%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU724^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 03:29:32 EDT 2024
% Result : Theorem 1.28s 0.87s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 586
% Syntax : Number of formulae : 645 ( 4 unt; 345 typ; 0 def)
% Number of atoms : 2954 ( 454 equ; 0 cnn)
% Maximal formula atoms : 936 ( 9 avg)
% Number of connectives : 11216 ( 717 ~; 735 |; 481 &;7506 @)
% ( 327 <=>;1450 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1035 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 349 ( 345 usr; 250 con; 0-4 aty)
% Number of variables : 2499 ( 156 ^2263 !; 80 ?;2499 :)
% 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,
epred1_0: $o ).
thf(decl_301,type,
esk1_2: $i > $i > $i ).
thf(decl_302,type,
esk2_2: $i > $i > $i ).
thf(decl_303,type,
esk3_2: $i > $i > $i ).
thf(decl_304,type,
esk4_1: $i > $i ).
thf(decl_305,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_306,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_307,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_308,type,
esk8_1: $i > $i ).
thf(decl_309,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_310,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_311,type,
esk11_2: $i > $i > $i ).
thf(decl_312,type,
esk12_2: $i > $i > $i ).
thf(decl_313,type,
esk13_1: $i > $i ).
thf(decl_314,type,
esk14_1: $i > $i ).
thf(decl_315,type,
esk15_1: $i > $i ).
thf(decl_316,type,
esk16_2: $i > $i > $i ).
thf(decl_317,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_318,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_319,type,
esk19_1: $i > $i ).
thf(decl_320,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_321,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_322,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_323,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_324,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_325,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_326,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_327,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_328,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_329,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_330,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_331,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_332,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_333,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_334,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_335,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_336,type,
esk36_2: $i > $i > $i ).
thf(decl_337,type,
esk37_2: $i > $i > $i ).
thf(decl_338,type,
esk38_2: $i > $i > $i ).
thf(decl_339,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_340,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_341,type,
esk41_2: $i > $i > $i ).
thf(decl_342,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_346,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_347,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_349,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_350,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_351,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_354,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_355,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_356,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_357,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_358,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_359,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_360,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_361,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_362,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_363,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_364,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_365,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_366,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_367,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_368,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_369,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_370,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_371,type,
esk71_0: $i ).
thf(decl_372,type,
esk72_0: $i ).
thf(decl_373,type,
esk73_0: $i ).
thf(decl_374,type,
esk74_0: $i ).
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(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(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(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(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(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(contrasubsetT1,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
=> ! [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(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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
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(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(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(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(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(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(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(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
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(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(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
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(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(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(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(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(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(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
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(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
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(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(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(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(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(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(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(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(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(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(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,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_254,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_255,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_256,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_257,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_258,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_259,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_260,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_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_282,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_283,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_284,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_285,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_286,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_287,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_288,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_289,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_290,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_291,plain,
( epred1_0
<=> ! [X823: $i] :
? [X824: $i] :
( ! [X825: $i] :
( ( in @ X825 @ X824 )
=> ! [X826: $i] :
( ( in @ X826 @ X825 )
=> ( in @ X826 @ X823 ) ) )
& ! [X827: $i,X828: $i] :
( ( ( in @ X827 @ X823 )
& ( in @ X828 @ X823 ) )
=> ( ! [X829: $i] :
( ( in @ X829 @ X824 )
=> ( ( in @ X827 @ X829 )
<=> ( in @ X828 @ X829 ) ) )
=> ( X827 = X828 ) ) )
& ! [X830: $i,X831: $i] :
( ( ( in @ X830 @ X824 )
& ( in @ X831 @ X824 ) )
=> ( ! [X832: $i] :
( ( in @ X832 @ X830 )
=> ( in @ X832 @ X831 ) )
| ! [X833: $i] :
( ( in @ X833 @ X831 )
=> ( in @ X833 @ X830 ) ) ) )
& ! [X834: $i] :
( ( ! [X835: $i] :
( ( in @ X835 @ X834 )
=> ( in @ X835 @ X823 ) )
& ? [X836: $i] : ( in @ X836 @ X834 ) )
=> ? [X837: $i,X838: $i] :
( ( in @ X837 @ X824 )
& ( in @ X838 @ X834 )
& ~ ? [X839: $i] :
( ( in @ X839 @ X837 )
& ( in @ X839 @ X834 ) )
& ! [X840: $i] :
( ( in @ X840 @ X824 )
=> ( ! [X841: $i] :
( ( in @ X841 @ X840 )
=> ( in @ X841 @ X837 ) )
| ( in @ X838 @ X840 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_292,negated_conjecture,
~ ( ! [X796: $i,X797: $i] :
( ! [X798: $i] :
( ( in @ X798 @ X796 )
<=> ( in @ X798 @ X797 ) )
=> ( X796 = X797 ) )
=> ( ! [X799: $i] :
~ ( in @ X799 @ emptyset )
=> ( ! [X800: $i,X801: $i,X802: $i] :
( ( in @ X802 @ ( setadjoin @ X800 @ X801 ) )
<=> ( ( X802 = X800 )
| ( in @ X802 @ X801 ) ) )
=> ( ! [X803: $i,X804: $i] :
( ( in @ X804 @ ( powerset @ X803 ) )
<=> ! [X805: $i] :
( ( in @ X805 @ X804 )
=> ( in @ X805 @ X803 ) ) )
=> ( ! [X806: $i,X807: $i] :
( ( in @ X807 @ ( setunion @ X806 ) )
<=> ? [X808: $i] :
( ( in @ X807 @ X808 )
& ( in @ X808 @ X806 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X809: $i] :
( ( in @ X809 @ omega )
=> ( in @ ( setadjoin @ X809 @ X809 ) @ omega ) )
=> ( ! [X810: $i] :
( ( ( in @ emptyset @ X810 )
& ! [X811: $i] :
( ( ( in @ X811 @ omega )
& ( in @ X811 @ X810 ) )
=> ( in @ ( setadjoin @ X811 @ X811 ) @ X810 ) ) )
=> ! [X812: $i] :
( ( in @ X812 @ omega )
=> ( in @ X812 @ X810 ) ) )
=> ( ! [X813: $i > $i > $o,X814: $i] :
( ! [X815: $i] :
( ( in @ X815 @ X814 )
=> ( exu @ ( X813 @ X815 ) ) )
=> ? [X816: $i] :
! [X817: $i] :
( ( in @ X817 @ X816 )
<=> ? [X818: $i] :
( ( in @ X818 @ X814 )
& ( X813 @ X818 @ X817 ) ) ) )
=> ( ! [X819: $i] :
( ? [X820: $i] : ( in @ X820 @ X819 )
=> ? [X821: $i] :
( ( in @ X821 @ X819 )
& ~ ? [X822: $i] :
( ( in @ X822 @ X821 )
& ( in @ X822 @ X819 ) ) ) )
=> ( epred1_0
=> ( ! [X842: $i > $o] :
( ( exu @ X842 )
=> ( X842
@ ( descr
@ ^ [Z0: $i] : ( X842 @ Z0 ) ) ) )
=> ( ! [X843: $i,X844: $i > $o,X845: $i] :
( ( in @ X845 @ X843 )
=> ( ( X844 @ X845 )
=> ( in @ X845 @ ( dsetconstr @ X843 @ X844 ) ) ) )
=> ( ! [X846: $i,X847: $i > $o,X848: $i] :
( ( in @ X848 @ ( dsetconstr @ X846 @ X847 ) )
=> ( in @ X848 @ X846 ) )
=> ( ! [X849: $i,X850: $i > $o,X851: $i] :
( ( in @ X851 @ ( dsetconstr @ X849 @ X850 ) )
=> ( X850 @ X851 ) )
=> ( ! [X852: $i > $o] :
( ( exu @ X852 )
=> ? [X853: $i] :
( ( X852 @ X853 )
& ! [X854: $i] :
( ( X852 @ X854 )
=> ( X853 = X854 ) ) ) )
=> ( ! [X855: $o,X856: $i] :
( ( in @ X856 @ ( prop2set @ X855 ) )
=> X855 )
=> ( ! [X857: $i] :
( ( in @ X857 @ emptyset )
=> ! [X858: $o] : X858 )
=> ( ! [X859: $i] :
( ( in @ X859 @ emptyset )
=> ~ $true )
=> ( ! [X860: $i] :
~ ( in @ X860 @ emptyset )
=> ( ! [X861: $i > $o] :
( ( exu @ X861 )
=> ? [X862: $i] : ( X861 @ X862 ) )
=> ( ! [X863: $i,X864: $i] :
( ! [X865: $i] :
( ( in @ X865 @ X863 )
=> ( in @ X865 @ X864 ) )
=> ( ! [X866: $i] :
( ( in @ X866 @ X864 )
=> ( in @ X866 @ X863 ) )
=> ( X863 = X864 ) ) )
=> ( ! [X867: $i] :
( ! [X868: $i] :
~ ( in @ X868 @ X867 )
=> ( X867 = emptyset ) )
=> ( ! [X869: $i] :
( ! [X870: $i] :
~ ( in @ X870 @ X869 )
=> ( X869 = emptyset ) )
=> ( ! [X871: $i,X872: $i > $o,X873: $i] :
( ( in @ X873 @ X871 )
=> ( ( in @ X873 @ ( dsetconstr @ X871 @ X872 ) )
<=> ( X872 @ X873 ) ) )
=> ( ! [X874: $i] :
( ( nonempty @ X874 )
=> ? [X875: $i] : ( in @ X875 @ X874 ) )
=> ( ! [X876: $i,X877: $i > $o,X878: $i] :
( ( in @ X878 @ X876 )
=> ( ( X877 @ X878 )
=> ( nonempty @ ( dsetconstr @ X876 @ X877 ) ) ) )
=> ( ! [X879: $i] :
( ? [X880: $i] : ( in @ X880 @ X879 )
=> ( nonempty @ X879 ) )
=> ( ! [X881: $i,X882: $i] : ( in @ X881 @ ( setadjoin @ X881 @ X882 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X883: $i,X884: $i,X885: $i] :
( ( in @ X885 @ X884 )
=> ( in @ X885 @ ( setadjoin @ X883 @ X884 ) ) )
=> ( ! [X886: $i,X887: $i,X888: $i] :
( ( in @ X888 @ ( setadjoin @ X886 @ X887 ) )
=> ! [X889: $o] :
( ( ( X888 = X886 )
=> X889 )
=> ( ( ( in @ X888 @ X887 )
=> X889 )
=> X889 ) ) )
=> ( ! [X890: $i,X891: $i,X892: $i] :
( ( in @ X892 @ ( setadjoin @ X890 @ X891 ) )
=> ( ( X892 = X890 )
| ( in @ X892 @ X891 ) ) )
=> ( ! [X893: $i] :
( ( dsetconstr @ X893
@ ^ [Z0: $i] : $true )
= X893 )
=> ( ! [X894: $i,X895: $i] :
( ! [X896: $i] :
( ( in @ X896 @ X895 )
=> ( in @ X896 @ X894 ) )
=> ( in @ X895 @ ( powerset @ X894 ) ) )
=> ( ! [X897: $i] : ( in @ emptyset @ ( powerset @ X897 ) )
=> ( ! [X898: $i] : ( in @ emptyset @ ( powerset @ X898 ) )
=> ( ! [X899: $i,X900: $i,X901: $i] :
( ( in @ X900 @ ( powerset @ X899 ) )
=> ( ( in @ X901 @ X900 )
=> ( in @ X901 @ X899 ) ) )
=> ( ! [X902: $i,X903: $i,X904: $i] :
( ( in @ X903 @ X904 )
=> ( ( in @ X904 @ X902 )
=> ( in @ X903 @ ( setunion @ X902 ) ) ) )
=> ( ! [X905: $i,X906: $i] :
( ( in @ X906 @ ( setunion @ X905 ) )
=> ! [X907: $o] :
( ! [X908: $i] :
( ( in @ X906 @ X908 )
=> ( ( in @ X908 @ X905 )
=> X907 ) )
=> X907 ) )
=> ( ! [X909: $i,X910: $i] :
( ( in @ X910 @ X909 )
=> ( in @ X910 @ ( powerset @ ( setunion @ X909 ) ) ) )
=> ( ! [X911: $i > $o] :
( ( exu @ X911 )
=> ? [X912: $i] :
! [X913: $i] :
( ( X911 @ X913 )
<=> ( X913 = X912 ) ) )
=> ( ! [X914: $i] :
( ( nonempty @ X914 )
=> ? [X915: $i] :
( ( in @ X915 @ X914 )
& $true ) )
=> ( ! [X916: $i,X917: $i] :
( ( in @ X916 @ ( setadjoin @ X917 @ emptyset ) )
=> ( X916 = X917 ) )
=> ( ! [X918: $i,X919: $i] :
( ( X918 != X919 )
=> ~ ( in @ X919 @ ( setadjoin @ X918 @ emptyset ) ) )
=> ( ! [X920: $i,X921: $i] :
( ( X920 = X921 )
=> ( in @ X920 @ ( setadjoin @ X921 @ emptyset ) ) )
=> ( ! [X922: $i,X923: $i] :
( ( in @ X922 @ ( setadjoin @ X923 @ emptyset ) )
=> ( in @ X923 @ ( setadjoin @ X922 @ emptyset ) ) )
=> ( ! [X924: $i,X925: $i,X926: $i] :
( ( in @ X926 @ ( setadjoin @ X924 @ ( setadjoin @ X925 @ emptyset ) ) )
=> ( ( X926 = X924 )
| ( X926 = X925 ) ) )
=> ( ! [X927: $i,X928: $i] : ( in @ X927 @ ( setadjoin @ X927 @ ( setadjoin @ X928 @ emptyset ) ) )
=> ( ! [X929: $i,X930: $i] : ( in @ X930 @ ( setadjoin @ X929 @ ( setadjoin @ X930 @ emptyset ) ) )
=> ( ! [X931: $i,X932: $i > $o] :
( ? [X933: $i] :
( ( in @ X933 @ X931 )
& ( X932 @ X933 ) )
=> ( ( ( dsetconstr @ X931 @ X932 )
= emptyset )
=> ~ $true ) )
=> ( ! [X934: $i > $o,X935: $i] :
( ( in @ X935 @ emptyset )
=> ( X934 @ X935 ) )
=> ( ! [X936: $i,X937: $i > $o] :
( ~ ! [X938: $i] :
( ( in @ X938 @ X936 )
=> ( X937 @ X938 ) )
=> ? [X939: $i] :
( ( in @ X939 @ X936 )
& ~ ( X937 @ X939 ) ) )
=> ( ! [X940: $i,X941: $i > $o] :
( ! [X942: $i] :
( ( in @ X942 @ X940 )
=> ~ ( X941 @ X942 ) )
=> ~ ? [X943: $i] :
( ( in @ X943 @ X940 )
& ( X941 @ X943 ) ) )
=> ( ! [X944: $i,X945: $i > $o] :
( ~ ? [X946: $i] :
( ( in @ X946 @ X944 )
& ( X945 @ X946 ) )
=> ! [X947: $i] :
( ( in @ X947 @ X944 )
=> ~ ( X945 @ X947 ) ) )
=> ( ! [X948: $i,X949: $i > $o] :
( ? [X950: $i] :
( ( in @ X950 @ X948 )
& ~ ( X949 @ X950 ) )
=> ~ ! [X951: $i] :
( ( in @ X951 @ X948 )
=> ( X949 @ X951 ) ) )
=> ( ! [X952: $o] :
( X952
=> ( in @ emptyset @ ( prop2set @ X952 ) ) )
=> ( prop2set2propI
=> ( ! [X953: $i,X954: $i > $o] :
( ~ ? [X955: $i] :
( ( in @ X955 @ X953 )
& ( X954 @ X955 ) )
=> ! [X956: $i] :
( ( in @ X956 @ X953 )
=> ~ ( X954 @ X956 ) ) )
=> ( ! [X957: $i,X958: $i > $o] :
( ~ ! [X959: $i] :
( ( in @ X959 @ X957 )
=> ( X958 @ X959 ) )
=> ? [X960: $i] :
( ( in @ X960 @ X957 )
& ~ ( X958 @ X960 ) ) )
=> ( ! [X961: $i > $o] :
( ? [X962: $i] :
( ( X961 @ X962 )
& ! [X963: $i] :
( ( X961 @ X963 )
=> ( X962 = X963 ) ) )
=> ( exu @ X961 ) )
=> ( ! [X964: $i > $o] :
( ? [X965: $i] : ( X964 @ X965 )
=> ( ! [X966: $i,X967: $i] :
( ( X964 @ X966 )
=> ( ( X964 @ X967 )
=> ( X966 = X967 ) ) )
=> ( exu @ X964 ) ) )
=> ( ! [X968: $i > $o] :
( ? [X969: $i] :
! [X970: $i] :
( ( X968 @ X970 )
<=> ( X970 = X969 ) )
=> ( exu @ X968 ) )
=> ( ! [X971: $i,X972: $i] :
( ( X971 = X972 )
=> ! [X973: $i,X974: $i] :
( ( X973 = X974 )
=> ( ( in @ X973 @ X971 )
=> ( in @ X974 @ X972 ) ) ) )
=> ( ! [X975: $i,X976: $i] :
( ( X975 = X976 )
=> ! [X977: $i,X978: $i] :
( ( X977 = X978 )
=> ( ( in @ X977 @ X975 )
<=> ( in @ X978 @ X976 ) ) ) )
=> ( ! [X979: $i > $o] :
( ( exu @ X979 )
=> ! [X980: $i,X981: $i] :
( ( X979 @ X980 )
=> ( ( X979 @ X981 )
=> ( X980 = X981 ) ) ) )
=> ( ! [X982: $i > $o,X983: $i > $o] :
( ! [X984: $i,X985: $i] :
( ( X984 = X985 )
=> ( ( X982 @ X984 )
<=> ( X983 @ X985 ) ) )
=> ( ( exu @ X982 )
<=> ( exu @ X983 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X986: $i,X987: $i] :
( ( X986 = X987 )
=> ! [X988: $i,X989: $i] :
( ( X988 = X989 )
=> ( ( setadjoin @ X986 @ X988 )
= ( setadjoin @ X987 @ X989 ) ) ) )
=> ( ! [X990: $i,X991: $i] :
( ( X990 = X991 )
=> ( ( powerset @ X990 )
= ( powerset @ X991 ) ) )
=> ( ! [X992: $i,X993: $i] :
( ( X992 = X993 )
=> ( ( setunion @ X992 )
= ( setunion @ X993 ) ) )
=> ( ( omega = omega )
=> ( ! [X994: $i > $o] :
( ( exu @ X994 )
=> ! [X995: $i,X996: $i] :
( ( X994 @ X995 )
=> ( ( X994 @ X996 )
=> ( X995 = X996 ) ) ) )
=> ( ! [X997: $i > $o,X998: $i > $o] :
( ! [X999: $i,X1000: $i] :
( ( X999 = X1000 )
=> ( ( X997 @ X999 )
<=> ( X998 @ X1000 ) ) )
=> ( ( exu @ X997 )
=> ( ( exu @ X998 )
=> ( ( descr @ X997 )
= ( descr @ X998 ) ) ) ) )
=> ( ! [X1001: $i,X1002: $i] :
( ( X1001 = X1002 )
=> ! [X1003: $i > $o,X1004: $i > $o] :
( ! [X1005: $i] :
( ( in @ X1005 @ X1001 )
=> ! [X1006: $i] :
( ( in @ X1006 @ X1002 )
=> ( ( X1005 = X1006 )
=> ( ( X1003 @ X1005 )
<=> ( X1004 @ X1006 ) ) ) ) )
=> ( ( dsetconstr @ X1001 @ X1003 )
= ( dsetconstr @ X1002 @ X1004 ) ) ) )
=> ( ! [X1007: $i,X1008: $i] :
( ! [X1009: $i] :
( ( in @ X1009 @ X1007 )
=> ( in @ X1009 @ X1008 ) )
=> ( subset @ X1007 @ X1008 ) )
=> ( ! [X1010: $i,X1011: $i] :
( ( X1010 = X1011 )
=> ( subset @ X1011 @ X1010 ) )
=> ( ! [X1012: $i,X1013: $i] :
( ( X1012 = X1013 )
=> ( subset @ X1012 @ X1013 ) )
=> ( ! [X1014: $i,X1015: $i] :
( ! [X1016: $i] :
( ( in @ X1016 @ X1014 )
=> ( in @ X1016 @ X1015 ) )
=> ( subset @ X1014 @ X1015 ) )
=> ( ! [X1017: $i] : ( subset @ emptyset @ X1017 )
=> ( ! [X1018: $i,X1019: $i,X1020: $i] :
( ( subset @ X1018 @ X1019 )
=> ( ( in @ X1020 @ X1018 )
=> ( in @ X1020 @ X1019 ) ) )
=> ( ! [X1021: $i,X1022: $i,X1023: $i] :
( ( subset @ X1021 @ X1022 )
=> ( ~ ( in @ X1023 @ X1022 )
=> ~ ( in @ X1023 @ X1021 ) ) )
=> ( ! [X1024: $i,X1025: $i,X1026: $i] :
( ( in @ X1026 @ X1024 )
=> ( ~ ( in @ X1026 @ X1025 )
=> ~ ( subset @ X1024 @ X1025 ) ) )
=> ( ! [X1027: $i,X1028: $i] :
( ~ ( subset @ X1027 @ X1028 )
=> ( X1027 != X1028 ) )
=> ( ! [X1029: $i,X1030: $i,X1031: $i] :
( ( in @ X1031 @ X1029 )
=> ( ~ ( in @ X1031 @ X1030 )
=> ( X1029 != X1030 ) ) )
=> ( ! [X1032: $i] : ( subset @ X1032 @ X1032 )
=> ( ! [X1033: $i,X1034: $i,X1035: $i] :
( ( subset @ X1033 @ X1034 )
=> ( ( subset @ X1034 @ X1035 )
=> ( subset @ X1033 @ X1035 ) ) )
=> ( ! [X1036: $i,X1037: $i] : ( subset @ X1037 @ ( setadjoin @ X1036 @ X1037 ) )
=> ( ! [X1038: $i,X1039: $i,X1040: $i] :
( ( subset @ X1038 @ X1040 )
=> ( subset @ X1038 @ ( setadjoin @ X1039 @ X1040 ) ) )
=> ( ! [X1041: $i,X1042: $i] :
( ( subset @ X1041 @ X1042 )
=> ( in @ X1041 @ ( powerset @ X1042 ) ) )
=> ( ! [X1043: $i,X1044: $i] :
( ( subset @ X1043 @ X1044 )
=> ( ( subset @ X1044 @ X1043 )
=> ( X1043 = X1044 ) ) )
=> ( ! [X1045: $i] :
( ( subset @ X1045 @ emptyset )
=> ( X1045 = emptyset ) )
=> ( ! [X1046: $i,X1047: $i] :
( ( subset @ X1047 @ X1046 )
=> ( in @ X1047 @ ( powerset @ X1046 ) ) )
=> ( ! [X1048: $i,X1049: $i] :
( ( in @ X1049 @ ( powerset @ X1048 ) )
=> ( subset @ X1049 @ X1048 ) )
=> ( ! [X1050: $i] : ( in @ X1050 @ ( powerset @ X1050 ) )
=> ( ! [X1051: $i,X1052: $i] :
( ( subset @ X1051 @ X1052 )
=> ( subset @ ( powerset @ X1051 ) @ ( powerset @ X1052 ) ) )
=> ( ! [X1053: $i,X1054: $i > $o] : ( in @ ( dsetconstr @ X1053 @ X1054 ) @ ( powerset @ X1053 ) )
=> ( ! [X1055: $i,X1056: $i > $o] : ( subset @ ( dsetconstr @ X1055 @ X1056 ) @ X1055 )
=> ( ! [X1057: $i,X1058: $i,X1059: $i] :
( ( in @ X1059 @ X1057 )
=> ( in @ X1059 @ ( binunion @ X1057 @ X1058 ) ) )
=> ( ! [X1060: $i,X1061: $i] : ( in @ X1061 @ ( setadjoin @ X1060 @ ( setadjoin @ X1061 @ emptyset ) ) )
=> ( ! [X1062: $i,X1063: $i,X1064: $i] :
( ( in @ X1064 @ X1063 )
=> ( in @ X1064 @ ( binunion @ X1062 @ X1063 ) ) )
=> ( ! [X1065: $i,X1066: $i,X1067: $i,X1068: $o] :
( ( in @ X1067 @ ( binunion @ X1065 @ X1066 ) )
=> ( ( ( in @ X1067 @ X1065 )
=> X1068 )
=> ( ( ( in @ X1067 @ X1066 )
=> X1068 )
=> X1068 ) ) )
=> ( ! [X1069: $i,X1070: $i,X1071: $i] :
( ( in @ X1071 @ ( binunion @ X1069 @ X1070 ) )
=> ( ( in @ X1071 @ X1069 )
| ( in @ X1071 @ X1070 ) ) )
=> ( ! [X1072: $i,X1073: $i] : ( subset @ X1072 @ ( binunion @ X1072 @ X1073 ) )
=> ( ! [X1074: $i,X1075: $i] : ( subset @ X1075 @ ( binunion @ X1074 @ X1075 ) )
=> ( ! [X1076: $i,X1077: $i,X1078: $i] :
( ( in @ X1078 @ X1076 )
=> ( ( in @ X1078 @ X1077 )
=> ( in @ X1078 @ ( binintersect @ X1076 @ X1077 ) ) ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i] :
( ( subset @ X1081 @ X1079 )
=> ( ( subset @ X1081 @ X1080 )
=> ( subset @ X1081 @ ( binintersect @ X1079 @ X1080 ) ) ) )
=> ( ! [X1082: $i,X1083: $i,X1084: $i] :
( ( in @ X1084 @ ( binintersect @ X1082 @ X1083 ) )
=> ( in @ X1084 @ X1082 ) )
=> ( ! [X1085: $i,X1086: $i] : ( subset @ ( binintersect @ X1085 @ X1086 ) @ X1085 )
=> ( ! [X1087: $i,X1088: $i] :
( ( subset @ X1087 @ X1088 )
=> ( ( binintersect @ X1087 @ X1088 )
= X1087 ) )
=> ( ! [X1089: $i,X1090: $i] :
( ( ( binintersect @ X1089 @ X1090 )
= X1090 )
=> ( subset @ X1090 @ X1089 ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( in @ X1093 @ ( binintersect @ X1091 @ X1092 ) )
=> ( in @ X1093 @ X1092 ) )
=> ( ! [X1094: $i,X1095: $i] :
( ~ ? [X1096: $i] :
( ( in @ X1096 @ X1094 )
& ( in @ X1096 @ X1095 ) )
=> ( ( binintersect @ X1094 @ X1095 )
= emptyset ) )
=> ( ! [X1097: $i,X1098: $i] : ( subset @ ( binintersect @ X1097 @ X1098 ) @ X1098 )
=> ( ! [X1099: $i,X1100: $i] :
( ( subset @ X1100 @ X1099 )
=> ( ( binintersect @ X1099 @ X1100 )
= X1100 ) )
=> ( ! [X1101: $i,X1102: $i] :
( ( ( binintersect @ X1101 @ X1102 )
= X1101 )
=> ( subset @ X1101 @ X1102 ) )
=> ( ! [X1103: $i,X1104: $i,X1105: $i] :
( ( binintersect @ X1103 @ ( binunion @ X1104 @ X1105 ) )
= ( binunion @ ( binintersect @ X1103 @ X1104 ) @ ( binintersect @ X1103 @ X1105 ) ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ( in @ X1108 @ X1106 )
=> ( ~ ( in @ X1108 @ X1107 )
=> ( in @ X1108 @ ( setminus @ X1106 @ X1107 ) ) ) )
=> ( ! [X1109: $i,X1110: $i,X1111: $i] :
( ( in @ X1111 @ ( setminus @ X1109 @ X1110 ) )
=> ( in @ X1111 @ X1109 ) )
=> ( ! [X1112: $i,X1113: $i,X1114: $i] :
( ( in @ X1114 @ ( setminus @ X1112 @ X1113 ) )
=> ~ ( in @ X1114 @ X1113 ) )
=> ( ! [X1115: $i,X1116: $i] :
( ( subset @ X1115 @ X1116 )
=> ( ( setminus @ X1115 @ X1116 )
= emptyset ) )
=> ( ! [X1117: $i,X1118: $i,X1119: $i] :
( ~ ( in @ X1119 @ ( setminus @ X1117 @ X1118 ) )
=> ( ( in @ X1119 @ X1117 )
=> ( in @ X1119 @ X1118 ) ) )
=> ( ! [X1120: $i,X1121: $i,X1122: $i] :
( ~ ( in @ X1122 @ ( setminus @ X1120 @ X1121 ) )
=> ( ~ ( in @ X1122 @ X1121 )
=> ~ ( in @ X1122 @ X1120 ) ) )
=> ( ! [X1123: $i,X1124: $i,X1125: $i] :
( ~ ( in @ X1125 @ X1123 )
=> ~ ( in @ X1125 @ ( setminus @ X1123 @ X1124 ) ) )
=> ( ! [X1126: $i,X1127: $i,X1128: $i] :
( ( in @ X1128 @ X1127 )
=> ~ ( in @ X1128 @ ( setminus @ X1126 @ X1127 ) ) )
=> ( ! [X1129: $i,X1130: $i] : ( subset @ ( setminus @ X1129 @ X1130 ) @ X1129 )
=> ( ! [X1131: $i,X1132: $i] :
( ( ( setminus @ X1131 @ X1132 )
= emptyset )
=> ( subset @ X1131 @ X1132 ) )
=> ( ! [X1133: $i,X1134: $i,X1135: $i] :
( ( in @ X1135 @ ( symdiff @ X1133 @ X1134 ) )
=> ! [X1136: $o] :
( ( ( in @ X1135 @ X1133 )
=> ( ~ ( in @ X1135 @ X1134 )
=> X1136 ) )
=> ( ( ~ ( in @ X1135 @ X1133 )
=> ( ( in @ X1135 @ X1134 )
=> X1136 ) )
=> X1136 ) ) )
=> ( ! [X1137: $i,X1138: $i,X1139: $i] :
( ( in @ X1139 @ X1137 )
=> ( ~ ( in @ X1139 @ X1138 )
=> ( in @ X1139 @ ( symdiff @ X1137 @ X1138 ) ) ) )
=> ( ! [X1140: $i,X1141: $i,X1142: $i] :
( ~ ( in @ X1142 @ X1140 )
=> ( ( in @ X1142 @ X1141 )
=> ( in @ X1142 @ ( symdiff @ X1140 @ X1141 ) ) ) )
=> ( ! [X1143: $i,X1144: $i,X1145: $i] :
( ( in @ X1145 @ X1143 )
=> ( ( in @ X1145 @ X1144 )
=> ~ ( in @ X1145 @ ( symdiff @ X1143 @ X1144 ) ) ) )
=> ( ! [X1146: $i,X1147: $i,X1148: $i] :
( ~ ( in @ X1148 @ X1146 )
=> ( ~ ( in @ X1148 @ X1147 )
=> ~ ( in @ X1148 @ ( symdiff @ X1146 @ X1147 ) ) ) )
=> ( ! [X1149: $i,X1150: $i] : ( in @ X1150 @ ( setadjoin @ X1149 @ ( setadjoin @ X1150 @ emptyset ) ) )
=> ( ! [X1151: $i,X1152: $i] : ( in @ X1151 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1151 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1151 @ ( setadjoin @ X1152 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1153: $i,X1154: $i] : ( in @ X1154 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1153 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1153 @ ( setadjoin @ X1154 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1155: $i,X1156: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1155 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1155 @ ( setadjoin @ X1156 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1157: $i,X1158: $i] : ( iskpair @ ( kpair @ X1157 @ X1158 ) )
=> ( ! [X1159: $i,X1160: $i] :
( ( in @ X1160 @ X1159 )
=> ( subset @ ( setadjoin @ X1160 @ emptyset ) @ X1159 ) )
=> ( ! [X1161: $i,X1162: $i] :
( ( in @ X1162 @ X1161 )
=> ( in @ ( setadjoin @ X1162 @ emptyset ) @ ( powerset @ X1161 ) ) )
=> ( ! [X1163: $i,X1164: $i,X1165: $i] :
( ( in @ X1165 @ X1163 )
=> ( in @ ( setadjoin @ X1165 @ emptyset ) @ ( powerset @ ( binunion @ X1163 @ X1164 ) ) ) )
=> ( ! [X1166: $i,X1167: $i,X1168: $i] :
( ( in @ X1168 @ ( setadjoin @ X1166 @ ( setadjoin @ X1167 @ emptyset ) ) )
=> ( ( X1168 = X1166 )
| ( X1168 = X1167 ) ) )
=> ( ! [X1169: $i,X1170: $i,X1171: $i] :
( ( in @ X1171 @ X1169 )
=> ! [X1172: $i] :
( ( in @ X1172 @ X1170 )
=> ( subset @ ( setadjoin @ X1171 @ ( setadjoin @ X1172 @ emptyset ) ) @ ( binunion @ X1169 @ X1170 ) ) ) )
=> ( ! [X1173: $i,X1174: $i,X1175: $i] :
( ( in @ X1175 @ X1173 )
=> ! [X1176: $i] :
( ( in @ X1176 @ X1174 )
=> ( in @ ( setadjoin @ X1175 @ ( setadjoin @ X1176 @ emptyset ) ) @ ( powerset @ ( binunion @ X1173 @ X1174 ) ) ) ) )
=> ( ! [X1177: $i,X1178: $i,X1179: $i] :
( ( in @ X1179 @ X1177 )
=> ! [X1180: $i] :
( ( in @ X1180 @ X1178 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1179 @ ( setadjoin @ X1180 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1177 @ X1178 ) ) ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ X1181 )
=> ! [X1184: $i] :
( ( in @ X1184 @ X1182 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1183 @ ( setadjoin @ X1184 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1181 @ X1182 ) ) ) ) ) )
=> ( ! [X1185: $i,X1186: $i,X1187: $i] :
( ( in @ X1187 @ X1185 )
=> ! [X1188: $i] :
( ( in @ X1188 @ X1186 )
=> ( in @ ( kpair @ X1187 @ X1188 ) @ ( powerset @ ( powerset @ ( binunion @ X1185 @ X1186 ) ) ) ) ) )
=> ( ! [X1189: $i,X1190: $i,X1191: $i] :
( ( in @ X1191 @ X1189 )
=> ! [X1192: $i] :
( ( in @ X1192 @ X1190 )
=> ( in @ ( kpair @ X1191 @ X1192 ) @ ( cartprod @ X1189 @ X1190 ) ) ) )
=> ( ! [X1193: $i,X1194: $i,X1195: $i] :
( ( in @ X1195 @ ( cartprod @ X1193 @ X1194 ) )
=> ? [X1196: $i] :
( ( in @ X1196 @ X1193 )
& ? [X1197: $i] :
( ( in @ X1197 @ X1194 )
& ( X1195
= ( kpair @ X1196 @ X1197 ) ) ) ) )
=> ( ! [X1198: $i,X1199: $i,X1200: $i] :
( ( in @ X1200 @ ( cartprod @ X1198 @ X1199 ) )
=> ( iskpair @ X1200 ) )
=> ( ! [X1201: $i,X1202: $i] :
( ( in @ X1202 @ ( setunion @ X1201 ) )
=> ? [X1203: $i] :
( ( in @ X1203 @ X1201 )
& ( in @ X1202 @ X1203 ) ) )
=> ( ! [X1204: $i] : ( subset @ ( setunion @ ( setadjoin @ X1204 @ emptyset ) ) @ X1204 )
=> ( ! [X1205: $i] : ( subset @ X1205 @ ( setunion @ ( setadjoin @ X1205 @ emptyset ) ) )
=> ( ! [X1206: $i] :
( ( setunion @ ( setadjoin @ X1206 @ emptyset ) )
= X1206 )
=> ( ! [X1207: $i,X1208: $i > $o] :
( ! [X1209: $i] :
( ( in @ X1209 @ X1207 )
=> ! [X1210: $i] :
( ( in @ X1210 @ X1207 )
=> ( ( X1208 @ X1209 )
=> ( ( X1208 @ X1210 )
=> ( X1209 = X1210 ) ) ) ) )
=> ( ? [X1211: $i] :
( ( in @ X1211 @ X1207 )
& ( X1208 @ X1211 ) )
=> ( singleton @ ( dsetconstr @ X1207 @ X1208 ) ) ) )
=> ( ! [X1212: $i,X1213: $i > $o] :
( ( ex1 @ X1212 @ X1213 )
=> ? [X1214: $i] :
( ( in @ X1214 @ X1212 )
& ( X1213 @ X1214 ) ) )
=> ( ! [X1215: $i,X1216: $i > $o,X1217: $i] :
( ( in @ X1217 @ X1215 )
=> ( ( X1216 @ X1217 )
=> ( ! [X1218: $i] :
( ( in @ X1218 @ X1215 )
=> ( ( X1216 @ X1218 )
=> ( X1218 = X1217 ) ) )
=> ( ex1 @ X1215 @ X1216 ) ) ) )
=> ( ! [X1219: $i,X1220: $i > $o] :
( ! [X1221: $i] :
( ( in @ X1221 @ X1219 )
=> ! [X1222: $i] :
( ( in @ X1222 @ X1219 )
=> ( ( X1220 @ X1221 )
=> ( ( X1220 @ X1222 )
=> ( X1221 = X1222 ) ) ) ) )
=> ( ? [X1223: $i] :
( ( in @ X1223 @ X1219 )
& ( X1220 @ X1223 ) )
=> ( ex1 @ X1219 @ X1220 ) ) )
=> ( ! [X1224: $i,X1225: $i] :
( ( ( setadjoin @ X1224 @ emptyset )
= ( setadjoin @ X1225 @ emptyset ) )
=> ( X1224 = X1225 ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i] :
( ( in @ ( setadjoin @ X1228 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1226 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1226 @ ( setadjoin @ X1227 @ emptyset ) ) @ emptyset ) ) )
=> ( X1226 = X1228 ) )
=> ( ! [X1229: $i] :
( ( iskpair @ X1229 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1229 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1229 ) ) ) )
=> ( ! [X1230: $i] :
( ( singleton @ X1230 )
=> ( in @ ( setunion @ X1230 ) @ X1230 ) )
=> ( ! [X1231: $i,X1232: $i] :
( ( kfst @ ( kpair @ X1231 @ X1232 ) )
= X1231 )
=> ( ! [X1233: $i,X1234: $i,X1235: $i] :
( ( in @ X1235 @ ( cartprod @ X1233 @ X1234 ) )
=> ( in @ ( kfst @ X1235 ) @ X1233 ) )
=> ( ! [X1236: $i,X1237: $i,X1238: $i,X1239: $i] :
( ( ( setadjoin @ ( setadjoin @ X1236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1236 @ ( setadjoin @ X1237 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1238 @ ( setadjoin @ X1239 @ emptyset ) ) @ emptyset ) ) )
=> ( X1236 = X1238 ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i,X1243: $i] :
( ( ( kpair @ X1240 @ X1241 )
= ( kpair @ X1242 @ X1243 ) )
=> ( X1240 = X1242 ) )
=> ( ! [X1244: $i,X1245: $i] :
( ( X1244 = X1245 )
=> ( ( setadjoin @ X1244 @ ( setadjoin @ X1245 @ emptyset ) )
= ( setadjoin @ X1244 @ emptyset ) ) )
=> ( ! [X1246: $i,X1247: $i] :
( ( X1246 = X1247 )
=> ( ( setadjoin @ ( setadjoin @ X1246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1246 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i,X1251: $i] :
( ( ( setadjoin @ ( setadjoin @ X1248 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1248 @ ( setadjoin @ X1249 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1250 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1250 @ ( setadjoin @ X1251 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1250 = X1251 )
=> ( X1249 = X1251 ) ) )
=> ( ! [X1252: $i,X1253: $i,X1254: $i] :
( ( ( setadjoin @ X1252 @ ( setadjoin @ X1253 @ emptyset ) )
= ( setadjoin @ X1254 @ emptyset ) )
=> ( X1252 = X1253 ) )
=> ( ! [X1255: $i,X1256: $i,X1257: $i,X1258: $i] :
( ( ( setadjoin @ ( setadjoin @ X1255 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1255 @ ( setadjoin @ X1256 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1257 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1257 @ ( setadjoin @ X1258 @ emptyset ) ) @ emptyset ) ) )
=> ( X1256 = X1258 ) )
=> ( ! [X1259: $i,X1260: $i,X1261: $i,X1262: $i] :
( ( ( kpair @ X1259 @ X1260 )
= ( kpair @ X1261 @ X1262 ) )
=> ( X1260 = X1262 ) )
=> ( ! [X1263: $i] :
( ( iskpair @ X1263 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1263 )
@ ^ [Z0: $i] :
( X1263
= ( kpair @ ( kfst @ X1263 ) @ Z0 ) ) ) ) )
=> ( ! [X1264: $i,X1265: $i] :
( ( ksnd @ ( kpair @ X1264 @ X1265 ) )
= X1265 )
=> ( ! [X1266: $i] :
( ( iskpair @ X1266 )
=> ( ( kpair @ ( kfst @ X1266 ) @ ( ksnd @ X1266 ) )
= X1266 ) )
=> ( ! [X1267: $i,X1268: $i,X1269: $i] :
( ( in @ X1269 @ ( cartprod @ X1267 @ X1268 ) )
=> ( in @ ( ksnd @ X1269 ) @ X1268 ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i,X1273: $i] :
( ( in @ ( kpair @ X1272 @ X1273 ) @ ( cartprod @ X1270 @ X1271 ) )
=> ( in @ X1272 @ X1270 ) )
=> ( ! [X1274: $i,X1275: $i,X1276: $i,X1277: $i] :
( ( in @ ( kpair @ X1276 @ X1277 ) @ ( cartprod @ X1274 @ X1275 ) )
=> ( in @ X1277 @ X1275 ) )
=> ( ! [X1278: $i,X1279: $i,X1280: $i] :
( ( in @ X1280 @ X1278 )
=> ! [X1281: $i] :
( ( in @ X1281 @ X1279 )
=> ( ( kpair @ X1280 @ X1281 )
= ( kpair @ X1280 @ X1281 ) ) ) )
=> ( ! [X1282: $i,X1283: $i,X1284: $i] :
( ( in @ X1284 @ X1282 )
=> ! [X1285: $i] :
( ( in @ X1285 @ X1283 )
=> ( ( kfst @ ( kpair @ X1284 @ X1285 ) )
= X1284 ) ) )
=> ( ! [X1286: $i,X1287: $i,X1288: $i] :
( ( in @ X1288 @ X1286 )
=> ! [X1289: $i] :
( ( in @ X1289 @ X1287 )
=> ( ( ksnd @ ( kpair @ X1288 @ X1289 ) )
= X1289 ) ) )
=> ( ! [X1290: $i,X1291: $i,X1292: $i] :
( ( in @ X1292 @ ( cartprod @ X1290 @ X1291 ) )
=> ( ( kpair @ ( kfst @ X1292 ) @ ( ksnd @ X1292 ) )
= X1292 ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i > $i > $o,X1296: $i] :
( ( in @ X1296 @ X1293 )
=> ! [X1297: $i] :
( ( in @ X1297 @ X1294 )
=> ( ( X1295 @ X1296 @ X1297 )
=> ( in @ ( kpair @ X1296 @ X1297 ) @ ( dpsetconstr @ X1293 @ X1294 @ X1295 ) ) ) ) )
=> ( ! [X1298: $i,X1299: $i,X1300: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1298 @ X1299 @ X1300 ) @ ( cartprod @ X1298 @ X1299 ) )
=> ( ! [X1301: $i,X1302: $i,X1303: $i > $i > $o] : ( breln @ X1301 @ X1302 @ ( dpsetconstr @ X1301 @ X1302 @ X1303 ) )
=> ( ! [X1304: $i,X1305: $i,X1306: $i > $i > $o,X1307: $i] :
( ( in @ X1307 @ X1304 )
=> ! [X1308: $i] :
( ( in @ X1308 @ X1305 )
=> ( ( in @ ( kpair @ X1307 @ X1308 ) @ ( dpsetconstr @ X1304 @ X1305 @ X1306 ) )
=> ( X1306 @ X1307 @ X1308 ) ) ) )
=> ( ! [X1309: $i,X1310: $i,X1311: $i > $i > $o,X1312: $i,X1313: $i] :
( ( in @ ( kpair @ X1312 @ X1313 ) @ ( dpsetconstr @ X1309 @ X1310 @ X1311 ) )
=> ( in @ X1312 @ X1309 ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i > $i > $o,X1317: $i,X1318: $i] :
( ( in @ ( kpair @ X1317 @ X1318 ) @ ( dpsetconstr @ X1314 @ X1315 @ X1316 ) )
=> ( in @ X1318 @ X1315 ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i > $i > $o,X1322: $i,X1323: $i] :
( ( in @ ( kpair @ X1322 @ X1323 ) @ ( dpsetconstr @ X1319 @ X1320 @ X1321 ) )
=> ( X1321 @ X1322 @ X1323 ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i] :
( ( func @ X1324 @ X1325 @ X1326 )
=> ! [X1327: $i] :
( ( in @ X1327 @ X1324 )
=> ( singleton
@ ( dsetconstr @ X1325
@ ^ [Z0: $i] : ( in @ ( kpair @ X1327 @ Z0 ) @ X1326 ) ) ) ) )
=> ( ! [X1328: $i,X1329: $i,X1330: $i] :
( ( func @ X1328 @ X1329 @ X1330 )
=> ! [X1331: $i] :
( ( in @ X1331 @ X1328 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1329
@ ^ [Z0: $i] : ( in @ ( kpair @ X1331 @ Z0 ) @ X1330 ) ) )
@ X1329 ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( func @ X1332 @ X1333 @ X1334 )
=> ! [X1335: $i] :
( ( in @ X1335 @ X1332 )
=> ( in @ ( ap @ X1332 @ X1333 @ X1334 @ X1335 ) @ X1333 ) ) )
=> ( ! [X1336: $i,X1337: $i,X1338: $i] :
( ( in @ X1338 @ ( funcSet @ X1336 @ X1337 ) )
=> ( func @ X1336 @ X1337 @ X1338 ) )
=> ( ! [X1339: $i,X1340: $i,X1341: $i] :
( ( in @ X1341 @ ( funcSet @ X1339 @ X1340 ) )
=> ! [X1342: $i] :
( ( in @ X1342 @ X1339 )
=> ( in @ ( ap @ X1339 @ X1340 @ X1341 @ X1342 ) @ X1340 ) ) )
=> ( ! [X1343: $i,X1344: $i,X1345: $i] :
( ( func @ X1343 @ X1344 @ X1345 )
=> ( in @ X1345 @ ( funcSet @ X1343 @ X1344 ) ) )
=> ( ! [X1346: $i,X1347: $i,X1348: $i > $i] :
( ! [X1349: $i] :
( ( in @ X1349 @ X1346 )
=> ( in @ ( X1348 @ X1349 ) @ X1347 ) )
=> ( func @ X1346 @ X1347
@ ( dpsetconstr @ X1346 @ X1347
@ ^ [Z0: $i] : ( $eq @ ( X1348 @ Z0 ) ) ) ) )
=> ( ! [X1350: $i,X1351: $i,X1352: $i > $i] :
( ! [X1353: $i] :
( ( in @ X1353 @ X1350 )
=> ( in @ ( X1352 @ X1353 ) @ X1351 ) )
=> ( func @ X1350 @ X1351 @ ( lam @ X1350 @ X1351 @ X1352 ) ) )
=> ( ! [X1354: $i,X1355: $i,X1356: $i > $i] :
( ! [X1357: $i] :
( ( in @ X1357 @ X1354 )
=> ( in @ ( X1356 @ X1357 ) @ X1355 ) )
=> ( in @ ( lam @ X1354 @ X1355 @ X1356 ) @ ( funcSet @ X1354 @ X1355 ) ) )
=> ( ! [X1358: $i,X1359: $i,X1360: $i] :
( ( breln @ X1358 @ X1359 @ X1360 )
=> ! [X1361: $i > $o] :
( ! [X1362: $i] :
( ( in @ X1362 @ X1358 )
=> ! [X1363: $i] :
( ( in @ X1363 @ X1359 )
=> ( ( in @ ( kpair @ X1362 @ X1363 ) @ X1360 )
=> ( X1361 @ ( kpair @ X1362 @ X1363 ) ) ) ) )
=> ! [X1364: $i] :
( ( in @ X1364 @ X1360 )
=> ( X1361 @ X1364 ) ) ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i] :
( ( breln @ X1365 @ X1366 @ X1367 )
=> ! [X1368: $i > $o] :
( ! [X1369: $i] :
( ( in @ X1369 @ X1365 )
=> ! [X1370: $i] :
( ( in @ X1370 @ X1366 )
=> ( ( in @ ( kpair @ X1369 @ X1370 ) @ X1367 )
=> ( X1368 @ ( kpair @ X1369 @ X1370 ) ) ) ) )
=> ! [X1371: $i] :
( ( in @ X1371 @ X1367 )
=> ( X1368 @ X1371 ) ) ) )
=> ( ! [X1372: $i,X1373: $i > $o] :
( ( ex1 @ X1372 @ X1373 )
=> ! [X1374: $i] :
( ( in @ X1374 @ X1372 )
=> ! [X1375: $i] :
( ( in @ X1375 @ X1372 )
=> ( ( X1373 @ X1374 )
=> ( ( X1373 @ X1375 )
=> ( X1374 = X1375 ) ) ) ) ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i] :
( ( func @ X1376 @ X1377 @ X1378 )
=> ! [X1379: $i] :
( ( in @ X1379 @ X1376 )
=> ( in @ ( kpair @ X1379 @ ( ap @ X1376 @ X1377 @ X1378 @ X1379 ) ) @ X1378 ) ) )
=> ( ! [X1380: $i,X1381: $i,X1382: $i] :
( ( in @ X1382 @ ( funcSet @ X1380 @ X1381 ) )
=> ! [X1383: $i] :
( ( in @ X1383 @ X1380 )
=> ( in @ ( kpair @ X1383 @ ( ap @ X1380 @ X1381 @ X1382 @ X1383 ) ) @ X1382 ) ) )
=> ( ! [X1384: $i,X1385: $i,X1386: $i] :
( ( func @ X1384 @ X1385 @ X1386 )
=> ! [X1387: $i] :
( ( in @ X1387 @ X1384 )
=> ! [X1388: $i] :
( ( in @ X1388 @ X1385 )
=> ( ( in @ ( kpair @ X1387 @ X1388 ) @ X1386 )
=> ( ( ap @ X1384 @ X1385 @ X1386 @ X1387 )
= X1388 ) ) ) ) )
=> ( ! [X1389: $i,X1390: $i,X1391: $i] :
( ( func @ X1389 @ X1390 @ X1391 )
=> ! [X1392: $i] :
( ( func @ X1389 @ X1390 @ X1392 )
=> ( ! [X1393: $i] :
( ( in @ X1393 @ X1389 )
=> ( ( ap @ X1389 @ X1390 @ X1391 @ X1393 )
= ( ap @ X1389 @ X1390 @ X1392 @ X1393 ) ) )
=> ! [X1394: $i] :
( ( in @ X1394 @ X1389 )
=> ! [X1395: $i] :
( ( in @ X1395 @ X1390 )
=> ( ( in @ ( kpair @ X1394 @ X1395 ) @ X1392 )
=> ( in @ ( kpair @ X1394 @ X1395 ) @ X1391 ) ) ) ) ) ) )
=> ( ! [X1396: $i,X1397: $i,X1398: $i] :
( ( in @ X1398 @ ( funcSet @ X1396 @ X1397 ) )
=> ! [X1399: $i] :
( ( in @ X1399 @ X1396 )
=> ! [X1400: $i] :
( ( in @ X1400 @ X1397 )
=> ( ( in @ ( kpair @ X1399 @ X1400 ) @ X1398 )
=> ( ( ap @ X1396 @ X1397 @ X1398 @ X1399 )
= X1400 ) ) ) ) )
=> ( ! [X1401: $i,X1402: $i,X1403: $i] :
( ( breln @ X1401 @ X1402 @ X1403 )
=> ! [X1404: $i] :
( ( breln @ X1401 @ X1402 @ X1404 )
=> ( ! [X1405: $i] :
( ( in @ X1405 @ X1401 )
=> ! [X1406: $i] :
( ( in @ X1406 @ X1402 )
=> ( ( in @ ( kpair @ X1405 @ X1406 ) @ X1403 )
=> ( in @ ( kpair @ X1405 @ X1406 ) @ X1404 ) ) ) )
=> ( subset @ X1403 @ X1404 ) ) ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i] :
( ( breln @ X1407 @ X1408 @ X1409 )
=> ! [X1410: $i] :
( ( breln @ X1407 @ X1408 @ X1410 )
=> ( ! [X1411: $i] :
( ( in @ X1411 @ X1407 )
=> ! [X1412: $i] :
( ( in @ X1412 @ X1408 )
=> ( ( in @ ( kpair @ X1411 @ X1412 ) @ X1409 )
=> ( in @ ( kpair @ X1411 @ X1412 ) @ X1410 ) ) ) )
=> ( ! [X1413: $i] :
( ( in @ X1413 @ X1407 )
=> ! [X1414: $i] :
( ( in @ X1414 @ X1408 )
=> ( ( in @ ( kpair @ X1413 @ X1414 ) @ X1410 )
=> ( in @ ( kpair @ X1413 @ X1414 ) @ X1409 ) ) ) )
=> ( X1409 = X1410 ) ) ) ) )
=> ( ! [X1415: $i,X1416: $i,X1417: $i] :
( ( func @ X1415 @ X1416 @ X1417 )
=> ! [X1418: $i] :
( ( func @ X1415 @ X1416 @ X1418 )
=> ( ! [X1419: $i] :
( ( in @ X1419 @ X1415 )
=> ( ( ap @ X1415 @ X1416 @ X1417 @ X1419 )
= ( ap @ X1415 @ X1416 @ X1418 @ X1419 ) ) )
=> ( X1417 = X1418 ) ) ) )
=> ( ! [X1420: $i,X1421: $i,X1422: $i] :
( ( in @ X1422 @ ( funcSet @ X1420 @ X1421 ) )
=> ! [X1423: $i] :
( ( in @ X1423 @ ( funcSet @ X1420 @ X1421 ) )
=> ( ! [X1424: $i] :
( ( in @ X1424 @ X1420 )
=> ( ( ap @ X1420 @ X1421 @ X1422 @ X1424 )
= ( ap @ X1420 @ X1421 @ X1423 @ X1424 ) ) )
=> ( X1422 = X1423 ) ) ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i] :
( ( in @ X1427 @ ( funcSet @ X1425 @ X1426 ) )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ( ( ap @ X1425 @ X1426 @ X1427 @ X1428 )
= ( ap @ X1425 @ X1426 @ X1427 @ X1428 ) ) ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i] :
( ( func @ X1429 @ X1430 @ X1431 )
=> ! [X1432: $i] :
( ( in @ X1432 @ X1429 )
=> ( ( ap @ X1429 @ X1430 @ X1431 @ X1432 )
= ( ap @ X1429 @ X1430 @ X1431 @ X1432 ) ) ) )
=> ( ! [X1433: $i,X1434: $i,X1435: $i > $i] :
( ! [X1436: $i] :
( ( in @ X1436 @ X1433 )
=> ( in @ ( X1435 @ X1436 ) @ X1434 ) )
=> ! [X1437: $i] :
( ( in @ X1437 @ X1433 )
=> ( ( ap @ X1433 @ X1434 @ ( lam @ X1433 @ X1434 @ X1435 ) @ X1437 )
= ( X1435 @ X1437 ) ) ) )
=> ( ! [X1438: $i,X1439: $i,X1440: $i] :
( ( func @ X1438 @ X1439 @ X1440 )
=> ( ( lam @ X1438 @ X1439 @ ( ap @ X1438 @ X1439 @ X1440 ) )
= X1440 ) )
=> ( ! [X1441: $i,X1442: $i,X1443: $i > $i] :
( ! [X1444: $i] :
( ( in @ X1444 @ X1441 )
=> ( in @ ( X1443 @ X1444 ) @ X1442 ) )
=> ( ( lam @ X1441 @ X1442 @ X1443 )
= ( lam @ X1441 @ X1442 @ X1443 ) ) )
=> ( ! [X1445: $i,X1446: $i,X1447: $i > $i] :
( ! [X1448: $i] :
( ( in @ X1448 @ X1445 )
=> ( in @ ( X1447 @ X1448 ) @ X1446 ) )
=> ! [X1449: $i] :
( ( in @ X1449 @ X1445 )
=> ( ( ap @ X1445 @ X1446 @ ( lam @ X1445 @ X1446 @ X1447 ) @ X1449 )
= ( X1447 @ X1449 ) ) ) )
=> ( ! [X1450: $i,X1451: $i,X1452: $i] :
( ( in @ X1452 @ ( funcSet @ X1450 @ X1451 ) )
=> ( ( lam @ X1450 @ X1451 @ ( ap @ X1450 @ X1451 @ X1452 ) )
= X1452 ) )
=> ( ! [X1453: $i,X1454: $o,X1455: $i] :
( ( in @ X1455 @ X1453 )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1453 )
=> ( ~ X1454
=> ( in @ X1456
@ ( dsetconstr @ X1453
@ ^ [Z0: $i] :
( ( X1454
& ( Z0 = X1455 ) )
| ( ~ X1454
& ( Z0 = X1456 ) ) ) ) ) ) ) )
=> ( ! [X1457: $i,X1458: $o,X1459: $i] :
( ( in @ X1459 @ X1457 )
=> ! [X1460: $i] :
( ( in @ X1460 @ X1457 )
=> ( ~ X1458
=> ( ( dsetconstr @ X1457
@ ^ [Z0: $i] :
( ( X1458
& ( Z0 = X1459 ) )
| ( ~ X1458
& ( Z0 = X1460 ) ) ) )
= ( setadjoin @ X1460 @ emptyset ) ) ) ) )
=> ( ! [X1461: $i,X1462: $o,X1463: $i] :
( ( in @ X1463 @ X1461 )
=> ! [X1464: $i] :
( ( in @ X1464 @ X1461 )
=> ( X1462
=> ( in @ X1463
@ ( dsetconstr @ X1461
@ ^ [Z0: $i] :
( ( X1462
& ( Z0 = X1463 ) )
| ( ~ X1462
& ( Z0 = X1464 ) ) ) ) ) ) ) )
=> ( ! [X1465: $i,X1466: $o,X1467: $i] :
( ( in @ X1467 @ X1465 )
=> ! [X1468: $i] :
( ( in @ X1468 @ X1465 )
=> ( X1466
=> ( ( dsetconstr @ X1465
@ ^ [Z0: $i] :
( ( X1466
& ( Z0 = X1467 ) )
| ( ~ X1466
& ( Z0 = X1468 ) ) ) )
= ( setadjoin @ X1467 @ emptyset ) ) ) ) )
=> ( ! [X1469: $i,X1470: $o,X1471: $i] :
( ( in @ X1471 @ X1469 )
=> ! [X1472: $i] :
( ( in @ X1472 @ X1469 )
=> ( singleton
@ ( dsetconstr @ X1469
@ ^ [Z0: $i] :
( ( X1470
& ( Z0 = X1471 ) )
| ( ~ X1470
& ( Z0 = X1472 ) ) ) ) ) ) )
=> ( ! [X1473: $i,X1474: $o,X1475: $i] :
( ( in @ X1475 @ X1473 )
=> ! [X1476: $i] :
( ( in @ X1476 @ X1473 )
=> ( in @ ( if @ X1473 @ X1474 @ X1475 @ X1476 ) @ X1473 ) ) )
=> ( ! [X1477: $i] :
( ( singleton @ X1477 )
=> ! [X1478: $i] :
( ( in @ X1478 @ X1477 )
=> ( ( setunion @ X1477 )
= X1478 ) ) )
=> ( ! [X1479: $i,X1480: $o,X1481: $i] :
( ( in @ X1481 @ X1479 )
=> ! [X1482: $i] :
( ( in @ X1482 @ X1479 )
=> ( X1480
=> ( ( if @ X1479 @ X1480 @ X1481 @ X1482 )
= X1481 ) ) ) )
=> ( ! [X1483: $i,X1484: $o,X1485: $i] :
( ( in @ X1485 @ X1483 )
=> ! [X1486: $i] :
( ( in @ X1486 @ X1483 )
=> ( ~ X1484
=> ( ( if @ X1483 @ X1484 @ X1485 @ X1486 )
= X1486 ) ) ) )
=> ( ! [X1487: $i,X1488: $o,X1489: $i] :
( ( in @ X1489 @ X1487 )
=> ! [X1490: $i] :
( ( in @ X1490 @ X1487 )
=> ( in @ ( if @ X1487 @ X1488 @ X1489 @ X1490 ) @ ( setadjoin @ X1489 @ ( setadjoin @ X1490 @ emptyset ) ) ) ) )
=> ( ! [X1491: $i,X1492: $i] :
( ( in @ X1492 @ ( powerset @ X1491 ) )
=> ! [X1493: $i] :
( ( in @ X1493 @ ( powerset @ X1491 ) )
=> ( in @ ( binintersect @ X1492 @ X1493 ) @ ( powerset @ X1491 ) ) ) )
=> ( ! [X1494: $i,X1495: $i] :
( ( in @ X1495 @ ( powerset @ X1494 ) )
=> ! [X1496: $i] :
( ( in @ X1496 @ ( powerset @ X1494 ) )
=> ( in @ ( binunion @ X1495 @ X1496 ) @ ( powerset @ X1494 ) ) ) )
=> ( ! [X1497: $i,X1498: $i] :
( ( in @ X1498 @ ( powerset @ X1497 ) )
=> ( in @ ( powerset @ X1498 ) @ ( powerset @ ( powerset @ X1497 ) ) ) )
=> ( ! [X1499: $i,X1500: $i] :
( ( in @ X1500 @ ( powerset @ X1499 ) )
=> ! [X1501: $i] :
( ( in @ X1501 @ ( powerset @ X1499 ) )
=> ( in @ ( setminus @ X1500 @ X1501 ) @ ( powerset @ X1499 ) ) ) )
=> ( ! [X1502: $i,X1503: $i] :
( ( in @ X1503 @ ( powerset @ X1502 ) )
=> ( in @ ( setminus @ X1502 @ X1503 ) @ ( powerset @ X1502 ) ) )
=> ( ! [X1504: $i,X1505: $i] :
( ( in @ X1505 @ ( powerset @ X1504 ) )
=> ! [X1506: $i] :
( ( in @ X1506 @ ( powerset @ X1504 ) )
=> ( ! [X1507: $i] :
( ( in @ X1507 @ X1504 )
=> ( ( in @ X1507 @ X1505 )
=> ( in @ X1507 @ X1506 ) ) )
=> ( ! [X1508: $i] :
( ( in @ X1508 @ X1504 )
=> ( ( in @ X1508 @ X1506 )
=> ( in @ X1508 @ X1505 ) ) )
=> ( X1505 = X1506 ) ) ) ) )
=> ( ! [X1509: $i,X1510: $i] :
( ( in @ X1510 @ ( powerset @ X1509 ) )
=> ! [X1511: $i] :
( ( in @ X1511 @ ( powerset @ X1509 ) )
=> ( ! [X1512: $i] :
( ( in @ X1512 @ X1509 )
=> ( ( in @ X1512 @ X1510 )
=> ( in @ X1512 @ X1511 ) ) )
=> ( subset @ X1510 @ X1511 ) ) ) )
=> ( ! [X1513: $i,X1514: $i] :
( ( in @ X1514 @ ( powerset @ X1513 ) )
=> ! [X1515: $i] :
( ( in @ X1515 @ ( powerset @ X1513 ) )
=> ( ! [X1516: $i] :
( ( in @ X1516 @ X1513 )
=> ( ( in @ X1516 @ X1514 )
=> ( in @ X1516 @ X1515 ) ) )
=> ( in @ X1514 @ ( powerset @ X1515 ) ) ) ) )
=> ( ! [X1517: $i,X1518: $i] :
( ( in @ X1518 @ ( powerset @ X1517 ) )
=> ! [X1519: $i] :
( ( in @ X1519 @ ( powerset @ X1517 ) )
=> ! [X1520: $i] :
( ( in @ X1520 @ X1517 )
=> ( ( in @ X1518 @ ( powerset @ X1519 ) )
=> ( ( in @ X1520 @ X1518 )
=> ( in @ X1520 @ X1519 ) ) ) ) ) )
=> ( ! [X1521: $i,X1522: $i] :
( ( in @ X1522 @ ( powerset @ X1521 ) )
=> ! [X1523: $i] :
( ( in @ X1523 @ X1521 )
=> ( ( in @ X1523 @ X1522 )
=> ~ ( in @ X1523 @ ( setminus @ X1521 @ X1522 ) ) ) ) )
=> ( ! [X1524: $i,X1525: $i] :
( ( in @ X1525 @ ( powerset @ X1524 ) )
=> ! [X1526: $i] :
( ( in @ X1526 @ X1524 )
=> ( ~ ( in @ X1526 @ ( setminus @ X1524 @ X1525 ) )
=> ( in @ X1526 @ X1525 ) ) ) )
=> ( ! [X1527: $i,X1528: $i] :
( ( in @ X1528 @ ( powerset @ X1527 ) )
=> ! [X1529: $i] :
( ( in @ X1529 @ ( powerset @ X1527 ) )
=> ! [X1530: $i] :
( ( in @ X1530 @ X1527 )
=> ( ~ ( in @ X1530 @ X1528 )
=> ~ ( in @ X1530 @ ( binintersect @ X1528 @ X1529 ) ) ) ) ) )
=> ( ! [X1531: $i,X1532: $i] :
( ( in @ X1532 @ ( powerset @ X1531 ) )
=> ! [X1533: $i] :
( ( in @ X1533 @ ( powerset @ X1531 ) )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1531 )
=> ( ~ ( in @ X1534 @ X1533 )
=> ~ ( in @ X1534 @ ( binintersect @ X1532 @ X1533 ) ) ) ) ) )
=> ( ! [X1535: $i,X1536: $i] :
( ( in @ X1536 @ ( powerset @ X1535 ) )
=> ! [X1537: $i] :
( ( in @ X1537 @ ( powerset @ X1535 ) )
=> ! [X1538: $i] :
( ( in @ X1538 @ X1535 )
=> ( ( subset @ X1536 @ ( setminus @ X1535 @ X1537 ) )
=> ( ( in @ X1538 @ X1537 )
=> ~ ( in @ X1538 @ X1536 ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(assume_negation,[status(cth)],[contrasubsetT1]),c_0_240]),contrasubsetT]),c_0_241]),emptysetsubset]),c_0_242]),brelnall1]),brelnall2]),subsetE]),c_0_243]),funcGraphProp1]),subsetE2]),funcGraphProp3]),funcGraphProp2]),notsubsetI]),funcextLem]),funcGraphProp4]),notequalI1]),subbreln]),eqbreln]),notequalI2]),funcext]),funcext2]),subsetRefl]),ap2apEq1]),subsetTrans]),ap2apEq2]),c_0_244]),c_0_245]),setadjoinSub]),c_0_246]),c_0_247]),c_0_248]),setadjoinSub2]),binintersectEL]),c_0_249]),c_0_250]),subset2powerset]),c_0_251]),c_0_252]),setextsub]),ifp]),theeq]),subsetemptysetimpeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),powersetI1]),binunionT_lem]),powersetT_lem]),powersetE1]),setminusT_lem]),complementT_lem]),inPowerset]),setextT]),subsetTI]),powersetsubset]),powersetTI1]),powersetTE1]),c_0_253]),complementTI1]),complementTE1]),c_0_254]),binintersectTELcontra]),binintersectTERcontra]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),ubforcartprodlem1]),ubforcartprodlem2]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),subsetI1]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),eqimpsubset2]),eqimpsubset1]),singletoninpowerset]),singletoninpowunion]),subsetI2]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_255]),c_0_256]),c_0_257]),c_0_258]),singletonsuniq]),setukpairinjL1]),c_0_259]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_260]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_261]),c_0_262]),c_0_263]),c_0_264]),c_0_265]),c_0_266]),c_0_267]),c_0_268]),c_0_269]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_270]),c_0_271]),c_0_272]),c_0_273]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_274]),c_0_275]),in__Cong]),inCongP]),c_0_276]),c_0_277]),c_0_278]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_279]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_280]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_281]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_282]),nonemptyE1]),c_0_283]),noeltsimpempty]),emptyI]),setext]),c_0_284]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),wellorderingAx]),foundationAx]),c_0_290]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_291]) ).
thf(c_0_293,negated_conjecture,
! 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$i,X1652: $i,X1653: $i,X1654: $i,X1655: $i,X1656: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1663: $i,X1664: $i,X1665: $i > $o,X1666: $i,X1667: $i > $o,X1668: $i,X1669: $i,X1670: $i > $o,X1671: $i,X1673: $i,X1674: $i > $o,X1676: $i,X1677: $i,X1678: $i > $o,X1680: $i,X1681: $i,X1682: $i > $o,X1683: $i,X1685: $o,X1686: $i,X1687: $i > $o,X1689: $i,X1690: $i,X1691: $i > $o,X1692: $i,X1694: $i > $o,X1695: $i,X1697: $i > $o,X1698: $i,X1701: $i > $o,X1702: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i > $o,X1713: $i,X1714: $i,X1715: $i > $o,X1716: $i > $o,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1724: $i,X1725: $i,X1726: $i,X1727: $i > $o,X1728: $i,X1729: $i,X1730: $i > $o,X1731: $i > $o,X1734: $i,X1735: $i,X1736: $i > $o,X1737: $i > $o,X1740: $i,X1741: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: 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$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,X1988: $i,X1989: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,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 > $i > $o,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i > $i > $o,X2034: $i,X2035: $i,X2036: $i > $i > $o,X2037: $i,X2038: $i,X2039: $i > $i > $o,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i > $i > $o,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i > $i > $o,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i > $i > $o,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 > $i,X2083: $i,X2084: $i,X2085: $i > $i,X2087: $i,X2088: $i,X2089: $i > $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i > $o,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i > $o,X2104: $i,X2105: $i,X2106: $i > $o,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i > $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i > $i,X2178: $i,X2179: $i,X2180: $i > $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $o,X2188: $i,X2189: $i,X2190: $i,X2191: $o,X2192: $i,X2193: $i,X2194: $i,X2195: $o,X2196: $i,X2197: $i,X2198: $i,X2199: $o,X2200: $i,X2201: $i,X2202: $i,X2203: $o,X2204: $i,X2205: $i,X2206: $i,X2207: $o,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $o,X2214: $i,X2215: $i,X2216: $i,X2217: $o,X2218: $i,X2219: $i,X2220: $i,X2221: $o,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2242: $i,X2243: $i,X2244: $i,X2246: $i,X2247: $i,X2248: $i,X2250: $i,X2251: $i,X2252: $i,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i] :
( ( ~ ( in @ ( esk1_2 @ X1539 @ X1540 ) @ X1539 )
| ~ ( in @ ( esk1_2 @ X1539 @ X1540 ) @ X1540 )
| ( X1539 = X1540 ) )
& ( ( in @ ( esk1_2 @ X1539 @ X1540 ) @ X1539 )
| ( in @ ( esk1_2 @ X1539 @ X1540 ) @ X1540 )
| ( X1539 = X1540 ) )
& ~ ( in @ X1542 @ emptyset )
& ( ~ ( in @ X1545 @ ( setadjoin @ X1543 @ X1544 ) )
| ( X1545 = X1543 )
| ( in @ X1545 @ X1544 ) )
& ( ( X1545 != X1543 )
| ( in @ X1545 @ ( setadjoin @ X1543 @ X1544 ) ) )
& ( ~ ( in @ X1545 @ X1544 )
| ( in @ X1545 @ ( setadjoin @ X1543 @ X1544 ) ) )
& ( ~ ( in @ X1547 @ ( powerset @ X1546 ) )
| ~ ( in @ X1548 @ X1547 )
| ( in @ X1548 @ X1546 ) )
& ( ( in @ ( esk2_2 @ X1549 @ X1550 ) @ X1550 )
| ( in @ X1550 @ ( powerset @ X1549 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1549 @ X1550 ) @ X1549 )
| ( in @ X1550 @ ( powerset @ X1549 ) ) )
& ( ( in @ X1553 @ ( esk3_2 @ X1552 @ X1553 ) )
| ~ ( in @ X1553 @ ( setunion @ X1552 ) ) )
& ( ( in @ ( esk3_2 @ X1552 @ X1553 ) @ X1552 )
| ~ ( in @ X1553 @ ( setunion @ X1552 ) ) )
& ( ~ ( in @ X1556 @ X1557 )
| ~ ( in @ X1557 @ X1555 )
| ( in @ X1556 @ ( setunion @ X1555 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1558 @ omega )
| ( in @ ( setadjoin @ X1558 @ X1558 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1559 ) @ omega )
| ~ ( in @ emptyset @ X1559 )
| ~ ( in @ X1561 @ omega )
| ( in @ X1561 @ X1559 ) )
& ( ( in @ ( esk4_1 @ X1559 ) @ X1559 )
| ~ ( in @ emptyset @ X1559 )
| ~ ( in @ X1561 @ omega )
| ( in @ X1561 @ X1559 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1559 ) @ ( esk4_1 @ X1559 ) ) @ X1559 )
| ~ ( in @ emptyset @ X1559 )
| ~ ( in @ X1561 @ omega )
| ( in @ X1561 @ X1559 ) )
& ( ( in @ ( esk7_3 @ X1562 @ X1563 @ X1566 ) @ X1563 )
| ~ ( in @ X1566 @ ( esk6_2 @ X1562 @ X1563 ) )
| ( in @ ( esk5_2 @ X1562 @ X1563 ) @ X1563 ) )
& ( ( X1562 @ ( esk7_3 @ X1562 @ X1563 @ X1566 ) @ X1566 )
| ~ ( in @ X1566 @ ( esk6_2 @ X1562 @ X1563 ) )
| ( in @ ( esk5_2 @ X1562 @ X1563 ) @ X1563 ) )
& ( ~ ( in @ X1569 @ X1563 )
| ~ ( X1562 @ X1569 @ X1568 )
| ( in @ X1568 @ ( esk6_2 @ X1562 @ X1563 ) )
| ( in @ ( esk5_2 @ X1562 @ X1563 ) @ X1563 ) )
& ( ( in @ ( esk7_3 @ X1562 @ X1563 @ X1566 ) @ X1563 )
| ~ ( in @ X1566 @ ( esk6_2 @ X1562 @ X1563 ) )
| ~ ( exu @ ( X1562 @ ( esk5_2 @ X1562 @ X1563 ) ) ) )
& ( ( X1562 @ ( esk7_3 @ X1562 @ X1563 @ X1566 ) @ X1566 )
| ~ ( in @ X1566 @ ( esk6_2 @ X1562 @ X1563 ) )
| ~ ( exu @ ( X1562 @ ( esk5_2 @ X1562 @ X1563 ) ) ) )
& ( ~ ( in @ X1569 @ X1563 )
| ~ ( X1562 @ X1569 @ X1568 )
| ( in @ X1568 @ ( esk6_2 @ X1562 @ X1563 ) )
| ~ ( exu @ ( X1562 @ ( esk5_2 @ X1562 @ X1563 ) ) ) )
& ( ( in @ ( esk8_1 @ X1570 ) @ X1570 )
| ~ ( in @ X1571 @ X1570 ) )
& ( ~ ( in @ X1573 @ ( esk8_1 @ X1570 ) )
| ~ ( in @ X1573 @ X1570 )
| ~ ( in @ X1571 @ X1570 ) )
& epred1_0
& ( ~ ( exu @ X1574 )
| ( X1574 @ ( descr @ X1574 ) ) )
& ( ~ ( in @ X1577 @ X1575 )
| ~ ( X1576 @ X1577 )
| ( in @ X1577 @ ( dsetconstr @ X1575 @ X1576 ) ) )
& ( ~ ( in @ X1580 @ ( dsetconstr @ X1578 @ X1579 ) )
| ( in @ X1580 @ X1578 ) )
& ( ~ ( in @ X1583 @ ( dsetconstr @ X1581 @ X1582 ) )
| ( X1582 @ X1583 ) )
& ( ( X1584 @ ( esk9_1 @ X1584 ) )
| ~ ( exu @ X1584 ) )
& ( ~ ( X1584 @ X1586 )
| ( ( esk9_1 @ X1584 )
= X1586 )
| ~ ( exu @ X1584 ) )
& ( ~ ( in @ X1588 @ ( prop2set @ X1587 ) )
| X1587 )
& ( ~ ( in @ X1589 @ emptyset )
| X1590 )
& ( ~ ( in @ X1591 @ emptyset )
| ~ $true )
& ~ ( in @ X1592 @ emptyset )
& ( ~ ( exu @ X1593 )
| ( X1593 @ ( esk10_1 @ X1593 ) ) )
& ( ( in @ ( esk12_2 @ X1595 @ X1596 ) @ X1596 )
| ( X1595 = X1596 )
| ( in @ ( esk11_2 @ X1595 @ X1596 ) @ X1595 ) )
& ( ~ ( in @ ( esk12_2 @ X1595 @ X1596 ) @ X1595 )
| ( X1595 = X1596 )
| ( in @ ( esk11_2 @ X1595 @ X1596 ) @ X1595 ) )
& ( ( in @ ( esk12_2 @ X1595 @ X1596 ) @ X1596 )
| ( X1595 = X1596 )
| ~ ( in @ ( esk11_2 @ X1595 @ X1596 ) @ X1596 ) )
& ( ~ ( in @ ( esk12_2 @ X1595 @ X1596 ) @ X1595 )
| ( X1595 = X1596 )
| ~ ( in @ ( esk11_2 @ X1595 @ X1596 ) @ X1596 ) )
& ( ( in @ ( esk13_1 @ X1599 ) @ X1599 )
| ( X1599 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1601 ) @ X1601 )
| ( X1601 = emptyset ) )
& ( ~ ( in @ X1605 @ ( dsetconstr @ X1603 @ X1604 ) )
| ( X1604 @ X1605 )
| ~ ( in @ X1605 @ X1603 ) )
& ( ~ ( X1604 @ X1605 )
| ( in @ X1605 @ ( dsetconstr @ X1603 @ X1604 ) )
| ~ ( in @ X1605 @ X1603 ) )
& ( ~ ( nonempty @ X1606 )
| ( in @ ( esk15_1 @ X1606 ) @ X1606 ) )
& ( ~ ( in @ X1610 @ X1608 )
| ~ ( X1609 @ X1610 )
| ( nonempty @ ( dsetconstr @ X1608 @ X1609 ) ) )
& ( ~ ( in @ X1612 @ X1611 )
| ( nonempty @ X1611 ) )
& ( in @ X1613 @ ( setadjoin @ X1613 @ X1614 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1617 @ X1616 )
| ( in @ X1617 @ ( setadjoin @ X1615 @ X1616 ) ) )
& ( ( in @ X1620 @ X1619 )
| X1621
| ( X1620 = X1618 )
| ~ ( in @ X1620 @ ( setadjoin @ X1618 @ X1619 ) ) )
& ( ~ X1621
| X1621
| ( X1620 = X1618 )
| ~ ( in @ X1620 @ ( setadjoin @ X1618 @ X1619 ) ) )
& ( ( in @ X1620 @ X1619 )
| X1621
| ~ X1621
| ~ ( in @ X1620 @ ( setadjoin @ X1618 @ X1619 ) ) )
& ( ~ X1621
| X1621
| ~ X1621
| ~ ( in @ X1620 @ ( setadjoin @ X1618 @ X1619 ) ) )
& ( ~ ( in @ X1624 @ ( setadjoin @ X1622 @ X1623 ) )
| ( X1624 = X1622 )
| ( in @ X1624 @ X1623 ) )
& ( ( dsetconstr @ X1625
@ ^ [Z0: $i] : $true )
= X1625 )
& ( ( in @ ( esk16_2 @ X1626 @ X1627 ) @ X1627 )
| ( in @ X1627 @ ( powerset @ X1626 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1626 @ X1627 ) @ X1626 )
| ( in @ X1627 @ ( powerset @ X1626 ) ) )
& ( in @ emptyset @ ( powerset @ X1629 ) )
& ( in @ emptyset @ ( powerset @ X1630 ) )
& ( ~ ( in @ X1632 @ ( powerset @ X1631 ) )
| ~ ( in @ X1633 @ X1632 )
| ( in @ X1633 @ X1631 ) )
& ( ~ ( in @ X1635 @ X1636 )
| ~ ( in @ X1636 @ X1634 )
| ( in @ X1635 @ ( setunion @ X1634 ) ) )
& ( ( in @ X1638 @ ( esk17_3 @ X1637 @ X1638 @ X1639 ) )
| X1639
| ~ ( in @ X1638 @ ( setunion @ X1637 ) ) )
& ( ( in @ ( esk17_3 @ X1637 @ X1638 @ X1639 ) @ X1637 )
| X1639
| ~ ( in @ X1638 @ ( setunion @ X1637 ) ) )
& ( ~ X1639
| X1639
| ~ ( in @ X1638 @ ( setunion @ X1637 ) ) )
& ( ~ ( in @ X1642 @ X1641 )
| ( in @ X1642 @ ( powerset @ ( setunion @ X1641 ) ) ) )
& ( ~ ( X1643 @ X1645 )
| ( X1645
= ( esk18_1 @ X1643 ) )
| ~ ( exu @ X1643 ) )
& ( ( X1646
!= ( esk18_1 @ X1643 ) )
| ( X1643 @ X1646 )
| ~ ( exu @ X1643 ) )
& ( ( in @ ( esk19_1 @ X1647 ) @ X1647 )
| ~ ( nonempty @ X1647 ) )
& ( $true
| ~ ( nonempty @ X1647 ) )
& ( ~ ( in @ X1649 @ ( setadjoin @ X1650 @ emptyset ) )
| ( X1649 = X1650 ) )
& ( ( X1651 = X1652 )
| ~ ( in @ X1652 @ ( setadjoin @ X1651 @ emptyset ) ) )
& ( ( X1653 != X1654 )
| ( in @ X1653 @ ( setadjoin @ X1654 @ emptyset ) ) )
& ( ~ ( in @ X1655 @ ( setadjoin @ X1656 @ emptyset ) )
| ( in @ X1656 @ ( setadjoin @ X1655 @ emptyset ) ) )
& ( ~ ( in @ X1659 @ ( setadjoin @ X1657 @ ( setadjoin @ X1658 @ emptyset ) ) )
| ( X1659 = X1657 )
| ( X1659 = X1658 ) )
& ( in @ X1660 @ ( setadjoin @ X1660 @ ( setadjoin @ X1661 @ emptyset ) ) )
& ( in @ X1663 @ ( setadjoin @ X1662 @ ( setadjoin @ X1663 @ emptyset ) ) )
& ( ~ ( in @ X1666 @ X1664 )
| ~ ( X1665 @ X1666 )
| ( ( dsetconstr @ X1664 @ X1665 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1668 @ emptyset )
| ( X1667 @ X1668 ) )
& ( ( in @ ( esk20_2 @ X1669 @ X1670 ) @ X1669 )
| ~ ( in @ X1671 @ X1669 )
| ( X1670 @ X1671 ) )
& ( ~ ( X1670 @ ( esk20_2 @ X1669 @ X1670 ) )
| ~ ( in @ X1671 @ X1669 )
| ( X1670 @ X1671 ) )
& ( ( in @ ( esk21_2 @ X1673 @ X1674 ) @ X1673 )
| ~ ( in @ X1676 @ X1673 )
| ~ ( X1674 @ X1676 ) )
& ( ( X1674 @ ( esk21_2 @ X1673 @ X1674 ) )
| ~ ( in @ X1676 @ X1673 )
| ~ ( X1674 @ X1676 ) )
& ( ( in @ ( esk22_2 @ X1677 @ X1678 ) @ X1677 )
| ~ ( in @ X1680 @ X1677 )
| ~ ( X1678 @ X1680 ) )
& ( ( X1678 @ ( esk22_2 @ X1677 @ X1678 ) )
| ~ ( in @ X1680 @ X1677 )
| ~ ( X1678 @ X1680 ) )
& ( ( in @ ( esk23_2 @ X1681 @ X1682 ) @ X1681 )
| ~ ( in @ X1683 @ X1681 )
| ( X1682 @ X1683 ) )
& ( ~ ( X1682 @ ( esk23_2 @ X1681 @ X1682 ) )
| ~ ( in @ X1683 @ X1681 )
| ( X1682 @ X1683 ) )
& ( ~ X1685
| ( in @ emptyset @ ( prop2set @ X1685 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1686 @ X1687 ) @ X1686 )
| ~ ( in @ X1689 @ X1686 )
| ~ ( X1687 @ X1689 ) )
& ( ( X1687 @ ( esk24_2 @ X1686 @ X1687 ) )
| ~ ( in @ X1689 @ X1686 )
| ~ ( X1687 @ X1689 ) )
& ( ( in @ ( esk25_2 @ X1690 @ X1691 ) @ X1690 )
| ~ ( in @ X1692 @ X1690 )
| ( X1691 @ X1692 ) )
& ( ~ ( X1691 @ ( esk25_2 @ X1690 @ X1691 ) )
| ~ ( in @ X1692 @ X1690 )
| ( X1691 @ X1692 ) )
& ( ( X1694 @ ( esk26_2 @ X1694 @ X1695 ) )
| ~ ( X1694 @ X1695 )
| ( exu @ X1694 ) )
& ( ( X1695
!= ( esk26_2 @ X1694 @ X1695 ) )
| ~ ( X1694 @ X1695 )
| ( exu @ X1694 ) )
& ( ( X1697 @ ( esk27_1 @ X1697 ) )
| ( exu @ X1697 )
| ~ ( X1697 @ X1698 ) )
& ( ( X1697 @ ( esk28_1 @ X1697 ) )
| ( exu @ X1697 )
| ~ ( X1697 @ X1698 ) )
& ( ( ( esk27_1 @ X1697 )
!= ( esk28_1 @ X1697 ) )
| ( exu @ X1697 )
| ~ ( X1697 @ X1698 ) )
& ( ~ ( X1701 @ ( esk29_2 @ X1701 @ X1702 ) )
| ( ( esk29_2 @ X1701 @ X1702 )
!= X1702 )
| ( exu @ X1701 ) )
& ( ( X1701 @ ( esk29_2 @ X1701 @ X1702 ) )
| ( ( esk29_2 @ X1701 @ X1702 )
= X1702 )
| ( exu @ X1701 ) )
& ( ( X1704 != X1705 )
| ( X1706 != X1707 )
| ~ ( in @ X1706 @ X1704 )
| ( in @ X1707 @ X1705 ) )
& ( ~ ( in @ X1710 @ X1708 )
| ( in @ X1711 @ X1709 )
| ( X1710 != X1711 )
| ( X1708 != X1709 ) )
& ( ~ ( in @ X1711 @ X1709 )
| ( in @ X1710 @ X1708 )
| ( X1710 != X1711 )
| ( X1708 != X1709 ) )
& ( ~ ( exu @ X1712 )
| ~ ( X1712 @ X1713 )
| ~ ( X1712 @ X1714 )
| ( X1713 = X1714 ) )
& ( ~ ( exu @ X1715 )
| ( exu @ X1716 )
| ( ( esk30_2 @ X1715 @ X1716 )
= ( esk31_2 @ X1715 @ X1716 ) ) )
& ( ~ ( exu @ X1716 )
| ( exu @ X1715 )
| ( ( esk30_2 @ X1715 @ X1716 )
= ( esk31_2 @ X1715 @ X1716 ) ) )
& ( ~ ( exu @ X1715 )
| ( exu @ X1716 )
| ~ ( X1715 @ ( esk30_2 @ X1715 @ X1716 ) )
| ~ ( X1716 @ ( esk31_2 @ X1715 @ X1716 ) ) )
& ( ~ ( exu @ X1716 )
| ( exu @ X1715 )
| ~ ( X1715 @ ( esk30_2 @ X1715 @ X1716 ) )
| ~ ( X1716 @ ( esk31_2 @ X1715 @ X1716 ) ) )
& ( ~ ( exu @ X1715 )
| ( exu @ X1716 )
| ( X1715 @ ( esk30_2 @ X1715 @ X1716 ) )
| ( X1716 @ ( esk31_2 @ X1715 @ X1716 ) ) )
& ( ~ ( exu @ X1716 )
| ( exu @ X1715 )
| ( X1715 @ ( esk30_2 @ X1715 @ X1716 ) )
| ( X1716 @ ( esk31_2 @ X1715 @ X1716 ) ) )
& ( emptyset = emptyset )
& ( ( X1719 != X1720 )
| ( X1721 != X1722 )
| ( ( setadjoin @ X1719 @ X1721 )
= ( setadjoin @ X1720 @ X1722 ) ) )
& ( ( X1723 != X1724 )
| ( ( powerset @ X1723 )
= ( powerset @ X1724 ) ) )
& ( ( X1725 != X1726 )
| ( ( setunion @ X1725 )
= ( setunion @ X1726 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1727 )
| ~ ( X1727 @ X1728 )
| ~ ( X1727 @ X1729 )
| ( X1728 = X1729 ) )
& ( ( ( esk32_2 @ X1730 @ X1731 )
= ( esk33_2 @ X1730 @ X1731 ) )
| ~ ( exu @ X1730 )
| ~ ( exu @ X1731 )
| ( ( descr @ X1730 )
= ( descr @ X1731 ) ) )
& ( ~ ( X1730 @ ( esk32_2 @ X1730 @ X1731 ) )
| ~ ( X1731 @ ( esk33_2 @ X1730 @ X1731 ) )
| ~ ( exu @ X1730 )
| ~ ( exu @ X1731 )
| ( ( descr @ X1730 )
= ( descr @ X1731 ) ) )
& ( ( X1730 @ ( esk32_2 @ X1730 @ X1731 ) )
| ( X1731 @ ( esk33_2 @ X1730 @ X1731 ) )
| ~ ( exu @ X1730 )
| ~ ( exu @ X1731 )
| ( ( descr @ X1730 )
= ( descr @ X1731 ) ) )
& ( ( in @ ( esk34_4 @ X1734 @ X1735 @ X1736 @ X1737 ) @ X1734 )
| ( ( dsetconstr @ X1734 @ X1736 )
= ( dsetconstr @ X1735 @ X1737 ) )
| ( X1734 != X1735 ) )
& ( ( in @ ( esk35_4 @ X1734 @ X1735 @ X1736 @ X1737 ) @ X1735 )
| ( ( dsetconstr @ X1734 @ X1736 )
= ( dsetconstr @ X1735 @ X1737 ) )
| ( X1734 != X1735 ) )
& ( ( ( esk34_4 @ X1734 @ X1735 @ X1736 @ X1737 )
= ( esk35_4 @ X1734 @ X1735 @ X1736 @ X1737 ) )
| ( ( dsetconstr @ X1734 @ X1736 )
= ( dsetconstr @ X1735 @ X1737 ) )
| ( X1734 != X1735 ) )
& ( ~ ( X1736 @ ( esk34_4 @ X1734 @ X1735 @ X1736 @ X1737 ) )
| ~ ( X1737 @ ( esk35_4 @ X1734 @ X1735 @ X1736 @ X1737 ) )
| ( ( dsetconstr @ X1734 @ X1736 )
= ( dsetconstr @ X1735 @ X1737 ) )
| ( X1734 != X1735 ) )
& ( ( X1736 @ ( esk34_4 @ X1734 @ X1735 @ X1736 @ X1737 ) )
| ( X1737 @ ( esk35_4 @ X1734 @ X1735 @ X1736 @ X1737 ) )
| ( ( dsetconstr @ X1734 @ X1736 )
= ( dsetconstr @ X1735 @ X1737 ) )
| ( X1734 != X1735 ) )
& ( ( in @ ( esk36_2 @ X1740 @ X1741 ) @ X1740 )
| ( subset @ X1740 @ X1741 ) )
& ( ~ ( in @ ( esk36_2 @ X1740 @ X1741 ) @ X1741 )
| ( subset @ X1740 @ X1741 ) )
& ( ( X1743 != X1744 )
| ( subset @ X1744 @ X1743 ) )
& ( ( X1745 != X1746 )
| ( subset @ X1745 @ X1746 ) )
& ( ( in @ ( esk37_2 @ X1747 @ X1748 ) @ X1747 )
| ( subset @ X1747 @ X1748 ) )
& ( ~ ( in @ ( esk37_2 @ X1747 @ X1748 ) @ X1748 )
| ( subset @ X1747 @ X1748 ) )
& ( subset @ emptyset @ X1750 )
& ( ~ ( subset @ X1751 @ X1752 )
| ~ ( in @ X1753 @ X1751 )
| ( in @ X1753 @ X1752 ) )
& ( ~ ( subset @ X1754 @ X1755 )
| ( in @ X1756 @ X1755 )
| ~ ( in @ X1756 @ X1754 ) )
& ( ~ ( in @ X1759 @ X1757 )
| ( in @ X1759 @ X1758 )
| ~ ( subset @ X1757 @ X1758 ) )
& ( ( subset @ X1760 @ X1761 )
| ( X1760 != X1761 ) )
& ( ~ ( in @ X1764 @ X1762 )
| ( in @ X1764 @ X1763 )
| ( X1762 != X1763 ) )
& ( subset @ X1765 @ X1765 )
& ( ~ ( subset @ X1766 @ X1767 )
| ~ ( subset @ X1767 @ X1768 )
| ( subset @ X1766 @ X1768 ) )
& ( subset @ X1770 @ ( setadjoin @ X1769 @ X1770 ) )
& ( ~ ( subset @ X1771 @ X1773 )
| ( subset @ X1771 @ ( setadjoin @ X1772 @ X1773 ) ) )
& ( ~ ( subset @ X1774 @ X1775 )
| ( in @ X1774 @ ( powerset @ X1775 ) ) )
& ( ~ ( subset @ X1776 @ X1777 )
| ~ ( subset @ X1777 @ X1776 )
| ( X1776 = X1777 ) )
& ( ~ ( subset @ X1778 @ emptyset )
| ( X1778 = emptyset ) )
& ( ~ ( subset @ X1780 @ X1779 )
| ( in @ X1780 @ ( powerset @ X1779 ) ) )
& ( ~ ( in @ X1782 @ ( powerset @ X1781 ) )
| ( subset @ X1782 @ X1781 ) )
& ( in @ X1783 @ ( powerset @ X1783 ) )
& ( ~ ( subset @ X1784 @ X1785 )
| ( subset @ ( powerset @ X1784 ) @ ( powerset @ X1785 ) ) )
& ( in @ ( dsetconstr @ X1786 @ X1787 ) @ ( powerset @ X1786 ) )
& ( subset @ ( dsetconstr @ X1788 @ X1789 ) @ X1788 )
& ( ~ ( in @ X1792 @ X1790 )
| ( in @ X1792 @ ( binunion @ X1790 @ X1791 ) ) )
& ( in @ X1794 @ ( setadjoin @ X1793 @ ( setadjoin @ X1794 @ emptyset ) ) )
& ( ~ ( in @ X1797 @ X1796 )
| ( in @ X1797 @ ( binunion @ X1795 @ X1796 ) ) )
& ( ( in @ X1800 @ X1799 )
| X1801
| ( in @ X1800 @ X1798 )
| ~ ( in @ X1800 @ ( binunion @ X1798 @ X1799 ) ) )
& ( ~ X1801
| X1801
| ( in @ X1800 @ X1798 )
| ~ ( in @ X1800 @ ( binunion @ X1798 @ X1799 ) ) )
& ( ( in @ X1800 @ X1799 )
| X1801
| ~ X1801
| ~ ( in @ X1800 @ ( binunion @ X1798 @ X1799 ) ) )
& ( ~ X1801
| X1801
| ~ X1801
| ~ ( in @ X1800 @ ( binunion @ X1798 @ X1799 ) ) )
& ( ~ ( in @ X1804 @ ( binunion @ X1802 @ X1803 ) )
| ( in @ X1804 @ X1802 )
| ( in @ X1804 @ X1803 ) )
& ( subset @ X1805 @ ( binunion @ X1805 @ X1806 ) )
& ( subset @ X1808 @ ( binunion @ X1807 @ X1808 ) )
& ( ~ ( in @ X1811 @ X1809 )
| ~ ( in @ X1811 @ X1810 )
| ( in @ X1811 @ ( binintersect @ X1809 @ X1810 ) ) )
& ( ~ ( subset @ X1814 @ X1812 )
| ~ ( subset @ X1814 @ X1813 )
| ( subset @ X1814 @ ( binintersect @ X1812 @ X1813 ) ) )
& ( ~ ( in @ X1817 @ ( binintersect @ X1815 @ X1816 ) )
| ( in @ X1817 @ X1815 ) )
& ( subset @ ( binintersect @ X1818 @ X1819 ) @ X1818 )
& ( ~ ( subset @ X1820 @ X1821 )
| ( ( binintersect @ X1820 @ X1821 )
= X1820 ) )
& ( ( ( binintersect @ X1822 @ X1823 )
!= X1823 )
| ( subset @ X1823 @ X1822 ) )
& ( ~ ( in @ X1826 @ ( binintersect @ X1824 @ X1825 ) )
| ( in @ X1826 @ X1825 ) )
& ( ( in @ ( esk38_2 @ X1827 @ X1828 ) @ X1827 )
| ( ( binintersect @ X1827 @ X1828 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1827 @ X1828 ) @ X1828 )
| ( ( binintersect @ X1827 @ X1828 )
= emptyset ) )
& ( subset @ ( binintersect @ X1830 @ X1831 ) @ X1831 )
& ( ~ ( subset @ X1833 @ X1832 )
| ( ( binintersect @ X1832 @ X1833 )
= X1833 ) )
& ( ( ( binintersect @ X1834 @ X1835 )
!= X1834 )
| ( subset @ X1834 @ X1835 ) )
& ( ( binintersect @ X1836 @ ( binunion @ X1837 @ X1838 ) )
= ( binunion @ ( binintersect @ X1836 @ X1837 ) @ ( binintersect @ X1836 @ X1838 ) ) )
& ( ~ ( in @ X1841 @ X1839 )
| ( in @ X1841 @ X1840 )
| ( in @ X1841 @ ( setminus @ X1839 @ X1840 ) ) )
& ( ~ ( in @ X1844 @ ( setminus @ X1842 @ X1843 ) )
| ( in @ X1844 @ X1842 ) )
& ( ~ ( in @ X1847 @ ( setminus @ X1845 @ X1846 ) )
| ~ ( in @ X1847 @ X1846 ) )
& ( ~ ( subset @ X1848 @ X1849 )
| ( ( setminus @ X1848 @ X1849 )
= emptyset ) )
& ( ( in @ X1852 @ ( setminus @ X1850 @ X1851 ) )
| ~ ( in @ X1852 @ X1850 )
| ( in @ X1852 @ X1851 ) )
& ( ( in @ X1855 @ ( setminus @ X1853 @ X1854 ) )
| ( in @ X1855 @ X1854 )
| ~ ( in @ X1855 @ X1853 ) )
& ( ( in @ X1858 @ X1856 )
| ~ ( in @ X1858 @ ( setminus @ X1856 @ X1857 ) ) )
& ( ~ ( in @ X1861 @ X1860 )
| ~ ( in @ X1861 @ ( setminus @ X1859 @ X1860 ) ) )
& ( subset @ ( setminus @ X1862 @ X1863 ) @ X1862 )
& ( ( ( setminus @ X1864 @ X1865 )
!= emptyset )
| ( subset @ X1864 @ X1865 ) )
& ( ~ ( in @ X1868 @ X1866 )
| X1869
| ( in @ X1868 @ X1866 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ( in @ X1868 @ X1867 )
| X1869
| ( in @ X1868 @ X1866 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ X1869
| X1869
| ( in @ X1868 @ X1866 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ ( in @ X1868 @ X1866 )
| X1869
| ~ ( in @ X1868 @ X1867 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ( in @ X1868 @ X1867 )
| X1869
| ~ ( in @ X1868 @ X1867 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ X1869
| X1869
| ~ ( in @ X1868 @ X1867 )
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ ( in @ X1868 @ X1866 )
| X1869
| ~ X1869
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ( in @ X1868 @ X1867 )
| X1869
| ~ X1869
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ X1869
| X1869
| ~ X1869
| ~ ( in @ X1868 @ ( symdiff @ X1866 @ X1867 ) ) )
& ( ~ ( in @ X1872 @ X1870 )
| ( in @ X1872 @ X1871 )
| ( in @ X1872 @ ( symdiff @ X1870 @ X1871 ) ) )
& ( ( in @ X1875 @ X1873 )
| ~ ( in @ X1875 @ X1874 )
| ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ ( in @ X1878 @ X1876 )
| ~ ( in @ X1878 @ X1877 )
| ~ ( in @ X1878 @ ( symdiff @ X1876 @ X1877 ) ) )
& ( ( in @ X1881 @ X1879 )
| ( in @ X1881 @ X1880 )
| ~ ( in @ X1881 @ ( symdiff @ X1879 @ X1880 ) ) )
& ( in @ X1883 @ ( setadjoin @ X1882 @ ( setadjoin @ X1883 @ emptyset ) ) )
& ( in @ X1884 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1884 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1884 @ ( setadjoin @ X1885 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1887 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1886 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1886 @ ( setadjoin @ X1887 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1888 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1888 @ ( setadjoin @ X1889 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1890 @ X1891 ) )
& ( ~ ( in @ X1893 @ X1892 )
| ( subset @ ( setadjoin @ X1893 @ emptyset ) @ X1892 ) )
& ( ~ ( in @ X1895 @ X1894 )
| ( in @ ( setadjoin @ X1895 @ emptyset ) @ ( powerset @ X1894 ) ) )
& ( ~ ( in @ X1898 @ X1896 )
| ( in @ ( setadjoin @ X1898 @ emptyset ) @ ( powerset @ ( binunion @ X1896 @ X1897 ) ) ) )
& ( ~ ( in @ X1901 @ ( setadjoin @ X1899 @ ( setadjoin @ X1900 @ emptyset ) ) )
| ( X1901 = X1899 )
| ( X1901 = X1900 ) )
& ( ~ ( in @ X1904 @ X1902 )
| ~ ( in @ X1905 @ X1903 )
| ( subset @ ( setadjoin @ X1904 @ ( setadjoin @ X1905 @ emptyset ) ) @ ( binunion @ X1902 @ X1903 ) ) )
& ( ~ ( in @ X1908 @ X1906 )
| ~ ( in @ X1909 @ X1907 )
| ( in @ ( setadjoin @ X1908 @ ( setadjoin @ X1909 @ emptyset ) ) @ ( powerset @ ( binunion @ X1906 @ X1907 ) ) ) )
& ( ~ ( in @ X1912 @ X1910 )
| ~ ( in @ X1913 @ X1911 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1912 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1912 @ ( setadjoin @ X1913 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1910 @ X1911 ) ) ) )
& ( ~ ( in @ X1916 @ X1914 )
| ~ ( in @ X1917 @ X1915 )
| ( in @ ( setadjoin @ ( setadjoin @ X1916 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1916 @ ( setadjoin @ X1917 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1914 @ X1915 ) ) ) ) )
& ( ~ ( in @ X1920 @ X1918 )
| ~ ( in @ X1921 @ X1919 )
| ( in @ ( kpair @ X1920 @ X1921 ) @ ( powerset @ ( powerset @ ( binunion @ X1918 @ X1919 ) ) ) ) )
& ( ~ ( in @ X1924 @ X1922 )
| ~ ( in @ X1925 @ X1923 )
| ( in @ ( kpair @ X1924 @ X1925 ) @ ( cartprod @ X1922 @ X1923 ) ) )
& ( ( in @ ( esk39_3 @ X1926 @ X1927 @ X1928 ) @ X1926 )
| ~ ( in @ X1928 @ ( cartprod @ X1926 @ X1927 ) ) )
& ( ( in @ ( esk40_3 @ X1926 @ X1927 @ X1928 ) @ X1927 )
| ~ ( in @ X1928 @ ( cartprod @ X1926 @ X1927 ) ) )
& ( ( X1928
= ( kpair @ ( esk39_3 @ X1926 @ X1927 @ X1928 ) @ ( esk40_3 @ X1926 @ X1927 @ X1928 ) ) )
| ~ ( in @ X1928 @ ( cartprod @ X1926 @ X1927 ) ) )
& ( ~ ( in @ X1933 @ ( cartprod @ X1931 @ X1932 ) )
| ( iskpair @ X1933 ) )
& ( ( in @ ( esk41_2 @ X1934 @ X1935 ) @ X1934 )
| ~ ( in @ X1935 @ ( setunion @ X1934 ) ) )
& ( ( in @ X1935 @ ( esk41_2 @ X1934 @ X1935 ) )
| ~ ( in @ X1935 @ ( setunion @ X1934 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1937 @ emptyset ) ) @ X1937 )
& ( subset @ X1938 @ ( setunion @ ( setadjoin @ X1938 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1939 @ emptyset ) )
= X1939 )
& ( ( in @ ( esk42_2 @ X1940 @ X1941 ) @ X1940 )
| ~ ( in @ X1944 @ X1940 )
| ~ ( X1941 @ X1944 )
| ( singleton @ ( dsetconstr @ X1940 @ X1941 ) ) )
& ( ( in @ ( esk43_2 @ X1940 @ X1941 ) @ X1940 )
| ~ ( in @ X1944 @ X1940 )
| ~ ( X1941 @ X1944 )
| ( singleton @ ( dsetconstr @ X1940 @ X1941 ) ) )
& ( ( X1941 @ ( esk42_2 @ X1940 @ X1941 ) )
| ~ ( in @ X1944 @ X1940 )
| ~ ( X1941 @ X1944 )
| ( singleton @ ( dsetconstr @ X1940 @ X1941 ) ) )
& ( ( X1941 @ ( esk43_2 @ X1940 @ X1941 ) )
| ~ ( in @ X1944 @ X1940 )
| ~ ( X1941 @ X1944 )
| ( singleton @ ( dsetconstr @ X1940 @ X1941 ) ) )
& ( ( ( esk42_2 @ X1940 @ X1941 )
!= ( esk43_2 @ X1940 @ X1941 ) )
| ~ ( in @ X1944 @ X1940 )
| ~ ( X1941 @ X1944 )
| ( singleton @ ( dsetconstr @ X1940 @ X1941 ) ) )
& ( ( in @ ( esk44_2 @ X1945 @ X1946 ) @ X1945 )
| ~ ( ex1 @ X1945 @ X1946 ) )
& ( ( X1946 @ ( esk44_2 @ X1945 @ X1946 ) )
| ~ ( ex1 @ X1945 @ X1946 ) )
& ( ( in @ ( esk45_3 @ X1948 @ X1949 @ X1950 ) @ X1948 )
| ( ex1 @ X1948 @ X1949 )
| ~ ( X1949 @ X1950 )
| ~ ( in @ X1950 @ X1948 ) )
& ( ( X1949 @ ( esk45_3 @ X1948 @ X1949 @ X1950 ) )
| ( ex1 @ X1948 @ X1949 )
| ~ ( X1949 @ X1950 )
| ~ ( in @ X1950 @ X1948 ) )
& ( ( ( esk45_3 @ X1948 @ X1949 @ X1950 )
!= X1950 )
| ( ex1 @ X1948 @ X1949 )
| ~ ( X1949 @ X1950 )
| ~ ( in @ X1950 @ X1948 ) )
& ( ( in @ ( esk46_2 @ X1952 @ X1953 ) @ X1952 )
| ~ ( in @ X1956 @ X1952 )
| ~ ( X1953 @ X1956 )
| ( ex1 @ X1952 @ X1953 ) )
& ( ( in @ ( esk47_2 @ X1952 @ X1953 ) @ X1952 )
| ~ ( in @ X1956 @ X1952 )
| ~ ( X1953 @ X1956 )
| ( ex1 @ X1952 @ X1953 ) )
& ( ( X1953 @ ( esk46_2 @ X1952 @ X1953 ) )
| ~ ( in @ X1956 @ X1952 )
| ~ ( X1953 @ X1956 )
| ( ex1 @ X1952 @ X1953 ) )
& ( ( X1953 @ ( esk47_2 @ X1952 @ X1953 ) )
| ~ ( in @ X1956 @ X1952 )
| ~ ( X1953 @ X1956 )
| ( ex1 @ X1952 @ X1953 ) )
& ( ( ( esk46_2 @ X1952 @ X1953 )
!= ( esk47_2 @ X1952 @ X1953 ) )
| ~ ( in @ X1956 @ X1952 )
| ~ ( X1953 @ X1956 )
| ( ex1 @ X1952 @ X1953 ) )
& ( ( ( setadjoin @ X1957 @ emptyset )
!= ( setadjoin @ X1958 @ emptyset ) )
| ( X1957 = X1958 ) )
& ( ~ ( in @ ( setadjoin @ X1961 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1959 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1959 @ ( setadjoin @ X1960 @ emptyset ) ) @ emptyset ) ) )
| ( X1959 = X1961 ) )
& ( ~ ( iskpair @ X1962 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1962 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1962 ) ) ) )
& ( ~ ( singleton @ X1963 )
| ( in @ ( setunion @ X1963 ) @ X1963 ) )
& ( ( kfst @ ( kpair @ X1964 @ X1965 ) )
= X1964 )
& ( ~ ( in @ X1968 @ ( cartprod @ X1966 @ X1967 ) )
| ( in @ ( kfst @ X1968 ) @ X1966 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1969 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1969 @ ( setadjoin @ X1970 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1971 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1971 @ ( setadjoin @ X1972 @ emptyset ) ) @ emptyset ) ) )
| ( X1969 = X1971 ) )
& ( ( ( kpair @ X1973 @ X1974 )
!= ( kpair @ X1975 @ X1976 ) )
| ( X1973 = X1975 ) )
& ( ( X1977 != X1978 )
| ( ( setadjoin @ X1977 @ ( setadjoin @ X1978 @ emptyset ) )
= ( setadjoin @ X1977 @ emptyset ) ) )
& ( ( X1979 != X1980 )
| ( ( setadjoin @ ( setadjoin @ X1979 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1979 @ ( setadjoin @ X1980 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1979 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1981 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1981 @ ( setadjoin @ X1982 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1983 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1983 @ ( setadjoin @ X1984 @ emptyset ) ) @ emptyset ) ) )
| ( X1983 != X1984 )
| ( X1982 = X1984 ) )
& ( ( ( setadjoin @ X1985 @ ( setadjoin @ X1986 @ emptyset ) )
!= ( setadjoin @ X1987 @ emptyset ) )
| ( X1985 = X1986 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1988 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1988 @ ( setadjoin @ X1989 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1990 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1990 @ ( setadjoin @ X1991 @ emptyset ) ) @ emptyset ) ) )
| ( X1989 = X1991 ) )
& ( ( ( kpair @ X1992 @ X1993 )
!= ( kpair @ X1994 @ X1995 ) )
| ( X1993 = X1995 ) )
& ( ~ ( iskpair @ X1996 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1996 )
@ ^ [Z0: $i] :
( X1996
= ( kpair @ ( kfst @ X1996 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1997 @ X1998 ) )
= X1998 )
& ( ~ ( iskpair @ X1999 )
| ( ( kpair @ ( kfst @ X1999 ) @ ( ksnd @ X1999 ) )
= X1999 ) )
& ( ~ ( in @ X2002 @ ( cartprod @ X2000 @ X2001 ) )
| ( in @ ( ksnd @ X2002 ) @ X2001 ) )
& ( ~ ( in @ ( kpair @ X2005 @ X2006 ) @ ( cartprod @ X2003 @ X2004 ) )
| ( in @ X2005 @ X2003 ) )
& ( ~ ( in @ ( kpair @ X2009 @ X2010 ) @ ( cartprod @ X2007 @ X2008 ) )
| ( in @ X2010 @ X2008 ) )
& ( ~ ( in @ X2013 @ X2011 )
| ~ ( in @ X2014 @ X2012 )
| ( ( kpair @ X2013 @ X2014 )
= ( kpair @ X2013 @ X2014 ) ) )
& ( ~ ( in @ X2017 @ X2015 )
| ~ ( in @ X2018 @ X2016 )
| ( ( kfst @ ( kpair @ X2017 @ X2018 ) )
= X2017 ) )
& ( ~ ( in @ X2021 @ X2019 )
| ~ ( in @ X2022 @ X2020 )
| ( ( ksnd @ ( kpair @ X2021 @ X2022 ) )
= X2022 ) )
& ( ~ ( in @ X2025 @ ( cartprod @ X2023 @ X2024 ) )
| ( ( kpair @ ( kfst @ X2025 ) @ ( ksnd @ X2025 ) )
= X2025 ) )
& ( ~ ( in @ X2029 @ X2026 )
| ~ ( in @ X2030 @ X2027 )
| ~ ( X2028 @ X2029 @ X2030 )
| ( in @ ( kpair @ X2029 @ X2030 ) @ ( dpsetconstr @ X2026 @ X2027 @ X2028 ) ) )
& ( subset @ ( dpsetconstr @ X2031 @ X2032 @ X2033 ) @ ( cartprod @ X2031 @ X2032 ) )
& ( breln @ X2034 @ X2035 @ ( dpsetconstr @ X2034 @ X2035 @ X2036 ) )
& ( ~ ( in @ X2040 @ X2037 )
| ~ ( in @ X2041 @ X2038 )
| ~ ( in @ ( kpair @ X2040 @ X2041 ) @ ( dpsetconstr @ X2037 @ X2038 @ X2039 ) )
| ( X2039 @ X2040 @ X2041 ) )
& ( ~ ( in @ ( kpair @ X2045 @ X2046 ) @ ( dpsetconstr @ X2042 @ X2043 @ X2044 ) )
| ( in @ X2045 @ X2042 ) )
& ( ~ ( in @ ( kpair @ X2050 @ X2051 ) @ ( dpsetconstr @ X2047 @ X2048 @ X2049 ) )
| ( in @ X2051 @ X2048 ) )
& ( ~ ( in @ ( kpair @ X2055 @ X2056 ) @ ( dpsetconstr @ X2052 @ X2053 @ X2054 ) )
| ( X2054 @ X2055 @ X2056 ) )
& ( ~ ( func @ X2057 @ X2058 @ X2059 )
| ~ ( in @ X2060 @ X2057 )
| ( singleton
@ ( dsetconstr @ X2058
@ ^ [Z0: $i] : ( in @ ( kpair @ X2060 @ Z0 ) @ X2059 ) ) ) )
& ( ~ ( func @ X2061 @ X2062 @ X2063 )
| ~ ( in @ X2064 @ X2061 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2062
@ ^ [Z0: $i] : ( in @ ( kpair @ X2064 @ Z0 ) @ X2063 ) ) )
@ X2062 ) )
& ( ~ ( func @ X2065 @ X2066 @ X2067 )
| ~ ( in @ X2068 @ X2065 )
| ( in @ ( ap @ X2065 @ X2066 @ X2067 @ X2068 ) @ X2066 ) )
& ( ~ ( in @ X2071 @ ( funcSet @ X2069 @ X2070 ) )
| ( func @ X2069 @ X2070 @ X2071 ) )
& ( ~ ( in @ X2074 @ ( funcSet @ X2072 @ X2073 ) )
| ~ ( in @ X2075 @ X2072 )
| ( in @ ( ap @ X2072 @ X2073 @ X2074 @ X2075 ) @ X2073 ) )
& ( ~ ( func @ X2076 @ X2077 @ X2078 )
| ( in @ X2078 @ ( funcSet @ X2076 @ X2077 ) ) )
& ( ( in @ ( esk48_3 @ X2079 @ X2080 @ X2081 ) @ X2079 )
| ( func @ X2079 @ X2080
@ ( dpsetconstr @ X2079 @ X2080
@ ^ [Z0: $i] : ( $eq @ ( X2081 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2081 @ ( esk48_3 @ X2079 @ X2080 @ X2081 ) ) @ X2080 )
| ( func @ X2079 @ X2080
@ ( dpsetconstr @ X2079 @ X2080
@ ^ [Z0: $i] : ( $eq @ ( X2081 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2083 @ X2084 @ X2085 ) @ X2083 )
| ( func @ X2083 @ X2084 @ ( lam @ X2083 @ X2084 @ X2085 ) ) )
& ( ~ ( in @ ( X2085 @ ( esk49_3 @ X2083 @ X2084 @ X2085 ) ) @ X2084 )
| ( func @ X2083 @ X2084 @ ( lam @ X2083 @ X2084 @ X2085 ) ) )
& ( ( in @ ( esk50_3 @ X2087 @ X2088 @ X2089 ) @ X2087 )
| ( in @ ( lam @ X2087 @ X2088 @ X2089 ) @ ( funcSet @ X2087 @ X2088 ) ) )
& ( ~ ( in @ ( X2089 @ ( esk50_3 @ X2087 @ X2088 @ X2089 ) ) @ X2088 )
| ( in @ ( lam @ X2087 @ X2088 @ X2089 ) @ ( funcSet @ X2087 @ X2088 ) ) )
& ( ( in @ ( esk51_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ X2091 )
| ~ ( in @ X2097 @ X2093 )
| ( X2094 @ X2097 )
| ~ ( breln @ X2091 @ X2092 @ X2093 ) )
& ( ( in @ ( esk52_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ X2092 )
| ~ ( in @ X2097 @ X2093 )
| ( X2094 @ X2097 )
| ~ ( breln @ X2091 @ X2092 @ X2093 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ ( esk52_4 @ X2091 @ X2092 @ X2093 @ X2094 ) ) @ X2093 )
| ~ ( in @ X2097 @ X2093 )
| ( X2094 @ X2097 )
| ~ ( breln @ X2091 @ X2092 @ X2093 ) )
& ( ~ ( X2094 @ ( kpair @ ( esk51_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ ( esk52_4 @ X2091 @ X2092 @ X2093 @ X2094 ) ) )
| ~ ( in @ X2097 @ X2093 )
| ( X2094 @ X2097 )
| ~ ( breln @ X2091 @ X2092 @ X2093 ) )
& ( ( in @ ( esk53_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ X2098 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( breln @ X2098 @ X2099 @ X2100 ) )
& ( ( in @ ( esk54_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ X2099 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( breln @ X2098 @ X2099 @ X2100 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ ( esk54_4 @ X2098 @ X2099 @ X2100 @ X2101 ) ) @ X2100 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( breln @ X2098 @ X2099 @ X2100 ) )
& ( ~ ( X2101 @ ( kpair @ ( esk53_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ ( esk54_4 @ X2098 @ X2099 @ X2100 @ X2101 ) ) )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( breln @ X2098 @ X2099 @ X2100 ) )
& ( ~ ( ex1 @ X2105 @ X2106 )
| ~ ( in @ X2107 @ X2105 )
| ~ ( in @ X2108 @ X2105 )
| ~ ( X2106 @ X2107 )
| ~ ( X2106 @ X2108 )
| ( X2107 = X2108 ) )
& ( ~ ( func @ X2109 @ X2110 @ X2111 )
| ~ ( in @ X2112 @ X2109 )
| ( in @ ( kpair @ X2112 @ ( ap @ X2109 @ X2110 @ X2111 @ X2112 ) ) @ X2111 ) )
& ( ~ ( in @ X2115 @ ( funcSet @ X2113 @ X2114 ) )
| ~ ( in @ X2116 @ X2113 )
| ( in @ ( kpair @ X2116 @ ( ap @ X2113 @ X2114 @ X2115 @ X2116 ) ) @ X2115 ) )
& ( ~ ( func @ X2117 @ X2118 @ X2119 )
| ~ ( in @ X2120 @ X2117 )
| ~ ( in @ X2121 @ X2118 )
| ~ ( in @ ( kpair @ X2120 @ X2121 ) @ X2119 )
| ( ( ap @ X2117 @ X2118 @ X2119 @ X2120 )
= X2121 ) )
& ( ( in @ ( esk55_4 @ X2122 @ X2123 @ X2124 @ X2125 ) @ X2122 )
| ~ ( in @ X2127 @ X2122 )
| ~ ( in @ X2128 @ X2123 )
| ~ ( in @ ( kpair @ X2127 @ X2128 ) @ X2125 )
| ( in @ ( kpair @ X2127 @ X2128 ) @ X2124 )
| ~ ( func @ X2122 @ X2123 @ X2125 )
| ~ ( func @ X2122 @ X2123 @ X2124 ) )
& ( ( ( ap @ X2122 @ X2123 @ X2124 @ ( esk55_4 @ X2122 @ X2123 @ X2124 @ X2125 ) )
!= ( ap @ X2122 @ X2123 @ X2125 @ ( esk55_4 @ X2122 @ X2123 @ X2124 @ X2125 ) ) )
| ~ ( in @ X2127 @ X2122 )
| ~ ( in @ X2128 @ X2123 )
| ~ ( in @ ( kpair @ X2127 @ X2128 ) @ X2125 )
| ( in @ ( kpair @ X2127 @ X2128 ) @ X2124 )
| ~ ( func @ X2122 @ X2123 @ X2125 )
| ~ ( func @ X2122 @ X2123 @ X2124 ) )
& ( ~ ( in @ X2131 @ ( funcSet @ X2129 @ X2130 ) )
| ~ ( in @ X2132 @ X2129 )
| ~ ( in @ X2133 @ X2130 )
| ~ ( in @ ( kpair @ X2132 @ X2133 ) @ X2131 )
| ( ( ap @ X2129 @ X2130 @ X2131 @ X2132 )
= X2133 ) )
& ( ( in @ ( esk56_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
| ( subset @ X2136 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2136 ) )
& ( ( in @ ( esk57_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
| ( subset @ X2136 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2136 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk57_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
| ( subset @ X2136 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2136 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk57_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
| ( subset @ X2136 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2137 )
| ~ ( breln @ X2134 @ X2135 @ X2136 ) )
& ( ( in @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ( X2142 = X2143 )
| ( in @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ( X2142 = X2143 )
| ( in @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ( X2142 = X2143 )
| ( in @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ( X2142 = X2143 )
| ( in @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ( X2142 = X2143 )
| ( in @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ( X2142 = X2143 )
| ( in @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ( X2142 = X2143 )
| ( in @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ( X2142 = X2143 )
| ( in @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ( X2142 = X2143 )
| ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ( X2142 = X2143 )
| ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ( X2142 = X2143 )
| ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ( X2142 = X2143 )
| ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2140 )
| ( X2142 = X2143 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ X2141 )
| ( X2142 = X2143 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ( X2142 = X2143 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk61_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 )
| ( X2142 = X2143 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2140 @ X2141 @ X2142 @ X2143 ) @ ( esk59_4 @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2143 )
| ~ ( breln @ X2140 @ X2141 @ X2142 ) )
& ( ( in @ ( esk62_4 @ X2148 @ X2149 @ X2150 @ X2151 ) @ X2148 )
| ( X2150 = X2151 )
| ~ ( func @ X2148 @ X2149 @ X2151 )
| ~ ( func @ X2148 @ X2149 @ X2150 ) )
& ( ( ( ap @ X2148 @ X2149 @ X2150 @ ( esk62_4 @ X2148 @ X2149 @ X2150 @ X2151 ) )
!= ( ap @ X2148 @ X2149 @ X2151 @ ( esk62_4 @ X2148 @ X2149 @ X2150 @ X2151 ) ) )
| ( X2150 = X2151 )
| ~ ( func @ X2148 @ X2149 @ X2151 )
| ~ ( func @ X2148 @ X2149 @ X2150 ) )
& ( ( in @ ( esk63_4 @ X2153 @ X2154 @ X2155 @ X2156 ) @ X2153 )
| ( X2155 = X2156 )
| ~ ( in @ X2156 @ ( funcSet @ X2153 @ X2154 ) )
| ~ ( in @ X2155 @ ( funcSet @ X2153 @ X2154 ) ) )
& ( ( ( ap @ X2153 @ X2154 @ X2155 @ ( esk63_4 @ X2153 @ X2154 @ X2155 @ X2156 ) )
!= ( ap @ X2153 @ X2154 @ X2156 @ ( esk63_4 @ X2153 @ X2154 @ X2155 @ X2156 ) ) )
| ( X2155 = X2156 )
| ~ ( in @ X2156 @ ( funcSet @ X2153 @ X2154 ) )
| ~ ( in @ X2155 @ ( funcSet @ X2153 @ X2154 ) ) )
& ( ~ ( in @ X2160 @ ( funcSet @ X2158 @ X2159 ) )
| ~ ( in @ X2161 @ X2158 )
| ( ( ap @ X2158 @ X2159 @ X2160 @ X2161 )
= ( ap @ X2158 @ X2159 @ X2160 @ X2161 ) ) )
& ( ~ ( func @ X2162 @ X2163 @ X2164 )
| ~ ( in @ X2165 @ X2162 )
| ( ( ap @ X2162 @ X2163 @ X2164 @ X2165 )
= ( ap @ X2162 @ X2163 @ X2164 @ X2165 ) ) )
& ( ( in @ ( esk64_3 @ X2166 @ X2167 @ X2168 ) @ X2166 )
| ~ ( in @ X2170 @ X2166 )
| ( ( ap @ X2166 @ X2167 @ ( lam @ X2166 @ X2167 @ X2168 ) @ X2170 )
= ( X2168 @ X2170 ) ) )
& ( ~ ( in @ ( X2168 @ ( esk64_3 @ X2166 @ X2167 @ X2168 ) ) @ X2167 )
| ~ ( in @ X2170 @ X2166 )
| ( ( ap @ X2166 @ X2167 @ ( lam @ X2166 @ X2167 @ X2168 ) @ X2170 )
= ( X2168 @ X2170 ) ) )
& ( ~ ( func @ X2171 @ X2172 @ X2173 )
| ( ( lam @ X2171 @ X2172 @ ( ap @ X2171 @ X2172 @ X2173 ) )
= X2173 ) )
& ( ( in @ ( esk65_3 @ X2174 @ X2175 @ X2176 ) @ X2174 )
| ( ( lam @ X2174 @ X2175 @ X2176 )
= ( lam @ X2174 @ X2175 @ X2176 ) ) )
& ( ~ ( in @ ( X2176 @ ( esk65_3 @ X2174 @ X2175 @ X2176 ) ) @ X2175 )
| ( ( lam @ X2174 @ X2175 @ X2176 )
= ( lam @ X2174 @ X2175 @ X2176 ) ) )
& ( ( in @ ( esk66_3 @ X2178 @ X2179 @ X2180 ) @ X2178 )
| ~ ( in @ X2182 @ X2178 )
| ( ( ap @ X2178 @ X2179 @ ( lam @ X2178 @ X2179 @ X2180 ) @ X2182 )
= ( X2180 @ X2182 ) ) )
& ( ~ ( in @ ( X2180 @ ( esk66_3 @ X2178 @ X2179 @ X2180 ) ) @ X2179 )
| ~ ( in @ X2182 @ X2178 )
| ( ( ap @ X2178 @ X2179 @ ( lam @ X2178 @ X2179 @ X2180 ) @ X2182 )
= ( X2180 @ X2182 ) ) )
& ( ~ ( in @ X2185 @ ( funcSet @ X2183 @ X2184 ) )
| ( ( lam @ X2183 @ X2184 @ ( ap @ X2183 @ X2184 @ X2185 ) )
= X2185 ) )
& ( ~ ( in @ X2188 @ X2186 )
| ~ ( in @ X2189 @ X2186 )
| X2187
| ( in @ X2189
@ ( dsetconstr @ X2186
@ ^ [Z0: $i] :
( ( X2187
& ( Z0 = X2188 ) )
| ( ~ X2187
& ( Z0 = X2189 ) ) ) ) ) )
& ( ~ ( in @ X2192 @ X2190 )
| ~ ( in @ X2193 @ X2190 )
| X2191
| ( ( dsetconstr @ X2190
@ ^ [Z0: $i] :
( ( X2191
& ( Z0 = X2192 ) )
| ( ~ X2191
& ( Z0 = X2193 ) ) ) )
= ( setadjoin @ X2193 @ emptyset ) ) )
& ( ~ ( in @ X2196 @ X2194 )
| ~ ( in @ X2197 @ X2194 )
| ~ X2195
| ( in @ X2196
@ ( dsetconstr @ X2194
@ ^ [Z0: $i] :
( ( X2195
& ( Z0 = X2196 ) )
| ( ~ X2195
& ( Z0 = X2197 ) ) ) ) ) )
& ( ~ ( in @ X2200 @ X2198 )
| ~ ( in @ X2201 @ X2198 )
| ~ X2199
| ( ( dsetconstr @ X2198
@ ^ [Z0: $i] :
( ( X2199
& ( Z0 = X2200 ) )
| ( ~ X2199
& ( Z0 = X2201 ) ) ) )
= ( setadjoin @ X2200 @ emptyset ) ) )
& ( ~ ( in @ X2204 @ X2202 )
| ~ ( in @ X2205 @ X2202 )
| ( singleton
@ ( dsetconstr @ X2202
@ ^ [Z0: $i] :
( ( X2203
& ( Z0 = X2204 ) )
| ( ~ X2203
& ( Z0 = X2205 ) ) ) ) ) )
& ( ~ ( in @ X2208 @ X2206 )
| ~ ( in @ X2209 @ X2206 )
| ( in @ ( if @ X2206 @ X2207 @ X2208 @ X2209 ) @ X2206 ) )
& ( ~ ( singleton @ X2210 )
| ~ ( in @ X2211 @ X2210 )
| ( ( setunion @ X2210 )
= X2211 ) )
& ( ~ ( in @ X2214 @ X2212 )
| ~ ( in @ X2215 @ X2212 )
| ~ X2213
| ( ( if @ X2212 @ X2213 @ X2214 @ X2215 )
= X2214 ) )
& ( ~ ( in @ X2218 @ X2216 )
| ~ ( in @ X2219 @ X2216 )
| X2217
| ( ( if @ X2216 @ X2217 @ X2218 @ X2219 )
= X2219 ) )
& ( ~ ( in @ X2222 @ X2220 )
| ~ ( in @ X2223 @ X2220 )
| ( in @ ( if @ X2220 @ X2221 @ X2222 @ X2223 ) @ ( setadjoin @ X2222 @ ( setadjoin @ X2223 @ emptyset ) ) ) )
& ( ~ ( in @ X2225 @ ( powerset @ X2224 ) )
| ~ ( in @ X2226 @ ( powerset @ X2224 ) )
| ( in @ ( binintersect @ X2225 @ X2226 ) @ ( powerset @ X2224 ) ) )
& ( ~ ( in @ X2228 @ ( powerset @ X2227 ) )
| ~ ( in @ X2229 @ ( powerset @ X2227 ) )
| ( in @ ( binunion @ X2228 @ X2229 ) @ ( powerset @ X2227 ) ) )
& ( ~ ( in @ X2231 @ ( powerset @ X2230 ) )
| ( in @ ( powerset @ X2231 ) @ ( powerset @ ( powerset @ X2230 ) ) ) )
& ( ~ ( in @ X2233 @ ( powerset @ X2232 ) )
| ~ ( in @ X2234 @ ( powerset @ X2232 ) )
| ( in @ ( setminus @ X2233 @ X2234 ) @ ( powerset @ X2232 ) ) )
& ( ~ ( in @ X2236 @ ( powerset @ X2235 ) )
| ( in @ ( setminus @ X2235 @ X2236 ) @ ( powerset @ X2235 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ( X2238 = X2239 )
| ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2237 )
| ( X2238 = X2239 )
| ~ ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ( X2238 = X2239 )
| ~ ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2237 @ X2238 @ X2239 ) @ X2238 )
| ( X2238 = X2239 )
| ~ ( in @ ( esk67_3 @ X2237 @ X2238 @ X2239 ) @ X2239 )
| ~ ( in @ X2239 @ ( powerset @ X2237 ) )
| ~ ( in @ X2238 @ ( powerset @ X2237 ) ) )
& ( ( in @ ( esk69_3 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ( subset @ X2243 @ X2244 )
| ~ ( in @ X2244 @ ( powerset @ X2242 ) )
| ~ ( in @ X2243 @ ( powerset @ X2242 ) ) )
& ( ( in @ ( esk69_3 @ X2242 @ X2243 @ X2244 ) @ X2243 )
| ( subset @ X2243 @ X2244 )
| ~ ( in @ X2244 @ ( powerset @ X2242 ) )
| ~ ( in @ X2243 @ ( powerset @ X2242 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2242 @ X2243 @ X2244 ) @ X2244 )
| ( subset @ X2243 @ X2244 )
| ~ ( in @ X2244 @ ( powerset @ X2242 ) )
| ~ ( in @ X2243 @ ( powerset @ X2242 ) ) )
& ( ( in @ ( esk70_3 @ X2246 @ X2247 @ X2248 ) @ X2246 )
| ( in @ X2247 @ ( powerset @ X2248 ) )
| ~ ( in @ X2248 @ ( powerset @ X2246 ) )
| ~ ( in @ X2247 @ ( powerset @ X2246 ) ) )
& ( ( in @ ( esk70_3 @ X2246 @ X2247 @ X2248 ) @ X2247 )
| ( in @ X2247 @ ( powerset @ X2248 ) )
| ~ ( in @ X2248 @ ( powerset @ X2246 ) )
| ~ ( in @ X2247 @ ( powerset @ X2246 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2246 @ X2247 @ X2248 ) @ X2248 )
| ( in @ X2247 @ ( powerset @ X2248 ) )
| ~ ( in @ X2248 @ ( powerset @ X2246 ) )
| ~ ( in @ X2247 @ ( powerset @ X2246 ) ) )
& ( ~ ( in @ X2251 @ ( powerset @ X2250 ) )
| ~ ( in @ X2252 @ ( powerset @ X2250 ) )
| ~ ( in @ X2253 @ X2250 )
| ~ ( in @ X2251 @ ( powerset @ X2252 ) )
| ~ ( in @ X2253 @ X2251 )
| ( in @ X2253 @ X2252 ) )
& ( ~ ( in @ X2255 @ ( powerset @ X2254 ) )
| ~ ( in @ X2256 @ X2254 )
| ~ ( in @ X2256 @ X2255 )
| ~ ( in @ X2256 @ ( setminus @ X2254 @ X2255 ) ) )
& ( ~ ( in @ X2258 @ ( powerset @ X2257 ) )
| ~ ( in @ X2259 @ X2257 )
| ( in @ X2259 @ ( setminus @ X2257 @ X2258 ) )
| ( in @ X2259 @ X2258 ) )
& ( ~ ( in @ X2261 @ ( powerset @ X2260 ) )
| ~ ( in @ X2262 @ ( powerset @ X2260 ) )
| ~ ( in @ X2263 @ X2260 )
| ( in @ X2263 @ X2261 )
| ~ ( in @ X2263 @ ( binintersect @ X2261 @ X2262 ) ) )
& ( ~ ( in @ X2265 @ ( powerset @ X2264 ) )
| ~ ( in @ X2266 @ ( powerset @ X2264 ) )
| ~ ( in @ X2267 @ X2264 )
| ( in @ X2267 @ X2266 )
| ~ ( in @ X2267 @ ( binintersect @ X2265 @ X2266 ) ) )
& ( ~ ( in @ X2269 @ ( powerset @ X2268 ) )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2271 @ X2268 )
| ~ ( subset @ X2269 @ ( setminus @ X2268 @ X2270 ) )
| ~ ( in @ X2271 @ X2270 )
| ~ ( in @ X2271 @ X2269 ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk74_0 @ esk71_0 )
& ( subset @ esk72_0 @ esk73_0 )
& ~ ( in @ esk74_0 @ esk73_0 )
& ( in @ esk74_0 @ esk72_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_292])])])])])])]) ).
thf(c_0_294,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
thf(c_0_295,negated_conjecture,
subset @ esk72_0 @ esk73_0,
inference(split_conjunct,[status(thm)],[c_0_293]) ).
thf(c_0_296,negated_conjecture,
~ ( in @ esk74_0 @ esk73_0 ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
thf(c_0_297,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk73_0 )
| ~ ( in @ X2 @ esk72_0 ) ),
inference(spm,[status(thm)],[c_0_294,c_0_295]) ).
thf(c_0_298,negated_conjecture,
in @ esk74_0 @ esk72_0,
inference(split_conjunct,[status(thm)],[c_0_293]) ).
thf(c_0_299,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_298])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU724^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 15:28:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running higher-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.28/0.87 # Version: 3.1.0-ho
% 1.28/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.28/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.28/0.87 # Starting ehoh_best5 with 300s (1) cores
% 1.28/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 1.28/0.87 # Starting new_bool_5 with 300s (1) cores
% 1.28/0.87 # Starting pre_casc_3 with 300s (1) cores
% 1.28/0.87 # Starting ho_unfolding_8 with 300s (1) cores
% 1.28/0.87 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.28/0.87 # Starting new_bool_3 with 300s (1) cores
% 1.28/0.87 # Starting new_ho_5 with 300s (1) cores
% 1.28/0.87 # new_ho_5 with pid 9060 completed with status 8
% 1.28/0.87 # new_bool_5 with pid 9055 completed with status 0
% 1.28/0.87 # Result found by new_bool_5
% 1.28/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.28/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.28/0.87 # Starting ehoh_best5 with 300s (1) cores
% 1.28/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 1.28/0.87 # Starting new_bool_5 with 300s (1) cores
% 1.28/0.87 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.28/0.87 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.28/0.87 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.28/0.87 # Starting ho_unfolding_8 with 55s (1) cores
% 1.28/0.87 # ho_unfolding_8 with pid 9070 completed with status 0
% 1.28/0.87 # Result found by ho_unfolding_8
% 1.28/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.28/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.28/0.87 # Starting ehoh_best5 with 300s (1) cores
% 1.28/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 1.28/0.87 # Starting new_bool_5 with 300s (1) cores
% 1.28/0.87 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.28/0.87 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.28/0.87 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.28/0.87 # Starting ho_unfolding_8 with 55s (1) cores
% 1.28/0.87 # Preprocessing time : 0.043 s
% 1.28/0.87 # Presaturation interreduction done
% 1.28/0.87
% 1.28/0.87 # Proof found!
% 1.28/0.87 # SZS status Theorem
% 1.28/0.87 # SZS output start CNFRefutation
% See solution above
% 1.28/0.87 # Parsed axioms : 523
% 1.28/0.87 # Removed by relevancy pruning/SinE : 283
% 1.28/0.87 # Initial clauses : 403
% 1.28/0.87 # Removed in clause preprocessing : 34
% 1.28/0.87 # Initial clauses in saturation : 369
% 1.28/0.87 # Processed clauses : 918
% 1.28/0.87 # ...of these trivial : 13
% 1.28/0.87 # ...subsumed : 101
% 1.28/0.87 # ...remaining for further processing : 804
% 1.28/0.87 # Other redundant clauses eliminated : 60
% 1.28/0.87 # Clauses deleted for lack of memory : 0
% 1.28/0.87 # Backward-subsumed : 3
% 1.28/0.87 # Backward-rewritten : 5
% 1.28/0.87 # Generated clauses : 10016
% 1.28/0.87 # ...of the previous two non-redundant : 9659
% 1.28/0.87 # ...aggressively subsumed : 0
% 1.28/0.87 # Contextual simplify-reflections : 2
% 1.28/0.87 # Paramodulations : 9921
% 1.28/0.87 # Factorizations : 2
% 1.28/0.87 # NegExts : 0
% 1.28/0.87 # Equation resolutions : 67
% 1.28/0.87 # Disequality decompositions : 0
% 1.28/0.87 # Total rewrite steps : 240
% 1.28/0.87 # ...of those cached : 163
% 1.28/0.87 # Propositional unsat checks : 0
% 1.28/0.87 # Propositional check models : 0
% 1.28/0.87 # Propositional check unsatisfiable : 0
% 1.28/0.87 # Propositional clauses : 0
% 1.28/0.87 # Propositional clauses after purity: 0
% 1.28/0.87 # Propositional unsat core size : 0
% 1.28/0.87 # Propositional preprocessing time : 0.000
% 1.28/0.87 # Propositional encoding time : 0.000
% 1.28/0.87 # Propositional solver time : 0.000
% 1.28/0.87 # Success case prop preproc time : 0.000
% 1.28/0.87 # Success case prop encoding time : 0.000
% 1.28/0.87 # Success case prop solver time : 0.000
% 1.28/0.87 # Current number of processed clauses : 457
% 1.28/0.87 # Positive orientable unit clauses : 56
% 1.28/0.87 # Positive unorientable unit clauses: 0
% 1.28/0.87 # Negative unit clauses : 19
% 1.28/0.87 # Non-unit-clauses : 382
% 1.28/0.87 # Current number of unprocessed clauses: 9326
% 1.28/0.87 # ...number of literals in the above : 37116
% 1.28/0.87 # Current number of archived formulas : 0
% 1.28/0.87 # Current number of archived clauses : 331
% 1.28/0.87 # Clause-clause subsumption calls (NU) : 50299
% 1.28/0.87 # Rec. Clause-clause subsumption calls : 23783
% 1.28/0.87 # Non-unit clause-clause subsumptions : 80
% 1.28/0.87 # Unit Clause-clause subsumption calls : 1655
% 1.28/0.87 # Rewrite failures with RHS unbound : 0
% 1.28/0.87 # BW rewrite match attempts : 37
% 1.28/0.87 # BW rewrite match successes : 4
% 1.28/0.87 # Condensation attempts : 0
% 1.28/0.87 # Condensation successes : 0
% 1.28/0.87 # Termbank termtop insertions : 219766
% 1.28/0.87 # Search garbage collected termcells : 23751
% 1.28/0.87
% 1.28/0.87 # -------------------------------------------------
% 1.28/0.87 # User time : 0.316 s
% 1.28/0.87 # System time : 0.031 s
% 1.28/0.87 # Total time : 0.347 s
% 1.28/0.87 # Maximum resident set size: 7784 pages
% 1.28/0.87
% 1.28/0.87 # -------------------------------------------------
% 1.28/0.87 # User time : 0.430 s
% 1.28/0.87 # System time : 0.065 s
% 1.28/0.87 # Total time : 0.495 s
% 1.28/0.87 # Maximum resident set size: 2616 pages
% 1.28/0.87 % E---3.1 exiting
% 1.28/0.87 % E exiting
%------------------------------------------------------------------------------