%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU743^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 03:29:45 EDT 2024
% Result : Theorem 24.13s 4.48s
% Output : CNFRefutation 24.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 646
% Syntax : Number of formulae : 740 ( 39 unt; 381 typ; 0 def)
% Number of atoms : 3450 ( 630 equ; 0 cnn)
% Maximal formula atoms : 1066 ( 9 avg)
% Number of connectives : 13951 ( 948 ~;1011 |; 579 &;9342 @)
% ( 353 <=>;1718 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1184 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 595 ( 595 >; 0 *; 0 +; 0 <<)
% Number of symbols : 385 ( 381 usr; 269 con; 0-4 aty)
% Number of variables : 2913 ( 182 ^2608 !; 123 ?;2913 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
epred1_0: $o ).
thf(decl_320,type,
esk1_2: $i > $i > $i ).
thf(decl_321,type,
esk2_2: $i > $i > $i ).
thf(decl_322,type,
esk3_2: $i > $i > $i ).
thf(decl_323,type,
esk4_1: $i > $i ).
thf(decl_324,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_325,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_326,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_327,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_328,type,
esk9_1: $i > $i ).
thf(decl_329,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_330,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_331,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_332,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_333,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_334,type,
esk15_2: $i > $i > $i ).
thf(decl_335,type,
esk16_2: $i > $i > $i ).
thf(decl_336,type,
esk17_1: $i > $i ).
thf(decl_337,type,
esk18_1: $i > $i ).
thf(decl_338,type,
esk19_1: $i > $i ).
thf(decl_339,type,
esk20_2: $i > $i > $i ).
thf(decl_340,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_341,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_342,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_343,type,
esk24_1: $i > $i ).
thf(decl_344,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_346,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_347,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_349,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_350,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_351,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_352,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_353,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_354,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_355,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_356,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_357,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_358,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_359,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_360,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_361,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_362,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_363,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_364,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_365,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_366,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_367,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_368,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_369,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_370,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_371,type,
esk52_2: $i > $i > $i ).
thf(decl_372,type,
esk53_2: $i > $i > $i ).
thf(decl_373,type,
esk54_2: $i > $i > $i ).
thf(decl_374,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_375,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_376,type,
esk57_2: $i > $i > $i ).
thf(decl_377,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_378,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_379,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_380,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_381,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_382,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_383,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_384,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_385,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_386,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_387,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_388,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_389,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_390,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_391,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_392,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_393,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_394,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_395,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_396,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_397,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_398,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_399,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_400,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_401,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_402,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_403,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_404,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_405,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_406,type,
esk87_0: $i ).
thf(decl_407,type,
esk88_0: $i ).
thf(decl_408,type,
esk89_0: $i ).
thf(decl_409,type,
esk90_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
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(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/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(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(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/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(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(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(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(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(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(intersectInPowersetIntersectUnions,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(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(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
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(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(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(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(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__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(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(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
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(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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
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(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(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(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(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(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(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(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(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(c_0_264,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_265,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_266,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_267,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_268,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_269,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_270,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_271,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_272,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_273,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_274,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_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,
( 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_277,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_278,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_279,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_280,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_281,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_282,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_283,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_284,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_285,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_286,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X864: $i] :
( ( X6 @ X2 @ X864 )
& ! [X865: $i] :
( ( X6 @ X2 @ X865 )
=> ( X864 = X865 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_264,c_0_265]) ).
thf(c_0_287,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X866: $i] :
( ( X1 @ X866 )
& ! [X867: $i] :
( ( X1 @ X867 )
=> ( X866 = X867 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_266,c_0_265]) ).
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,
( 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_290,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_291,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X868: $i] :
( ( X1 @ X868 )
& ! [X869: $i] :
( ( X1 @ X869 )
=> ( X868 = X869 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_267,c_0_265]) ).
thf(c_0_292,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X870: $i] :
( ( X1 @ X870 )
& ! [X871: $i] :
( ( X1 @ X871 )
=> ( X870 = X871 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_268,c_0_265]) ).
thf(c_0_293,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_294,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_269]) ).
thf(c_0_295,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_270,c_0_269]) ).
thf(c_0_296,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_269]) ).
thf(c_0_297,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_298,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X872: $i] :
( ( X1 @ X872 )
& ! [X873: $i] :
( ( X1 @ X873 )
=> ( X872 = X873 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_271,c_0_265]) ).
thf(c_0_299,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_269]) ).
thf(c_0_300,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_301,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X874: $i] :
( ( X1 @ X874 )
& ! [X875: $i] :
( ( X1 @ X875 )
=> ( X874 = X875 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_272,c_0_265]) ).
thf(c_0_302,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X876: $i] :
( ( X1 @ X876 )
& ! [X877: $i] :
( ( X1 @ X877 )
=> ( X876 = X877 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_273,c_0_265]) ).
thf(c_0_303,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X878: $i] :
( ( X1 @ X878 )
& ! [X879: $i] :
( ( X1 @ X879 )
=> ( X878 = X879 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_274,c_0_265]) ).
thf(c_0_304,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X880: $i] :
( ( X1 @ X880 )
& ! [X881: $i] :
( ( X1 @ X881 )
=> ( X880 = X881 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_275,c_0_265]) ).
thf(c_0_305,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X882: $i] :
( ( X1 @ X882 )
& ! [X883: $i] :
( ( X1 @ X883 )
=> ( X882 = X883 ) ) )
<=> ? [X884: $i] :
( ( X17 @ X884 )
& ! [X885: $i] :
( ( X17 @ X885 )
=> ( X884 = X885 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_276,c_0_265]) ).
thf(c_0_306,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X886: $i] :
( ( X1 @ X886 )
& ! [X887: $i] :
( ( X1 @ X887 )
=> ( X886 = X887 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_277,c_0_265]) ).
thf(c_0_307,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X888: $i] :
( ( X1 @ X888 )
& ! [X889: $i] :
( ( X1 @ X889 )
=> ( X888 = X889 ) ) )
=> ( ? [X890: $i] :
( ( X17 @ X890 )
& ! [X891: $i] :
( ( X17 @ X891 )
=> ( X890 = X891 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_278,c_0_265]) ).
thf(c_0_308,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_309,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_310,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_311,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_312,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_279,c_0_280]) ).
thf(c_0_313,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_281,c_0_280]) ).
thf(c_0_314,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_282,c_0_280]) ).
thf(c_0_315,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_316,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_317,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_318,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_319,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_283,c_0_284]) ).
thf(c_0_320,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_321,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_322,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_323,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_324,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_325,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_326,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_327,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_328,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_329,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_284]) ).
thf(c_0_330,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_284]) ).
thf(c_0_331,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_285,c_0_280]) ).
thf(c_0_332,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_284]) ).
thf(c_0_333,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_284]) ).
thf(c_0_334,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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,plain,
( epred1_0
<=> ! [X921: $i] :
? [X922: $i] :
( ! [X923: $i] :
( ( in @ X923 @ X922 )
=> ! [X924: $i] :
( ( in @ X924 @ X923 )
=> ( in @ X924 @ X921 ) ) )
& ! [X925: $i,X926: $i] :
( ( ( in @ X925 @ X921 )
& ( in @ X926 @ X921 ) )
=> ( ! [X927: $i] :
( ( in @ X927 @ X922 )
=> ( ( in @ X925 @ X927 )
<=> ( in @ X926 @ X927 ) ) )
=> ( X925 = X926 ) ) )
& ! [X928: $i,X929: $i] :
( ( ( in @ X928 @ X922 )
& ( in @ X929 @ X922 ) )
=> ( ! [X930: $i] :
( ( in @ X930 @ X928 )
=> ( in @ X930 @ X929 ) )
| ! [X931: $i] :
( ( in @ X931 @ X929 )
=> ( in @ X931 @ X928 ) ) ) )
& ! [X932: $i] :
( ( ! [X933: $i] :
( ( in @ X933 @ X932 )
=> ( in @ X933 @ X921 ) )
& ? [X934: $i] : ( in @ X934 @ X932 ) )
=> ? [X935: $i,X936: $i] :
( ( in @ X935 @ X922 )
& ( in @ X936 @ X932 )
& ~ ? [X937: $i] :
( ( in @ X937 @ X935 )
& ( in @ X937 @ X932 ) )
& ! [X938: $i] :
( ( in @ X938 @ X922 )
=> ( ! [X939: $i] :
( ( in @ X939 @ X938 )
=> ( in @ X939 @ X935 ) )
| ( in @ X936 @ X938 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_345,negated_conjecture,
~ ( ! [X892: $i,X893: $i] :
( ! [X894: $i] :
( ( in @ X894 @ X892 )
<=> ( in @ X894 @ X893 ) )
=> ( X892 = X893 ) )
=> ( ! [X895: $i] :
~ ( in @ X895 @ emptyset )
=> ( ! [X896: $i,X897: $i,X898: $i] :
( ( in @ X898 @ ( setadjoin @ X896 @ X897 ) )
<=> ( ( X898 = X896 )
| ( in @ X898 @ X897 ) ) )
=> ( ! [X899: $i,X900: $i] :
( ( in @ X900 @ ( powerset @ X899 ) )
<=> ! [X901: $i] :
( ( in @ X901 @ X900 )
=> ( in @ X901 @ X899 ) ) )
=> ( ! [X902: $i,X903: $i] :
( ( in @ X903 @ ( setunion @ X902 ) )
<=> ? [X904: $i] :
( ( in @ X903 @ X904 )
& ( in @ X904 @ X902 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X905: $i] :
( ( in @ X905 @ omega )
=> ( in @ ( setadjoin @ X905 @ X905 ) @ omega ) )
=> ( ! [X906: $i] :
( ( ( in @ emptyset @ X906 )
& ! [X907: $i] :
( ( ( in @ X907 @ omega )
& ( in @ X907 @ X906 ) )
=> ( in @ ( setadjoin @ X907 @ X907 ) @ X906 ) ) )
=> ! [X908: $i] :
( ( in @ X908 @ omega )
=> ( in @ X908 @ X906 ) ) )
=> ( ! [X909: $i > $i > $o,X910: $i] :
( ! [X911: $i] :
( ( in @ X911 @ X910 )
=> ? [X912: $i] :
( ( X909 @ X911 @ X912 )
& ! [X913: $i] :
( ( X909 @ X911 @ X913 )
=> ( X912 = X913 ) ) ) )
=> ? [X914: $i] :
! [X915: $i] :
( ( in @ X915 @ X914 )
<=> ? [X916: $i] :
( ( in @ X916 @ X910 )
& ( X909 @ X916 @ X915 ) ) ) )
=> ( ! [X917: $i] :
( ? [X918: $i] : ( in @ X918 @ X917 )
=> ? [X919: $i] :
( ( in @ X919 @ X917 )
& ~ ? [X920: $i] :
( ( in @ X920 @ X919 )
& ( in @ X920 @ X917 ) ) ) )
=> ( epred1_0
=> ( ! [X940: $i > $o] :
( ? [X941: $i] :
( ( X940 @ X941 )
& ! [X942: $i] :
( ( X940 @ X942 )
=> ( X941 = X942 ) ) )
=> ( X940
@ ( descr
@ ^ [Z0: $i] : ( X940 @ Z0 ) ) ) )
=> ( ! [X943: $i,X944: $i > $o,X945: $i] :
( ( in @ X945 @ X943 )
=> ( ( X944 @ X945 )
=> ( in @ X945 @ ( dsetconstr @ X943 @ X944 ) ) ) )
=> ( ! [X946: $i,X947: $i > $o,X948: $i] :
( ( in @ X948 @ ( dsetconstr @ X946 @ X947 ) )
=> ( in @ X948 @ X946 ) )
=> ( ! [X949: $i,X950: $i > $o,X951: $i] :
( ( in @ X951 @ ( dsetconstr @ X949 @ X950 ) )
=> ( X950 @ X951 ) )
=> ( ! [X952: $i > $o] :
( ? [X953: $i] :
( ( X952 @ X953 )
& ! [X954: $i] :
( ( X952 @ X954 )
=> ( X953 = X954 ) ) )
=> ? [X955: $i] :
( ( X952 @ X955 )
& ! [X956: $i] :
( ( X952 @ X956 )
=> ( X955 = X956 ) ) ) )
=> ( ! [X957: $o,X958: $i] :
( ( in @ X958 @ ( prop2set @ X957 ) )
=> X957 )
=> ( ! [X959: $i] :
( ( in @ X959 @ emptyset )
=> ! [X960: $o] : X960 )
=> ( ! [X961: $i] :
( ( in @ X961 @ emptyset )
=> ~ $true )
=> ( ! [X962: $i] :
~ ( in @ X962 @ emptyset )
=> ( ! [X963: $i > $o] :
( ? [X964: $i] :
( ( X963 @ X964 )
& ! [X965: $i] :
( ( X963 @ X965 )
=> ( X964 = X965 ) ) )
=> ? [X966: $i] : ( X963 @ X966 ) )
=> ( ! [X967: $i,X968: $i] :
( ! [X969: $i] :
( ( in @ X969 @ X967 )
=> ( in @ X969 @ X968 ) )
=> ( ! [X970: $i] :
( ( in @ X970 @ X968 )
=> ( in @ X970 @ X967 ) )
=> ( X967 = X968 ) ) )
=> ( ! [X971: $i] :
( ! [X972: $i] :
~ ( in @ X972 @ X971 )
=> ( X971 = emptyset ) )
=> ( ! [X973: $i] :
( ! [X974: $i] :
~ ( in @ X974 @ X973 )
=> ( X973 = emptyset ) )
=> ( ! [X975: $i,X976: $i > $o,X977: $i] :
( ( in @ X977 @ X975 )
=> ( ( in @ X977 @ ( dsetconstr @ X975 @ X976 ) )
<=> ( X976 @ X977 ) ) )
=> ( ! [X978: $i] :
( ( X978 != emptyset )
=> ? [X979: $i] : ( in @ X979 @ X978 ) )
=> ( ! [X980: $i,X981: $i > $o,X982: $i] :
( ( in @ X982 @ X980 )
=> ( ( X981 @ X982 )
=> ( ( dsetconstr @ X980 @ X981 )
!= emptyset ) ) )
=> ( ! [X983: $i] :
( ? [X984: $i] : ( in @ X984 @ X983 )
=> ( X983 != emptyset ) )
=> ( ! [X985: $i,X986: $i] : ( in @ X985 @ ( setadjoin @ X985 @ X986 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X987: $i,X988: $i,X989: $i] :
( ( in @ X989 @ X988 )
=> ( in @ X989 @ ( setadjoin @ X987 @ X988 ) ) )
=> ( ! [X990: $i,X991: $i,X992: $i] :
( ( in @ X992 @ ( setadjoin @ X990 @ X991 ) )
=> ! [X993: $o] :
( ( ( X992 = X990 )
=> X993 )
=> ( ( ( in @ X992 @ X991 )
=> X993 )
=> X993 ) ) )
=> ( ! [X994: $i,X995: $i,X996: $i] :
( ( in @ X996 @ ( setadjoin @ X994 @ X995 ) )
=> ( ( X996 = X994 )
| ( in @ X996 @ X995 ) ) )
=> ( ! [X997: $i] :
( ( dsetconstr @ X997
@ ^ [Z0: $i] : $true )
= X997 )
=> ( ! [X998: $i,X999: $i] :
( ! [X1000: $i] :
( ( in @ X1000 @ X999 )
=> ( in @ X1000 @ X998 ) )
=> ( in @ X999 @ ( powerset @ X998 ) ) )
=> ( ! [X1001: $i] : ( in @ emptyset @ ( powerset @ X1001 ) )
=> ( ! [X1002: $i] : ( in @ emptyset @ ( powerset @ X1002 ) )
=> ( ! [X1003: $i,X1004: $i,X1005: $i] :
( ( in @ X1004 @ ( powerset @ X1003 ) )
=> ( ( in @ X1005 @ X1004 )
=> ( in @ X1005 @ X1003 ) ) )
=> ( ! [X1006: $i,X1007: $i,X1008: $i] :
( ( in @ X1007 @ X1008 )
=> ( ( in @ X1008 @ X1006 )
=> ( in @ X1007 @ ( setunion @ X1006 ) ) ) )
=> ( ! [X1009: $i,X1010: $i] :
( ( in @ X1010 @ ( setunion @ X1009 ) )
=> ! [X1011: $o] :
( ! [X1012: $i] :
( ( in @ X1010 @ X1012 )
=> ( ( in @ X1012 @ X1009 )
=> X1011 ) )
=> X1011 ) )
=> ( ! [X1013: $i,X1014: $i] :
( ( in @ X1014 @ X1013 )
=> ( in @ X1014 @ ( powerset @ ( setunion @ X1013 ) ) ) )
=> ( ! [X1015: $i > $o] :
( ? [X1016: $i] :
( ( X1015 @ X1016 )
& ! [X1017: $i] :
( ( X1015 @ X1017 )
=> ( X1016 = X1017 ) ) )
=> ? [X1018: $i] :
! [X1019: $i] :
( ( X1015 @ X1019 )
<=> ( X1019 = X1018 ) ) )
=> ( ! [X1020: $i] :
( ( X1020 != emptyset )
=> ? [X1021: $i] :
( ( in @ X1021 @ X1020 )
& $true ) )
=> ( ! [X1022: $i,X1023: $i] :
( ( in @ X1022 @ ( setadjoin @ X1023 @ emptyset ) )
=> ( X1022 = X1023 ) )
=> ( ! [X1024: $i,X1025: $i] :
( ( X1024 != X1025 )
=> ~ ( in @ X1025 @ ( setadjoin @ X1024 @ emptyset ) ) )
=> ( ! [X1026: $i,X1027: $i] :
( ( X1026 = X1027 )
=> ( in @ X1026 @ ( setadjoin @ X1027 @ emptyset ) ) )
=> ( ! [X1028: $i,X1029: $i] :
( ( in @ X1028 @ ( setadjoin @ X1029 @ emptyset ) )
=> ( in @ X1029 @ ( setadjoin @ X1028 @ emptyset ) ) )
=> ( ! [X1030: $i,X1031: $i,X1032: $i] :
( ( in @ X1032 @ ( setadjoin @ X1030 @ ( setadjoin @ X1031 @ emptyset ) ) )
=> ( ( X1032 = X1030 )
| ( X1032 = X1031 ) ) )
=> ( ! [X1033: $i,X1034: $i] : ( in @ X1033 @ ( setadjoin @ X1033 @ ( setadjoin @ X1034 @ emptyset ) ) )
=> ( ! [X1035: $i,X1036: $i] : ( in @ X1036 @ ( setadjoin @ X1035 @ ( setadjoin @ X1036 @ emptyset ) ) )
=> ( ! [X1037: $i,X1038: $i > $o] :
( ? [X1039: $i] :
( ( in @ X1039 @ X1037 )
& ( X1038 @ X1039 ) )
=> ( ( ( dsetconstr @ X1037 @ X1038 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1040: $i > $o,X1041: $i] :
( ( in @ X1041 @ emptyset )
=> ( X1040 @ X1041 ) )
=> ( ! [X1042: $i,X1043: $i > $o] :
( ~ ! [X1044: $i] :
( ( in @ X1044 @ X1042 )
=> ( X1043 @ X1044 ) )
=> ? [X1045: $i] :
( ( in @ X1045 @ X1042 )
& ~ ( X1043 @ X1045 ) ) )
=> ( ! [X1046: $i,X1047: $i > $o] :
( ! [X1048: $i] :
( ( in @ X1048 @ X1046 )
=> ~ ( X1047 @ X1048 ) )
=> ~ ? [X1049: $i] :
( ( in @ X1049 @ X1046 )
& ( X1047 @ X1049 ) ) )
=> ( ! [X1050: $i,X1051: $i > $o] :
( ~ ? [X1052: $i] :
( ( in @ X1052 @ X1050 )
& ( X1051 @ X1052 ) )
=> ! [X1053: $i] :
( ( in @ X1053 @ X1050 )
=> ~ ( X1051 @ X1053 ) ) )
=> ( ! [X1054: $i,X1055: $i > $o] :
( ? [X1056: $i] :
( ( in @ X1056 @ X1054 )
& ~ ( X1055 @ X1056 ) )
=> ~ ! [X1057: $i] :
( ( in @ X1057 @ X1054 )
=> ( X1055 @ X1057 ) ) )
=> ( ! [X1058: $o] :
( X1058
=> ( in @ emptyset @ ( prop2set @ X1058 ) ) )
=> ( ! [X1059: $o] :
( X1059
=> ( set2prop @ ( prop2set @ X1059 ) ) )
=> ( ! [X1060: $i,X1061: $i > $o] :
( ~ ? [X1062: $i] :
( ( in @ X1062 @ X1060 )
& ( X1061 @ X1062 ) )
=> ! [X1063: $i] :
( ( in @ X1063 @ X1060 )
=> ~ ( X1061 @ X1063 ) ) )
=> ( ! [X1064: $i,X1065: $i > $o] :
( ~ ! [X1066: $i] :
( ( in @ X1066 @ X1064 )
=> ( X1065 @ X1066 ) )
=> ? [X1067: $i] :
( ( in @ X1067 @ X1064 )
& ~ ( X1065 @ X1067 ) ) )
=> ( ! [X1068: $i > $o] :
( ? [X1069: $i] :
( ( X1068 @ X1069 )
& ! [X1070: $i] :
( ( X1068 @ X1070 )
=> ( X1069 = X1070 ) ) )
=> ? [X1071: $i] :
( ( X1068 @ X1071 )
& ! [X1072: $i] :
( ( X1068 @ X1072 )
=> ( X1071 = X1072 ) ) ) )
=> ( ! [X1073: $i > $o] :
( ? [X1074: $i] : ( X1073 @ X1074 )
=> ( ! [X1075: $i,X1076: $i] :
( ( X1073 @ X1075 )
=> ( ( X1073 @ X1076 )
=> ( X1075 = X1076 ) ) )
=> ? [X1077: $i] :
( ( X1073 @ X1077 )
& ! [X1078: $i] :
( ( X1073 @ X1078 )
=> ( X1077 = X1078 ) ) ) ) )
=> ( ! [X1079: $i > $o] :
( ? [X1080: $i] :
! [X1081: $i] :
( ( X1079 @ X1081 )
<=> ( X1081 = X1080 ) )
=> ? [X1082: $i] :
( ( X1079 @ X1082 )
& ! [X1083: $i] :
( ( X1079 @ X1083 )
=> ( X1082 = X1083 ) ) ) )
=> ( ! [X1084: $i,X1085: $i] :
( ( X1084 = X1085 )
=> ! [X1086: $i,X1087: $i] :
( ( X1086 = X1087 )
=> ( ( in @ X1086 @ X1084 )
=> ( in @ X1087 @ X1085 ) ) ) )
=> ( ! [X1088: $i,X1089: $i] :
( ( X1088 = X1089 )
=> ! [X1090: $i,X1091: $i] :
( ( X1090 = X1091 )
=> ( ( in @ X1090 @ X1088 )
<=> ( in @ X1091 @ X1089 ) ) ) )
=> ( ! [X1092: $i > $o] :
( ? [X1093: $i] :
( ( X1092 @ X1093 )
& ! [X1094: $i] :
( ( X1092 @ X1094 )
=> ( X1093 = X1094 ) ) )
=> ! [X1095: $i,X1096: $i] :
( ( X1092 @ X1095 )
=> ( ( X1092 @ X1096 )
=> ( X1095 = X1096 ) ) ) )
=> ( ! [X1097: $i > $o,X1098: $i > $o] :
( ! [X1099: $i,X1100: $i] :
( ( X1099 = X1100 )
=> ( ( X1097 @ X1099 )
<=> ( X1098 @ X1100 ) ) )
=> ( ? [X1101: $i] :
( ( X1097 @ X1101 )
& ! [X1102: $i] :
( ( X1097 @ X1102 )
=> ( X1101 = X1102 ) ) )
<=> ? [X1103: $i] :
( ( X1098 @ X1103 )
& ! [X1104: $i] :
( ( X1098 @ X1104 )
=> ( X1103 = X1104 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1105: $i,X1106: $i] :
( ( X1105 = X1106 )
=> ! [X1107: $i,X1108: $i] :
( ( X1107 = X1108 )
=> ( ( setadjoin @ X1105 @ X1107 )
= ( setadjoin @ X1106 @ X1108 ) ) ) )
=> ( ! [X1109: $i,X1110: $i] :
( ( X1109 = X1110 )
=> ( ( powerset @ X1109 )
= ( powerset @ X1110 ) ) )
=> ( ! [X1111: $i,X1112: $i] :
( ( X1111 = X1112 )
=> ( ( setunion @ X1111 )
= ( setunion @ X1112 ) ) )
=> ( ( omega = omega )
=> ( ! [X1113: $i > $o] :
( ? [X1114: $i] :
( ( X1113 @ X1114 )
& ! [X1115: $i] :
( ( X1113 @ X1115 )
=> ( X1114 = X1115 ) ) )
=> ! [X1116: $i,X1117: $i] :
( ( X1113 @ X1116 )
=> ( ( X1113 @ X1117 )
=> ( X1116 = X1117 ) ) ) )
=> ( ! [X1118: $i > $o,X1119: $i > $o] :
( ! [X1120: $i,X1121: $i] :
( ( X1120 = X1121 )
=> ( ( X1118 @ X1120 )
<=> ( X1119 @ X1121 ) ) )
=> ( ? [X1122: $i] :
( ( X1118 @ X1122 )
& ! [X1123: $i] :
( ( X1118 @ X1123 )
=> ( X1122 = X1123 ) ) )
=> ( ? [X1124: $i] :
( ( X1119 @ X1124 )
& ! [X1125: $i] :
( ( X1119 @ X1125 )
=> ( X1124 = X1125 ) ) )
=> ( ( descr @ X1118 )
= ( descr @ X1119 ) ) ) ) )
=> ( ! [X1126: $i,X1127: $i] :
( ( X1126 = X1127 )
=> ! [X1128: $i > $o,X1129: $i > $o] :
( ! [X1130: $i] :
( ( in @ X1130 @ X1126 )
=> ! [X1131: $i] :
( ( in @ X1131 @ X1127 )
=> ( ( X1130 = X1131 )
=> ( ( X1128 @ X1130 )
<=> ( X1129 @ X1131 ) ) ) ) )
=> ( ( dsetconstr @ X1126 @ X1128 )
= ( dsetconstr @ X1127 @ X1129 ) ) ) )
=> ( ! [X1132: $i,X1133: $i] :
( ! [X1134: $i] :
( ( in @ X1134 @ X1132 )
=> ( in @ X1134 @ X1133 ) )
=> ( subset @ X1132 @ X1133 ) )
=> ( ! [X1135: $i,X1136: $i] :
( ( X1135 = X1136 )
=> ( subset @ X1136 @ X1135 ) )
=> ( ! [X1137: $i,X1138: $i] :
( ( X1137 = X1138 )
=> ( subset @ X1137 @ X1138 ) )
=> ( ! [X1139: $i,X1140: $i] :
( ! [X1141: $i] :
( ( in @ X1141 @ X1139 )
=> ( in @ X1141 @ X1140 ) )
=> ( subset @ X1139 @ X1140 ) )
=> ( ! [X1142: $i] : ( subset @ emptyset @ X1142 )
=> ( ! [X1143: $i,X1144: $i,X1145: $i] :
( ( subset @ X1143 @ X1144 )
=> ( ( in @ X1145 @ X1143 )
=> ( in @ X1145 @ X1144 ) ) )
=> ( ! [X1146: $i,X1147: $i,X1148: $i] :
( ( subset @ X1146 @ X1147 )
=> ( ~ ( in @ X1148 @ X1147 )
=> ~ ( in @ X1148 @ X1146 ) ) )
=> ( ! [X1149: $i,X1150: $i,X1151: $i] :
( ( in @ X1151 @ X1149 )
=> ( ~ ( in @ X1151 @ X1150 )
=> ~ ( subset @ X1149 @ X1150 ) ) )
=> ( ! [X1152: $i,X1153: $i] :
( ~ ( subset @ X1152 @ X1153 )
=> ( X1152 != X1153 ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ X1154 )
=> ( ~ ( in @ X1156 @ X1155 )
=> ( X1154 != X1155 ) ) )
=> ( ! [X1157: $i] : ( subset @ X1157 @ X1157 )
=> ( ! [X1158: $i,X1159: $i,X1160: $i] :
( ( subset @ X1158 @ X1159 )
=> ( ( subset @ X1159 @ X1160 )
=> ( subset @ X1158 @ X1160 ) ) )
=> ( ! [X1161: $i,X1162: $i] : ( subset @ X1162 @ ( setadjoin @ X1161 @ X1162 ) )
=> ( ! [X1163: $i,X1164: $i,X1165: $i] :
( ( subset @ X1163 @ X1165 )
=> ( subset @ X1163 @ ( setadjoin @ X1164 @ X1165 ) ) )
=> ( ! [X1166: $i,X1167: $i] :
( ( subset @ X1166 @ X1167 )
=> ( in @ X1166 @ ( powerset @ X1167 ) ) )
=> ( ! [X1168: $i,X1169: $i] :
( ( subset @ X1168 @ X1169 )
=> ( ( subset @ X1169 @ X1168 )
=> ( X1168 = X1169 ) ) )
=> ( ! [X1170: $i] :
( ( subset @ X1170 @ emptyset )
=> ( X1170 = emptyset ) )
=> ( ! [X1171: $i,X1172: $i] :
( ( subset @ X1172 @ X1171 )
=> ( in @ X1172 @ ( powerset @ X1171 ) ) )
=> ( ! [X1173: $i,X1174: $i] :
( ( in @ X1174 @ ( powerset @ X1173 ) )
=> ( subset @ X1174 @ X1173 ) )
=> ( ! [X1175: $i] : ( in @ X1175 @ ( powerset @ X1175 ) )
=> ( ! [X1176: $i,X1177: $i] :
( ( subset @ X1176 @ X1177 )
=> ( subset @ ( powerset @ X1176 ) @ ( powerset @ X1177 ) ) )
=> ( ! [X1178: $i,X1179: $i > $o] : ( in @ ( dsetconstr @ X1178 @ X1179 ) @ ( powerset @ X1178 ) )
=> ( ! [X1180: $i,X1181: $i > $o] : ( subset @ ( dsetconstr @ X1180 @ X1181 ) @ X1180 )
=> ( ! [X1182: $i,X1183: $i,X1184: $i] :
( ( in @ X1184 @ X1182 )
=> ( in @ X1184 @ ( binunion @ X1182 @ X1183 ) ) )
=> ( ! [X1185: $i,X1186: $i] : ( in @ X1186 @ ( setadjoin @ X1185 @ ( setadjoin @ X1186 @ emptyset ) ) )
=> ( ! [X1187: $i,X1188: $i,X1189: $i] :
( ( in @ X1189 @ X1188 )
=> ( in @ X1189 @ ( binunion @ X1187 @ X1188 ) ) )
=> ( ! [X1190: $i,X1191: $i,X1192: $i,X1193: $o] :
( ( in @ X1192 @ ( binunion @ X1190 @ X1191 ) )
=> ( ( ( in @ X1192 @ X1190 )
=> X1193 )
=> ( ( ( in @ X1192 @ X1191 )
=> X1193 )
=> X1193 ) ) )
=> ( ! [X1194: $i,X1195: $i,X1196: $i] :
( ( in @ X1196 @ ( binunion @ X1194 @ X1195 ) )
=> ( ( in @ X1196 @ X1194 )
| ( in @ X1196 @ X1195 ) ) )
=> ( ! [X1197: $i,X1198: $i] : ( subset @ X1197 @ ( binunion @ X1197 @ X1198 ) )
=> ( ! [X1199: $i,X1200: $i] : ( subset @ X1200 @ ( binunion @ X1199 @ X1200 ) )
=> ( ! [X1201: $i,X1202: $i,X1203: $i] :
( ( in @ X1203 @ X1201 )
=> ( ( in @ X1203 @ X1202 )
=> ( in @ X1203 @ ( binintersect @ X1201 @ X1202 ) ) ) )
=> ( ! [X1204: $i,X1205: $i,X1206: $i] :
( ( subset @ X1206 @ X1204 )
=> ( ( subset @ X1206 @ X1205 )
=> ( subset @ X1206 @ ( binintersect @ X1204 @ X1205 ) ) ) )
=> ( ! [X1207: $i,X1208: $i,X1209: $i] :
( ( in @ X1209 @ ( binintersect @ X1207 @ X1208 ) )
=> ( in @ X1209 @ X1207 ) )
=> ( ! [X1210: $i,X1211: $i] : ( subset @ ( binintersect @ X1210 @ X1211 ) @ X1210 )
=> ( ! [X1212: $i,X1213: $i] :
( ( subset @ X1212 @ X1213 )
=> ( ( binintersect @ X1212 @ X1213 )
= X1212 ) )
=> ( ! [X1214: $i,X1215: $i] :
( ( ( binintersect @ X1214 @ X1215 )
= X1215 )
=> ( subset @ X1215 @ X1214 ) )
=> ( ! [X1216: $i,X1217: $i,X1218: $i] :
( ( in @ X1218 @ ( binintersect @ X1216 @ X1217 ) )
=> ( in @ X1218 @ X1217 ) )
=> ( ! [X1219: $i,X1220: $i] :
( ~ ? [X1221: $i] :
( ( in @ X1221 @ X1219 )
& ( in @ X1221 @ X1220 ) )
=> ( ( binintersect @ X1219 @ X1220 )
= emptyset ) )
=> ( ! [X1222: $i,X1223: $i] : ( subset @ ( binintersect @ X1222 @ X1223 ) @ X1223 )
=> ( ! [X1224: $i,X1225: $i] :
( ( subset @ X1225 @ X1224 )
=> ( ( binintersect @ X1224 @ X1225 )
= X1225 ) )
=> ( ! [X1226: $i,X1227: $i] :
( ( ( binintersect @ X1226 @ X1227 )
= X1226 )
=> ( subset @ X1226 @ X1227 ) )
=> ( ! [X1228: $i,X1229: $i,X1230: $i] :
( ( binintersect @ X1228 @ ( binunion @ X1229 @ X1230 ) )
= ( binunion @ ( binintersect @ X1228 @ X1229 ) @ ( binintersect @ X1228 @ X1230 ) ) )
=> ( ! [X1231: $i,X1232: $i,X1233: $i] :
( ( in @ X1233 @ X1231 )
=> ( ~ ( in @ X1233 @ X1232 )
=> ( in @ X1233 @ ( setminus @ X1231 @ X1232 ) ) ) )
=> ( ! [X1234: $i,X1235: $i,X1236: $i] :
( ( in @ X1236 @ ( setminus @ X1234 @ X1235 ) )
=> ( in @ X1236 @ X1234 ) )
=> ( ! [X1237: $i,X1238: $i,X1239: $i] :
( ( in @ X1239 @ ( setminus @ X1237 @ X1238 ) )
=> ~ ( in @ X1239 @ X1238 ) )
=> ( ! [X1240: $i,X1241: $i] :
( ( subset @ X1240 @ X1241 )
=> ( ( setminus @ X1240 @ X1241 )
= emptyset ) )
=> ( ! [X1242: $i,X1243: $i,X1244: $i] :
( ~ ( in @ X1244 @ ( setminus @ X1242 @ X1243 ) )
=> ( ( in @ X1244 @ X1242 )
=> ( in @ X1244 @ X1243 ) ) )
=> ( ! [X1245: $i,X1246: $i,X1247: $i] :
( ~ ( in @ X1247 @ ( setminus @ X1245 @ X1246 ) )
=> ( ~ ( in @ X1247 @ X1246 )
=> ~ ( in @ X1247 @ X1245 ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ~ ( in @ X1250 @ X1248 )
=> ~ ( in @ X1250 @ ( setminus @ X1248 @ X1249 ) ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i] :
( ( in @ X1253 @ X1252 )
=> ~ ( in @ X1253 @ ( setminus @ X1251 @ X1252 ) ) )
=> ( ! [X1254: $i,X1255: $i] : ( subset @ ( setminus @ X1254 @ X1255 ) @ X1254 )
=> ( ! [X1256: $i,X1257: $i] :
( ( ( setminus @ X1256 @ X1257 )
= emptyset )
=> ( subset @ X1256 @ X1257 ) )
=> ( ! [X1258: $i,X1259: $i,X1260: $i] :
( ( in @ X1260 @ ( symdiff @ X1258 @ X1259 ) )
=> ! [X1261: $o] :
( ( ( in @ X1260 @ X1258 )
=> ( ~ ( in @ X1260 @ X1259 )
=> X1261 ) )
=> ( ( ~ ( in @ X1260 @ X1258 )
=> ( ( in @ X1260 @ X1259 )
=> X1261 ) )
=> X1261 ) ) )
=> ( ! [X1262: $i,X1263: $i,X1264: $i] :
( ( in @ X1264 @ X1262 )
=> ( ~ ( in @ X1264 @ X1263 )
=> ( in @ X1264 @ ( symdiff @ X1262 @ X1263 ) ) ) )
=> ( ! [X1265: $i,X1266: $i,X1267: $i] :
( ~ ( in @ X1267 @ X1265 )
=> ( ( in @ X1267 @ X1266 )
=> ( in @ X1267 @ ( symdiff @ X1265 @ X1266 ) ) ) )
=> ( ! [X1268: $i,X1269: $i,X1270: $i] :
( ( in @ X1270 @ X1268 )
=> ( ( in @ X1270 @ X1269 )
=> ~ ( in @ X1270 @ ( symdiff @ X1268 @ X1269 ) ) ) )
=> ( ! [X1271: $i,X1272: $i,X1273: $i] :
( ~ ( in @ X1273 @ X1271 )
=> ( ~ ( in @ X1273 @ X1272 )
=> ~ ( in @ X1273 @ ( symdiff @ X1271 @ X1272 ) ) ) )
=> ( ! [X1274: $i,X1275: $i] : ( in @ X1275 @ ( setadjoin @ X1274 @ ( setadjoin @ X1275 @ emptyset ) ) )
=> ( ! [X1276: $i,X1277: $i] : ( in @ X1276 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1276 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1276 @ ( setadjoin @ X1277 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1278: $i,X1279: $i] : ( in @ X1279 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1278 @ ( setadjoin @ X1279 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1280: $i,X1281: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1280 @ ( setadjoin @ X1281 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1282: $i,X1283: $i] : ( iskpair @ ( kpair @ X1282 @ X1283 ) )
=> ( ! [X1284: $i,X1285: $i] :
( ( in @ X1285 @ X1284 )
=> ( subset @ ( setadjoin @ X1285 @ emptyset ) @ X1284 ) )
=> ( ! [X1286: $i,X1287: $i] :
( ( in @ X1287 @ X1286 )
=> ( in @ ( setadjoin @ X1287 @ emptyset ) @ ( powerset @ X1286 ) ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i] :
( ( in @ X1290 @ X1288 )
=> ( in @ ( setadjoin @ X1290 @ emptyset ) @ ( powerset @ ( binunion @ X1288 @ X1289 ) ) ) )
=> ( ! [X1291: $i,X1292: $i,X1293: $i] :
( ( in @ X1293 @ ( setadjoin @ X1291 @ ( setadjoin @ X1292 @ emptyset ) ) )
=> ( ( X1293 = X1291 )
| ( X1293 = X1292 ) ) )
=> ( ! [X1294: $i,X1295: $i,X1296: $i] :
( ( in @ X1296 @ X1294 )
=> ! [X1297: $i] :
( ( in @ X1297 @ X1295 )
=> ( subset @ ( setadjoin @ X1296 @ ( setadjoin @ X1297 @ emptyset ) ) @ ( binunion @ X1294 @ X1295 ) ) ) )
=> ( ! [X1298: $i,X1299: $i,X1300: $i] :
( ( in @ X1300 @ X1298 )
=> ! [X1301: $i] :
( ( in @ X1301 @ X1299 )
=> ( in @ ( setadjoin @ X1300 @ ( setadjoin @ X1301 @ emptyset ) ) @ ( powerset @ ( binunion @ X1298 @ X1299 ) ) ) ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i] :
( ( in @ X1304 @ X1302 )
=> ! [X1305: $i] :
( ( in @ X1305 @ X1303 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1304 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1304 @ ( setadjoin @ X1305 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1302 @ X1303 ) ) ) ) )
=> ( ! [X1306: $i,X1307: $i,X1308: $i] :
( ( in @ X1308 @ X1306 )
=> ! [X1309: $i] :
( ( in @ X1309 @ X1307 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1308 @ ( setadjoin @ X1309 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1306 @ X1307 ) ) ) ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i] :
( ( in @ X1312 @ X1310 )
=> ! [X1313: $i] :
( ( in @ X1313 @ X1311 )
=> ( in @ ( kpair @ X1312 @ X1313 ) @ ( powerset @ ( powerset @ ( binunion @ X1310 @ X1311 ) ) ) ) ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( in @ X1316 @ X1314 )
=> ! [X1317: $i] :
( ( in @ X1317 @ X1315 )
=> ( in @ ( kpair @ X1316 @ X1317 ) @ ( cartprod @ X1314 @ X1315 ) ) ) )
=> ( ! [X1318: $i,X1319: $i,X1320: $i] :
( ( in @ X1320 @ ( cartprod @ X1318 @ X1319 ) )
=> ? [X1321: $i] :
( ( in @ X1321 @ X1318 )
& ? [X1322: $i] :
( ( in @ X1322 @ X1319 )
& ( X1320
= ( kpair @ X1321 @ X1322 ) ) ) ) )
=> ( ! [X1323: $i,X1324: $i,X1325: $i] :
( ( in @ X1325 @ ( cartprod @ X1323 @ X1324 ) )
=> ( iskpair @ X1325 ) )
=> ( ! [X1326: $i,X1327: $i] :
( ( in @ X1327 @ ( setunion @ X1326 ) )
=> ? [X1328: $i] :
( ( in @ X1328 @ X1326 )
& ( in @ X1327 @ X1328 ) ) )
=> ( ! [X1329: $i] : ( subset @ ( setunion @ ( setadjoin @ X1329 @ emptyset ) ) @ X1329 )
=> ( ! [X1330: $i] : ( subset @ X1330 @ ( setunion @ ( setadjoin @ X1330 @ emptyset ) ) )
=> ( ! [X1331: $i] :
( ( setunion @ ( setadjoin @ X1331 @ emptyset ) )
= X1331 )
=> ( ! [X1332: $i,X1333: $i > $o] :
( ! [X1334: $i] :
( ( in @ X1334 @ X1332 )
=> ! [X1335: $i] :
( ( in @ X1335 @ X1332 )
=> ( ( X1333 @ X1334 )
=> ( ( X1333 @ X1335 )
=> ( X1334 = X1335 ) ) ) ) )
=> ( ? [X1336: $i] :
( ( in @ X1336 @ X1332 )
& ( X1333 @ X1336 ) )
=> ( singleton @ ( dsetconstr @ X1332 @ X1333 ) ) ) )
=> ( ! [X1337: $i,X1338: $i > $o] :
( ( singleton @ ( dsetconstr @ X1337 @ X1338 ) )
=> ? [X1339: $i] :
( ( in @ X1339 @ X1337 )
& ( X1338 @ X1339 ) ) )
=> ( ! [X1340: $i,X1341: $i > $o,X1342: $i] :
( ( in @ X1342 @ X1340 )
=> ( ( X1341 @ X1342 )
=> ( ! [X1343: $i] :
( ( in @ X1343 @ X1340 )
=> ( ( X1341 @ X1343 )
=> ( X1343 = X1342 ) ) )
=> ( singleton @ ( dsetconstr @ X1340 @ X1341 ) ) ) ) )
=> ( ! [X1344: $i,X1345: $i > $o] :
( ! [X1346: $i] :
( ( in @ X1346 @ X1344 )
=> ! [X1347: $i] :
( ( in @ X1347 @ X1344 )
=> ( ( X1345 @ X1346 )
=> ( ( X1345 @ X1347 )
=> ( X1346 = X1347 ) ) ) ) )
=> ( ? [X1348: $i] :
( ( in @ X1348 @ X1344 )
& ( X1345 @ X1348 ) )
=> ( singleton @ ( dsetconstr @ X1344 @ X1345 ) ) ) )
=> ( ! [X1349: $i,X1350: $i] :
( ( ( setadjoin @ X1349 @ emptyset )
= ( setadjoin @ X1350 @ emptyset ) )
=> ( X1349 = X1350 ) )
=> ( ! [X1351: $i,X1352: $i,X1353: $i] :
( ( in @ ( setadjoin @ X1353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1351 @ ( setadjoin @ X1352 @ emptyset ) ) @ emptyset ) ) )
=> ( X1351 = X1353 ) )
=> ( ! [X1354: $i] :
( ( iskpair @ X1354 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1354 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1354 ) ) ) )
=> ( ! [X1355: $i] :
( ( singleton @ X1355 )
=> ( in @ ( setunion @ X1355 ) @ X1355 ) )
=> ( ! [X1356: $i,X1357: $i] :
( ( kfst @ ( kpair @ X1356 @ X1357 ) )
= X1356 )
=> ( ! [X1358: $i,X1359: $i,X1360: $i] :
( ( in @ X1360 @ ( cartprod @ X1358 @ X1359 ) )
=> ( in @ ( kfst @ X1360 ) @ X1358 ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i,X1364: $i] :
( ( ( setadjoin @ ( setadjoin @ X1361 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1361 @ ( setadjoin @ X1362 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1363 @ ( setadjoin @ X1364 @ emptyset ) ) @ emptyset ) ) )
=> ( X1361 = X1363 ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i,X1368: $i] :
( ( ( kpair @ X1365 @ X1366 )
= ( kpair @ X1367 @ X1368 ) )
=> ( X1365 = X1367 ) )
=> ( ! [X1369: $i,X1370: $i] :
( ( X1369 = X1370 )
=> ( ( setadjoin @ X1369 @ ( setadjoin @ X1370 @ emptyset ) )
= ( setadjoin @ X1369 @ emptyset ) ) )
=> ( ! [X1371: $i,X1372: $i] :
( ( X1371 = X1372 )
=> ( ( setadjoin @ ( setadjoin @ X1371 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1371 @ ( setadjoin @ X1372 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1371 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i,X1376: $i] :
( ( ( setadjoin @ ( setadjoin @ X1373 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1373 @ ( setadjoin @ X1374 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1375 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1375 @ ( setadjoin @ X1376 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1375 = X1376 )
=> ( X1374 = X1376 ) ) )
=> ( ! [X1377: $i,X1378: $i,X1379: $i] :
( ( ( setadjoin @ X1377 @ ( setadjoin @ X1378 @ emptyset ) )
= ( setadjoin @ X1379 @ emptyset ) )
=> ( X1377 = X1378 ) )
=> ( ! [X1380: $i,X1381: $i,X1382: $i,X1383: $i] :
( ( ( setadjoin @ ( setadjoin @ X1380 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1380 @ ( setadjoin @ X1381 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1382 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1382 @ ( setadjoin @ X1383 @ emptyset ) ) @ emptyset ) ) )
=> ( X1381 = X1383 ) )
=> ( ! [X1384: $i,X1385: $i,X1386: $i,X1387: $i] :
( ( ( kpair @ X1384 @ X1385 )
= ( kpair @ X1386 @ X1387 ) )
=> ( X1385 = X1387 ) )
=> ( ! [X1388: $i] :
( ( iskpair @ X1388 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1388 )
@ ^ [Z0: $i] :
( X1388
= ( kpair @ ( kfst @ X1388 ) @ Z0 ) ) ) ) )
=> ( ! [X1389: $i,X1390: $i] :
( ( ksnd @ ( kpair @ X1389 @ X1390 ) )
= X1390 )
=> ( ! [X1391: $i] :
( ( iskpair @ X1391 )
=> ( ( kpair @ ( kfst @ X1391 ) @ ( ksnd @ X1391 ) )
= X1391 ) )
=> ( ! [X1392: $i,X1393: $i,X1394: $i] :
( ( in @ X1394 @ ( cartprod @ X1392 @ X1393 ) )
=> ( in @ ( ksnd @ X1394 ) @ X1393 ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i,X1398: $i] :
( ( in @ ( kpair @ X1397 @ X1398 ) @ ( cartprod @ X1395 @ X1396 ) )
=> ( in @ X1397 @ X1395 ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i,X1402: $i] :
( ( in @ ( kpair @ X1401 @ X1402 ) @ ( cartprod @ X1399 @ X1400 ) )
=> ( in @ X1402 @ X1400 ) )
=> ( ! [X1403: $i,X1404: $i,X1405: $i] :
( ( in @ X1405 @ X1403 )
=> ! [X1406: $i] :
( ( in @ X1406 @ X1404 )
=> ( ( kpair @ X1405 @ X1406 )
= ( kpair @ X1405 @ X1406 ) ) ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i] :
( ( in @ X1409 @ X1407 )
=> ! [X1410: $i] :
( ( in @ X1410 @ X1408 )
=> ( ( kfst @ ( kpair @ X1409 @ X1410 ) )
= X1409 ) ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i] :
( ( in @ X1413 @ X1411 )
=> ! [X1414: $i] :
( ( in @ X1414 @ X1412 )
=> ( ( ksnd @ ( kpair @ X1413 @ X1414 ) )
= X1414 ) ) )
=> ( ! [X1415: $i,X1416: $i,X1417: $i] :
( ( in @ X1417 @ ( cartprod @ X1415 @ X1416 ) )
=> ( ( kpair @ ( kfst @ X1417 ) @ ( ksnd @ X1417 ) )
= X1417 ) )
=> ( ! [X1418: $i,X1419: $i,X1420: $i > $i > $o,X1421: $i] :
( ( in @ X1421 @ X1418 )
=> ! [X1422: $i] :
( ( in @ X1422 @ X1419 )
=> ( ( X1420 @ X1421 @ X1422 )
=> ( in @ ( kpair @ X1421 @ X1422 ) @ ( dpsetconstr @ X1418 @ X1419 @ X1420 ) ) ) ) )
=> ( ! [X1423: $i,X1424: $i,X1425: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1423 @ X1424 @ X1425 ) @ ( cartprod @ X1423 @ X1424 ) )
=> ( ! [X1426: $i,X1427: $i,X1428: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1426 @ X1427 @ X1428 ) @ ( cartprod @ X1426 @ X1427 ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i > $i > $o,X1432: $i] :
( ( in @ X1432 @ X1429 )
=> ! [X1433: $i] :
( ( in @ X1433 @ X1430 )
=> ( ( in @ ( kpair @ X1432 @ X1433 ) @ ( dpsetconstr @ X1429 @ X1430 @ X1431 ) )
=> ( X1431 @ X1432 @ X1433 ) ) ) )
=> ( ! [X1434: $i,X1435: $i,X1436: $i > $i > $o,X1437: $i,X1438: $i] :
( ( in @ ( kpair @ X1437 @ X1438 ) @ ( dpsetconstr @ X1434 @ X1435 @ X1436 ) )
=> ( in @ X1437 @ X1434 ) )
=> ( ! [X1439: $i,X1440: $i,X1441: $i > $i > $o,X1442: $i,X1443: $i] :
( ( in @ ( kpair @ X1442 @ X1443 ) @ ( dpsetconstr @ X1439 @ X1440 @ X1441 ) )
=> ( in @ X1443 @ X1440 ) )
=> ( ! [X1444: $i,X1445: $i,X1446: $i > $i > $o,X1447: $i,X1448: $i] :
( ( in @ ( kpair @ X1447 @ X1448 ) @ ( dpsetconstr @ X1444 @ X1445 @ X1446 ) )
=> ( X1446 @ X1447 @ X1448 ) )
=> ( ! [X1449: $i,X1450: $i,X1451: $i] :
( ( func @ X1449 @ X1450 @ X1451 )
=> ! [X1452: $i] :
( ( in @ X1452 @ X1449 )
=> ( singleton
@ ( dsetconstr @ X1450
@ ^ [Z0: $i] : ( in @ ( kpair @ X1452 @ Z0 ) @ X1451 ) ) ) ) )
=> ( ! [X1453: $i,X1454: $i,X1455: $i] :
( ( func @ X1453 @ X1454 @ X1455 )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1453 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1454
@ ^ [Z0: $i] : ( in @ ( kpair @ X1456 @ Z0 ) @ X1455 ) ) )
@ X1454 ) ) )
=> ( ! [X1457: $i,X1458: $i,X1459: $i] :
( ( func @ X1457 @ X1458 @ X1459 )
=> ! [X1460: $i] :
( ( in @ X1460 @ X1457 )
=> ( in @ ( ap @ X1457 @ X1458 @ X1459 @ X1460 ) @ X1458 ) ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i] :
( ( in @ X1463 @ ( funcSet @ X1461 @ X1462 ) )
=> ( func @ X1461 @ X1462 @ X1463 ) )
=> ( ! [X1464: $i,X1465: $i,X1466: $i] :
( ( in @ X1466 @ ( funcSet @ X1464 @ X1465 ) )
=> ! [X1467: $i] :
( ( in @ X1467 @ X1464 )
=> ( in @ ( ap @ X1464 @ X1465 @ X1466 @ X1467 ) @ X1465 ) ) )
=> ( ! [X1468: $i,X1469: $i,X1470: $i] :
( ( func @ X1468 @ X1469 @ X1470 )
=> ( in @ X1470 @ ( funcSet @ X1468 @ X1469 ) ) )
=> ( ! [X1471: $i,X1472: $i,X1473: $i > $i] :
( ! [X1474: $i] :
( ( in @ X1474 @ X1471 )
=> ( in @ ( X1473 @ X1474 ) @ X1472 ) )
=> ( func @ X1471 @ X1472
@ ( dpsetconstr @ X1471 @ X1472
@ ^ [Z0: $i] : ( $eq @ ( X1473 @ Z0 ) ) ) ) )
=> ( ! [X1475: $i,X1476: $i,X1477: $i > $i] :
( ! [X1478: $i] :
( ( in @ X1478 @ X1475 )
=> ( in @ ( X1477 @ X1478 ) @ X1476 ) )
=> ( func @ X1475 @ X1476 @ ( lam @ X1475 @ X1476 @ X1477 ) ) )
=> ( ! [X1479: $i,X1480: $i,X1481: $i > $i] :
( ! [X1482: $i] :
( ( in @ X1482 @ X1479 )
=> ( in @ ( X1481 @ X1482 ) @ X1480 ) )
=> ( in @ ( lam @ X1479 @ X1480 @ X1481 ) @ ( funcSet @ X1479 @ X1480 ) ) )
=> ( ! [X1483: $i,X1484: $i,X1485: $i] :
( ( subset @ X1485 @ ( cartprod @ X1483 @ X1484 ) )
=> ! [X1486: $i > $o] :
( ! [X1487: $i] :
( ( in @ X1487 @ X1483 )
=> ! [X1488: $i] :
( ( in @ X1488 @ X1484 )
=> ( ( in @ ( kpair @ X1487 @ X1488 ) @ X1485 )
=> ( X1486 @ ( kpair @ X1487 @ X1488 ) ) ) ) )
=> ! [X1489: $i] :
( ( in @ X1489 @ X1485 )
=> ( X1486 @ X1489 ) ) ) )
=> ( ! [X1490: $i,X1491: $i,X1492: $i] :
( ( subset @ X1492 @ ( cartprod @ X1490 @ X1491 ) )
=> ! [X1493: $i > $o] :
( ! [X1494: $i] :
( ( in @ X1494 @ X1490 )
=> ! [X1495: $i] :
( ( in @ X1495 @ X1491 )
=> ( ( in @ ( kpair @ X1494 @ X1495 ) @ X1492 )
=> ( X1493 @ ( kpair @ X1494 @ X1495 ) ) ) ) )
=> ! [X1496: $i] :
( ( in @ X1496 @ X1492 )
=> ( X1493 @ X1496 ) ) ) )
=> ( ! [X1497: $i,X1498: $i > $o] :
( ( singleton @ ( dsetconstr @ X1497 @ X1498 ) )
=> ! [X1499: $i] :
( ( in @ X1499 @ X1497 )
=> ! [X1500: $i] :
( ( in @ X1500 @ X1497 )
=> ( ( X1498 @ X1499 )
=> ( ( X1498 @ X1500 )
=> ( X1499 = X1500 ) ) ) ) ) )
=> ( ! [X1501: $i,X1502: $i,X1503: $i] :
( ( func @ X1501 @ X1502 @ X1503 )
=> ! [X1504: $i] :
( ( in @ X1504 @ X1501 )
=> ( in @ ( kpair @ X1504 @ ( ap @ X1501 @ X1502 @ X1503 @ X1504 ) ) @ X1503 ) ) )
=> ( ! [X1505: $i,X1506: $i,X1507: $i] :
( ( in @ X1507 @ ( funcSet @ X1505 @ X1506 ) )
=> ! [X1508: $i] :
( ( in @ X1508 @ X1505 )
=> ( in @ ( kpair @ X1508 @ ( ap @ X1505 @ X1506 @ X1507 @ X1508 ) ) @ X1507 ) ) )
=> ( ! [X1509: $i,X1510: $i,X1511: $i] :
( ( func @ X1509 @ X1510 @ X1511 )
=> ! [X1512: $i] :
( ( in @ X1512 @ X1509 )
=> ! [X1513: $i] :
( ( in @ X1513 @ X1510 )
=> ( ( in @ ( kpair @ X1512 @ X1513 ) @ X1511 )
=> ( ( ap @ X1509 @ X1510 @ X1511 @ X1512 )
= X1513 ) ) ) ) )
=> ( ! [X1514: $i,X1515: $i,X1516: $i] :
( ( func @ X1514 @ X1515 @ X1516 )
=> ! [X1517: $i] :
( ( func @ X1514 @ X1515 @ X1517 )
=> ( ! [X1518: $i] :
( ( in @ X1518 @ X1514 )
=> ( ( ap @ X1514 @ X1515 @ X1516 @ X1518 )
= ( ap @ X1514 @ X1515 @ X1517 @ X1518 ) ) )
=> ! [X1519: $i] :
( ( in @ X1519 @ X1514 )
=> ! [X1520: $i] :
( ( in @ X1520 @ X1515 )
=> ( ( in @ ( kpair @ X1519 @ X1520 ) @ X1517 )
=> ( in @ ( kpair @ X1519 @ X1520 ) @ X1516 ) ) ) ) ) ) )
=> ( ! [X1521: $i,X1522: $i,X1523: $i] :
( ( in @ X1523 @ ( funcSet @ X1521 @ X1522 ) )
=> ! [X1524: $i] :
( ( in @ X1524 @ X1521 )
=> ! [X1525: $i] :
( ( in @ X1525 @ X1522 )
=> ( ( in @ ( kpair @ X1524 @ X1525 ) @ X1523 )
=> ( ( ap @ X1521 @ X1522 @ X1523 @ X1524 )
= X1525 ) ) ) ) )
=> ( ! [X1526: $i,X1527: $i,X1528: $i] :
( ( subset @ X1528 @ ( cartprod @ X1526 @ X1527 ) )
=> ! [X1529: $i] :
( ( subset @ X1529 @ ( cartprod @ X1526 @ X1527 ) )
=> ( ! [X1530: $i] :
( ( in @ X1530 @ X1526 )
=> ! [X1531: $i] :
( ( in @ X1531 @ X1527 )
=> ( ( in @ ( kpair @ X1530 @ X1531 ) @ X1528 )
=> ( in @ ( kpair @ X1530 @ X1531 ) @ X1529 ) ) ) )
=> ( subset @ X1528 @ X1529 ) ) ) )
=> ( ! [X1532: $i,X1533: $i,X1534: $i] :
( ( subset @ X1534 @ ( cartprod @ X1532 @ X1533 ) )
=> ! [X1535: $i] :
( ( subset @ X1535 @ ( cartprod @ X1532 @ X1533 ) )
=> ( ! [X1536: $i] :
( ( in @ X1536 @ X1532 )
=> ! [X1537: $i] :
( ( in @ X1537 @ X1533 )
=> ( ( in @ ( kpair @ X1536 @ X1537 ) @ X1534 )
=> ( in @ ( kpair @ X1536 @ X1537 ) @ X1535 ) ) ) )
=> ( ! [X1538: $i] :
( ( in @ X1538 @ X1532 )
=> ! [X1539: $i] :
( ( in @ X1539 @ X1533 )
=> ( ( in @ ( kpair @ X1538 @ X1539 ) @ X1535 )
=> ( in @ ( kpair @ X1538 @ X1539 ) @ X1534 ) ) ) )
=> ( X1534 = X1535 ) ) ) ) )
=> ( ! [X1540: $i,X1541: $i,X1542: $i] :
( ( func @ X1540 @ X1541 @ X1542 )
=> ! [X1543: $i] :
( ( func @ X1540 @ X1541 @ X1543 )
=> ( ! [X1544: $i] :
( ( in @ X1544 @ X1540 )
=> ( ( ap @ X1540 @ X1541 @ X1542 @ X1544 )
= ( ap @ X1540 @ X1541 @ X1543 @ X1544 ) ) )
=> ( X1542 = X1543 ) ) ) )
=> ( ! [X1545: $i,X1546: $i,X1547: $i] :
( ( in @ X1547 @ ( funcSet @ X1545 @ X1546 ) )
=> ! [X1548: $i] :
( ( in @ X1548 @ ( funcSet @ X1545 @ X1546 ) )
=> ( ! [X1549: $i] :
( ( in @ X1549 @ X1545 )
=> ( ( ap @ X1545 @ X1546 @ X1547 @ X1549 )
= ( ap @ X1545 @ X1546 @ X1548 @ X1549 ) ) )
=> ( X1547 = X1548 ) ) ) )
=> ( ! [X1550: $i,X1551: $i,X1552: $i] :
( ( in @ X1552 @ ( funcSet @ X1550 @ X1551 ) )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1550 )
=> ( ( ap @ X1550 @ X1551 @ X1552 @ X1553 )
= ( ap @ X1550 @ X1551 @ X1552 @ X1553 ) ) ) )
=> ( ! [X1554: $i,X1555: $i,X1556: $i] :
( ( func @ X1554 @ X1555 @ X1556 )
=> ! [X1557: $i] :
( ( in @ X1557 @ X1554 )
=> ( ( ap @ X1554 @ X1555 @ X1556 @ X1557 )
= ( ap @ X1554 @ X1555 @ X1556 @ X1557 ) ) ) )
=> ( ! [X1558: $i,X1559: $i,X1560: $i > $i] :
( ! [X1561: $i] :
( ( in @ X1561 @ X1558 )
=> ( in @ ( X1560 @ X1561 ) @ X1559 ) )
=> ! [X1562: $i] :
( ( in @ X1562 @ X1558 )
=> ( ( ap @ X1558 @ X1559 @ ( lam @ X1558 @ X1559 @ X1560 ) @ X1562 )
= ( X1560 @ X1562 ) ) ) )
=> ( ! [X1563: $i,X1564: $i,X1565: $i] :
( ( func @ X1563 @ X1564 @ X1565 )
=> ( ( lam @ X1563 @ X1564 @ ( ap @ X1563 @ X1564 @ X1565 ) )
= X1565 ) )
=> ( ! [X1566: $i,X1567: $i,X1568: $i > $i] :
( ! [X1569: $i] :
( ( in @ X1569 @ X1566 )
=> ( in @ ( X1568 @ X1569 ) @ X1567 ) )
=> ( ( lam @ X1566 @ X1567 @ X1568 )
= ( lam @ X1566 @ X1567 @ X1568 ) ) )
=> ( ! [X1570: $i,X1571: $i,X1572: $i > $i] :
( ! [X1573: $i] :
( ( in @ X1573 @ X1570 )
=> ( in @ ( X1572 @ X1573 ) @ X1571 ) )
=> ! [X1574: $i] :
( ( in @ X1574 @ X1570 )
=> ( ( ap @ X1570 @ X1571 @ ( lam @ X1570 @ X1571 @ X1572 ) @ X1574 )
= ( X1572 @ X1574 ) ) ) )
=> ( ! [X1575: $i,X1576: $i,X1577: $i] :
( ( in @ X1577 @ ( funcSet @ X1575 @ X1576 ) )
=> ( ( lam @ X1575 @ X1576 @ ( ap @ X1575 @ X1576 @ X1577 ) )
= X1577 ) )
=> ( ! [X1578: $i,X1579: $o,X1580: $i] :
( ( in @ X1580 @ X1578 )
=> ! [X1581: $i] :
( ( in @ X1581 @ X1578 )
=> ( ~ X1579
=> ( in @ X1581
@ ( dsetconstr @ X1578
@ ^ [Z0: $i] :
( ( X1579
& ( Z0 = X1580 ) )
| ( ~ X1579
& ( Z0 = X1581 ) ) ) ) ) ) ) )
=> ( ! [X1582: $i,X1583: $o,X1584: $i] :
( ( in @ X1584 @ X1582 )
=> ! [X1585: $i] :
( ( in @ X1585 @ X1582 )
=> ( ~ X1583
=> ( ( dsetconstr @ X1582
@ ^ [Z0: $i] :
( ( X1583
& ( Z0 = X1584 ) )
| ( ~ X1583
& ( Z0 = X1585 ) ) ) )
= ( setadjoin @ X1585 @ emptyset ) ) ) ) )
=> ( ! [X1586: $i,X1587: $o,X1588: $i] :
( ( in @ X1588 @ X1586 )
=> ! [X1589: $i] :
( ( in @ X1589 @ X1586 )
=> ( X1587
=> ( in @ X1588
@ ( dsetconstr @ X1586
@ ^ [Z0: $i] :
( ( X1587
& ( Z0 = X1588 ) )
| ( ~ X1587
& ( Z0 = X1589 ) ) ) ) ) ) ) )
=> ( ! [X1590: $i,X1591: $o,X1592: $i] :
( ( in @ X1592 @ X1590 )
=> ! [X1593: $i] :
( ( in @ X1593 @ X1590 )
=> ( X1591
=> ( ( dsetconstr @ X1590
@ ^ [Z0: $i] :
( ( X1591
& ( Z0 = X1592 ) )
| ( ~ X1591
& ( Z0 = X1593 ) ) ) )
= ( setadjoin @ X1592 @ emptyset ) ) ) ) )
=> ( ! [X1594: $i,X1595: $o,X1596: $i] :
( ( in @ X1596 @ X1594 )
=> ! [X1597: $i] :
( ( in @ X1597 @ X1594 )
=> ( singleton
@ ( dsetconstr @ X1594
@ ^ [Z0: $i] :
( ( X1595
& ( Z0 = X1596 ) )
| ( ~ X1595
& ( Z0 = X1597 ) ) ) ) ) ) )
=> ( ! [X1598: $i,X1599: $o,X1600: $i] :
( ( in @ X1600 @ X1598 )
=> ! [X1601: $i] :
( ( in @ X1601 @ X1598 )
=> ( in @ ( if @ X1598 @ X1599 @ X1600 @ X1601 ) @ X1598 ) ) )
=> ( ! [X1602: $i] :
( ( singleton @ X1602 )
=> ! [X1603: $i] :
( ( in @ X1603 @ X1602 )
=> ( ( setunion @ X1602 )
= X1603 ) ) )
=> ( ! [X1604: $i,X1605: $o,X1606: $i] :
( ( in @ X1606 @ X1604 )
=> ! [X1607: $i] :
( ( in @ X1607 @ X1604 )
=> ( X1605
=> ( ( if @ X1604 @ X1605 @ X1606 @ X1607 )
= X1606 ) ) ) )
=> ( ! [X1608: $i,X1609: $o,X1610: $i] :
( ( in @ X1610 @ X1608 )
=> ! [X1611: $i] :
( ( in @ X1611 @ X1608 )
=> ( ~ X1609
=> ( ( if @ X1608 @ X1609 @ X1610 @ X1611 )
= X1611 ) ) ) )
=> ( ! [X1612: $i,X1613: $o,X1614: $i] :
( ( in @ X1614 @ X1612 )
=> ! [X1615: $i] :
( ( in @ X1615 @ X1612 )
=> ( in @ ( if @ X1612 @ X1613 @ X1614 @ X1615 ) @ ( setadjoin @ X1614 @ ( setadjoin @ X1615 @ emptyset ) ) ) ) )
=> ( ! [X1616: $i,X1617: $i] :
( ( in @ X1617 @ ( powerset @ X1616 ) )
=> ! [X1618: $i] :
( ( in @ X1618 @ ( powerset @ X1616 ) )
=> ( in @ ( binintersect @ X1617 @ X1618 ) @ ( powerset @ X1616 ) ) ) )
=> ( ! [X1619: $i,X1620: $i] :
( ( in @ X1620 @ ( powerset @ X1619 ) )
=> ! [X1621: $i] :
( ( in @ X1621 @ ( powerset @ X1619 ) )
=> ( in @ ( binunion @ X1620 @ X1621 ) @ ( powerset @ X1619 ) ) ) )
=> ( ! [X1622: $i,X1623: $i] :
( ( in @ X1623 @ ( powerset @ X1622 ) )
=> ( in @ ( powerset @ X1623 ) @ ( powerset @ ( powerset @ X1622 ) ) ) )
=> ( ! [X1624: $i,X1625: $i] :
( ( in @ X1625 @ ( powerset @ X1624 ) )
=> ! [X1626: $i] :
( ( in @ X1626 @ ( powerset @ X1624 ) )
=> ( in @ ( setminus @ X1625 @ X1626 ) @ ( powerset @ X1624 ) ) ) )
=> ( ! [X1627: $i,X1628: $i] :
( ( in @ X1628 @ ( powerset @ X1627 ) )
=> ( in @ ( setminus @ X1627 @ X1628 ) @ ( powerset @ X1627 ) ) )
=> ( ! [X1629: $i,X1630: $i] :
( ( in @ X1630 @ ( powerset @ X1629 ) )
=> ! [X1631: $i] :
( ( in @ X1631 @ ( powerset @ X1629 ) )
=> ( ! [X1632: $i] :
( ( in @ X1632 @ X1629 )
=> ( ( in @ X1632 @ X1630 )
=> ( in @ X1632 @ X1631 ) ) )
=> ( ! [X1633: $i] :
( ( in @ X1633 @ X1629 )
=> ( ( in @ X1633 @ X1631 )
=> ( in @ X1633 @ X1630 ) ) )
=> ( X1630 = X1631 ) ) ) ) )
=> ( ! [X1634: $i,X1635: $i] :
( ( in @ X1635 @ ( powerset @ X1634 ) )
=> ! [X1636: $i] :
( ( in @ X1636 @ ( powerset @ X1634 ) )
=> ( ! [X1637: $i] :
( ( in @ X1637 @ X1634 )
=> ( ( in @ X1637 @ X1635 )
=> ( in @ X1637 @ X1636 ) ) )
=> ( subset @ X1635 @ X1636 ) ) ) )
=> ( ! [X1638: $i,X1639: $i] :
( ( in @ X1639 @ ( powerset @ X1638 ) )
=> ! [X1640: $i] :
( ( in @ X1640 @ ( powerset @ X1638 ) )
=> ( ! [X1641: $i] :
( ( in @ X1641 @ X1638 )
=> ( ( in @ X1641 @ X1639 )
=> ( in @ X1641 @ X1640 ) ) )
=> ( in @ X1639 @ ( powerset @ X1640 ) ) ) ) )
=> ( ! [X1642: $i,X1643: $i] :
( ( in @ X1643 @ ( powerset @ X1642 ) )
=> ! [X1644: $i] :
( ( in @ X1644 @ ( powerset @ X1642 ) )
=> ! [X1645: $i] :
( ( in @ X1645 @ X1642 )
=> ( ( in @ X1643 @ ( powerset @ X1644 ) )
=> ( ( in @ X1645 @ X1643 )
=> ( in @ X1645 @ X1644 ) ) ) ) ) )
=> ( ! [X1646: $i,X1647: $i] :
( ( in @ X1647 @ ( powerset @ X1646 ) )
=> ! [X1648: $i] :
( ( in @ X1648 @ X1646 )
=> ( ( in @ X1648 @ X1647 )
=> ~ ( in @ X1648 @ ( setminus @ X1646 @ X1647 ) ) ) ) )
=> ( ! [X1649: $i,X1650: $i] :
( ( in @ X1650 @ ( powerset @ X1649 ) )
=> ! [X1651: $i] :
( ( in @ X1651 @ X1649 )
=> ( ~ ( in @ X1651 @ ( setminus @ X1649 @ X1650 ) )
=> ( in @ X1651 @ X1650 ) ) ) )
=> ( ! [X1652: $i,X1653: $i] :
( ( in @ X1653 @ ( powerset @ X1652 ) )
=> ! [X1654: $i] :
( ( in @ X1654 @ ( powerset @ X1652 ) )
=> ! [X1655: $i] :
( ( in @ X1655 @ X1652 )
=> ( ~ ( in @ X1655 @ X1653 )
=> ~ ( in @ X1655 @ ( binintersect @ X1653 @ X1654 ) ) ) ) ) )
=> ( ! [X1656: $i,X1657: $i] :
( ( in @ X1657 @ ( powerset @ X1656 ) )
=> ! [X1658: $i] :
( ( in @ X1658 @ ( powerset @ X1656 ) )
=> ! [X1659: $i] :
( ( in @ X1659 @ X1656 )
=> ( ~ ( in @ X1659 @ X1658 )
=> ~ ( in @ X1659 @ ( binintersect @ X1657 @ X1658 ) ) ) ) ) )
=> ( ! [X1660: $i,X1661: $i] :
( ( in @ X1661 @ ( powerset @ X1660 ) )
=> ! [X1662: $i] :
( ( in @ X1662 @ ( powerset @ X1660 ) )
=> ! [X1663: $i] :
( ( in @ X1663 @ X1660 )
=> ( ( subset @ X1661 @ ( setminus @ X1660 @ X1662 ) )
=> ( ( in @ X1663 @ X1662 )
=> ~ ( in @ X1663 @ X1661 ) ) ) ) ) )
=> ( ! [X1664: $i,X1665: $i] :
( ( in @ X1665 @ ( powerset @ X1664 ) )
=> ! [X1666: $i] :
( ( in @ X1666 @ ( powerset @ X1664 ) )
=> ! [X1667: $i] :
( ( in @ X1667 @ X1664 )
=> ( ( subset @ X1665 @ X1666 )
=> ( ~ ( in @ X1667 @ X1666 )
=> ~ ( in @ X1667 @ X1665 ) ) ) ) ) )
=> ( ! [X1668: $i,X1669: $i] :
( ( in @ X1669 @ ( powerset @ X1668 ) )
=> ! [X1670: $i] :
( ( in @ X1670 @ ( powerset @ X1668 ) )
=> ( ( subset @ X1669 @ X1670 )
=> ( subset @ ( setminus @ X1668 @ X1670 ) @ ( setminus @ X1668 @ X1669 ) ) ) ) )
=> ( ! [X1671: $i,X1672: $i] :
( ( in @ X1672 @ ( powerset @ X1671 ) )
=> ! [X1673: $i] :
( ( in @ X1673 @ ( powerset @ X1671 ) )
=> ( ( subset @ ( setminus @ X1671 @ X1673 ) @ ( setminus @ X1671 @ X1672 ) )
=> ( subset @ X1672 @ X1673 ) ) ) )
=> ( ! [X1674: $i,X1675: $i] :
( ( in @ X1675 @ ( powerset @ X1674 ) )
=> ! [X1676: $i] :
( ( in @ X1676 @ X1674 )
=> ( ( in @ X1676 @ X1675 )
=> ( in @ X1676 @ ( setminus @ X1674 @ ( setminus @ X1674 @ X1675 ) ) ) ) ) )
=> ( ! [X1677: $i,X1678: $i] :
( ( in @ X1678 @ ( powerset @ X1677 ) )
=> ! [X1679: $i] :
( ( in @ X1679 @ X1677 )
=> ( ( in @ X1679 @ ( setminus @ X1677 @ ( setminus @ X1677 @ X1678 ) ) )
=> ( in @ X1679 @ X1678 ) ) ) )
=> ( ! [X1680: $i,X1681: $i] :
( ( in @ X1681 @ ( powerset @ X1680 ) )
=> ( subset @ X1681 @ ( setminus @ X1680 @ ( setminus @ X1680 @ X1681 ) ) ) )
=> ( ! [X1682: $i,X1683: $i] :
( ( in @ X1683 @ ( powerset @ X1682 ) )
=> ( subset @ ( setminus @ X1682 @ ( setminus @ X1682 @ X1683 ) ) @ X1683 ) )
=> ( ! [X1684: $i,X1685: $i] :
( ( in @ X1685 @ ( powerset @ X1684 ) )
=> ( X1685
= ( setminus @ X1684 @ ( setminus @ X1684 @ X1685 ) ) ) )
=> ( ! [X1686: $i,X1687: $i] :
( ( in @ X1687 @ ( powerset @ X1686 ) )
=> ! [X1688: $i] :
( ( in @ X1688 @ ( powerset @ X1686 ) )
=> ! [X1689: $i] :
( ( in @ X1689 @ X1686 )
=> ( ( in @ X1689 @ ( setminus @ X1686 @ X1687 ) )
=> ~ ( in @ X1689 @ ( binintersect @ X1687 @ X1688 ) ) ) ) ) )
=> ( ! [X1690: $i,X1691: $i] :
( ( in @ X1691 @ ( powerset @ X1690 ) )
=> ! [X1692: $i] :
( ( in @ X1692 @ ( powerset @ X1690 ) )
=> ! [X1693: $i] :
( ( in @ X1693 @ X1690 )
=> ( ( in @ X1693 @ ( setminus @ X1690 @ X1691 ) )
=> ( in @ X1693 @ ( setminus @ X1690 @ ( binintersect @ X1691 @ X1692 ) ) ) ) ) ) )
=> ( ! [X1694: $i,X1695: $i] :
( ( in @ X1695 @ ( powerset @ X1694 ) )
=> ! [X1696: $i] :
( ( in @ X1696 @ ( powerset @ X1694 ) )
=> ( subset @ ( setminus @ X1694 @ X1695 ) @ ( setminus @ X1694 @ ( binintersect @ X1695 @ X1696 ) ) ) ) )
=> ( ! [X1697: $i,X1698: $i] :
( ( in @ X1698 @ ( powerset @ X1697 ) )
=> ! [X1699: $i] :
( ( in @ X1699 @ ( powerset @ X1697 ) )
=> ( in @ ( setminus @ X1697 @ X1698 ) @ ( powerset @ ( setminus @ X1697 @ ( binintersect @ X1698 @ X1699 ) ) ) ) ) )
=> ( ! [X1700: $i,X1701: $i] :
( ( in @ X1701 @ ( powerset @ X1700 ) )
=> ! [X1702: $i] :
( ( in @ X1702 @ ( powerset @ X1700 ) )
=> ( ( subset @ X1701 @ ( setminus @ X1700 @ X1702 ) )
=> ! [X1703: $i] :
( ( in @ X1703 @ X1700 )
=> ( ( in @ X1703 @ X1702 )
=> ( in @ X1703 @ ( setminus @ X1700 @ X1701 ) ) ) ) ) ) )
=> ( ! [X1704: $i,X1705: $i] :
( ( in @ X1705 @ ( powerset @ X1704 ) )
=> ! [X1706: $i] :
( ( in @ X1706 @ ( powerset @ X1704 ) )
=> ( ( subset @ X1705 @ ( setminus @ X1704 @ X1706 ) )
=> ( subset @ X1706 @ ( setminus @ X1704 @ X1705 ) ) ) ) )
=> ( ! [X1707: $i,X1708: $i] :
( ( in @ X1708 @ ( powerset @ X1707 ) )
=> ! [X1709: $i] :
( ( in @ X1709 @ ( powerset @ X1707 ) )
=> ! [X1710: $i] :
( ( in @ X1710 @ X1707 )
=> ( ~ ( in @ X1710 @ ( binunion @ X1708 @ X1709 ) )
=> ~ ( in @ X1710 @ X1708 ) ) ) ) )
=> ( ! [X1711: $i,X1712: $i] :
( ( in @ X1712 @ ( powerset @ X1711 ) )
=> ! [X1713: $i] :
( ( in @ X1713 @ ( powerset @ X1711 ) )
=> ! [X1714: $i] :
( ( in @ X1714 @ X1711 )
=> ( ~ ( in @ X1714 @ ( binunion @ X1712 @ X1713 ) )
=> ~ ( in @ X1714 @ X1713 ) ) ) ) )
=> ( ! [X1715: $i,X1716: $i] :
( ( in @ X1716 @ ( powerset @ X1715 ) )
=> ! [X1717: $i] :
( ( in @ X1717 @ ( powerset @ X1715 ) )
=> ! [X1718: $i] :
( ( in @ X1718 @ ( powerset @ X1715 ) )
=> ! [X1719: $i] :
( ( in @ X1719 @ X1715 )
=> ( ( in @ X1719 @ ( binintersect @ X1716 @ X1717 ) )
=> ( in @ X1719 @ ( binunion @ X1716 @ X1718 ) ) ) ) ) ) )
=> ( ! [X1720: $i,X1721: $i] :
( ( in @ X1721 @ ( powerset @ X1720 ) )
=> ! [X1722: $i] :
( ( in @ X1722 @ ( powerset @ X1720 ) )
=> ! [X1723: $i] :
( ( in @ X1723 @ ( powerset @ X1720 ) )
=> ! [X1724: $i] :
( ( in @ X1724 @ X1720 )
=> ( ( in @ X1724 @ ( binintersect @ X1721 @ X1722 ) )
=> ( in @ X1724 @ ( binunion @ X1722 @ X1723 ) ) ) ) ) ) )
=> ( ! [X1725: $i,X1726: $i] :
( ( in @ X1726 @ ( powerset @ X1725 ) )
=> ! [X1727: $i] :
( ( in @ X1727 @ ( powerset @ X1725 ) )
=> ! [X1728: $i] :
( ( in @ X1728 @ ( powerset @ X1725 ) )
=> ! [X1729: $i] :
( ( in @ X1729 @ X1725 )
=> ( ( in @ X1729 @ ( binintersect @ X1726 @ X1727 ) )
=> ( in @ X1729 @ ( binintersect @ ( binunion @ X1726 @ X1728 ) @ ( binunion @ X1727 @ X1728 ) ) ) ) ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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set2propI]),notdexE]),notdallE]),c_0_301]),c_0_302]),c_0_303]),inCongP]),in__Cong]),c_0_304]),c_0_305]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_306]),c_0_307]),c_0_308]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_309]),c_0_310]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_311]),c_0_312]),c_0_313]),c_0_314]),singletonsuniq]),setukpairinjL1]),c_0_315]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_316]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_317]),c_0_318]),c_0_319]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),c_0_324]),c_0_325]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_326]),c_0_327]),c_0_328]),c_0_329]),c_0_330]),c_0_331]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_332]),c_0_333]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_334]),c_0_335]),c_0_336]),c_0_337]),c_0_338]),c_0_339]),c_0_340]),c_0_341]),c_0_342]),c_0_343]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),setminusT_lem]),complementT_lem]),setextT]),subsetTI]),powersetTI1]),powersetTE1]),complementTI1]),complementTE1]),binintersectTELcontra]),binintersectTERcontra]),contrasubsetT]),contrasubsetT1]),contrasubsetT2]),contrasubsetT3]),doubleComplementI1]),doubleComplementE1]),doubleComplementSub1]),doubleComplementSub2]),doubleComplementEq]),complementTnotintersectT]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),complementInPowersetComplementIntersect]),contraSubsetComplement]),complementTcontraSubset]),binunionTILcontra]),binunionTIRcontra]),inIntersectImpInUnion]),inIntersectImpInUnion2]),inIntersectImpInIntersectUnions])])]),c_0_344]) ).
thf(c_0_346,negated_conjecture,
! 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$o,X2172: $i,X2173: $i > $o,X2174: $i,X2176: $i,X2177: $i > $o,X2180: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i,X2204: $i,X2205: $i,X2206: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2245: $i,X2246: $i,X2247: $i,X2248: $i,X2249: $i,X2250: $i,X2251: $i,X2252: $i > $i > $o,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i > $i > $o,X2258: $i,X2259: $i,X2260: $i > $i > $o,X2261: $i,X2262: $i,X2263: $i > $i > $o,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i > $i > $o,X2269: $i,X2270: $i,X2271: $i,X2272: $i,X2273: $i > $i > $o,X2274: $i,X2275: $i,X2276: $i,X2277: $i,X2278: $i > $i > $o,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2287: $i,X2288: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i,X2293: $i,X2294: $i,X2295: $i,X2296: $i,X2297: $i,X2298: $i,X2299: $i,X2300: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i > $i,X2307: $i,X2308: $i,X2309: $i > $i,X2311: $i,X2312: $i,X2313: $i > $i,X2315: $i,X2316: $i,X2317: $i,X2318: $i > $o,X2321: $i,X2322: $i,X2323: $i,X2324: $i,X2325: $i > $o,X2328: $i,X2329: $i,X2330: $i > $o,X2331: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $i,X2338: $i,X2339: $i,X2340: $i,X2341: $i,X2342: $i,X2343: $i,X2344: $i,X2345: $i,X2346: $i,X2347: $i,X2348: $i,X2349: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2388: $i,X2389: $i,X2390: $i,X2391: $i,X2392: $i > $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i > $i,X2402: $i,X2403: $i,X2404: $i > $i,X2406: $i,X2407: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $o,X2412: $i,X2413: $i,X2414: $i,X2415: $o,X2416: $i,X2417: $i,X2418: $i,X2419: $o,X2420: $i,X2421: $i,X2422: $i,X2423: $o,X2424: $i,X2425: $i,X2426: $i,X2427: $o,X2428: $i,X2429: $i,X2430: $i,X2431: $o,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2436: $i,X2437: $o,X2438: $i,X2439: $i,X2440: $i,X2441: $o,X2442: $i,X2443: $i,X2444: $i,X2445: $o,X2446: $i,X2447: $i,X2448: $i,X2449: $i,X2450: $i,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i,X2456: $i,X2457: $i,X2458: $i,X2459: $i,X2460: $i,X2461: $i,X2462: $i,X2463: $i,X2466: $i,X2467: $i,X2468: $i,X2470: $i,X2471: $i,X2472: $i,X2474: $i,X2475: $i,X2476: $i,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2490: $i,X2491: $i,X2492: $i,X2493: $i,X2494: $i,X2495: $i,X2496: $i,X2497: $i,X2498: $i,X2499: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i,X2517: $i,X2518: $i,X2519: $i,X2520: $i,X2521: $i,X2522: $i,X2523: $i,X2524: $i,X2525: $i,X2526: $i,X2527: $i,X2528: $i,X2529: $i,X2530: $i,X2531: $i,X2532: $i,X2533: $i,X2534: $i,X2535: $i,X2536: $i,X2537: $i,X2538: $i,X2539: $i,X2540: $i,X2541: $i,X2542: $i,X2543: $i,X2544: $i,X2545: $i,X2546: $i,X2547: $i,X2548: $i,X2549: $i,X2550: $i,X2551: $i,X2552: $i,X2553: $i,X2554: $i,X2555: $i,X2556: $i,X2557: $i,X2558: $i,X2559: $i,X2560: $i,X2561: $i] :
( ( ~ ( in @ ( esk1_2 @ X1730 @ X1731 ) @ X1730 )
| ~ ( in @ ( esk1_2 @ X1730 @ X1731 ) @ X1731 )
| ( X1730 = X1731 ) )
& ( ( in @ ( esk1_2 @ X1730 @ X1731 ) @ X1730 )
| ( in @ ( esk1_2 @ X1730 @ X1731 ) @ X1731 )
| ( X1730 = X1731 ) )
& ~ ( in @ X1733 @ emptyset )
& ( ~ ( in @ X1736 @ ( setadjoin @ X1734 @ X1735 ) )
| ( X1736 = X1734 )
| ( in @ X1736 @ X1735 ) )
& ( ( X1736 != X1734 )
| ( in @ X1736 @ ( setadjoin @ X1734 @ X1735 ) ) )
& ( ~ ( in @ X1736 @ X1735 )
| ( in @ X1736 @ ( setadjoin @ X1734 @ X1735 ) ) )
& ( ~ ( in @ X1738 @ ( powerset @ X1737 ) )
| ~ ( in @ X1739 @ X1738 )
| ( in @ X1739 @ X1737 ) )
& ( ( in @ ( esk2_2 @ X1740 @ X1741 ) @ X1741 )
| ( in @ X1741 @ ( powerset @ X1740 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1740 @ X1741 ) @ X1740 )
| ( in @ X1741 @ ( powerset @ X1740 ) ) )
& ( ( in @ X1744 @ ( esk3_2 @ X1743 @ X1744 ) )
| ~ ( in @ X1744 @ ( setunion @ X1743 ) ) )
& ( ( in @ ( esk3_2 @ X1743 @ X1744 ) @ X1743 )
| ~ ( in @ X1744 @ ( setunion @ X1743 ) ) )
& ( ~ ( in @ X1747 @ X1748 )
| ~ ( in @ X1748 @ X1746 )
| ( in @ X1747 @ ( setunion @ X1746 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1749 @ omega )
| ( in @ ( setadjoin @ X1749 @ X1749 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1750 ) @ omega )
| ~ ( in @ emptyset @ X1750 )
| ~ ( in @ X1752 @ omega )
| ( in @ X1752 @ X1750 ) )
& ( ( in @ ( esk4_1 @ X1750 ) @ X1750 )
| ~ ( in @ emptyset @ X1750 )
| ~ ( in @ X1752 @ omega )
| ( in @ X1752 @ X1750 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1750 ) @ ( esk4_1 @ X1750 ) ) @ X1750 )
| ~ ( in @ emptyset @ X1750 )
| ~ ( in @ X1752 @ omega )
| ( in @ X1752 @ X1750 ) )
& ( ( in @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1754 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( in @ ( esk5_2 @ X1753 @ X1754 ) @ X1754 ) )
& ( ( X1753 @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1759 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( in @ ( esk5_2 @ X1753 @ X1754 ) @ X1754 ) )
& ( ~ ( in @ X1762 @ X1754 )
| ~ ( X1753 @ X1762 @ X1761 )
| ( in @ X1761 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( in @ ( esk5_2 @ X1753 @ X1754 ) @ X1754 ) )
& ( ( in @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1754 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ( X1753 @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1759 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ~ ( in @ X1762 @ X1754 )
| ~ ( X1753 @ X1762 @ X1761 )
| ( in @ X1761 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ( in @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1754 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1756
!= ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ( X1753 @ ( esk8_3 @ X1753 @ X1754 @ X1759 ) @ X1759 )
| ~ ( in @ X1759 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1756
!= ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ~ ( in @ X1762 @ X1754 )
| ~ ( X1753 @ X1762 @ X1761 )
| ( in @ X1761 @ ( esk7_2 @ X1753 @ X1754 ) )
| ( X1756
!= ( esk6_3 @ X1753 @ X1754 @ X1756 ) )
| ~ ( X1753 @ ( esk5_2 @ X1753 @ X1754 ) @ X1756 ) )
& ( ( in @ ( esk9_1 @ X1763 ) @ X1763 )
| ~ ( in @ X1764 @ X1763 ) )
& ( ~ ( in @ X1766 @ ( esk9_1 @ X1763 ) )
| ~ ( in @ X1766 @ X1763 )
| ~ ( in @ X1764 @ X1763 ) )
& epred1_0
& ( ( X1767 @ ( esk10_2 @ X1767 @ X1768 ) )
| ~ ( X1767 @ X1768 )
| ( X1767 @ ( descr @ X1767 ) ) )
& ( ( X1768
!= ( esk10_2 @ X1767 @ X1768 ) )
| ~ ( X1767 @ X1768 )
| ( X1767 @ ( descr @ X1767 ) ) )
& ( ~ ( in @ X1772 @ X1770 )
| ~ ( X1771 @ X1772 )
| ( in @ X1772 @ ( dsetconstr @ X1770 @ X1771 ) ) )
& ( ~ ( in @ X1775 @ ( dsetconstr @ X1773 @ X1774 ) )
| ( in @ X1775 @ X1773 ) )
& ( ~ ( in @ X1778 @ ( dsetconstr @ X1776 @ X1777 ) )
| ( X1777 @ X1778 ) )
& ( ( X1779 @ ( esk12_1 @ X1779 ) )
| ( X1779 @ ( esk11_2 @ X1779 @ X1780 ) )
| ~ ( X1779 @ X1780 ) )
& ( ~ ( X1779 @ X1783 )
| ( ( esk12_1 @ X1779 )
= X1783 )
| ( X1779 @ ( esk11_2 @ X1779 @ X1780 ) )
| ~ ( X1779 @ X1780 ) )
& ( ( X1779 @ ( esk12_1 @ X1779 ) )
| ( X1780
!= ( esk11_2 @ X1779 @ X1780 ) )
| ~ ( X1779 @ X1780 ) )
& ( ~ ( X1779 @ X1783 )
| ( ( esk12_1 @ X1779 )
= X1783 )
| ( X1780
!= ( esk11_2 @ X1779 @ X1780 ) )
| ~ ( X1779 @ X1780 ) )
& ( ~ ( in @ X1785 @ ( prop2set @ X1784 ) )
| X1784 )
& ( ~ ( in @ X1786 @ emptyset )
| X1787 )
& ( ~ ( in @ X1788 @ emptyset )
| ~ $true )
& ~ ( in @ X1789 @ emptyset )
& ( ( X1790 @ ( esk13_2 @ X1790 @ X1791 ) )
| ~ ( X1790 @ X1791 )
| ( X1790 @ ( esk14_1 @ X1790 ) ) )
& ( ( X1791
!= ( esk13_2 @ X1790 @ X1791 ) )
| ~ ( X1790 @ X1791 )
| ( X1790 @ ( esk14_1 @ X1790 ) ) )
& ( ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1795 )
| ( X1794 = X1795 )
| ( in @ ( esk15_2 @ X1794 @ X1795 ) @ X1794 ) )
& ( ~ ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1794 )
| ( X1794 = X1795 )
| ( in @ ( esk15_2 @ X1794 @ X1795 ) @ X1794 ) )
& ( ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1795 )
| ( X1794 = X1795 )
| ~ ( in @ ( esk15_2 @ X1794 @ X1795 ) @ X1795 ) )
& ( ~ ( in @ ( esk16_2 @ X1794 @ X1795 ) @ X1794 )
| ( X1794 = X1795 )
| ~ ( in @ ( esk15_2 @ X1794 @ X1795 ) @ X1795 ) )
& ( ( in @ ( esk17_1 @ X1798 ) @ X1798 )
| ( X1798 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1800 ) @ X1800 )
| ( X1800 = emptyset ) )
& ( ~ ( in @ X1804 @ ( dsetconstr @ X1802 @ X1803 ) )
| ( X1803 @ X1804 )
| ~ ( in @ X1804 @ X1802 ) )
& ( ~ ( X1803 @ X1804 )
| ( in @ X1804 @ ( dsetconstr @ X1802 @ X1803 ) )
| ~ ( in @ X1804 @ X1802 ) )
& ( ( X1805 = emptyset )
| ( in @ ( esk19_1 @ X1805 ) @ X1805 ) )
& ( ~ ( in @ X1809 @ X1807 )
| ~ ( X1808 @ X1809 )
| ( ( dsetconstr @ X1807 @ X1808 )
!= emptyset ) )
& ( ~ ( in @ X1811 @ X1810 )
| ( X1810 != emptyset ) )
& ( in @ X1812 @ ( setadjoin @ X1812 @ X1813 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1816 @ X1815 )
| ( in @ X1816 @ ( setadjoin @ X1814 @ X1815 ) ) )
& ( ( in @ X1819 @ X1818 )
| X1820
| ( X1819 = X1817 )
| ~ ( in @ X1819 @ ( setadjoin @ X1817 @ X1818 ) ) )
& ( ~ X1820
| X1820
| ( X1819 = X1817 )
| ~ ( in @ X1819 @ ( setadjoin @ X1817 @ X1818 ) ) )
& ( ( in @ X1819 @ X1818 )
| X1820
| ~ X1820
| ~ ( in @ X1819 @ ( setadjoin @ X1817 @ X1818 ) ) )
& ( ~ X1820
| X1820
| ~ X1820
| ~ ( in @ X1819 @ ( setadjoin @ X1817 @ X1818 ) ) )
& ( ~ ( in @ X1823 @ ( setadjoin @ X1821 @ X1822 ) )
| ( X1823 = X1821 )
| ( in @ X1823 @ X1822 ) )
& ( ( dsetconstr @ X1824
@ ^ [Z0: $i] : $true )
= X1824 )
& ( ( in @ ( esk20_2 @ X1825 @ X1826 ) @ X1826 )
| ( in @ X1826 @ ( powerset @ X1825 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1825 @ X1826 ) @ X1825 )
| ( in @ X1826 @ ( powerset @ X1825 ) ) )
& ( in @ emptyset @ ( powerset @ X1828 ) )
& ( in @ emptyset @ ( powerset @ X1829 ) )
& ( ~ ( in @ X1831 @ ( powerset @ X1830 ) )
| ~ ( in @ X1832 @ X1831 )
| ( in @ X1832 @ X1830 ) )
& ( ~ ( in @ X1834 @ X1835 )
| ~ ( in @ X1835 @ X1833 )
| ( in @ X1834 @ ( setunion @ X1833 ) ) )
& ( ( in @ X1837 @ ( esk21_3 @ X1836 @ X1837 @ X1838 ) )
| X1838
| ~ ( in @ X1837 @ ( setunion @ X1836 ) ) )
& ( ( in @ ( esk21_3 @ X1836 @ X1837 @ X1838 ) @ X1836 )
| X1838
| ~ ( in @ X1837 @ ( setunion @ X1836 ) ) )
& ( ~ X1838
| X1838
| ~ ( in @ X1837 @ ( setunion @ X1836 ) ) )
& ( ~ ( in @ X1841 @ X1840 )
| ( in @ X1841 @ ( powerset @ ( setunion @ X1840 ) ) ) )
& ( ~ ( X1842 @ X1846 )
| ( X1846
= ( esk23_1 @ X1842 ) )
| ( X1842 @ ( esk22_2 @ X1842 @ X1843 ) )
| ~ ( X1842 @ X1843 ) )
& ( ( X1847
!= ( esk23_1 @ X1842 ) )
| ( X1842 @ X1847 )
| ( X1842 @ ( esk22_2 @ X1842 @ X1843 ) )
| ~ ( X1842 @ X1843 ) )
& ( ~ ( X1842 @ X1846 )
| ( X1846
= ( esk23_1 @ X1842 ) )
| ( X1843
!= ( esk22_2 @ X1842 @ X1843 ) )
| ~ ( X1842 @ X1843 ) )
& ( ( X1847
!= ( esk23_1 @ X1842 ) )
| ( X1842 @ X1847 )
| ( X1843
!= ( esk22_2 @ X1842 @ X1843 ) )
| ~ ( X1842 @ X1843 ) )
& ( ( in @ ( esk24_1 @ X1848 ) @ X1848 )
| ( X1848 = emptyset ) )
& ( $true
| ( X1848 = emptyset ) )
& ( ~ ( in @ X1850 @ ( setadjoin @ X1851 @ emptyset ) )
| ( X1850 = X1851 ) )
& ( ( X1852 = X1853 )
| ~ ( in @ X1853 @ ( setadjoin @ X1852 @ emptyset ) ) )
& ( ( X1854 != X1855 )
| ( in @ X1854 @ ( setadjoin @ X1855 @ emptyset ) ) )
& ( ~ ( in @ X1856 @ ( setadjoin @ X1857 @ emptyset ) )
| ( in @ X1857 @ ( setadjoin @ X1856 @ emptyset ) ) )
& ( ~ ( in @ X1860 @ ( setadjoin @ X1858 @ ( setadjoin @ X1859 @ emptyset ) ) )
| ( X1860 = X1858 )
| ( X1860 = X1859 ) )
& ( in @ X1861 @ ( setadjoin @ X1861 @ ( setadjoin @ X1862 @ emptyset ) ) )
& ( in @ X1864 @ ( setadjoin @ X1863 @ ( setadjoin @ X1864 @ emptyset ) ) )
& ( ~ ( in @ X1867 @ X1865 )
| ~ ( X1866 @ X1867 )
| ( ( dsetconstr @ X1865 @ X1866 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1869 @ emptyset )
| ( X1868 @ X1869 ) )
& ( ( in @ ( esk25_2 @ X1870 @ X1871 ) @ X1870 )
| ~ ( in @ X1872 @ X1870 )
| ( X1871 @ X1872 ) )
& ( ~ ( X1871 @ ( esk25_2 @ X1870 @ X1871 ) )
| ~ ( in @ X1872 @ X1870 )
| ( X1871 @ X1872 ) )
& ( ( in @ ( esk26_2 @ X1874 @ X1875 ) @ X1874 )
| ~ ( in @ X1877 @ X1874 )
| ~ ( X1875 @ X1877 ) )
& ( ( X1875 @ ( esk26_2 @ X1874 @ X1875 ) )
| ~ ( in @ X1877 @ X1874 )
| ~ ( X1875 @ X1877 ) )
& ( ( in @ ( esk27_2 @ X1878 @ X1879 ) @ X1878 )
| ~ ( in @ X1881 @ X1878 )
| ~ ( X1879 @ X1881 ) )
& ( ( X1879 @ ( esk27_2 @ X1878 @ X1879 ) )
| ~ ( in @ X1881 @ X1878 )
| ~ ( X1879 @ X1881 ) )
& ( ( in @ ( esk28_2 @ X1882 @ X1883 ) @ X1882 )
| ~ ( in @ X1884 @ X1882 )
| ( X1883 @ X1884 ) )
& ( ~ ( X1883 @ ( esk28_2 @ X1882 @ X1883 ) )
| ~ ( in @ X1884 @ X1882 )
| ( X1883 @ X1884 ) )
& ( ~ X1886
| ( in @ emptyset @ ( prop2set @ X1886 ) ) )
& ( ~ X1887
| ( set2prop @ ( prop2set @ X1887 ) ) )
& ( ( in @ ( esk29_2 @ X1888 @ X1889 ) @ X1888 )
| ~ ( in @ X1891 @ X1888 )
| ~ ( X1889 @ X1891 ) )
& ( ( X1889 @ ( esk29_2 @ X1888 @ X1889 ) )
| ~ ( in @ X1891 @ X1888 )
| ~ ( X1889 @ X1891 ) )
& ( ( in @ ( esk30_2 @ X1892 @ X1893 ) @ X1892 )
| ~ ( in @ X1894 @ X1892 )
| ( X1893 @ X1894 ) )
& ( ~ ( X1893 @ ( esk30_2 @ X1892 @ X1893 ) )
| ~ ( in @ X1894 @ X1892 )
| ( X1893 @ X1894 ) )
& ( ( X1896 @ ( esk32_1 @ X1896 ) )
| ( X1896 @ ( esk31_2 @ X1896 @ X1897 ) )
| ~ ( X1896 @ X1897 ) )
& ( ~ ( X1896 @ X1900 )
| ( ( esk32_1 @ X1896 )
= X1900 )
| ( X1896 @ ( esk31_2 @ X1896 @ X1897 ) )
| ~ ( X1896 @ X1897 ) )
& ( ( X1896 @ ( esk32_1 @ X1896 ) )
| ( X1897
!= ( esk31_2 @ X1896 @ X1897 ) )
| ~ ( X1896 @ X1897 ) )
& ( ~ ( X1896 @ X1900 )
| ( ( esk32_1 @ X1896 )
= X1900 )
| ( X1897
!= ( esk31_2 @ X1896 @ X1897 ) )
| ~ ( X1896 @ X1897 ) )
& ( ( X1901 @ ( esk35_1 @ X1901 ) )
| ( X1901 @ ( esk33_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ~ ( X1901 @ X1906 )
| ( ( esk35_1 @ X1901 )
= X1906 )
| ( X1901 @ ( esk33_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ( X1901 @ ( esk35_1 @ X1901 ) )
| ( X1901 @ ( esk34_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ~ ( X1901 @ X1906 )
| ( ( esk35_1 @ X1901 )
= X1906 )
| ( X1901 @ ( esk34_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ( X1901 @ ( esk35_1 @ X1901 ) )
| ( ( esk33_1 @ X1901 )
!= ( esk34_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ~ ( X1901 @ X1906 )
| ( ( esk35_1 @ X1901 )
= X1906 )
| ( ( esk33_1 @ X1901 )
!= ( esk34_1 @ X1901 ) )
| ~ ( X1901 @ X1902 ) )
& ( ( X1907 @ ( esk37_1 @ X1907 ) )
| ~ ( X1907 @ ( esk36_2 @ X1907 @ X1908 ) )
| ( ( esk36_2 @ X1907 @ X1908 )
!= X1908 ) )
& ( ~ ( X1907 @ X1911 )
| ( ( esk37_1 @ X1907 )
= X1911 )
| ~ ( X1907 @ ( esk36_2 @ X1907 @ X1908 ) )
| ( ( esk36_2 @ X1907 @ X1908 )
!= X1908 ) )
& ( ( X1907 @ ( esk37_1 @ X1907 ) )
| ( X1907 @ ( esk36_2 @ X1907 @ X1908 ) )
| ( ( esk36_2 @ X1907 @ X1908 )
= X1908 ) )
& ( ~ ( X1907 @ X1911 )
| ( ( esk37_1 @ X1907 )
= X1911 )
| ( X1907 @ ( esk36_2 @ X1907 @ X1908 ) )
| ( ( esk36_2 @ X1907 @ X1908 )
= X1908 ) )
& ( ( X1912 != X1913 )
| ( X1914 != X1915 )
| ~ ( in @ X1914 @ X1912 )
| ( in @ X1915 @ X1913 ) )
& ( ~ ( in @ X1918 @ X1916 )
| ( in @ X1919 @ X1917 )
| ( X1918 != X1919 )
| ( X1916 != X1917 ) )
& ( ~ ( in @ X1919 @ X1917 )
| ( in @ X1918 @ X1916 )
| ( X1918 != X1919 )
| ( X1916 != X1917 ) )
& ( ( X1920 @ ( esk38_2 @ X1920 @ X1921 ) )
| ~ ( X1920 @ X1921 )
| ~ ( X1920 @ X1923 )
| ~ ( X1920 @ X1924 )
| ( X1923 = X1924 ) )
& ( ( X1921
!= ( esk38_2 @ X1920 @ X1921 ) )
| ~ ( X1920 @ X1921 )
| ~ ( X1920 @ X1923 )
| ~ ( X1920 @ X1924 )
| ( X1923 = X1924 ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( ( esk39_2 @ X1925 @ X1926 )
= ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ~ ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ~ ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1925 @ ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1926 @ ( esk42_2 @ X1925 @ X1926 ) )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1926 @ X1932 )
| ( ( esk42_2 @ X1925 @ X1926 )
= X1932 )
| ( X1929
!= ( esk41_3 @ X1925 @ X1926 @ X1929 ) )
| ~ ( X1925 @ X1929 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1926 @ ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ( X1925 @ ( esk44_2 @ X1925 @ X1926 ) )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( ~ ( X1925 @ X1936 )
| ( ( esk44_2 @ X1925 @ X1926 )
= X1936 )
| ( X1933
!= ( esk43_3 @ X1925 @ X1926 @ X1933 ) )
| ~ ( X1926 @ X1933 )
| ( X1925 @ ( esk39_2 @ X1925 @ X1926 ) )
| ( X1926 @ ( esk40_2 @ X1925 @ X1926 ) ) )
& ( emptyset = emptyset )
& ( ( X1937 != X1938 )
| ( X1939 != X1940 )
| ( ( setadjoin @ X1937 @ X1939 )
= ( setadjoin @ X1938 @ X1940 ) ) )
& ( ( X1941 != X1942 )
| ( ( powerset @ X1941 )
= ( powerset @ X1942 ) ) )
& ( ( X1943 != X1944 )
| ( ( setunion @ X1943 )
= ( setunion @ X1944 ) ) )
& ( omega = omega )
& ( ( X1945 @ ( esk45_2 @ X1945 @ X1946 ) )
| ~ ( X1945 @ X1946 )
| ~ ( X1945 @ X1948 )
| ~ ( X1945 @ X1949 )
| ( X1948 = X1949 ) )
& ( ( X1946
!= ( esk45_2 @ X1945 @ X1946 ) )
| ~ ( X1945 @ X1946 )
| ~ ( X1945 @ X1948 )
| ~ ( X1945 @ X1949 )
| ( X1948 = X1949 ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( ( esk46_2 @ X1950 @ X1951 )
= ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( ( esk46_2 @ X1950 @ X1951 )
= ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( ( esk46_2 @ X1950 @ X1951 )
= ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( ( esk46_2 @ X1950 @ X1951 )
= ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ~ ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ~ ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ~ ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ~ ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ~ ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ~ ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ~ ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ~ ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1950 @ ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1951 @ ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( X1956
!= ( esk49_3 @ X1950 @ X1951 @ X1956 ) )
| ~ ( X1951 @ X1956 )
| ( ( descr @ X1950 )
= ( descr @ X1951 ) )
| ( X1954
!= ( esk48_3 @ X1950 @ X1951 @ X1954 ) )
| ~ ( X1950 @ X1954 )
| ( X1950 @ ( esk46_2 @ X1950 @ X1951 ) )
| ( X1951 @ ( esk47_2 @ X1950 @ X1951 ) ) )
& ( ( in @ ( esk50_4 @ X1958 @ X1959 @ X1960 @ X1961 ) @ X1958 )
| ( ( dsetconstr @ X1958 @ X1960 )
= ( dsetconstr @ X1959 @ X1961 ) )
| ( X1958 != X1959 ) )
& ( ( in @ ( esk51_4 @ X1958 @ X1959 @ X1960 @ X1961 ) @ X1959 )
| ( ( dsetconstr @ X1958 @ X1960 )
= ( dsetconstr @ X1959 @ X1961 ) )
| ( X1958 != X1959 ) )
& ( ( ( esk50_4 @ X1958 @ X1959 @ X1960 @ X1961 )
= ( esk51_4 @ X1958 @ X1959 @ X1960 @ X1961 ) )
| ( ( dsetconstr @ X1958 @ X1960 )
= ( dsetconstr @ X1959 @ X1961 ) )
| ( X1958 != X1959 ) )
& ( ~ ( X1960 @ ( esk50_4 @ X1958 @ X1959 @ X1960 @ X1961 ) )
| ~ ( X1961 @ ( esk51_4 @ X1958 @ X1959 @ X1960 @ X1961 ) )
| ( ( dsetconstr @ X1958 @ X1960 )
= ( dsetconstr @ X1959 @ X1961 ) )
| ( X1958 != X1959 ) )
& ( ( X1960 @ ( esk50_4 @ X1958 @ X1959 @ X1960 @ X1961 ) )
| ( X1961 @ ( esk51_4 @ X1958 @ X1959 @ X1960 @ X1961 ) )
| ( ( dsetconstr @ X1958 @ X1960 )
= ( dsetconstr @ X1959 @ X1961 ) )
| ( X1958 != X1959 ) )
& ( ( in @ ( esk52_2 @ X1964 @ X1965 ) @ X1964 )
| ( subset @ X1964 @ X1965 ) )
& ( ~ ( in @ ( esk52_2 @ X1964 @ X1965 ) @ X1965 )
| ( subset @ X1964 @ X1965 ) )
& ( ( X1967 != X1968 )
| ( subset @ X1968 @ X1967 ) )
& ( ( X1969 != X1970 )
| ( subset @ X1969 @ X1970 ) )
& ( ( in @ ( esk53_2 @ X1971 @ X1972 ) @ X1971 )
| ( subset @ X1971 @ X1972 ) )
& ( ~ ( in @ ( esk53_2 @ X1971 @ X1972 ) @ X1972 )
| ( subset @ X1971 @ X1972 ) )
& ( subset @ emptyset @ X1974 )
& ( ~ ( subset @ X1975 @ X1976 )
| ~ ( in @ X1977 @ X1975 )
| ( in @ X1977 @ X1976 ) )
& ( ~ ( subset @ X1978 @ X1979 )
| ( in @ X1980 @ X1979 )
| ~ ( in @ X1980 @ X1978 ) )
& ( ~ ( in @ X1983 @ X1981 )
| ( in @ X1983 @ X1982 )
| ~ ( subset @ X1981 @ X1982 ) )
& ( ( subset @ X1984 @ X1985 )
| ( X1984 != X1985 ) )
& ( ~ ( in @ X1988 @ X1986 )
| ( in @ X1988 @ X1987 )
| ( X1986 != X1987 ) )
& ( subset @ X1989 @ X1989 )
& ( ~ ( subset @ X1990 @ X1991 )
| ~ ( subset @ X1991 @ X1992 )
| ( subset @ X1990 @ X1992 ) )
& ( subset @ X1994 @ ( setadjoin @ X1993 @ X1994 ) )
& ( ~ ( subset @ X1995 @ X1997 )
| ( subset @ X1995 @ ( setadjoin @ X1996 @ X1997 ) ) )
& ( ~ ( subset @ X1998 @ X1999 )
| ( in @ X1998 @ ( powerset @ X1999 ) ) )
& ( ~ ( subset @ X2000 @ X2001 )
| ~ ( subset @ X2001 @ X2000 )
| ( X2000 = X2001 ) )
& ( ~ ( subset @ X2002 @ emptyset )
| ( X2002 = emptyset ) )
& ( ~ ( subset @ X2004 @ X2003 )
| ( in @ X2004 @ ( powerset @ X2003 ) ) )
& ( ~ ( in @ X2006 @ ( powerset @ X2005 ) )
| ( subset @ X2006 @ X2005 ) )
& ( in @ X2007 @ ( powerset @ X2007 ) )
& ( ~ ( subset @ X2008 @ X2009 )
| ( subset @ ( powerset @ X2008 ) @ ( powerset @ X2009 ) ) )
& ( in @ ( dsetconstr @ X2010 @ X2011 ) @ ( powerset @ X2010 ) )
& ( subset @ ( dsetconstr @ X2012 @ X2013 ) @ X2012 )
& ( ~ ( in @ X2016 @ X2014 )
| ( in @ X2016 @ ( binunion @ X2014 @ X2015 ) ) )
& ( in @ X2018 @ ( setadjoin @ X2017 @ ( setadjoin @ X2018 @ emptyset ) ) )
& ( ~ ( in @ X2021 @ X2020 )
| ( in @ X2021 @ ( binunion @ X2019 @ X2020 ) ) )
& ( ( in @ X2024 @ X2023 )
| X2025
| ( in @ X2024 @ X2022 )
| ~ ( in @ X2024 @ ( binunion @ X2022 @ X2023 ) ) )
& ( ~ X2025
| X2025
| ( in @ X2024 @ X2022 )
| ~ ( in @ X2024 @ ( binunion @ X2022 @ X2023 ) ) )
& ( ( in @ X2024 @ X2023 )
| X2025
| ~ X2025
| ~ ( in @ X2024 @ ( binunion @ X2022 @ X2023 ) ) )
& ( ~ X2025
| X2025
| ~ X2025
| ~ ( in @ X2024 @ ( binunion @ X2022 @ X2023 ) ) )
& ( ~ ( in @ X2028 @ ( binunion @ X2026 @ X2027 ) )
| ( in @ X2028 @ X2026 )
| ( in @ X2028 @ X2027 ) )
& ( subset @ X2029 @ ( binunion @ X2029 @ X2030 ) )
& ( subset @ X2032 @ ( binunion @ X2031 @ X2032 ) )
& ( ~ ( in @ X2035 @ X2033 )
| ~ ( in @ X2035 @ X2034 )
| ( in @ X2035 @ ( binintersect @ X2033 @ X2034 ) ) )
& ( ~ ( subset @ X2038 @ X2036 )
| ~ ( subset @ X2038 @ X2037 )
| ( subset @ X2038 @ ( binintersect @ X2036 @ X2037 ) ) )
& ( ~ ( in @ X2041 @ ( binintersect @ X2039 @ X2040 ) )
| ( in @ X2041 @ X2039 ) )
& ( subset @ ( binintersect @ X2042 @ X2043 ) @ X2042 )
& ( ~ ( subset @ X2044 @ X2045 )
| ( ( binintersect @ X2044 @ X2045 )
= X2044 ) )
& ( ( ( binintersect @ X2046 @ X2047 )
!= X2047 )
| ( subset @ X2047 @ X2046 ) )
& ( ~ ( in @ X2050 @ ( binintersect @ X2048 @ X2049 ) )
| ( in @ X2050 @ X2049 ) )
& ( ( in @ ( esk54_2 @ X2051 @ X2052 ) @ X2051 )
| ( ( binintersect @ X2051 @ X2052 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X2051 @ X2052 ) @ X2052 )
| ( ( binintersect @ X2051 @ X2052 )
= emptyset ) )
& ( subset @ ( binintersect @ X2054 @ X2055 ) @ X2055 )
& ( ~ ( subset @ X2057 @ X2056 )
| ( ( binintersect @ X2056 @ X2057 )
= X2057 ) )
& ( ( ( binintersect @ X2058 @ X2059 )
!= X2058 )
| ( subset @ X2058 @ X2059 ) )
& ( ( binintersect @ X2060 @ ( binunion @ X2061 @ X2062 ) )
= ( binunion @ ( binintersect @ X2060 @ X2061 ) @ ( binintersect @ X2060 @ X2062 ) ) )
& ( ~ ( in @ X2065 @ X2063 )
| ( in @ X2065 @ X2064 )
| ( in @ X2065 @ ( setminus @ X2063 @ X2064 ) ) )
& ( ~ ( in @ X2068 @ ( setminus @ X2066 @ X2067 ) )
| ( in @ X2068 @ X2066 ) )
& ( ~ ( in @ X2071 @ ( setminus @ X2069 @ X2070 ) )
| ~ ( in @ X2071 @ X2070 ) )
& ( ~ ( subset @ X2072 @ X2073 )
| ( ( setminus @ X2072 @ X2073 )
= emptyset ) )
& ( ( in @ X2076 @ ( setminus @ X2074 @ X2075 ) )
| ~ ( in @ X2076 @ X2074 )
| ( in @ X2076 @ X2075 ) )
& ( ( in @ X2079 @ ( setminus @ X2077 @ X2078 ) )
| ( in @ X2079 @ X2078 )
| ~ ( in @ X2079 @ X2077 ) )
& ( ( in @ X2082 @ X2080 )
| ~ ( in @ X2082 @ ( setminus @ X2080 @ X2081 ) ) )
& ( ~ ( in @ X2085 @ X2084 )
| ~ ( in @ X2085 @ ( setminus @ X2083 @ X2084 ) ) )
& ( subset @ ( setminus @ X2086 @ X2087 ) @ X2086 )
& ( ( ( setminus @ X2088 @ X2089 )
!= emptyset )
| ( subset @ X2088 @ X2089 ) )
& ( ~ ( in @ X2092 @ X2090 )
| X2093
| ( in @ X2092 @ X2090 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ( in @ X2092 @ X2091 )
| X2093
| ( in @ X2092 @ X2090 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ X2093
| X2093
| ( in @ X2092 @ X2090 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ ( in @ X2092 @ X2090 )
| X2093
| ~ ( in @ X2092 @ X2091 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ( in @ X2092 @ X2091 )
| X2093
| ~ ( in @ X2092 @ X2091 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ X2093
| X2093
| ~ ( in @ X2092 @ X2091 )
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ ( in @ X2092 @ X2090 )
| X2093
| ~ X2093
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ( in @ X2092 @ X2091 )
| X2093
| ~ X2093
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ X2093
| X2093
| ~ X2093
| ~ ( in @ X2092 @ ( symdiff @ X2090 @ X2091 ) ) )
& ( ~ ( in @ X2096 @ X2094 )
| ( in @ X2096 @ X2095 )
| ( in @ X2096 @ ( symdiff @ X2094 @ X2095 ) ) )
& ( ( in @ X2099 @ X2097 )
| ~ ( in @ X2099 @ X2098 )
| ( in @ X2099 @ ( symdiff @ X2097 @ X2098 ) ) )
& ( ~ ( in @ X2102 @ X2100 )
| ~ ( in @ X2102 @ X2101 )
| ~ ( in @ X2102 @ ( symdiff @ X2100 @ X2101 ) ) )
& ( ( in @ X2105 @ X2103 )
| ( in @ X2105 @ X2104 )
| ~ ( in @ X2105 @ ( symdiff @ X2103 @ X2104 ) ) )
& ( in @ X2107 @ ( setadjoin @ X2106 @ ( setadjoin @ X2107 @ emptyset ) ) )
& ( in @ X2108 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2108 @ ( setadjoin @ X2109 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2111 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2110 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2110 @ ( setadjoin @ X2111 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2112 @ ( setadjoin @ X2113 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2114 @ X2115 ) )
& ( ~ ( in @ X2117 @ X2116 )
| ( subset @ ( setadjoin @ X2117 @ emptyset ) @ X2116 ) )
& ( ~ ( in @ X2119 @ X2118 )
| ( in @ ( setadjoin @ X2119 @ emptyset ) @ ( powerset @ X2118 ) ) )
& ( ~ ( in @ X2122 @ X2120 )
| ( in @ ( setadjoin @ X2122 @ emptyset ) @ ( powerset @ ( binunion @ X2120 @ X2121 ) ) ) )
& ( ~ ( in @ X2125 @ ( setadjoin @ X2123 @ ( setadjoin @ X2124 @ emptyset ) ) )
| ( X2125 = X2123 )
| ( X2125 = X2124 ) )
& ( ~ ( in @ X2128 @ X2126 )
| ~ ( in @ X2129 @ X2127 )
| ( subset @ ( setadjoin @ X2128 @ ( setadjoin @ X2129 @ emptyset ) ) @ ( binunion @ X2126 @ X2127 ) ) )
& ( ~ ( in @ X2132 @ X2130 )
| ~ ( in @ X2133 @ X2131 )
| ( in @ ( setadjoin @ X2132 @ ( setadjoin @ X2133 @ emptyset ) ) @ ( powerset @ ( binunion @ X2130 @ X2131 ) ) ) )
& ( ~ ( in @ X2136 @ X2134 )
| ~ ( in @ X2137 @ X2135 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2136 @ ( setadjoin @ X2137 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2134 @ X2135 ) ) ) )
& ( ~ ( in @ X2140 @ X2138 )
| ~ ( in @ X2141 @ X2139 )
| ( in @ ( setadjoin @ ( setadjoin @ X2140 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2140 @ ( setadjoin @ X2141 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2138 @ X2139 ) ) ) ) )
& ( ~ ( in @ X2144 @ X2142 )
| ~ ( in @ X2145 @ X2143 )
| ( in @ ( kpair @ X2144 @ X2145 ) @ ( powerset @ ( powerset @ ( binunion @ X2142 @ X2143 ) ) ) ) )
& ( ~ ( in @ X2148 @ X2146 )
| ~ ( in @ X2149 @ X2147 )
| ( in @ ( kpair @ X2148 @ X2149 ) @ ( cartprod @ X2146 @ X2147 ) ) )
& ( ( in @ ( esk55_3 @ X2150 @ X2151 @ X2152 ) @ X2150 )
| ~ ( in @ X2152 @ ( cartprod @ X2150 @ X2151 ) ) )
& ( ( in @ ( esk56_3 @ X2150 @ X2151 @ X2152 ) @ X2151 )
| ~ ( in @ X2152 @ ( cartprod @ X2150 @ X2151 ) ) )
& ( ( X2152
= ( kpair @ ( esk55_3 @ X2150 @ X2151 @ X2152 ) @ ( esk56_3 @ X2150 @ X2151 @ X2152 ) ) )
| ~ ( in @ X2152 @ ( cartprod @ X2150 @ X2151 ) ) )
& ( ~ ( in @ X2157 @ ( cartprod @ X2155 @ X2156 ) )
| ( iskpair @ X2157 ) )
& ( ( in @ ( esk57_2 @ X2158 @ X2159 ) @ X2158 )
| ~ ( in @ X2159 @ ( setunion @ X2158 ) ) )
& ( ( in @ X2159 @ ( esk57_2 @ X2158 @ X2159 ) )
| ~ ( in @ X2159 @ ( setunion @ X2158 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2161 @ emptyset ) ) @ X2161 )
& ( subset @ X2162 @ ( setunion @ ( setadjoin @ X2162 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2163 @ emptyset ) )
= X2163 )
& ( ( in @ ( esk58_2 @ X2164 @ X2165 ) @ X2164 )
| ~ ( in @ X2168 @ X2164 )
| ~ ( X2165 @ X2168 )
| ( singleton @ ( dsetconstr @ X2164 @ X2165 ) ) )
& ( ( in @ ( esk59_2 @ X2164 @ X2165 ) @ X2164 )
| ~ ( in @ X2168 @ X2164 )
| ~ ( X2165 @ X2168 )
| ( singleton @ ( dsetconstr @ X2164 @ X2165 ) ) )
& ( ( X2165 @ ( esk58_2 @ X2164 @ X2165 ) )
| ~ ( in @ X2168 @ X2164 )
| ~ ( X2165 @ X2168 )
| ( singleton @ ( dsetconstr @ X2164 @ X2165 ) ) )
& ( ( X2165 @ ( esk59_2 @ X2164 @ X2165 ) )
| ~ ( in @ X2168 @ X2164 )
| ~ ( X2165 @ X2168 )
| ( singleton @ ( dsetconstr @ X2164 @ X2165 ) ) )
& ( ( ( esk58_2 @ X2164 @ X2165 )
!= ( esk59_2 @ X2164 @ X2165 ) )
| ~ ( in @ X2168 @ X2164 )
| ~ ( X2165 @ X2168 )
| ( singleton @ ( dsetconstr @ X2164 @ X2165 ) ) )
& ( ( in @ ( esk60_2 @ X2169 @ X2170 ) @ X2169 )
| ~ ( singleton @ ( dsetconstr @ X2169 @ X2170 ) ) )
& ( ( X2170 @ ( esk60_2 @ X2169 @ X2170 ) )
| ~ ( singleton @ ( dsetconstr @ X2169 @ X2170 ) ) )
& ( ( in @ ( esk61_3 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ( singleton @ ( dsetconstr @ X2172 @ X2173 ) )
| ~ ( X2173 @ X2174 )
| ~ ( in @ X2174 @ X2172 ) )
& ( ( X2173 @ ( esk61_3 @ X2172 @ X2173 @ X2174 ) )
| ( singleton @ ( dsetconstr @ X2172 @ X2173 ) )
| ~ ( X2173 @ X2174 )
| ~ ( in @ X2174 @ X2172 ) )
& ( ( ( esk61_3 @ X2172 @ X2173 @ X2174 )
!= X2174 )
| ( singleton @ ( dsetconstr @ X2172 @ X2173 ) )
| ~ ( X2173 @ X2174 )
| ~ ( in @ X2174 @ X2172 ) )
& ( ( in @ ( esk62_2 @ X2176 @ X2177 ) @ X2176 )
| ~ ( in @ X2180 @ X2176 )
| ~ ( X2177 @ X2180 )
| ( singleton @ ( dsetconstr @ X2176 @ X2177 ) ) )
& ( ( in @ ( esk63_2 @ X2176 @ X2177 ) @ X2176 )
| ~ ( in @ X2180 @ X2176 )
| ~ ( X2177 @ X2180 )
| ( singleton @ ( dsetconstr @ X2176 @ X2177 ) ) )
& ( ( X2177 @ ( esk62_2 @ X2176 @ X2177 ) )
| ~ ( in @ X2180 @ X2176 )
| ~ ( X2177 @ X2180 )
| ( singleton @ ( dsetconstr @ X2176 @ X2177 ) ) )
& ( ( X2177 @ ( esk63_2 @ X2176 @ X2177 ) )
| ~ ( in @ X2180 @ X2176 )
| ~ ( X2177 @ X2180 )
| ( singleton @ ( dsetconstr @ X2176 @ X2177 ) ) )
& ( ( ( esk62_2 @ X2176 @ X2177 )
!= ( esk63_2 @ X2176 @ X2177 ) )
| ~ ( in @ X2180 @ X2176 )
| ~ ( X2177 @ X2180 )
| ( singleton @ ( dsetconstr @ X2176 @ X2177 ) ) )
& ( ( ( setadjoin @ X2181 @ emptyset )
!= ( setadjoin @ X2182 @ emptyset ) )
| ( X2181 = X2182 ) )
& ( ~ ( in @ ( setadjoin @ X2185 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2183 @ ( setadjoin @ X2184 @ emptyset ) ) @ emptyset ) ) )
| ( X2183 = X2185 ) )
& ( ~ ( iskpair @ X2186 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2186 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2186 ) ) ) )
& ( ~ ( singleton @ X2187 )
| ( in @ ( setunion @ X2187 ) @ X2187 ) )
& ( ( kfst @ ( kpair @ X2188 @ X2189 ) )
= X2188 )
& ( ~ ( in @ X2192 @ ( cartprod @ X2190 @ X2191 ) )
| ( in @ ( kfst @ X2192 ) @ X2190 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2193 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2193 @ ( setadjoin @ X2194 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2195 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2195 @ ( setadjoin @ X2196 @ emptyset ) ) @ emptyset ) ) )
| ( X2193 = X2195 ) )
& ( ( ( kpair @ X2197 @ X2198 )
!= ( kpair @ X2199 @ X2200 ) )
| ( X2197 = X2199 ) )
& ( ( X2201 != X2202 )
| ( ( setadjoin @ X2201 @ ( setadjoin @ X2202 @ emptyset ) )
= ( setadjoin @ X2201 @ emptyset ) ) )
& ( ( X2203 != X2204 )
| ( ( setadjoin @ ( setadjoin @ X2203 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2203 @ ( setadjoin @ X2204 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2203 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2205 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2205 @ ( setadjoin @ X2206 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2207 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2207 @ ( setadjoin @ X2208 @ emptyset ) ) @ emptyset ) ) )
| ( X2207 != X2208 )
| ( X2206 = X2208 ) )
& ( ( ( setadjoin @ X2209 @ ( setadjoin @ X2210 @ emptyset ) )
!= ( setadjoin @ X2211 @ emptyset ) )
| ( X2209 = X2210 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2212 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2212 @ ( setadjoin @ X2213 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2214 @ ( setadjoin @ X2215 @ emptyset ) ) @ emptyset ) ) )
| ( X2213 = X2215 ) )
& ( ( ( kpair @ X2216 @ X2217 )
!= ( kpair @ X2218 @ X2219 ) )
| ( X2217 = X2219 ) )
& ( ~ ( iskpair @ X2220 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2220 )
@ ^ [Z0: $i] :
( X2220
= ( kpair @ ( kfst @ X2220 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2221 @ X2222 ) )
= X2222 )
& ( ~ ( iskpair @ X2223 )
| ( ( kpair @ ( kfst @ X2223 ) @ ( ksnd @ X2223 ) )
= X2223 ) )
& ( ~ ( in @ X2226 @ ( cartprod @ X2224 @ X2225 ) )
| ( in @ ( ksnd @ X2226 ) @ X2225 ) )
& ( ~ ( in @ ( kpair @ X2229 @ X2230 ) @ ( cartprod @ X2227 @ X2228 ) )
| ( in @ X2229 @ X2227 ) )
& ( ~ ( in @ ( kpair @ X2233 @ X2234 ) @ ( cartprod @ X2231 @ X2232 ) )
| ( in @ X2234 @ X2232 ) )
& ( ~ ( in @ X2237 @ X2235 )
| ~ ( in @ X2238 @ X2236 )
| ( ( kpair @ X2237 @ X2238 )
= ( kpair @ X2237 @ X2238 ) ) )
& ( ~ ( in @ X2241 @ X2239 )
| ~ ( in @ X2242 @ X2240 )
| ( ( kfst @ ( kpair @ X2241 @ X2242 ) )
= X2241 ) )
& ( ~ ( in @ X2245 @ X2243 )
| ~ ( in @ X2246 @ X2244 )
| ( ( ksnd @ ( kpair @ X2245 @ X2246 ) )
= X2246 ) )
& ( ~ ( in @ X2249 @ ( cartprod @ X2247 @ X2248 ) )
| ( ( kpair @ ( kfst @ X2249 ) @ ( ksnd @ X2249 ) )
= X2249 ) )
& ( ~ ( in @ X2253 @ X2250 )
| ~ ( in @ X2254 @ X2251 )
| ~ ( X2252 @ X2253 @ X2254 )
| ( in @ ( kpair @ X2253 @ X2254 ) @ ( dpsetconstr @ X2250 @ X2251 @ X2252 ) ) )
& ( subset @ ( dpsetconstr @ X2255 @ X2256 @ X2257 ) @ ( cartprod @ X2255 @ X2256 ) )
& ( subset @ ( dpsetconstr @ X2258 @ X2259 @ X2260 ) @ ( cartprod @ X2258 @ X2259 ) )
& ( ~ ( in @ X2264 @ X2261 )
| ~ ( in @ X2265 @ X2262 )
| ~ ( in @ ( kpair @ X2264 @ X2265 ) @ ( dpsetconstr @ X2261 @ X2262 @ X2263 ) )
| ( X2263 @ X2264 @ X2265 ) )
& ( ~ ( in @ ( kpair @ X2269 @ X2270 ) @ ( dpsetconstr @ X2266 @ X2267 @ X2268 ) )
| ( in @ X2269 @ X2266 ) )
& ( ~ ( in @ ( kpair @ X2274 @ X2275 ) @ ( dpsetconstr @ X2271 @ X2272 @ X2273 ) )
| ( in @ X2275 @ X2272 ) )
& ( ~ ( in @ ( kpair @ X2279 @ X2280 ) @ ( dpsetconstr @ X2276 @ X2277 @ X2278 ) )
| ( X2278 @ X2279 @ X2280 ) )
& ( ~ ( func @ X2281 @ X2282 @ X2283 )
| ~ ( in @ X2284 @ X2281 )
| ( singleton
@ ( dsetconstr @ X2282
@ ^ [Z0: $i] : ( in @ ( kpair @ X2284 @ Z0 ) @ X2283 ) ) ) )
& ( ~ ( func @ X2285 @ X2286 @ X2287 )
| ~ ( in @ X2288 @ X2285 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2286
@ ^ [Z0: $i] : ( in @ ( kpair @ X2288 @ Z0 ) @ X2287 ) ) )
@ X2286 ) )
& ( ~ ( func @ X2289 @ X2290 @ X2291 )
| ~ ( in @ X2292 @ X2289 )
| ( in @ ( ap @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2290 ) )
& ( ~ ( in @ X2295 @ ( funcSet @ X2293 @ X2294 ) )
| ( func @ X2293 @ X2294 @ X2295 ) )
& ( ~ ( in @ X2298 @ ( funcSet @ X2296 @ X2297 ) )
| ~ ( in @ X2299 @ X2296 )
| ( in @ ( ap @ X2296 @ X2297 @ X2298 @ X2299 ) @ X2297 ) )
& ( ~ ( func @ X2300 @ X2301 @ X2302 )
| ( in @ X2302 @ ( funcSet @ X2300 @ X2301 ) ) )
& ( ( in @ ( esk64_3 @ X2303 @ X2304 @ X2305 ) @ X2303 )
| ( func @ X2303 @ X2304
@ ( dpsetconstr @ X2303 @ X2304
@ ^ [Z0: $i] : ( $eq @ ( X2305 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2305 @ ( esk64_3 @ X2303 @ X2304 @ X2305 ) ) @ X2304 )
| ( func @ X2303 @ X2304
@ ( dpsetconstr @ X2303 @ X2304
@ ^ [Z0: $i] : ( $eq @ ( X2305 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2307 @ X2308 @ X2309 ) @ X2307 )
| ( func @ X2307 @ X2308 @ ( lam @ X2307 @ X2308 @ X2309 ) ) )
& ( ~ ( in @ ( X2309 @ ( esk65_3 @ X2307 @ X2308 @ X2309 ) ) @ X2308 )
| ( func @ X2307 @ X2308 @ ( lam @ X2307 @ X2308 @ X2309 ) ) )
& ( ( in @ ( esk66_3 @ X2311 @ X2312 @ X2313 ) @ X2311 )
| ( in @ ( lam @ X2311 @ X2312 @ X2313 ) @ ( funcSet @ X2311 @ X2312 ) ) )
& ( ~ ( in @ ( X2313 @ ( esk66_3 @ X2311 @ X2312 @ X2313 ) ) @ X2312 )
| ( in @ ( lam @ X2311 @ X2312 @ X2313 ) @ ( funcSet @ X2311 @ X2312 ) ) )
& ( ( in @ ( esk67_4 @ X2315 @ X2316 @ X2317 @ X2318 ) @ X2315 )
| ~ ( in @ X2321 @ X2317 )
| ( X2318 @ X2321 )
| ~ ( subset @ X2317 @ ( cartprod @ X2315 @ X2316 ) ) )
& ( ( in @ ( esk68_4 @ X2315 @ X2316 @ X2317 @ X2318 ) @ X2316 )
| ~ ( in @ X2321 @ X2317 )
| ( X2318 @ X2321 )
| ~ ( subset @ X2317 @ ( cartprod @ X2315 @ X2316 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2315 @ X2316 @ X2317 @ X2318 ) @ ( esk68_4 @ X2315 @ X2316 @ X2317 @ X2318 ) ) @ X2317 )
| ~ ( in @ X2321 @ X2317 )
| ( X2318 @ X2321 )
| ~ ( subset @ X2317 @ ( cartprod @ X2315 @ X2316 ) ) )
& ( ~ ( X2318 @ ( kpair @ ( esk67_4 @ X2315 @ X2316 @ X2317 @ X2318 ) @ ( esk68_4 @ X2315 @ X2316 @ X2317 @ X2318 ) ) )
| ~ ( in @ X2321 @ X2317 )
| ( X2318 @ X2321 )
| ~ ( subset @ X2317 @ ( cartprod @ X2315 @ X2316 ) ) )
& ( ( in @ ( esk69_4 @ X2322 @ X2323 @ X2324 @ X2325 ) @ X2322 )
| ~ ( in @ X2328 @ X2324 )
| ( X2325 @ X2328 )
| ~ ( subset @ X2324 @ ( cartprod @ X2322 @ X2323 ) ) )
& ( ( in @ ( esk70_4 @ X2322 @ X2323 @ X2324 @ X2325 ) @ X2323 )
| ~ ( in @ X2328 @ X2324 )
| ( X2325 @ X2328 )
| ~ ( subset @ X2324 @ ( cartprod @ X2322 @ X2323 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2322 @ X2323 @ X2324 @ X2325 ) @ ( esk70_4 @ X2322 @ X2323 @ X2324 @ X2325 ) ) @ X2324 )
| ~ ( in @ X2328 @ X2324 )
| ( X2325 @ X2328 )
| ~ ( subset @ X2324 @ ( cartprod @ X2322 @ X2323 ) ) )
& ( ~ ( X2325 @ ( kpair @ ( esk69_4 @ X2322 @ X2323 @ X2324 @ X2325 ) @ ( esk70_4 @ X2322 @ X2323 @ X2324 @ X2325 ) ) )
| ~ ( in @ X2328 @ X2324 )
| ( X2325 @ X2328 )
| ~ ( subset @ X2324 @ ( cartprod @ X2322 @ X2323 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2329 @ X2330 ) )
| ~ ( in @ X2331 @ X2329 )
| ~ ( in @ X2332 @ X2329 )
| ~ ( X2330 @ X2331 )
| ~ ( X2330 @ X2332 )
| ( X2331 = X2332 ) )
& ( ~ ( func @ X2333 @ X2334 @ X2335 )
| ~ ( in @ X2336 @ X2333 )
| ( in @ ( kpair @ X2336 @ ( ap @ X2333 @ X2334 @ X2335 @ X2336 ) ) @ X2335 ) )
& ( ~ ( in @ X2339 @ ( funcSet @ X2337 @ X2338 ) )
| ~ ( in @ X2340 @ X2337 )
| ( in @ ( kpair @ X2340 @ ( ap @ X2337 @ X2338 @ X2339 @ X2340 ) ) @ X2339 ) )
& ( ~ ( func @ X2341 @ X2342 @ X2343 )
| ~ ( in @ X2344 @ X2341 )
| ~ ( in @ X2345 @ X2342 )
| ~ ( in @ ( kpair @ X2344 @ X2345 ) @ X2343 )
| ( ( ap @ X2341 @ X2342 @ X2343 @ X2344 )
= X2345 ) )
& ( ( in @ ( esk71_4 @ X2346 @ X2347 @ X2348 @ X2349 ) @ X2346 )
| ~ ( in @ X2351 @ X2346 )
| ~ ( in @ X2352 @ X2347 )
| ~ ( in @ ( kpair @ X2351 @ X2352 ) @ X2349 )
| ( in @ ( kpair @ X2351 @ X2352 ) @ X2348 )
| ~ ( func @ X2346 @ X2347 @ X2349 )
| ~ ( func @ X2346 @ X2347 @ X2348 ) )
& ( ( ( ap @ X2346 @ X2347 @ X2348 @ ( esk71_4 @ X2346 @ X2347 @ X2348 @ X2349 ) )
!= ( ap @ X2346 @ X2347 @ X2349 @ ( esk71_4 @ X2346 @ X2347 @ X2348 @ X2349 ) ) )
| ~ ( in @ X2351 @ X2346 )
| ~ ( in @ X2352 @ X2347 )
| ~ ( in @ ( kpair @ X2351 @ X2352 ) @ X2349 )
| ( in @ ( kpair @ X2351 @ X2352 ) @ X2348 )
| ~ ( func @ X2346 @ X2347 @ X2349 )
| ~ ( func @ X2346 @ X2347 @ X2348 ) )
& ( ~ ( in @ X2355 @ ( funcSet @ X2353 @ X2354 ) )
| ~ ( in @ X2356 @ X2353 )
| ~ ( in @ X2357 @ X2354 )
| ~ ( in @ ( kpair @ X2356 @ X2357 ) @ X2355 )
| ( ( ap @ X2353 @ X2354 @ X2355 @ X2356 )
= X2357 ) )
& ( ( in @ ( esk72_4 @ X2358 @ X2359 @ X2360 @ X2361 ) @ X2358 )
| ( subset @ X2360 @ X2361 )
| ~ ( subset @ X2361 @ ( cartprod @ X2358 @ X2359 ) )
| ~ ( subset @ X2360 @ ( cartprod @ X2358 @ X2359 ) ) )
& ( ( in @ ( esk73_4 @ X2358 @ X2359 @ X2360 @ X2361 ) @ X2359 )
| ( subset @ X2360 @ X2361 )
| ~ ( subset @ X2361 @ ( cartprod @ X2358 @ X2359 ) )
| ~ ( subset @ X2360 @ ( cartprod @ X2358 @ X2359 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2358 @ X2359 @ X2360 @ X2361 ) @ ( esk73_4 @ X2358 @ X2359 @ X2360 @ X2361 ) ) @ X2360 )
| ( subset @ X2360 @ X2361 )
| ~ ( subset @ X2361 @ ( cartprod @ X2358 @ X2359 ) )
| ~ ( subset @ X2360 @ ( cartprod @ X2358 @ X2359 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2358 @ X2359 @ X2360 @ X2361 ) @ ( esk73_4 @ X2358 @ X2359 @ X2360 @ X2361 ) ) @ X2361 )
| ( subset @ X2360 @ X2361 )
| ~ ( subset @ X2361 @ ( cartprod @ X2358 @ X2359 ) )
| ~ ( subset @ X2360 @ ( cartprod @ X2358 @ X2359 ) ) )
& ( ( in @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ( X2366 = X2367 )
| ( in @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ( X2366 = X2367 )
| ( in @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ( X2366 = X2367 )
| ( in @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ( X2366 = X2367 )
| ( in @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ( X2366 = X2367 )
| ( in @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ( X2366 = X2367 )
| ( in @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ( X2366 = X2367 )
| ( in @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ( X2366 = X2367 )
| ( in @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ( X2366 = X2367 )
| ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ( X2366 = X2367 )
| ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ( X2366 = X2367 )
| ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ( X2366 = X2367 )
| ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2364 )
| ( X2366 = X2367 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 )
| ( X2366 = X2367 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ( X2366 = X2367 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk77_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2366 )
| ( X2366 = X2367 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2364 @ X2365 @ X2366 @ X2367 ) @ ( esk75_4 @ X2364 @ X2365 @ X2366 @ X2367 ) ) @ X2367 )
| ~ ( subset @ X2367 @ ( cartprod @ X2364 @ X2365 ) )
| ~ ( subset @ X2366 @ ( cartprod @ X2364 @ X2365 ) ) )
& ( ( in @ ( esk78_4 @ X2372 @ X2373 @ X2374 @ X2375 ) @ X2372 )
| ( X2374 = X2375 )
| ~ ( func @ X2372 @ X2373 @ X2375 )
| ~ ( func @ X2372 @ X2373 @ X2374 ) )
& ( ( ( ap @ X2372 @ X2373 @ X2374 @ ( esk78_4 @ X2372 @ X2373 @ X2374 @ X2375 ) )
!= ( ap @ X2372 @ X2373 @ X2375 @ ( esk78_4 @ X2372 @ X2373 @ X2374 @ X2375 ) ) )
| ( X2374 = X2375 )
| ~ ( func @ X2372 @ X2373 @ X2375 )
| ~ ( func @ X2372 @ X2373 @ X2374 ) )
& ( ( in @ ( esk79_4 @ X2377 @ X2378 @ X2379 @ X2380 ) @ X2377 )
| ( X2379 = X2380 )
| ~ ( in @ X2380 @ ( funcSet @ X2377 @ X2378 ) )
| ~ ( in @ X2379 @ ( funcSet @ X2377 @ X2378 ) ) )
& ( ( ( ap @ X2377 @ X2378 @ X2379 @ ( esk79_4 @ X2377 @ X2378 @ X2379 @ X2380 ) )
!= ( ap @ X2377 @ X2378 @ X2380 @ ( esk79_4 @ X2377 @ X2378 @ X2379 @ X2380 ) ) )
| ( X2379 = X2380 )
| ~ ( in @ X2380 @ ( funcSet @ X2377 @ X2378 ) )
| ~ ( in @ X2379 @ ( funcSet @ X2377 @ X2378 ) ) )
& ( ~ ( in @ X2384 @ ( funcSet @ X2382 @ X2383 ) )
| ~ ( in @ X2385 @ X2382 )
| ( ( ap @ X2382 @ X2383 @ X2384 @ X2385 )
= ( ap @ X2382 @ X2383 @ X2384 @ X2385 ) ) )
& ( ~ ( func @ X2386 @ X2387 @ X2388 )
| ~ ( in @ X2389 @ X2386 )
| ( ( ap @ X2386 @ X2387 @ X2388 @ X2389 )
= ( ap @ X2386 @ X2387 @ X2388 @ X2389 ) ) )
& ( ( in @ ( esk80_3 @ X2390 @ X2391 @ X2392 ) @ X2390 )
| ~ ( in @ X2394 @ X2390 )
| ( ( ap @ X2390 @ X2391 @ ( lam @ X2390 @ X2391 @ X2392 ) @ X2394 )
= ( X2392 @ X2394 ) ) )
& ( ~ ( in @ ( X2392 @ ( esk80_3 @ X2390 @ X2391 @ X2392 ) ) @ X2391 )
| ~ ( in @ X2394 @ X2390 )
| ( ( ap @ X2390 @ X2391 @ ( lam @ X2390 @ X2391 @ X2392 ) @ X2394 )
= ( X2392 @ X2394 ) ) )
& ( ~ ( func @ X2395 @ X2396 @ X2397 )
| ( ( lam @ X2395 @ X2396 @ ( ap @ X2395 @ X2396 @ X2397 ) )
= X2397 ) )
& ( ( in @ ( esk81_3 @ X2398 @ X2399 @ X2400 ) @ X2398 )
| ( ( lam @ X2398 @ X2399 @ X2400 )
= ( lam @ X2398 @ X2399 @ X2400 ) ) )
& ( ~ ( in @ ( X2400 @ ( esk81_3 @ X2398 @ X2399 @ X2400 ) ) @ X2399 )
| ( ( lam @ X2398 @ X2399 @ X2400 )
= ( lam @ X2398 @ X2399 @ X2400 ) ) )
& ( ( in @ ( esk82_3 @ X2402 @ X2403 @ X2404 ) @ X2402 )
| ~ ( in @ X2406 @ X2402 )
| ( ( ap @ X2402 @ X2403 @ ( lam @ X2402 @ X2403 @ X2404 ) @ X2406 )
= ( X2404 @ X2406 ) ) )
& ( ~ ( in @ ( X2404 @ ( esk82_3 @ X2402 @ X2403 @ X2404 ) ) @ X2403 )
| ~ ( in @ X2406 @ X2402 )
| ( ( ap @ X2402 @ X2403 @ ( lam @ X2402 @ X2403 @ X2404 ) @ X2406 )
= ( X2404 @ X2406 ) ) )
& ( ~ ( in @ X2409 @ ( funcSet @ X2407 @ X2408 ) )
| ( ( lam @ X2407 @ X2408 @ ( ap @ X2407 @ X2408 @ X2409 ) )
= X2409 ) )
& ( ~ ( in @ X2412 @ X2410 )
| ~ ( in @ X2413 @ X2410 )
| X2411
| ( in @ X2413
@ ( dsetconstr @ X2410
@ ^ [Z0: $i] :
( ( X2411
& ( Z0 = X2412 ) )
| ( ~ X2411
& ( Z0 = X2413 ) ) ) ) ) )
& ( ~ ( in @ X2416 @ X2414 )
| ~ ( in @ X2417 @ X2414 )
| X2415
| ( ( dsetconstr @ X2414
@ ^ [Z0: $i] :
( ( X2415
& ( Z0 = X2416 ) )
| ( ~ X2415
& ( Z0 = X2417 ) ) ) )
= ( setadjoin @ X2417 @ emptyset ) ) )
& ( ~ ( in @ X2420 @ X2418 )
| ~ ( in @ X2421 @ X2418 )
| ~ X2419
| ( in @ X2420
@ ( dsetconstr @ X2418
@ ^ [Z0: $i] :
( ( X2419
& ( Z0 = X2420 ) )
| ( ~ X2419
& ( Z0 = X2421 ) ) ) ) ) )
& ( ~ ( in @ X2424 @ X2422 )
| ~ ( in @ X2425 @ X2422 )
| ~ X2423
| ( ( dsetconstr @ X2422
@ ^ [Z0: $i] :
( ( X2423
& ( Z0 = X2424 ) )
| ( ~ X2423
& ( Z0 = X2425 ) ) ) )
= ( setadjoin @ X2424 @ emptyset ) ) )
& ( ~ ( in @ X2428 @ X2426 )
| ~ ( in @ X2429 @ X2426 )
| ( singleton
@ ( dsetconstr @ X2426
@ ^ [Z0: $i] :
( ( X2427
& ( Z0 = X2428 ) )
| ( ~ X2427
& ( Z0 = X2429 ) ) ) ) ) )
& ( ~ ( in @ X2432 @ X2430 )
| ~ ( in @ X2433 @ X2430 )
| ( in @ ( if @ X2430 @ X2431 @ X2432 @ X2433 ) @ X2430 ) )
& ( ~ ( singleton @ X2434 )
| ~ ( in @ X2435 @ X2434 )
| ( ( setunion @ X2434 )
= X2435 ) )
& ( ~ ( in @ X2438 @ X2436 )
| ~ ( in @ X2439 @ X2436 )
| ~ X2437
| ( ( if @ X2436 @ X2437 @ X2438 @ X2439 )
= X2438 ) )
& ( ~ ( in @ X2442 @ X2440 )
| ~ ( in @ X2443 @ X2440 )
| X2441
| ( ( if @ X2440 @ X2441 @ X2442 @ X2443 )
= X2443 ) )
& ( ~ ( in @ X2446 @ X2444 )
| ~ ( in @ X2447 @ X2444 )
| ( in @ ( if @ X2444 @ X2445 @ X2446 @ X2447 ) @ ( setadjoin @ X2446 @ ( setadjoin @ X2447 @ emptyset ) ) ) )
& ( ~ ( in @ X2449 @ ( powerset @ X2448 ) )
| ~ ( in @ X2450 @ ( powerset @ X2448 ) )
| ( in @ ( binintersect @ X2449 @ X2450 ) @ ( powerset @ X2448 ) ) )
& ( ~ ( in @ X2452 @ ( powerset @ X2451 ) )
| ~ ( in @ X2453 @ ( powerset @ X2451 ) )
| ( in @ ( binunion @ X2452 @ X2453 ) @ ( powerset @ X2451 ) ) )
& ( ~ ( in @ X2455 @ ( powerset @ X2454 ) )
| ( in @ ( powerset @ X2455 ) @ ( powerset @ ( powerset @ X2454 ) ) ) )
& ( ~ ( in @ X2457 @ ( powerset @ X2456 ) )
| ~ ( in @ X2458 @ ( powerset @ X2456 ) )
| ( in @ ( setminus @ X2457 @ X2458 ) @ ( powerset @ X2456 ) ) )
& ( ~ ( in @ X2460 @ ( powerset @ X2459 ) )
| ( in @ ( setminus @ X2459 @ X2460 ) @ ( powerset @ X2459 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ( X2462 = X2463 )
| ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2461 )
| ( X2462 = X2463 )
| ~ ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ( X2462 = X2463 )
| ~ ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2461 @ X2462 @ X2463 ) @ X2462 )
| ( X2462 = X2463 )
| ~ ( in @ ( esk83_3 @ X2461 @ X2462 @ X2463 ) @ X2463 )
| ~ ( in @ X2463 @ ( powerset @ X2461 ) )
| ~ ( in @ X2462 @ ( powerset @ X2461 ) ) )
& ( ( in @ ( esk85_3 @ X2466 @ X2467 @ X2468 ) @ X2466 )
| ( subset @ X2467 @ X2468 )
| ~ ( in @ X2468 @ ( powerset @ X2466 ) )
| ~ ( in @ X2467 @ ( powerset @ X2466 ) ) )
& ( ( in @ ( esk85_3 @ X2466 @ X2467 @ X2468 ) @ X2467 )
| ( subset @ X2467 @ X2468 )
| ~ ( in @ X2468 @ ( powerset @ X2466 ) )
| ~ ( in @ X2467 @ ( powerset @ X2466 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2466 @ X2467 @ X2468 ) @ X2468 )
| ( subset @ X2467 @ X2468 )
| ~ ( in @ X2468 @ ( powerset @ X2466 ) )
| ~ ( in @ X2467 @ ( powerset @ X2466 ) ) )
& ( ( in @ ( esk86_3 @ X2470 @ X2471 @ X2472 ) @ X2470 )
| ( in @ X2471 @ ( powerset @ X2472 ) )
| ~ ( in @ X2472 @ ( powerset @ X2470 ) )
| ~ ( in @ X2471 @ ( powerset @ X2470 ) ) )
& ( ( in @ ( esk86_3 @ X2470 @ X2471 @ X2472 ) @ X2471 )
| ( in @ X2471 @ ( powerset @ X2472 ) )
| ~ ( in @ X2472 @ ( powerset @ X2470 ) )
| ~ ( in @ X2471 @ ( powerset @ X2470 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2470 @ X2471 @ X2472 ) @ X2472 )
| ( in @ X2471 @ ( powerset @ X2472 ) )
| ~ ( in @ X2472 @ ( powerset @ X2470 ) )
| ~ ( in @ X2471 @ ( powerset @ X2470 ) ) )
& ( ~ ( in @ X2475 @ ( powerset @ X2474 ) )
| ~ ( in @ X2476 @ ( powerset @ X2474 ) )
| ~ ( in @ X2477 @ X2474 )
| ~ ( in @ X2475 @ ( powerset @ X2476 ) )
| ~ ( in @ X2477 @ X2475 )
| ( in @ X2477 @ X2476 ) )
& ( ~ ( in @ X2479 @ ( powerset @ X2478 ) )
| ~ ( in @ X2480 @ X2478 )
| ~ ( in @ X2480 @ X2479 )
| ~ ( in @ X2480 @ ( setminus @ X2478 @ X2479 ) ) )
& ( ~ ( in @ X2482 @ ( powerset @ X2481 ) )
| ~ ( in @ X2483 @ X2481 )
| ( in @ X2483 @ ( setminus @ X2481 @ X2482 ) )
| ( in @ X2483 @ X2482 ) )
& ( ~ ( in @ X2485 @ ( powerset @ X2484 ) )
| ~ ( in @ X2486 @ ( powerset @ X2484 ) )
| ~ ( in @ X2487 @ X2484 )
| ( in @ X2487 @ X2485 )
| ~ ( in @ X2487 @ ( binintersect @ X2485 @ X2486 ) ) )
& ( ~ ( in @ X2489 @ ( powerset @ X2488 ) )
| ~ ( in @ X2490 @ ( powerset @ X2488 ) )
| ~ ( in @ X2491 @ X2488 )
| ( in @ X2491 @ X2490 )
| ~ ( in @ X2491 @ ( binintersect @ X2489 @ X2490 ) ) )
& ( ~ ( in @ X2493 @ ( powerset @ X2492 ) )
| ~ ( in @ X2494 @ ( powerset @ X2492 ) )
| ~ ( in @ X2495 @ X2492 )
| ~ ( subset @ X2493 @ ( setminus @ X2492 @ X2494 ) )
| ~ ( in @ X2495 @ X2494 )
| ~ ( in @ X2495 @ X2493 ) )
& ( ~ ( in @ X2497 @ ( powerset @ X2496 ) )
| ~ ( in @ X2498 @ ( powerset @ X2496 ) )
| ~ ( in @ X2499 @ X2496 )
| ~ ( subset @ X2497 @ X2498 )
| ( in @ X2499 @ X2498 )
| ~ ( in @ X2499 @ X2497 ) )
& ( ~ ( in @ X2501 @ ( powerset @ X2500 ) )
| ~ ( in @ X2502 @ ( powerset @ X2500 ) )
| ~ ( subset @ X2501 @ X2502 )
| ( subset @ ( setminus @ X2500 @ X2502 ) @ ( setminus @ X2500 @ X2501 ) ) )
& ( ~ ( in @ X2504 @ ( powerset @ X2503 ) )
| ~ ( in @ X2505 @ ( powerset @ X2503 ) )
| ~ ( subset @ ( setminus @ X2503 @ X2505 ) @ ( setminus @ X2503 @ X2504 ) )
| ( subset @ X2504 @ X2505 ) )
& ( ~ ( in @ X2507 @ ( powerset @ X2506 ) )
| ~ ( in @ X2508 @ X2506 )
| ~ ( in @ X2508 @ X2507 )
| ( in @ X2508 @ ( setminus @ X2506 @ ( setminus @ X2506 @ X2507 ) ) ) )
& ( ~ ( in @ X2510 @ ( powerset @ X2509 ) )
| ~ ( in @ X2511 @ X2509 )
| ~ ( in @ X2511 @ ( setminus @ X2509 @ ( setminus @ X2509 @ X2510 ) ) )
| ( in @ X2511 @ X2510 ) )
& ( ~ ( in @ X2513 @ ( powerset @ X2512 ) )
| ( subset @ X2513 @ ( setminus @ X2512 @ ( setminus @ X2512 @ X2513 ) ) ) )
& ( ~ ( in @ X2515 @ ( powerset @ X2514 ) )
| ( subset @ ( setminus @ X2514 @ ( setminus @ X2514 @ X2515 ) ) @ X2515 ) )
& ( ~ ( in @ X2517 @ ( powerset @ X2516 ) )
| ( X2517
= ( setminus @ X2516 @ ( setminus @ X2516 @ X2517 ) ) ) )
& ( ~ ( in @ X2519 @ ( powerset @ X2518 ) )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2521 @ X2518 )
| ~ ( in @ X2521 @ ( setminus @ X2518 @ X2519 ) )
| ~ ( in @ X2521 @ ( binintersect @ X2519 @ X2520 ) ) )
& ( ~ ( in @ X2523 @ ( powerset @ X2522 ) )
| ~ ( in @ X2524 @ ( powerset @ X2522 ) )
| ~ ( in @ X2525 @ X2522 )
| ~ ( in @ X2525 @ ( setminus @ X2522 @ X2523 ) )
| ( in @ X2525 @ ( setminus @ X2522 @ ( binintersect @ X2523 @ X2524 ) ) ) )
& ( ~ ( in @ X2527 @ ( powerset @ X2526 ) )
| ~ ( in @ X2528 @ ( powerset @ X2526 ) )
| ( subset @ ( setminus @ X2526 @ X2527 ) @ ( setminus @ X2526 @ ( binintersect @ X2527 @ X2528 ) ) ) )
& ( ~ ( in @ X2530 @ ( powerset @ X2529 ) )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ( in @ ( setminus @ X2529 @ X2530 ) @ ( powerset @ ( setminus @ X2529 @ ( binintersect @ X2530 @ X2531 ) ) ) ) )
& ( ~ ( in @ X2533 @ ( powerset @ X2532 ) )
| ~ ( in @ X2534 @ ( powerset @ X2532 ) )
| ~ ( subset @ X2533 @ ( setminus @ X2532 @ X2534 ) )
| ~ ( in @ X2535 @ X2532 )
| ~ ( in @ X2535 @ X2534 )
| ( in @ X2535 @ ( setminus @ X2532 @ X2533 ) ) )
& ( ~ ( in @ X2537 @ ( powerset @ X2536 ) )
| ~ ( in @ X2538 @ ( powerset @ X2536 ) )
| ~ ( subset @ X2537 @ ( setminus @ X2536 @ X2538 ) )
| ( subset @ X2538 @ ( setminus @ X2536 @ X2537 ) ) )
& ( ~ ( in @ X2540 @ ( powerset @ X2539 ) )
| ~ ( in @ X2541 @ ( powerset @ X2539 ) )
| ~ ( in @ X2542 @ X2539 )
| ( in @ X2542 @ ( binunion @ X2540 @ X2541 ) )
| ~ ( in @ X2542 @ X2540 ) )
& ( ~ ( in @ X2544 @ ( powerset @ X2543 ) )
| ~ ( in @ X2545 @ ( powerset @ X2543 ) )
| ~ ( in @ X2546 @ X2543 )
| ( in @ X2546 @ ( binunion @ X2544 @ X2545 ) )
| ~ ( in @ X2546 @ X2545 ) )
& ( ~ ( in @ X2548 @ ( powerset @ X2547 ) )
| ~ ( in @ X2549 @ ( powerset @ X2547 ) )
| ~ ( in @ X2550 @ ( powerset @ X2547 ) )
| ~ ( in @ X2551 @ X2547 )
| ~ ( in @ X2551 @ ( binintersect @ X2548 @ X2549 ) )
| ( in @ X2551 @ ( binunion @ X2548 @ X2550 ) ) )
& ( ~ ( in @ X2553 @ ( powerset @ X2552 ) )
| ~ ( in @ X2554 @ ( powerset @ X2552 ) )
| ~ ( in @ X2555 @ ( powerset @ X2552 ) )
| ~ ( in @ X2556 @ X2552 )
| ~ ( in @ X2556 @ ( binintersect @ X2553 @ X2554 ) )
| ( in @ X2556 @ ( binunion @ X2554 @ X2555 ) ) )
& ( ~ ( in @ X2558 @ ( powerset @ X2557 ) )
| ~ ( in @ X2559 @ ( powerset @ X2557 ) )
| ~ ( in @ X2560 @ ( powerset @ X2557 ) )
| ~ ( in @ X2561 @ X2557 )
| ~ ( in @ X2561 @ ( binintersect @ X2558 @ X2559 ) )
| ( in @ X2561 @ ( binintersect @ ( binunion @ X2558 @ X2560 ) @ ( binunion @ X2559 @ X2560 ) ) ) )
& ( in @ esk88_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk89_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk90_0 @ ( powerset @ esk87_0 ) )
& ~ ( in @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( powerset @ ( binintersect @ ( binunion @ esk88_0 @ esk90_0 ) @ ( binunion @ esk89_0 @ esk90_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_345])])])])])])]) ).
thf(c_0_347,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_348,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ ( binintersect @ X3 @ X4 ) )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_349,negated_conjecture,
~ ( in @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( powerset @ ( binintersect @ ( binunion @ esk88_0 @ esk90_0 ) @ ( binunion @ esk89_0 @ esk90_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_350,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ ( binintersect @ X3 @ X4 ) ) )
| ~ ( subset @ X2 @ X4 )
| ~ ( subset @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_347,c_0_348]) ).
thf(c_0_351,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ X4 )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_352,negated_conjecture,
! [X2: $i,X3: $i] : ( subset @ X2 @ ( binunion @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_353,negated_conjecture,
( ~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( binunion @ esk89_0 @ esk90_0 ) )
| ~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( binunion @ esk88_0 @ esk90_0 ) ) ),
inference(spm,[status(thm)],[c_0_349,c_0_350]) ).
thf(c_0_354,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( subset @ X2 @ ( binunion @ X3 @ X4 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_351,c_0_352]) ).
thf(c_0_355,negated_conjecture,
! [X2: $i,X3: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_356,negated_conjecture,
~ ( subset @ ( binintersect @ esk88_0 @ esk89_0 ) @ ( binunion @ esk88_0 @ esk90_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_354]),c_0_355])]) ).
thf(c_0_357,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
thf(c_0_358,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_354]),c_0_357])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU743^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.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 15:35:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.46 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
% 24.13/4.48 # Version: 3.1.0-ho
% 24.13/4.48 # Preprocessing class: HSLMSLSSLLLCHFA.
% 24.13/4.48 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 24.13/4.48 # Starting ehoh_best5 with 300s (1) cores
% 24.13/4.48 # Starting almost_fo_3_lam with 300s (1) cores
% 24.13/4.48 # Starting new_bool_5 with 300s (1) cores
% 24.13/4.48 # Starting pre_casc_3 with 300s (1) cores
% 24.13/4.48 # Starting ho_unfolding_8 with 300s (1) cores
% 24.13/4.48 # Starting new_ho_10_cnf2 with 300s (1) cores
% 24.13/4.48 # Starting new_bool_3 with 300s (1) cores
% 24.13/4.48 # Starting new_ho_5 with 300s (1) cores
% 24.13/4.48 # pre_casc_3 with pid 29833 completed with status 8
% 24.13/4.48 # new_ho_5 with pid 29837 completed with status 8
% 24.13/4.48 # almost_fo_3_lam with pid 29831 completed with status 0
% 24.13/4.48 # Result found by almost_fo_3_lam
% 24.13/4.48 # Preprocessing class: HSLMSLSSLLLCHFA.
% 24.13/4.48 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 24.13/4.48 # Starting ehoh_best5 with 300s (1) cores
% 24.13/4.48 # Starting almost_fo_3_lam with 300s (1) cores
% 24.13/4.48 # No SInE strategy applied
% 24.13/4.48 # Search class: HGHSM-FSLM32-MHFMMSBN
% 24.13/4.48 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 24.13/4.48 # Starting ho_unfolding_8 with 55s (1) cores
% 24.13/4.48 # ho_unfolding_8 with pid 29854 completed with status 0
% 24.13/4.48 # Result found by ho_unfolding_8
% 24.13/4.48 # Preprocessing class: HSLMSLSSLLLCHFA.
% 24.13/4.48 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 24.13/4.48 # Starting ehoh_best5 with 300s (1) cores
% 24.13/4.48 # Starting almost_fo_3_lam with 300s (1) cores
% 24.13/4.48 # No SInE strategy applied
% 24.13/4.48 # Search class: HGHSM-FSLM32-MHFMMSBN
% 24.13/4.48 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 24.13/4.48 # Starting ho_unfolding_8 with 55s (1) cores
% 24.13/4.48 # Preprocessing time : 0.067 s
% 24.13/4.48 # Presaturation interreduction done
% 24.13/4.48
% 24.13/4.48 # Proof found!
% 24.13/4.48 # SZS status Theorem
% 24.13/4.48 # SZS output start CNFRefutation
% See solution above
% 24.13/4.49 # Parsed axioms : 561
% 24.13/4.49 # Removed by relevancy pruning/SinE : 0
% 24.13/4.49 # Initial clauses : 741
% 24.13/4.49 # Removed in clause preprocessing : 326
% 24.13/4.49 # Initial clauses in saturation : 415
% 24.13/4.49 # Processed clauses : 5575
% 24.13/4.49 # ...of these trivial : 37
% 24.13/4.49 # ...subsumed : 2753
% 24.13/4.49 # ...remaining for further processing : 2785
% 24.13/4.49 # Other redundant clauses eliminated : 69
% 24.13/4.49 # Clauses deleted for lack of memory : 0
% 24.13/4.49 # Backward-subsumed : 264
% 24.13/4.49 # Backward-rewritten : 38
% 24.13/4.49 # Generated clauses : 186514
% 24.13/4.49 # ...of the previous two non-redundant : 184768
% 24.13/4.49 # ...aggressively subsumed : 0
% 24.13/4.49 # Contextual simplify-reflections : 36
% 24.13/4.49 # Paramodulations : 186319
% 24.13/4.49 # Factorizations : 62
% 24.13/4.49 # NegExts : 40
% 24.13/4.49 # Equation resolutions : 77
% 24.13/4.49 # Disequality decompositions : 0
% 24.13/4.49 # Total rewrite steps : 19333
% 24.13/4.49 # ...of those cached : 18936
% 24.13/4.49 # Propositional unsat checks : 0
% 24.13/4.49 # Propositional check models : 0
% 24.13/4.49 # Propositional check unsatisfiable : 0
% 24.13/4.49 # Propositional clauses : 0
% 24.13/4.49 # Propositional clauses after purity: 0
% 24.13/4.49 # Propositional unsat core size : 0
% 24.13/4.49 # Propositional preprocessing time : 0.000
% 24.13/4.49 # Propositional encoding time : 0.000
% 24.13/4.49 # Propositional solver time : 0.000
% 24.13/4.49 # Success case prop preproc time : 0.000
% 24.13/4.49 # Success case prop encoding time : 0.000
% 24.13/4.49 # Success case prop solver time : 0.000
% 24.13/4.49 # Current number of processed clauses : 2106
% 24.13/4.49 # Positive orientable unit clauses : 70
% 24.13/4.49 # Positive unorientable unit clauses: 0
% 24.13/4.49 # Negative unit clauses : 116
% 24.13/4.49 # Non-unit-clauses : 1920
% 24.13/4.49 # Current number of unprocessed clauses: 179807
% 24.13/4.49 # ...number of literals in the above : 708978
% 24.13/4.49 # Current number of archived formulas : 0
% 24.13/4.49 # Current number of archived clauses : 664
% 24.13/4.49 # Clause-clause subsumption calls (NU) : 511933
% 24.13/4.49 # Rec. Clause-clause subsumption calls : 249730
% 24.13/4.49 # Non-unit clause-clause subsumptions : 1779
% 24.13/4.49 # Unit Clause-clause subsumption calls : 11104
% 24.13/4.49 # Rewrite failures with RHS unbound : 0
% 24.13/4.49 # BW rewrite match attempts : 100
% 24.13/4.49 # BW rewrite match successes : 19
% 24.13/4.49 # Condensation attempts : 0
% 24.13/4.49 # Condensation successes : 0
% 24.13/4.49 # Termbank termtop insertions : 3725913
% 24.13/4.49 # Search garbage collected termcells : 27052
% 24.13/4.49
% 24.13/4.49 # -------------------------------------------------
% 24.13/4.49 # User time : 3.778 s
% 24.13/4.49 # System time : 0.130 s
% 24.13/4.49 # Total time : 3.908 s
% 24.13/4.49 # Maximum resident set size: 8360 pages
% 24.13/4.49
% 24.13/4.49 # -------------------------------------------------
% 24.13/4.49 # User time : 3.980 s
% 24.13/4.49 # System time : 0.199 s
% 24.13/4.49 # Total time : 4.180 s
% 24.13/4.49 # Maximum resident set size: 2492 pages
% 24.13/4.49 % E---3.1 exiting
% 24.13/4.49 % E exiting
%------------------------------------------------------------------------------