ X2095 ) )
& ( ~ ( in @ X2099 @ X2096 )
| ~ ( in @ X2100 @ X2097 )
| ~ ( in @ ( kpair @ X2099 @ X2100 ) @ ( dpsetconstr @ X2096 @ X2097 @ X2098 ) )
| ( X2098 @ X2099 @ X2100 ) )
& ( ~ ( in @ ( kpair @ X2104 @ X2105 ) @ ( dpsetconstr @ X2101 @ X2102 @ X2103 ) )
| ( in @ X2104 @ X2101 ) )
& ( ~ ( in @ ( kpair @ X2109 @ X2110 ) @ ( dpsetconstr @ X2106 @ X2107 @ X2108 ) )
| ( in @ X2110 @ X2107 ) )
& ( ~ ( in @ ( kpair @ X2114 @ X2115 ) @ ( dpsetconstr @ X2111 @ X2112 @ X2113 ) )
| ( X2113 @ X2114 @ X2115 ) )
& ( ~ ( func @ X2116 @ X2117 @ X2118 )
| ~ ( in @ X2119 @ X2116 )
| ( singleton
@ ( dsetconstr @ X2117
@ ^ [Z0: $i] : ( in @ ( kpair @ X2119 @ Z0 ) @ X2118 ) ) ) )
& ( ~ ( func @ X2120 @ X2121 @ X2122 )
| ~ ( in @ X2123 @ X2120 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2121
@ ^ [Z0: $i] : ( in @ ( kpair @ X2123 @ Z0 ) @ X2122 ) ) )
@ X2121 ) )
& ( ~ ( func @ X2124 @ X2125 @ X2126 )
| ~ ( in @ X2127 @ X2124 )
| ( in @ ( ap @ X2124 @ X2125 @ X2126 @ X2127 ) @ X2125 ) )
& ( ~ ( in @ X2130 @ ( funcSet @ X2128 @ X2129 ) )
| ( func @ X2128 @ X2129 @ X2130 ) )
& ( ~ ( in @ X2133 @ ( funcSet @ X2131 @ X2132 ) )
| ~ ( in @ X2134 @ X2131 )
| ( in @ ( ap @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 ) )
& ( ~ ( func @ X2135 @ X2136 @ X2137 )
| ( in @ X2137 @ ( funcSet @ X2135 @ X2136 ) ) )
& ( ( in @ ( esk48_3 @ X2138 @ X2139 @ X2140 ) @ X2138 )
| ( func @ X2138 @ X2139
@ ( dpsetconstr @ X2138 @ X2139
@ ^ [Z0: $i] : ( $eq @ ( X2140 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2140 @ ( esk48_3 @ X2138 @ X2139 @ X2140 ) ) @ X2139 )
| ( func @ X2138 @ X2139
@ ( dpsetconstr @ X2138 @ X2139
@ ^ [Z0: $i] : ( $eq @ ( X2140 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2142 @ X2143 @ X2144 ) @ X2142 )
| ( func @ X2142 @ X2143 @ ( lam @ X2142 @ X2143 @ X2144 ) ) )
& ( ~ ( in @ ( X2144 @ ( esk49_3 @ X2142 @ X2143 @ X2144 ) ) @ X2143 )
| ( func @ X2142 @ X2143 @ ( lam @ X2142 @ X2143 @ X2144 ) ) )
& ( ( in @ ( esk50_3 @ X2146 @ X2147 @ X2148 ) @ X2146 )
| ( in @ ( lam @ X2146 @ X2147 @ X2148 ) @ ( funcSet @ X2146 @ X2147 ) ) )
& ( ~ ( in @ ( X2148 @ ( esk50_3 @ X2146 @ X2147 @ X2148 ) ) @ X2147 )
| ( in @ ( lam @ X2146 @ X2147 @ X2148 ) @ ( funcSet @ X2146 @ X2147 ) ) )
& ( ( in @ ( esk51_4 @ X2150 @ X2151 @ X2152 @ X2153 ) @ X2150 )
| ~ ( in @ X2156 @ X2152 )
| ( X2153 @ X2156 )
| ~ ( breln @ X2150 @ X2151 @ X2152 ) )
& ( ( in @ ( esk52_4 @ X2150 @ X2151 @ X2152 @ X2153 ) @ X2151 )
| ~ ( in @ X2156 @ X2152 )
| ( X2153 @ X2156 )
| ~ ( breln @ X2150 @ X2151 @ X2152 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2150 @ X2151 @ X2152 @ X2153 ) @ ( esk52_4 @ X2150 @ X2151 @ X2152 @ X2153 ) ) @ X2152 )
| ~ ( in @ X2156 @ X2152 )
| ( X2153 @ X2156 )
| ~ ( breln @ X2150 @ X2151 @ X2152 ) )
& ( ~ ( X2153 @ ( kpair @ ( esk51_4 @ X2150 @ X2151 @ X2152 @ X2153 ) @ ( esk52_4 @ X2150 @ X2151 @ X2152 @ X2153 ) ) )
| ~ ( in @ X2156 @ X2152 )
| ( X2153 @ X2156 )
| ~ ( breln @ X2150 @ X2151 @ X2152 ) )
& ( ( in @ ( esk53_4 @ X2157 @ X2158 @ X2159 @ X2160 ) @ X2157 )
| ~ ( in @ X2163 @ X2159 )
| ( X2160 @ X2163 )
| ~ ( breln @ X2157 @ X2158 @ X2159 ) )
& ( ( in @ ( esk54_4 @ X2157 @ X2158 @ X2159 @ X2160 ) @ X2158 )
| ~ ( in @ X2163 @ X2159 )
| ( X2160 @ X2163 )
| ~ ( breln @ X2157 @ X2158 @ X2159 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2157 @ X2158 @ X2159 @ X2160 ) @ ( esk54_4 @ X2157 @ X2158 @ X2159 @ X2160 ) ) @ X2159 )
| ~ ( in @ X2163 @ X2159 )
| ( X2160 @ X2163 )
| ~ ( breln @ X2157 @ X2158 @ X2159 ) )
& ( ~ ( X2160 @ ( kpair @ ( esk53_4 @ X2157 @ X2158 @ X2159 @ X2160 ) @ ( esk54_4 @ X2157 @ X2158 @ X2159 @ X2160 ) ) )
| ~ ( in @ X2163 @ X2159 )
| ( X2160 @ X2163 )
| ~ ( breln @ X2157 @ X2158 @ X2159 ) )
& ( ~ ( ex1 @ X2164 @ X2165 )
| ~ ( in @ X2166 @ X2164 )
| ~ ( in @ X2167 @ X2164 )
| ~ ( X2165 @ X2166 )
| ~ ( X2165 @ X2167 )
| ( X2166 = X2167 ) )
& ( ~ ( func @ X2168 @ X2169 @ X2170 )
| ~ ( in @ X2171 @ X2168 )
| ( in @ ( kpair @ X2171 @ ( ap @ X2168 @ X2169 @ X2170 @ X2171 ) ) @ X2170 ) )
& ( ~ ( in @ X2174 @ ( funcSet @ X2172 @ X2173 ) )
| ~ ( in @ X2175 @ X2172 )
| ( in @ ( kpair @ X2175 @ ( ap @ X2172 @ X2173 @ X2174 @ X2175 ) ) @ X2174 ) )
& ( ~ ( func @ X2176 @ X2177 @ X2178 )
| ~ ( in @ X2179 @ X2176 )
| ~ ( in @ X2180 @ X2177 )
| ~ ( in @ ( kpair @ X2179 @ X2180 ) @ X2178 )
| ( ( ap @ X2176 @ X2177 @ X2178 @ X2179 )
= X2180 ) )
& ( ( in @ ( esk55_4 @ X2181 @ X2182 @ X2183 @ X2184 ) @ X2181 )
| ~ ( in @ X2186 @ X2181 )
| ~ ( in @ X2187 @ X2182 )
| ~ ( in @ ( kpair @ X2186 @ X2187 ) @ X2184 )
| ( in @ ( kpair @ X2186 @ X2187 ) @ X2183 )
| ~ ( func @ X2181 @ X2182 @ X2184 )
| ~ ( func @ X2181 @ X2182 @ X2183 ) )
& ( ( ( ap @ X2181 @ X2182 @ X2183 @ ( esk55_4 @ X2181 @ X2182 @ X2183 @ X2184 ) )
!= ( ap @ X2181 @ X2182 @ X2184 @ ( esk55_4 @ X2181 @ X2182 @ X2183 @ X2184 ) ) )
| ~ ( in @ X2186 @ X2181 )
| ~ ( in @ X2187 @ X2182 )
| ~ ( in @ ( kpair @ X2186 @ X2187 ) @ X2184 )
| ( in @ ( kpair @ X2186 @ X2187 ) @ X2183 )
| ~ ( func @ X2181 @ X2182 @ X2184 )
| ~ ( func @ X2181 @ X2182 @ X2183 ) )
& ( ~ ( in @ X2190 @ ( funcSet @ X2188 @ X2189 ) )
| ~ ( in @ X2191 @ X2188 )
| ~ ( in @ X2192 @ X2189 )
| ~ ( in @ ( kpair @ X2191 @ X2192 ) @ X2190 )
| ( ( ap @ X2188 @ X2189 @ X2190 @ X2191 )
= X2192 ) )
& ( ( in @ ( esk56_4 @ X2193 @ X2194 @ X2195 @ X2196 ) @ X2193 )
| ( subset @ X2195 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2195 ) )
& ( ( in @ ( esk57_4 @ X2193 @ X2194 @ X2195 @ X2196 ) @ X2194 )
| ( subset @ X2195 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2195 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2193 @ X2194 @ X2195 @ X2196 ) @ ( esk57_4 @ X2193 @ X2194 @ X2195 @ X2196 ) ) @ X2195 )
| ( subset @ X2195 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2195 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2193 @ X2194 @ X2195 @ X2196 ) @ ( esk57_4 @ X2193 @ X2194 @ X2195 @ X2196 ) ) @ X2196 )
| ( subset @ X2195 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2196 )
| ~ ( breln @ X2193 @ X2194 @ X2195 ) )
& ( ( in @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ( X2201 = X2202 )
| ( in @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ( X2201 = X2202 )
| ( in @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ( X2201 = X2202 )
| ( in @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ( X2201 = X2202 )
| ( in @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ( X2201 = X2202 )
| ( in @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ( X2201 = X2202 )
| ( in @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ( X2201 = X2202 )
| ( in @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ( X2201 = X2202 )
| ( in @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ( X2201 = X2202 )
| ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ( X2201 = X2202 )
| ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ( X2201 = X2202 )
| ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ( X2201 = X2202 )
| ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ( X2201 = X2202 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ( X2201 = X2202 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ( X2201 = X2202 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk61_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ( X2201 = X2202 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk59_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2202 )
| ~ ( breln @ X2199 @ X2200 @ X2201 ) )
& ( ( in @ ( esk62_4 @ X2207 @ X2208 @ X2209 @ X2210 ) @ X2207 )
| ( X2209 = X2210 )
| ~ ( func @ X2207 @ X2208 @ X2210 )
| ~ ( func @ X2207 @ X2208 @ X2209 ) )
& ( ( ( ap @ X2207 @ X2208 @ X2209 @ ( esk62_4 @ X2207 @ X2208 @ X2209 @ X2210 ) )
!= ( ap @ X2207 @ X2208 @ X2210 @ ( esk62_4 @ X2207 @ X2208 @ X2209 @ X2210 ) ) )
| ( X2209 = X2210 )
| ~ ( func @ X2207 @ X2208 @ X2210 )
| ~ ( func @ X2207 @ X2208 @ X2209 ) )
& ( ( in @ ( esk63_4 @ X2212 @ X2213 @ X2214 @ X2215 ) @ X2212 )
| ( X2214 = X2215 )
| ~ ( in @ X2215 @ ( funcSet @ X2212 @ X2213 ) )
| ~ ( in @ X2214 @ ( funcSet @ X2212 @ X2213 ) ) )
& ( ( ( ap @ X2212 @ X2213 @ X2214 @ ( esk63_4 @ X2212 @ X2213 @ X2214 @ X2215 ) )
!= ( ap @ X2212 @ X2213 @ X2215 @ ( esk63_4 @ X2212 @ X2213 @ X2214 @ X2215 ) ) )
| ( X2214 = X2215 )
| ~ ( in @ X2215 @ ( funcSet @ X2212 @ X2213 ) )
| ~ ( in @ X2214 @ ( funcSet @ X2212 @ X2213 ) ) )
& ( ~ ( in @ X2219 @ ( funcSet @ X2217 @ X2218 ) )
| ~ ( in @ X2220 @ X2217 )
| ( ( ap @ X2217 @ X2218 @ X2219 @ X2220 )
= ( ap @ X2217 @ X2218 @ X2219 @ X2220 ) ) )
& ( ~ ( func @ X2221 @ X2222 @ X2223 )
| ~ ( in @ X2224 @ X2221 )
| ( ( ap @ X2221 @ X2222 @ X2223 @ X2224 )
= ( ap @ X2221 @ X2222 @ X2223 @ X2224 ) ) )
& ( ( in @ ( esk64_3 @ X2225 @ X2226 @ X2227 ) @ X2225 )
| ~ ( in @ X2229 @ X2225 )
| ( ( ap @ X2225 @ X2226 @ ( lam @ X2225 @ X2226 @ X2227 ) @ X2229 )
= ( X2227 @ X2229 ) ) )
& ( ~ ( in @ ( X2227 @ ( esk64_3 @ X2225 @ X2226 @ X2227 ) ) @ X2226 )
| ~ ( in @ X2229 @ X2225 )
| ( ( ap @ X2225 @ X2226 @ ( lam @ X2225 @ X2226 @ X2227 ) @ X2229 )
= ( X2227 @ X2229 ) ) )
& ( ~ ( func @ X2230 @ X2231 @ X2232 )
| ( ( lam @ X2230 @ X2231 @ ( ap @ X2230 @ X2231 @ X2232 ) )
= X2232 ) )
& ( ( in @ ( esk65_3 @ X2233 @ X2234 @ X2235 ) @ X2233 )
| ( ( lam @ X2233 @ X2234 @ X2235 )
= ( lam @ X2233 @ X2234 @ X2235 ) ) )
& ( ~ ( in @ ( X2235 @ ( esk65_3 @ X2233 @ X2234 @ X2235 ) ) @ X2234 )
| ( ( lam @ X2233 @ X2234 @ X2235 )
= ( lam @ X2233 @ X2234 @ X2235 ) ) )
& ( ( in @ ( esk66_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ~ ( in @ X2241 @ X2237 )
| ( ( ap @ X2237 @ X2238 @ ( lam @ X2237 @ X2238 @ X2239 ) @ X2241 )
= ( X2239 @ X2241 ) ) )
& ( ~ ( in @ ( X2239 @ ( esk66_3 @ X2237 @ X2238 @ X2239 ) ) @ X2238 )
| ~ ( in @ X2241 @ X2237 )
| ( ( ap @ X2237 @ X2238 @ ( lam @ X2237 @ X2238 @ X2239 ) @ X2241 )
= ( X2239 @ X2241 ) ) )
& ( ~ ( in @ X2244 @ ( funcSet @ X2242 @ X2243 ) )
| ( ( lam @ X2242 @ X2243 @ ( ap @ X2242 @ X2243 @ X2244 ) )
= X2244 ) )
& ( ~ ( in @ X2247 @ X2245 )
| ~ ( in @ X2248 @ X2245 )
| X2246
| ( in @ X2248
@ ( dsetconstr @ X2245
@ ^ [Z0: $i] :
( ( X2246
& ( Z0 = X2247 ) )
| ( ~ X2246
& ( Z0 = X2248 ) ) ) ) ) )
& ( ~ ( in @ X2251 @ X2249 )
| ~ ( in @ X2252 @ X2249 )
| X2250
| ( ( dsetconstr @ X2249
@ ^ [Z0: $i] :
( ( X2250
& ( Z0 = X2251 ) )
| ( ~ X2250
& ( Z0 = X2252 ) ) ) )
= ( setadjoin @ X2252 @ emptyset ) ) )
& ( ~ ( in @ X2255 @ X2253 )
| ~ ( in @ X2256 @ X2253 )
| ~ X2254
| ( in @ X2255
@ ( dsetconstr @ X2253
@ ^ [Z0: $i] :
( ( X2254
& ( Z0 = X2255 ) )
| ( ~ X2254
& ( Z0 = X2256 ) ) ) ) ) )
& ( ~ ( in @ X2259 @ X2257 )
| ~ ( in @ X2260 @ X2257 )
| ~ X2258
| ( ( dsetconstr @ X2257
@ ^ [Z0: $i] :
( ( X2258
& ( Z0 = X2259 ) )
| ( ~ X2258
& ( Z0 = X2260 ) ) ) )
= ( setadjoin @ X2259 @ emptyset ) ) )
& ( ~ ( in @ X2263 @ X2261 )
| ~ ( in @ X2264 @ X2261 )
| ( singleton
@ ( dsetconstr @ X2261
@ ^ [Z0: $i] :
( ( X2262
& ( Z0 = X2263 ) )
| ( ~ X2262
& ( Z0 = X2264 ) ) ) ) ) )
& ( ~ ( in @ X2267 @ X2265 )
| ~ ( in @ X2268 @ X2265 )
| ( in @ ( if @ X2265 @ X2266 @ X2267 @ X2268 ) @ X2265 ) )
& ( ~ ( singleton @ X2269 )
| ~ ( in @ X2270 @ X2269 )
| ( ( setunion @ X2269 )
= X2270 ) )
& ( ~ ( in @ X2273 @ X2271 )
| ~ ( in @ X2274 @ X2271 )
| ~ X2272
| ( ( if @ X2271 @ X2272 @ X2273 @ X2274 )
= X2273 ) )
& ( ~ ( in @ X2277 @ X2275 )
| ~ ( in @ X2278 @ X2275 )
| X2276
| ( ( if @ X2275 @ X2276 @ X2277 @ X2278 )
= X2278 ) )
& ( ~ ( in @ X2281 @ X2279 )
| ~ ( in @ X2282 @ X2279 )
| ( in @ ( if @ X2279 @ X2280 @ X2281 @ X2282 ) @ ( setadjoin @ X2281 @ ( setadjoin @ X2282 @ emptyset ) ) ) )
& ( ~ ( in @ X2284 @ ( powerset @ X2283 ) )
| ~ ( in @ X2285 @ ( powerset @ X2283 ) )
| ( in @ ( binintersect @ X2284 @ X2285 ) @ ( powerset @ X2283 ) ) )
& ( ~ ( in @ X2287 @ ( powerset @ X2286 ) )
| ~ ( in @ X2288 @ ( powerset @ X2286 ) )
| ( in @ ( binunion @ X2287 @ X2288 ) @ ( powerset @ X2286 ) ) )
& ( ~ ( in @ X2290 @ ( powerset @ X2289 ) )
| ( in @ ( powerset @ X2290 ) @ ( powerset @ ( powerset @ X2289 ) ) ) )
& ( ~ ( in @ X2292 @ ( powerset @ X2291 ) )
| ~ ( in @ X2293 @ ( powerset @ X2291 ) )
| ( in @ ( setminus @ X2292 @ X2293 ) @ ( powerset @ X2291 ) ) )
& ( ~ ( in @ X2295 @ ( powerset @ X2294 ) )
| ( in @ ( setminus @ X2294 @ X2295 ) @ ( powerset @ X2294 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ( X2297 = X2298 )
| ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2296 )
| ( X2297 = X2298 )
| ~ ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ( X2297 = X2298 )
| ~ ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2296 @ X2297 @ X2298 ) @ X2297 )
| ( X2297 = X2298 )
| ~ ( in @ ( esk67_3 @ X2296 @ X2297 @ X2298 ) @ X2298 )
| ~ ( in @ X2298 @ ( powerset @ X2296 ) )
| ~ ( in @ X2297 @ ( powerset @ X2296 ) ) )
& ( ( in @ ( esk69_3 @ X2301 @ X2302 @ X2303 ) @ X2301 )
| ( subset @ X2302 @ X2303 )
| ~ ( in @ X2303 @ ( powerset @ X2301 ) )
| ~ ( in @ X2302 @ ( powerset @ X2301 ) ) )
& ( ( in @ ( esk69_3 @ X2301 @ X2302 @ X2303 ) @ X2302 )
| ( subset @ X2302 @ X2303 )
| ~ ( in @ X2303 @ ( powerset @ X2301 ) )
| ~ ( in @ X2302 @ ( powerset @ X2301 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2301 @ X2302 @ X2303 ) @ X2303 )
| ( subset @ X2302 @ X2303 )
| ~ ( in @ X2303 @ ( powerset @ X2301 ) )
| ~ ( in @ X2302 @ ( powerset @ X2301 ) ) )
& ( ( in @ ( esk70_3 @ X2305 @ X2306 @ X2307 ) @ X2305 )
| ( in @ X2306 @ ( powerset @ X2307 ) )
| ~ ( in @ X2307 @ ( powerset @ X2305 ) )
| ~ ( in @ X2306 @ ( powerset @ X2305 ) ) )
& ( ( in @ ( esk70_3 @ X2305 @ X2306 @ X2307 ) @ X2306 )
| ( in @ X2306 @ ( powerset @ X2307 ) )
| ~ ( in @ X2307 @ ( powerset @ X2305 ) )
| ~ ( in @ X2306 @ ( powerset @ X2305 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2305 @ X2306 @ X2307 ) @ X2307 )
| ( in @ X2306 @ ( powerset @ X2307 ) )
| ~ ( in @ X2307 @ ( powerset @ X2305 ) )
| ~ ( in @ X2306 @ ( powerset @ X2305 ) ) )
& ( ~ ( in @ X2310 @ ( powerset @ X2309 ) )
| ~ ( in @ X2311 @ ( powerset @ X2309 ) )
| ~ ( in @ X2312 @ X2309 )
| ~ ( in @ X2310 @ ( powerset @ X2311 ) )
| ~ ( in @ X2312 @ X2310 )
| ( in @ X2312 @ X2311 ) )
& ( ~ ( in @ X2314 @ ( powerset @ X2313 ) )
| ~ ( in @ X2315 @ X2313 )
| ~ ( in @ X2315 @ X2314 )
| ~ ( in @ X2315 @ ( setminus @ X2313 @ X2314 ) ) )
& ( ~ ( in @ X2317 @ ( powerset @ X2316 ) )
| ~ ( in @ X2318 @ X2316 )
| ( in @ X2318 @ ( setminus @ X2316 @ X2317 ) )
| ( in @ X2318 @ X2317 ) )
& ( ~ ( in @ X2320 @ ( powerset @ X2319 ) )
| ~ ( in @ X2321 @ ( powerset @ X2319 ) )
| ~ ( in @ X2322 @ X2319 )
| ( in @ X2322 @ X2320 )
| ~ ( in @ X2322 @ ( binintersect @ X2320 @ X2321 ) ) )
& ( ~ ( in @ X2324 @ ( powerset @ X2323 ) )
| ~ ( in @ X2325 @ ( powerset @ X2323 ) )
| ~ ( in @ X2326 @ X2323 )
| ( in @ X2326 @ X2325 )
| ~ ( in @ X2326 @ ( binintersect @ X2324 @ X2325 ) ) )
& ( ~ ( in @ X2328 @ ( powerset @ X2327 ) )
| ~ ( in @ X2329 @ ( powerset @ X2327 ) )
| ~ ( in @ X2330 @ X2327 )
| ~ ( subset @ X2328 @ ( setminus @ X2327 @ X2329 ) )
| ~ ( in @ X2330 @ X2329 )
| ~ ( in @ X2330 @ X2328 ) )
& ( ~ ( in @ X2332 @ ( powerset @ X2331 ) )
| ~ ( in @ X2333 @ ( powerset @ X2331 ) )
| ~ ( in @ X2334 @ X2331 )
| ~ ( subset @ X2332 @ X2333 )
| ( in @ X2334 @ X2333 )
| ~ ( in @ X2334 @ X2332 ) )
& ( ~ ( in @ X2336 @ ( powerset @ X2335 ) )
| ~ ( in @ X2337 @ ( powerset @ X2335 ) )
| ~ ( subset @ X2336 @ X2337 )
| ( subset @ ( setminus @ X2335 @ X2337 ) @ ( setminus @ X2335 @ X2336 ) ) )
& ( ~ ( in @ X2339 @ ( powerset @ X2338 ) )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( subset @ ( setminus @ X2338 @ X2340 ) @ ( setminus @ X2338 @ X2339 ) )
| ( subset @ X2339 @ X2340 ) )
& ( ~ ( in @ X2342 @ ( powerset @ X2341 ) )
| ~ ( in @ X2343 @ X2341 )
| ~ ( in @ X2343 @ X2342 )
| ( in @ X2343 @ ( setminus @ X2341 @ ( setminus @ X2341 @ X2342 ) ) ) )
& ( ~ ( in @ X2345 @ ( powerset @ X2344 ) )
| ~ ( in @ X2346 @ X2344 )
| ~ ( in @ X2346 @ ( setminus @ X2344 @ ( setminus @ X2344 @ X2345 ) ) )
| ( in @ X2346 @ X2345 ) )
& ( ~ ( in @ X2348 @ ( powerset @ X2347 ) )
| ( subset @ X2348 @ ( setminus @ X2347 @ ( setminus @ X2347 @ X2348 ) ) ) )
& ( ~ ( in @ X2350 @ ( powerset @ X2349 ) )
| ( subset @ ( setminus @ X2349 @ ( setminus @ X2349 @ X2350 ) ) @ X2350 ) )
& ( ~ ( in @ X2352 @ ( powerset @ X2351 ) )
| ( X2352
= ( setminus @ X2351 @ ( setminus @ X2351 @ X2352 ) ) ) )
& ( ~ ( in @ X2354 @ ( powerset @ X2353 ) )
| ~ ( in @ X2355 @ ( powerset @ X2353 ) )
| ~ ( in @ X2356 @ X2353 )
| ~ ( in @ X2356 @ ( setminus @ X2353 @ X2354 ) )
| ~ ( in @ X2356 @ ( binintersect @ X2354 @ X2355 ) ) )
& ( ~ ( in @ X2358 @ ( powerset @ X2357 ) )
| ~ ( in @ X2359 @ ( powerset @ X2357 ) )
| ~ ( in @ X2360 @ X2357 )
| ~ ( in @ X2360 @ ( setminus @ X2357 @ X2358 ) )
| ( in @ X2360 @ ( setminus @ X2357 @ ( binintersect @ X2358 @ X2359 ) ) ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ~ ( subset @ ( setminus @ esk71_0 @ esk72_0 ) @ ( setminus @ esk71_0 @ ( binintersect @ esk72_0 @ esk73_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_302])])])])])])]) ).
thf(c_0_304,negated_conjecture,
~ ( subset @ ( setminus @ esk71_0 @ esk72_0 ) @ ( setminus @ esk71_0 @ ( binintersect @ esk72_0 @ esk73_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_305,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X2 ) )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_306,negated_conjecture,
in @ esk72_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_307,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_308,negated_conjecture,
~ ( in @ ( binintersect @ esk72_0 @ esk73_0 ) @ ( powerset @ esk71_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_305]),c_0_306]),c_0_307])]) ).
thf(c_0_309,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( binintersect @ X2 @ X4 ) @ ( powerset @ X3 ) )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_310,negated_conjecture,
in @ esk73_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
thf(c_0_311,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_309]),c_0_310]),c_0_306])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU734^1 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:20:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.56/1.05 # Version: 3.1.0-ho
% 2.56/1.05 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.56/1.05 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.05 # Starting ehoh_best5 with 300s (1) cores
% 2.56/1.05 # Starting almost_fo_3_lam with 300s (1) cores
% 2.56/1.05 # Starting new_bool_5 with 300s (1) cores
% 2.56/1.05 # Starting pre_casc_3 with 300s (1) cores
% 2.56/1.05 # Starting ho_unfolding_8 with 300s (1) cores
% 2.56/1.05 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.56/1.05 # Starting new_bool_3 with 300s (1) cores
% 2.56/1.05 # Starting new_ho_5 with 300s (1) cores
% 2.56/1.05 # new_ho_5 with pid 28100 completed with status 8
% 2.56/1.05 # new_bool_5 with pid 28095 completed with status 0
% 2.56/1.05 # Result found by new_bool_5
% 2.56/1.05 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.56/1.05 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.05 # Starting ehoh_best5 with 300s (1) cores
% 2.56/1.05 # Starting almost_fo_3_lam with 300s (1) cores
% 2.56/1.05 # Starting new_bool_5 with 300s (1) cores
% 2.56/1.05 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.56/1.05 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.56/1.05 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.56/1.05 # Starting ho_unfolding_8 with 55s (1) cores
% 2.56/1.05 # ho_unfolding_8 with pid 28161 completed with status 0
% 2.56/1.05 # Result found by ho_unfolding_8
% 2.56/1.05 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.56/1.05 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.56/1.05 # Starting ehoh_best5 with 300s (1) cores
% 2.56/1.05 # Starting almost_fo_3_lam with 300s (1) cores
% 2.56/1.05 # Starting new_bool_5 with 300s (1) cores
% 2.56/1.05 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.56/1.05 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.56/1.05 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.56/1.05 # Starting ho_unfolding_8 with 55s (1) cores
% 2.56/1.05 # Preprocessing time : 0.081 s
% 2.56/1.05 # Presaturation interreduction done
% 2.56/1.05
% 2.56/1.05 # Proof found!
% 2.56/1.05 # SZS status Theorem
% 2.56/1.05 # SZS output start CNFRefutation
% See solution above
% 2.56/1.06 # Parsed axioms : 543
% 2.56/1.06 # Removed by relevancy pruning/SinE : 293
% 2.56/1.06 # Initial clauses : 410
% 2.56/1.06 # Removed in clause preprocessing : 34
% 2.56/1.06 # Initial clauses in saturation : 376
% 2.56/1.06 # Processed clauses : 739
% 2.56/1.06 # ...of these trivial : 11
% 2.56/1.06 # ...subsumed : 38
% 2.56/1.06 # ...remaining for further processing : 690
% 2.56/1.06 # Other redundant clauses eliminated : 54
% 2.56/1.06 # Clauses deleted for lack of memory : 0
% 2.56/1.06 # Backward-subsumed : 0
% 2.56/1.06 # Backward-rewritten : 3
% 2.56/1.06 # Generated clauses : 7390
% 2.56/1.06 # ...of the previous two non-redundant : 7157
% 2.56/1.06 # ...aggressively subsumed : 0
% 2.56/1.06 # Contextual simplify-reflections : 5
% 2.56/1.06 # Paramodulations : 7301
% 2.56/1.06 # Factorizations : 2
% 2.56/1.06 # NegExts : 0
% 2.56/1.06 # Equation resolutions : 61
% 2.56/1.06 # Disequality decompositions : 0
% 2.56/1.06 # Total rewrite steps : 202
% 2.56/1.06 # ...of those cached : 133
% 2.56/1.06 # Propositional unsat checks : 0
% 2.56/1.06 # Propositional check models : 0
% 2.56/1.06 # Propositional check unsatisfiable : 0
% 2.56/1.06 # Propositional clauses : 0
% 2.56/1.06 # Propositional clauses after purity: 0
% 2.56/1.06 # Propositional unsat core size : 0
% 2.56/1.06 # Propositional preprocessing time : 0.000
% 2.56/1.06 # Propositional encoding time : 0.000
% 2.56/1.06 # Propositional solver time : 0.000
% 2.56/1.06 # Success case prop preproc time : 0.000
% 2.56/1.06 # Success case prop encoding time : 0.000
% 2.56/1.06 # Success case prop solver time : 0.000
% 2.56/1.06 # Current number of processed clauses : 342
% 2.56/1.06 # Positive orientable unit clauses : 41
% 2.56/1.06 # Positive unorientable unit clauses: 0
% 2.56/1.06 # Negative unit clauses : 9
% 2.56/1.06 # Non-unit-clauses : 292
% 2.56/1.06 # Current number of unprocessed clauses: 7117
% 2.56/1.06 # ...number of literals in the above : 29838
% 2.56/1.06 # Current number of archived formulas : 0
% 2.56/1.06 # Current number of archived clauses : 332
% 2.56/1.06 # Clause-clause subsumption calls (NU) : 55792
% 2.56/1.06 # Rec. Clause-clause subsumption calls : 24133
% 2.56/1.06 # Non-unit clause-clause subsumptions : 36
% 2.56/1.06 # Unit Clause-clause subsumption calls : 1146
% 2.56/1.06 # Rewrite failures with RHS unbound : 0
% 2.56/1.06 # BW rewrite match attempts : 38
% 2.56/1.06 # BW rewrite match successes : 3
% 2.56/1.06 # Condensation attempts : 0
% 2.56/1.06 # Condensation successes : 0
% 2.56/1.06 # Termbank termtop insertions : 190206
% 2.56/1.06 # Search garbage collected termcells : 24711
% 2.56/1.06
% 2.56/1.06 # -------------------------------------------------
% 2.56/1.06 # User time : 0.489 s
% 2.56/1.06 # System time : 0.026 s
% 2.56/1.06 # Total time : 0.515 s
% 2.56/1.06 # Maximum resident set size: 7996 pages
% 2.56/1.06
% 2.56/1.06 # -------------------------------------------------
% 2.56/1.06 # User time : 0.637 s
% 2.56/1.06 # System time : 0.080 s
% 2.56/1.06 # Total time : 0.717 s
% 2.56/1.06 # Maximum resident set size: 2624 pages
% 2.56/1.06 % E---3.1 exiting
% 2.56/1.06 % E exiting
%------------------------------------------------------------------------------