%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU713^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 03:29:23 EDT 2024
% Result : Theorem 11.76s 2.42s
% Output : CNFRefutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 579
% Syntax : Number of formulae : 672 ( 40 unt; 345 typ; 0 def)
% Number of atoms : 2918 ( 616 equ; 0 cnn)
% Maximal formula atoms : 879 ( 8 avg)
% Number of connectives : 11768 ( 784 ~; 862 |; 536 &;7826 @)
% ( 322 <=>;1438 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1036 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 582 ( 582 >; 0 *; 0 +; 0 <<)
% Number of symbols : 349 ( 345 usr; 238 con; 0-4 aty)
% Number of variables : 2585 ( 182 ^2280 !; 123 ?;2585 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
epred1_0: $o ).
thf(decl_290,type,
esk1_2: $i > $i > $i ).
thf(decl_291,type,
esk2_2: $i > $i > $i ).
thf(decl_292,type,
esk3_2: $i > $i > $i ).
thf(decl_293,type,
esk4_1: $i > $i ).
thf(decl_294,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_295,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_296,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_297,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_298,type,
esk9_1: $i > $i ).
thf(decl_299,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_300,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_301,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_302,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_303,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_304,type,
esk15_2: $i > $i > $i ).
thf(decl_305,type,
esk16_2: $i > $i > $i ).
thf(decl_306,type,
esk17_1: $i > $i ).
thf(decl_307,type,
esk18_1: $i > $i ).
thf(decl_308,type,
esk19_1: $i > $i ).
thf(decl_309,type,
esk20_2: $i > $i > $i ).
thf(decl_310,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_311,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_312,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_313,type,
esk24_1: $i > $i ).
thf(decl_314,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_316,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_317,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_318,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_319,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_320,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_321,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_322,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_323,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_324,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_325,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_326,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_327,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_328,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_329,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_330,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_331,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_332,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_333,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_334,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_335,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_336,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_337,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_338,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_339,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_340,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_341,type,
esk52_2: $i > $i > $i ).
thf(decl_342,type,
esk53_2: $i > $i > $i ).
thf(decl_343,type,
esk54_2: $i > $i > $i ).
thf(decl_344,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_345,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_346,type,
esk57_2: $i > $i > $i ).
thf(decl_347,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_349,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_350,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_351,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_354,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_355,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_356,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_357,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_358,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_359,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_360,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_361,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_362,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_363,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_364,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_365,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_366,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_367,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_368,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_369,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_370,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_371,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_372,type,
esk83_0: $i ).
thf(decl_373,type,
esk84_0: $i ).
thf(decl_374,type,
esk85_0: $i ).
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(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(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(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(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(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(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(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(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(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(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(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(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(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(setminusT_lem,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
=> ! [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(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
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(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(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(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(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(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(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(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(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
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(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(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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
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(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
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(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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
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(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(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(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(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(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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
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(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(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(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(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_233,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_234,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_235,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_236,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_237,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_238,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_239,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_240,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_241,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_242,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_243,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_244,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_245,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_246,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_247,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_248,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_249,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_250,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_251,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_252,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_253,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_254,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_255,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_256,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_257,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_258,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_259,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_233]) ).
thf(c_0_260,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_233]) ).
thf(c_0_261,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_234,c_0_235]) ).
thf(c_0_262,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_233]) ).
thf(c_0_263,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_233]) ).
thf(c_0_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_275,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_276,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_236,c_0_235]) ).
thf(c_0_277,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_237,c_0_235]) ).
thf(c_0_278,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_238,c_0_235]) ).
thf(c_0_279,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_280,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_281,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_282,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_283,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_239,c_0_233]) ).
thf(c_0_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X779: $i] :
( ( X1 @ X779 )
& ! [X780: $i] :
( ( X1 @ X780 )
=> ( X779 = X780 ) ) )
=> ( ? [X781: $i] :
( ( X17 @ X781 )
& ! [X782: $i] :
( ( X17 @ X782 )
=> ( X781 = X782 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_240,c_0_241]) ).
thf(c_0_292,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X777: $i] :
( ( X1 @ X777 )
& ! [X778: $i] :
( ( X1 @ X778 )
=> ( X777 = X778 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_242,c_0_241]) ).
thf(c_0_293,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X773: $i] :
( ( X1 @ X773 )
& ! [X774: $i] :
( ( X1 @ X774 )
=> ( X773 = X774 ) ) )
<=> ? [X775: $i] :
( ( X17 @ X775 )
& ! [X776: $i] :
( ( X17 @ X776 )
=> ( X775 = X776 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_243,c_0_241]) ).
thf(c_0_294,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X771: $i] :
( ( X1 @ X771 )
& ! [X772: $i] :
( ( X1 @ X772 )
=> ( X771 = X772 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_244,c_0_241]) ).
thf(c_0_295,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X769: $i] :
( ( X1 @ X769 )
& ! [X770: $i] :
( ( X1 @ X770 )
=> ( X769 = X770 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_245,c_0_241]) ).
thf(c_0_296,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X767: $i] :
( ( X1 @ X767 )
& ! [X768: $i] :
( ( X1 @ X768 )
=> ( X767 = X768 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_246,c_0_241]) ).
thf(c_0_297,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X765: $i] :
( ( X1 @ X765 )
& ! [X766: $i] :
( ( X1 @ X766 )
=> ( X765 = X766 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_247,c_0_241]) ).
thf(c_0_298,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_299,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_248]) ).
thf(c_0_300,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X763: $i] :
( ( X1 @ X763 )
& ! [X764: $i] :
( ( X1 @ X764 )
=> ( X763 = X764 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_249,c_0_241]) ).
thf(c_0_301,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_302,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_248]) ).
thf(c_0_303,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_250,c_0_248]) ).
thf(c_0_304,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_248]) ).
thf(c_0_305,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_306,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X761: $i] :
( ( X1 @ X761 )
& ! [X762: $i] :
( ( X1 @ X762 )
=> ( X761 = X762 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_251,c_0_241]) ).
thf(c_0_307,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X759: $i] :
( ( X1 @ X759 )
& ! [X760: $i] :
( ( X1 @ X760 )
=> ( X759 = X760 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_252,c_0_241]) ).
thf(c_0_308,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_309,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_310,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_311,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X757: $i] :
( ( X1 @ X757 )
& ! [X758: $i] :
( ( X1 @ X758 )
=> ( X757 = X758 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_253,c_0_241]) ).
thf(c_0_312,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X755: $i] :
( ( X6 @ X2 @ X755 )
& ! [X756: $i] :
( ( X6 @ X2 @ X756 )
=> ( X755 = X756 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_254,c_0_241]) ).
thf(c_0_313,plain,
( epred1_0
<=> ! [X812: $i] :
? [X813: $i] :
( ! [X814: $i] :
( ( in @ X814 @ X813 )
=> ! [X815: $i] :
( ( in @ X815 @ X814 )
=> ( in @ X815 @ X812 ) ) )
& ! [X816: $i,X817: $i] :
( ( ( in @ X816 @ X812 )
& ( in @ X817 @ X812 ) )
=> ( ! [X818: $i] :
( ( in @ X818 @ X813 )
=> ( ( in @ X816 @ X818 )
<=> ( in @ X817 @ X818 ) ) )
=> ( X816 = X817 ) ) )
& ! [X819: $i,X820: $i] :
( ( ( in @ X819 @ X813 )
& ( in @ X820 @ X813 ) )
=> ( ! [X821: $i] :
( ( in @ X821 @ X819 )
=> ( in @ X821 @ X820 ) )
| ! [X822: $i] :
( ( in @ X822 @ X820 )
=> ( in @ X822 @ X819 ) ) ) )
& ! [X823: $i] :
( ( ! [X824: $i] :
( ( in @ X824 @ X823 )
=> ( in @ X824 @ X812 ) )
& ? [X825: $i] : ( in @ X825 @ X823 ) )
=> ? [X826: $i,X827: $i] :
( ( in @ X826 @ X813 )
& ( in @ X827 @ X823 )
& ~ ? [X828: $i] :
( ( in @ X828 @ X826 )
& ( in @ X828 @ X823 ) )
& ! [X829: $i] :
( ( in @ X829 @ X813 )
=> ( ! [X830: $i] :
( ( in @ X830 @ X829 )
=> ( in @ X830 @ X826 ) )
| ( in @ X827 @ X829 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_314,negated_conjecture,
~ ( ! [X783: $i,X784: $i] :
( ! [X785: $i] :
( ( in @ X785 @ X783 )
<=> ( in @ X785 @ X784 ) )
=> ( X783 = X784 ) )
=> ( ! [X786: $i] :
~ ( in @ X786 @ emptyset )
=> ( ! [X787: $i,X788: $i,X789: $i] :
( ( in @ X789 @ ( setadjoin @ X787 @ X788 ) )
<=> ( ( X789 = X787 )
| ( in @ X789 @ X788 ) ) )
=> ( ! [X790: $i,X791: $i] :
( ( in @ X791 @ ( powerset @ X790 ) )
<=> ! [X792: $i] :
( ( in @ X792 @ X791 )
=> ( in @ X792 @ X790 ) ) )
=> ( ! [X793: $i,X794: $i] :
( ( in @ X794 @ ( setunion @ X793 ) )
<=> ? [X795: $i] :
( ( in @ X794 @ X795 )
& ( in @ X795 @ X793 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X796: $i] :
( ( in @ X796 @ omega )
=> ( in @ ( setadjoin @ X796 @ X796 ) @ omega ) )
=> ( ! [X797: $i] :
( ( ( in @ emptyset @ X797 )
& ! [X798: $i] :
( ( ( in @ X798 @ omega )
& ( in @ X798 @ X797 ) )
=> ( in @ ( setadjoin @ X798 @ X798 ) @ X797 ) ) )
=> ! [X799: $i] :
( ( in @ X799 @ omega )
=> ( in @ X799 @ X797 ) ) )
=> ( ! [X800: $i > $i > $o,X801: $i] :
( ! [X802: $i] :
( ( in @ X802 @ X801 )
=> ? [X803: $i] :
( ( X800 @ X802 @ X803 )
& ! [X804: $i] :
( ( X800 @ X802 @ X804 )
=> ( X803 = X804 ) ) ) )
=> ? [X805: $i] :
! [X806: $i] :
( ( in @ X806 @ X805 )
<=> ? [X807: $i] :
( ( in @ X807 @ X801 )
& ( X800 @ X807 @ X806 ) ) ) )
=> ( ! [X808: $i] :
( ? [X809: $i] : ( in @ X809 @ X808 )
=> ? [X810: $i] :
( ( in @ X810 @ X808 )
& ~ ? [X811: $i] :
( ( in @ X811 @ X810 )
& ( in @ X811 @ X808 ) ) ) )
=> ( epred1_0
=> ( ! [X831: $i > $o] :
( ? [X832: $i] :
( ( X831 @ X832 )
& ! [X833: $i] :
( ( X831 @ X833 )
=> ( X832 = X833 ) ) )
=> ( X831
@ ( descr
@ ^ [Z0: $i] : ( X831 @ Z0 ) ) ) )
=> ( ! [X834: $i,X835: $i > $o,X836: $i] :
( ( in @ X836 @ X834 )
=> ( ( X835 @ X836 )
=> ( in @ X836 @ ( dsetconstr @ X834 @ X835 ) ) ) )
=> ( ! [X837: $i,X838: $i > $o,X839: $i] :
( ( in @ X839 @ ( dsetconstr @ X837 @ X838 ) )
=> ( in @ X839 @ X837 ) )
=> ( ! [X840: $i,X841: $i > $o,X842: $i] :
( ( in @ X842 @ ( dsetconstr @ X840 @ X841 ) )
=> ( X841 @ X842 ) )
=> ( ! [X843: $i > $o] :
( ? [X844: $i] :
( ( X843 @ X844 )
& ! [X845: $i] :
( ( X843 @ X845 )
=> ( X844 = X845 ) ) )
=> ? [X846: $i] :
( ( X843 @ X846 )
& ! [X847: $i] :
( ( X843 @ X847 )
=> ( X846 = X847 ) ) ) )
=> ( ! [X848: $o,X849: $i] :
( ( in @ X849 @ ( prop2set @ X848 ) )
=> X848 )
=> ( ! [X850: $i] :
( ( in @ X850 @ emptyset )
=> ! [X851: $o] : X851 )
=> ( ! [X852: $i] :
( ( in @ X852 @ emptyset )
=> ~ $true )
=> ( ! [X853: $i] :
~ ( in @ X853 @ emptyset )
=> ( ! [X854: $i > $o] :
( ? [X855: $i] :
( ( X854 @ X855 )
& ! [X856: $i] :
( ( X854 @ X856 )
=> ( X855 = X856 ) ) )
=> ? [X857: $i] : ( X854 @ X857 ) )
=> ( ! [X858: $i,X859: $i] :
( ! [X860: $i] :
( ( in @ X860 @ X858 )
=> ( in @ X860 @ X859 ) )
=> ( ! [X861: $i] :
( ( in @ X861 @ X859 )
=> ( in @ X861 @ X858 ) )
=> ( X858 = X859 ) ) )
=> ( ! [X862: $i] :
( ! [X863: $i] :
~ ( in @ X863 @ X862 )
=> ( X862 = emptyset ) )
=> ( ! [X864: $i] :
( ! [X865: $i] :
~ ( in @ X865 @ X864 )
=> ( X864 = emptyset ) )
=> ( ! [X866: $i,X867: $i > $o,X868: $i] :
( ( in @ X868 @ X866 )
=> ( ( in @ X868 @ ( dsetconstr @ X866 @ X867 ) )
<=> ( X867 @ X868 ) ) )
=> ( ! [X869: $i] :
( ( X869 != emptyset )
=> ? [X870: $i] : ( in @ X870 @ X869 ) )
=> ( ! [X871: $i,X872: $i > $o,X873: $i] :
( ( in @ X873 @ X871 )
=> ( ( X872 @ X873 )
=> ( ( dsetconstr @ X871 @ X872 )
!= emptyset ) ) )
=> ( ! [X874: $i] :
( ? [X875: $i] : ( in @ X875 @ X874 )
=> ( X874 != emptyset ) )
=> ( ! [X876: $i,X877: $i] : ( in @ X876 @ ( setadjoin @ X876 @ X877 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X878: $i,X879: $i,X880: $i] :
( ( in @ X880 @ X879 )
=> ( in @ X880 @ ( setadjoin @ X878 @ X879 ) ) )
=> ( ! [X881: $i,X882: $i,X883: $i] :
( ( in @ X883 @ ( setadjoin @ X881 @ X882 ) )
=> ! [X884: $o] :
( ( ( X883 = X881 )
=> X884 )
=> ( ( ( in @ X883 @ X882 )
=> X884 )
=> X884 ) ) )
=> ( ! [X885: $i,X886: $i,X887: $i] :
( ( in @ X887 @ ( setadjoin @ X885 @ X886 ) )
=> ( ( X887 = X885 )
| ( in @ X887 @ X886 ) ) )
=> ( ! [X888: $i] :
( ( dsetconstr @ X888
@ ^ [Z0: $i] : $true )
= X888 )
=> ( ! [X889: $i,X890: $i] :
( ! [X891: $i] :
( ( in @ X891 @ X890 )
=> ( in @ X891 @ X889 ) )
=> ( in @ X890 @ ( powerset @ X889 ) ) )
=> ( ! [X892: $i] : ( in @ emptyset @ ( powerset @ X892 ) )
=> ( ! [X893: $i] : ( in @ emptyset @ ( powerset @ X893 ) )
=> ( ! [X894: $i,X895: $i,X896: $i] :
( ( in @ X895 @ ( powerset @ X894 ) )
=> ( ( in @ X896 @ X895 )
=> ( in @ X896 @ X894 ) ) )
=> ( ! [X897: $i,X898: $i,X899: $i] :
( ( in @ X898 @ X899 )
=> ( ( in @ X899 @ X897 )
=> ( in @ X898 @ ( setunion @ X897 ) ) ) )
=> ( ! [X900: $i,X901: $i] :
( ( in @ X901 @ ( setunion @ X900 ) )
=> ! [X902: $o] :
( ! [X903: $i] :
( ( in @ X901 @ X903 )
=> ( ( in @ X903 @ X900 )
=> X902 ) )
=> X902 ) )
=> ( ! [X904: $i,X905: $i] :
( ( in @ X905 @ X904 )
=> ( in @ X905 @ ( powerset @ ( setunion @ X904 ) ) ) )
=> ( ! [X906: $i > $o] :
( ? [X907: $i] :
( ( X906 @ X907 )
& ! [X908: $i] :
( ( X906 @ X908 )
=> ( X907 = X908 ) ) )
=> ? [X909: $i] :
! [X910: $i] :
( ( X906 @ X910 )
<=> ( X910 = X909 ) ) )
=> ( ! [X911: $i] :
( ( X911 != emptyset )
=> ? [X912: $i] :
( ( in @ X912 @ X911 )
& $true ) )
=> ( ! [X913: $i,X914: $i] :
( ( in @ X913 @ ( setadjoin @ X914 @ emptyset ) )
=> ( X913 = X914 ) )
=> ( ! [X915: $i,X916: $i] :
( ( X915 != X916 )
=> ~ ( in @ X916 @ ( setadjoin @ X915 @ emptyset ) ) )
=> ( ! [X917: $i,X918: $i] :
( ( X917 = X918 )
=> ( in @ X917 @ ( setadjoin @ X918 @ emptyset ) ) )
=> ( ! [X919: $i,X920: $i] :
( ( in @ X919 @ ( setadjoin @ X920 @ emptyset ) )
=> ( in @ X920 @ ( setadjoin @ X919 @ emptyset ) ) )
=> ( ! [X921: $i,X922: $i,X923: $i] :
( ( in @ X923 @ ( setadjoin @ X921 @ ( setadjoin @ X922 @ emptyset ) ) )
=> ( ( X923 = X921 )
| ( X923 = X922 ) ) )
=> ( ! [X924: $i,X925: $i] : ( in @ X924 @ ( setadjoin @ X924 @ ( setadjoin @ X925 @ emptyset ) ) )
=> ( ! [X926: $i,X927: $i] : ( in @ X927 @ ( setadjoin @ X926 @ ( setadjoin @ X927 @ emptyset ) ) )
=> ( ! [X928: $i,X929: $i > $o] :
( ? [X930: $i] :
( ( in @ X930 @ X928 )
& ( X929 @ X930 ) )
=> ( ( ( dsetconstr @ X928 @ X929 )
= emptyset )
=> ~ $true ) )
=> ( ! [X931: $i > $o,X932: $i] :
( ( in @ X932 @ emptyset )
=> ( X931 @ X932 ) )
=> ( ! [X933: $i,X934: $i > $o] :
( ~ ! [X935: $i] :
( ( in @ X935 @ X933 )
=> ( X934 @ X935 ) )
=> ? [X936: $i] :
( ( in @ X936 @ X933 )
& ~ ( X934 @ X936 ) ) )
=> ( ! [X937: $i,X938: $i > $o] :
( ! [X939: $i] :
( ( in @ X939 @ X937 )
=> ~ ( X938 @ X939 ) )
=> ~ ? [X940: $i] :
( ( in @ X940 @ X937 )
& ( X938 @ X940 ) ) )
=> ( ! [X941: $i,X942: $i > $o] :
( ~ ? [X943: $i] :
( ( in @ X943 @ X941 )
& ( X942 @ X943 ) )
=> ! [X944: $i] :
( ( in @ X944 @ X941 )
=> ~ ( X942 @ X944 ) ) )
=> ( ! [X945: $i,X946: $i > $o] :
( ? [X947: $i] :
( ( in @ X947 @ X945 )
& ~ ( X946 @ X947 ) )
=> ~ ! [X948: $i] :
( ( in @ X948 @ X945 )
=> ( X946 @ X948 ) ) )
=> ( ! [X949: $o] :
( X949
=> ( in @ emptyset @ ( prop2set @ X949 ) ) )
=> ( prop2set2propI
=> ( ! [X950: $i,X951: $i > $o] :
( ~ ? [X952: $i] :
( ( in @ X952 @ X950 )
& ( X951 @ X952 ) )
=> ! [X953: $i] :
( ( in @ X953 @ X950 )
=> ~ ( X951 @ X953 ) ) )
=> ( ! [X954: $i,X955: $i > $o] :
( ~ ! [X956: $i] :
( ( in @ X956 @ X954 )
=> ( X955 @ X956 ) )
=> ? [X957: $i] :
( ( in @ X957 @ X954 )
& ~ ( X955 @ X957 ) ) )
=> ( ! [X958: $i > $o] :
( ? [X959: $i] :
( ( X958 @ X959 )
& ! [X960: $i] :
( ( X958 @ X960 )
=> ( X959 = X960 ) ) )
=> ? [X961: $i] :
( ( X958 @ X961 )
& ! [X962: $i] :
( ( X958 @ X962 )
=> ( X961 = X962 ) ) ) )
=> ( ! [X963: $i > $o] :
( ? [X964: $i] : ( X963 @ X964 )
=> ( ! [X965: $i,X966: $i] :
( ( X963 @ X965 )
=> ( ( X963 @ X966 )
=> ( X965 = X966 ) ) )
=> ? [X967: $i] :
( ( X963 @ X967 )
& ! [X968: $i] :
( ( X963 @ X968 )
=> ( X967 = X968 ) ) ) ) )
=> ( ! [X969: $i > $o] :
( ? [X970: $i] :
! [X971: $i] :
( ( X969 @ X971 )
<=> ( X971 = X970 ) )
=> ? [X972: $i] :
( ( X969 @ X972 )
& ! [X973: $i] :
( ( X969 @ X973 )
=> ( X972 = X973 ) ) ) )
=> ( ! [X974: $i,X975: $i] :
( ( X974 = X975 )
=> ! [X976: $i,X977: $i] :
( ( X976 = X977 )
=> ( ( in @ X976 @ X974 )
=> ( in @ X977 @ X975 ) ) ) )
=> ( ! [X978: $i,X979: $i] :
( ( X978 = X979 )
=> ! [X980: $i,X981: $i] :
( ( X980 = X981 )
=> ( ( in @ X980 @ X978 )
<=> ( in @ X981 @ X979 ) ) ) )
=> ( ! [X982: $i > $o] :
( ? [X983: $i] :
( ( X982 @ X983 )
& ! [X984: $i] :
( ( X982 @ X984 )
=> ( X983 = X984 ) ) )
=> ! [X985: $i,X986: $i] :
( ( X982 @ X985 )
=> ( ( X982 @ X986 )
=> ( X985 = X986 ) ) ) )
=> ( ! [X987: $i > $o,X988: $i > $o] :
( ! [X989: $i,X990: $i] :
( ( X989 = X990 )
=> ( ( X987 @ X989 )
<=> ( X988 @ X990 ) ) )
=> ( ? [X991: $i] :
( ( X987 @ X991 )
& ! [X992: $i] :
( ( X987 @ X992 )
=> ( X991 = X992 ) ) )
<=> ? [X993: $i] :
( ( X988 @ X993 )
& ! [X994: $i] :
( ( X988 @ X994 )
=> ( X993 = X994 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X995: $i,X996: $i] :
( ( X995 = X996 )
=> ! [X997: $i,X998: $i] :
( ( X997 = X998 )
=> ( ( setadjoin @ X995 @ X997 )
= ( setadjoin @ X996 @ X998 ) ) ) )
=> ( ! [X999: $i,X1000: $i] :
( ( X999 = X1000 )
=> ( ( powerset @ X999 )
= ( powerset @ X1000 ) ) )
=> ( ! [X1001: $i,X1002: $i] :
( ( X1001 = X1002 )
=> ( ( setunion @ X1001 )
= ( setunion @ X1002 ) ) )
=> ( ( omega = omega )
=> ( ! [X1003: $i > $o] :
( ? [X1004: $i] :
( ( X1003 @ X1004 )
& ! [X1005: $i] :
( ( X1003 @ X1005 )
=> ( X1004 = X1005 ) ) )
=> ! [X1006: $i,X1007: $i] :
( ( X1003 @ X1006 )
=> ( ( X1003 @ X1007 )
=> ( X1006 = X1007 ) ) ) )
=> ( ! [X1008: $i > $o,X1009: $i > $o] :
( ! [X1010: $i,X1011: $i] :
( ( X1010 = X1011 )
=> ( ( X1008 @ X1010 )
<=> ( X1009 @ X1011 ) ) )
=> ( ? [X1012: $i] :
( ( X1008 @ X1012 )
& ! [X1013: $i] :
( ( X1008 @ X1013 )
=> ( X1012 = X1013 ) ) )
=> ( ? [X1014: $i] :
( ( X1009 @ X1014 )
& ! [X1015: $i] :
( ( X1009 @ X1015 )
=> ( X1014 = X1015 ) ) )
=> ( ( descr @ X1008 )
= ( descr @ X1009 ) ) ) ) )
=> ( ! [X1016: $i,X1017: $i] :
( ( X1016 = X1017 )
=> ! [X1018: $i > $o,X1019: $i > $o] :
( ! [X1020: $i] :
( ( in @ X1020 @ X1016 )
=> ! [X1021: $i] :
( ( in @ X1021 @ X1017 )
=> ( ( X1020 = X1021 )
=> ( ( X1018 @ X1020 )
<=> ( X1019 @ X1021 ) ) ) ) )
=> ( ( dsetconstr @ X1016 @ X1018 )
= ( dsetconstr @ X1017 @ X1019 ) ) ) )
=> ( ! [X1022: $i,X1023: $i] :
( ! [X1024: $i] :
( ( in @ X1024 @ X1022 )
=> ( in @ X1024 @ X1023 ) )
=> ( subset @ X1022 @ X1023 ) )
=> ( ! [X1025: $i,X1026: $i] :
( ( X1025 = X1026 )
=> ( subset @ X1026 @ X1025 ) )
=> ( ! [X1027: $i,X1028: $i] :
( ( X1027 = X1028 )
=> ( subset @ X1027 @ X1028 ) )
=> ( ! [X1029: $i,X1030: $i] :
( ! [X1031: $i] :
( ( in @ X1031 @ X1029 )
=> ( in @ X1031 @ X1030 ) )
=> ( subset @ X1029 @ X1030 ) )
=> ( ! [X1032: $i] : ( subset @ emptyset @ X1032 )
=> ( ! [X1033: $i,X1034: $i,X1035: $i] :
( ( subset @ X1033 @ X1034 )
=> ( ( in @ X1035 @ X1033 )
=> ( in @ X1035 @ X1034 ) ) )
=> ( ! [X1036: $i,X1037: $i,X1038: $i] :
( ( subset @ X1036 @ X1037 )
=> ( ~ ( in @ X1038 @ X1037 )
=> ~ ( in @ X1038 @ X1036 ) ) )
=> ( ! [X1039: $i,X1040: $i,X1041: $i] :
( ( in @ X1041 @ X1039 )
=> ( ~ ( in @ X1041 @ X1040 )
=> ~ ( subset @ X1039 @ X1040 ) ) )
=> ( ! [X1042: $i,X1043: $i] :
( ~ ( subset @ X1042 @ X1043 )
=> ( X1042 != X1043 ) )
=> ( ! [X1044: $i,X1045: $i,X1046: $i] :
( ( in @ X1046 @ X1044 )
=> ( ~ ( in @ X1046 @ X1045 )
=> ( X1044 != X1045 ) ) )
=> ( ! [X1047: $i] : ( subset @ X1047 @ X1047 )
=> ( ! [X1048: $i,X1049: $i,X1050: $i] :
( ( subset @ X1048 @ X1049 )
=> ( ( subset @ X1049 @ X1050 )
=> ( subset @ X1048 @ X1050 ) ) )
=> ( ! [X1051: $i,X1052: $i] : ( subset @ X1052 @ ( setadjoin @ X1051 @ X1052 ) )
=> ( ! [X1053: $i,X1054: $i,X1055: $i] :
( ( subset @ X1053 @ X1055 )
=> ( subset @ X1053 @ ( setadjoin @ X1054 @ X1055 ) ) )
=> ( ! [X1056: $i,X1057: $i] :
( ( subset @ X1056 @ X1057 )
=> ( in @ X1056 @ ( powerset @ X1057 ) ) )
=> ( ! [X1058: $i,X1059: $i] :
( ( subset @ X1058 @ X1059 )
=> ( ( subset @ X1059 @ X1058 )
=> ( X1058 = X1059 ) ) )
=> ( ! [X1060: $i] :
( ( subset @ X1060 @ emptyset )
=> ( X1060 = emptyset ) )
=> ( ! [X1061: $i,X1062: $i] :
( ( subset @ X1062 @ X1061 )
=> ( in @ X1062 @ ( powerset @ X1061 ) ) )
=> ( ! [X1063: $i,X1064: $i] :
( ( in @ X1064 @ ( powerset @ X1063 ) )
=> ( subset @ X1064 @ X1063 ) )
=> ( ! [X1065: $i] : ( in @ X1065 @ ( powerset @ X1065 ) )
=> ( ! [X1066: $i,X1067: $i] :
( ( subset @ X1066 @ X1067 )
=> ( subset @ ( powerset @ X1066 ) @ ( powerset @ X1067 ) ) )
=> ( ! [X1068: $i,X1069: $i > $o] : ( in @ ( dsetconstr @ X1068 @ X1069 ) @ ( powerset @ X1068 ) )
=> ( ! [X1070: $i,X1071: $i > $o] : ( subset @ ( dsetconstr @ X1070 @ X1071 ) @ X1070 )
=> ( ! [X1072: $i,X1073: $i,X1074: $i] :
( ( in @ X1074 @ X1072 )
=> ( in @ X1074 @ ( binunion @ X1072 @ X1073 ) ) )
=> ( ! [X1075: $i,X1076: $i] : ( in @ X1076 @ ( setadjoin @ X1075 @ ( setadjoin @ X1076 @ emptyset ) ) )
=> ( ! [X1077: $i,X1078: $i,X1079: $i] :
( ( in @ X1079 @ X1078 )
=> ( in @ X1079 @ ( binunion @ X1077 @ X1078 ) ) )
=> ( ! [X1080: $i,X1081: $i,X1082: $i,X1083: $o] :
( ( in @ X1082 @ ( binunion @ X1080 @ X1081 ) )
=> ( ( ( in @ X1082 @ X1080 )
=> X1083 )
=> ( ( ( in @ X1082 @ X1081 )
=> X1083 )
=> X1083 ) ) )
=> ( ! [X1084: $i,X1085: $i,X1086: $i] :
( ( in @ X1086 @ ( binunion @ X1084 @ X1085 ) )
=> ( ( in @ X1086 @ X1084 )
| ( in @ X1086 @ X1085 ) ) )
=> ( ! [X1087: $i,X1088: $i] : ( subset @ X1087 @ ( binunion @ X1087 @ X1088 ) )
=> ( ! [X1089: $i,X1090: $i] : ( subset @ X1090 @ ( binunion @ X1089 @ X1090 ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( in @ X1093 @ X1091 )
=> ( ( in @ X1093 @ X1092 )
=> ( in @ X1093 @ ( binintersect @ X1091 @ X1092 ) ) ) )
=> ( ! [X1094: $i,X1095: $i,X1096: $i] :
( ( subset @ X1096 @ X1094 )
=> ( ( subset @ X1096 @ X1095 )
=> ( subset @ X1096 @ ( binintersect @ X1094 @ X1095 ) ) ) )
=> ( ! [X1097: $i,X1098: $i,X1099: $i] :
( ( in @ X1099 @ ( binintersect @ X1097 @ X1098 ) )
=> ( in @ X1099 @ X1097 ) )
=> ( ! [X1100: $i,X1101: $i] : ( subset @ ( binintersect @ X1100 @ X1101 ) @ X1100 )
=> ( ! [X1102: $i,X1103: $i] :
( ( subset @ X1102 @ X1103 )
=> ( ( binintersect @ X1102 @ X1103 )
= X1102 ) )
=> ( ! [X1104: $i,X1105: $i] :
( ( ( binintersect @ X1104 @ X1105 )
= X1105 )
=> ( subset @ X1105 @ X1104 ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ( in @ X1108 @ ( binintersect @ X1106 @ X1107 ) )
=> ( in @ X1108 @ X1107 ) )
=> ( ! [X1109: $i,X1110: $i] :
( ~ ? [X1111: $i] :
( ( in @ X1111 @ X1109 )
& ( in @ X1111 @ X1110 ) )
=> ( ( binintersect @ X1109 @ X1110 )
= emptyset ) )
=> ( ! [X1112: $i,X1113: $i] : ( subset @ ( binintersect @ X1112 @ X1113 ) @ X1113 )
=> ( ! [X1114: $i,X1115: $i] :
( ( subset @ X1115 @ X1114 )
=> ( ( binintersect @ X1114 @ X1115 )
= X1115 ) )
=> ( ! [X1116: $i,X1117: $i] :
( ( ( binintersect @ X1116 @ X1117 )
= X1116 )
=> ( subset @ X1116 @ X1117 ) )
=> ( ! [X1118: $i,X1119: $i,X1120: $i] :
( ( binintersect @ X1118 @ ( binunion @ X1119 @ X1120 ) )
= ( binunion @ ( binintersect @ X1118 @ X1119 ) @ ( binintersect @ X1118 @ X1120 ) ) )
=> ( ! [X1121: $i,X1122: $i,X1123: $i] :
( ( in @ X1123 @ X1121 )
=> ( ~ ( in @ X1123 @ X1122 )
=> ( in @ X1123 @ ( setminus @ X1121 @ X1122 ) ) ) )
=> ( ! [X1124: $i,X1125: $i,X1126: $i] :
( ( in @ X1126 @ ( setminus @ X1124 @ X1125 ) )
=> ( in @ X1126 @ X1124 ) )
=> ( ! [X1127: $i,X1128: $i,X1129: $i] :
( ( in @ X1129 @ ( setminus @ X1127 @ X1128 ) )
=> ~ ( in @ X1129 @ X1128 ) )
=> ( ! [X1130: $i,X1131: $i] :
( ( subset @ X1130 @ X1131 )
=> ( ( setminus @ X1130 @ X1131 )
= emptyset ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ~ ( in @ X1134 @ ( setminus @ X1132 @ X1133 ) )
=> ( ( in @ X1134 @ X1132 )
=> ( in @ X1134 @ X1133 ) ) )
=> ( ! [X1135: $i,X1136: $i,X1137: $i] :
( ~ ( in @ X1137 @ ( setminus @ X1135 @ X1136 ) )
=> ( ~ ( in @ X1137 @ X1136 )
=> ~ ( in @ X1137 @ X1135 ) ) )
=> ( ! [X1138: $i,X1139: $i,X1140: $i] :
( ~ ( in @ X1140 @ X1138 )
=> ~ ( in @ X1140 @ ( setminus @ X1138 @ X1139 ) ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i] :
( ( in @ X1143 @ X1142 )
=> ~ ( in @ X1143 @ ( setminus @ X1141 @ X1142 ) ) )
=> ( ! [X1144: $i,X1145: $i] : ( subset @ ( setminus @ X1144 @ X1145 ) @ X1144 )
=> ( ! [X1146: $i,X1147: $i] :
( ( ( setminus @ X1146 @ X1147 )
= emptyset )
=> ( subset @ X1146 @ X1147 ) )
=> ( ! [X1148: $i,X1149: $i,X1150: $i] :
( ( in @ X1150 @ ( symdiff @ X1148 @ X1149 ) )
=> ! [X1151: $o] :
( ( ( in @ X1150 @ X1148 )
=> ( ~ ( in @ X1150 @ X1149 )
=> X1151 ) )
=> ( ( ~ ( in @ X1150 @ X1148 )
=> ( ( in @ X1150 @ X1149 )
=> X1151 ) )
=> X1151 ) ) )
=> ( ! [X1152: $i,X1153: $i,X1154: $i] :
( ( in @ X1154 @ X1152 )
=> ( ~ ( in @ X1154 @ X1153 )
=> ( in @ X1154 @ ( symdiff @ X1152 @ X1153 ) ) ) )
=> ( ! [X1155: $i,X1156: $i,X1157: $i] :
( ~ ( in @ X1157 @ X1155 )
=> ( ( in @ X1157 @ X1156 )
=> ( in @ X1157 @ ( symdiff @ X1155 @ X1156 ) ) ) )
=> ( ! [X1158: $i,X1159: $i,X1160: $i] :
( ( in @ X1160 @ X1158 )
=> ( ( in @ X1160 @ X1159 )
=> ~ ( in @ X1160 @ ( symdiff @ X1158 @ X1159 ) ) ) )
=> ( ! [X1161: $i,X1162: $i,X1163: $i] :
( ~ ( in @ X1163 @ X1161 )
=> ( ~ ( in @ X1163 @ X1162 )
=> ~ ( in @ X1163 @ ( symdiff @ X1161 @ X1162 ) ) ) )
=> ( ! [X1164: $i,X1165: $i] : ( in @ X1165 @ ( setadjoin @ X1164 @ ( setadjoin @ X1165 @ emptyset ) ) )
=> ( ! [X1166: $i,X1167: $i] : ( in @ X1166 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1166 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1166 @ ( setadjoin @ X1167 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1168: $i,X1169: $i] : ( in @ X1169 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1168 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1168 @ ( setadjoin @ X1169 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1170: $i,X1171: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1170 @ ( setadjoin @ X1171 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1172: $i,X1173: $i] : ( iskpair @ ( kpair @ X1172 @ X1173 ) )
=> ( ! [X1174: $i,X1175: $i] :
( ( in @ X1175 @ X1174 )
=> ( subset @ ( setadjoin @ X1175 @ emptyset ) @ X1174 ) )
=> ( ! [X1176: $i,X1177: $i] :
( ( in @ X1177 @ X1176 )
=> ( in @ ( setadjoin @ X1177 @ emptyset ) @ ( powerset @ X1176 ) ) )
=> ( ! [X1178: $i,X1179: $i,X1180: $i] :
( ( in @ X1180 @ X1178 )
=> ( in @ ( setadjoin @ X1180 @ emptyset ) @ ( powerset @ ( binunion @ X1178 @ X1179 ) ) ) )
=> ( ! [X1181: $i,X1182: $i,X1183: $i] :
( ( in @ X1183 @ ( setadjoin @ X1181 @ ( setadjoin @ X1182 @ emptyset ) ) )
=> ( ( X1183 = X1181 )
| ( X1183 = X1182 ) ) )
=> ( ! [X1184: $i,X1185: $i,X1186: $i] :
( ( in @ X1186 @ X1184 )
=> ! [X1187: $i] :
( ( in @ X1187 @ X1185 )
=> ( subset @ ( setadjoin @ X1186 @ ( setadjoin @ X1187 @ emptyset ) ) @ ( binunion @ X1184 @ X1185 ) ) ) )
=> ( ! [X1188: $i,X1189: $i,X1190: $i] :
( ( in @ X1190 @ X1188 )
=> ! [X1191: $i] :
( ( in @ X1191 @ X1189 )
=> ( in @ ( setadjoin @ X1190 @ ( setadjoin @ X1191 @ emptyset ) ) @ ( powerset @ ( binunion @ X1188 @ X1189 ) ) ) ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i] :
( ( in @ X1194 @ X1192 )
=> ! [X1195: $i] :
( ( in @ X1195 @ X1193 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1194 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1194 @ ( setadjoin @ X1195 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1192 @ X1193 ) ) ) ) )
=> ( ! [X1196: $i,X1197: $i,X1198: $i] :
( ( in @ X1198 @ X1196 )
=> ! [X1199: $i] :
( ( in @ X1199 @ X1197 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1198 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1198 @ ( setadjoin @ X1199 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1196 @ X1197 ) ) ) ) ) )
=> ( ! [X1200: $i,X1201: $i,X1202: $i] :
( ( in @ X1202 @ X1200 )
=> ! [X1203: $i] :
( ( in @ X1203 @ X1201 )
=> ( in @ ( kpair @ X1202 @ X1203 ) @ ( powerset @ ( powerset @ ( binunion @ X1200 @ X1201 ) ) ) ) ) )
=> ( ! [X1204: $i,X1205: $i,X1206: $i] :
( ( in @ X1206 @ X1204 )
=> ! [X1207: $i] :
( ( in @ X1207 @ X1205 )
=> ( in @ ( kpair @ X1206 @ X1207 ) @ ( cartprod @ X1204 @ X1205 ) ) ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ( in @ X1210 @ ( cartprod @ X1208 @ X1209 ) )
=> ? [X1211: $i] :
( ( in @ X1211 @ X1208 )
& ? [X1212: $i] :
( ( in @ X1212 @ X1209 )
& ( X1210
= ( kpair @ X1211 @ X1212 ) ) ) ) )
=> ( ! [X1213: $i,X1214: $i,X1215: $i] :
( ( in @ X1215 @ ( cartprod @ X1213 @ X1214 ) )
=> ( iskpair @ X1215 ) )
=> ( ! [X1216: $i,X1217: $i] :
( ( in @ X1217 @ ( setunion @ X1216 ) )
=> ? [X1218: $i] :
( ( in @ X1218 @ X1216 )
& ( in @ X1217 @ X1218 ) ) )
=> ( ! [X1219: $i] : ( subset @ ( setunion @ ( setadjoin @ X1219 @ emptyset ) ) @ X1219 )
=> ( ! [X1220: $i] : ( subset @ X1220 @ ( setunion @ ( setadjoin @ X1220 @ emptyset ) ) )
=> ( ! [X1221: $i] :
( ( setunion @ ( setadjoin @ X1221 @ emptyset ) )
= X1221 )
=> ( ! [X1222: $i,X1223: $i > $o] :
( ! [X1224: $i] :
( ( in @ X1224 @ X1222 )
=> ! [X1225: $i] :
( ( in @ X1225 @ X1222 )
=> ( ( X1223 @ X1224 )
=> ( ( X1223 @ X1225 )
=> ( X1224 = X1225 ) ) ) ) )
=> ( ? [X1226: $i] :
( ( in @ X1226 @ X1222 )
& ( X1223 @ X1226 ) )
=> ( singleton @ ( dsetconstr @ X1222 @ X1223 ) ) ) )
=> ( ! [X1227: $i,X1228: $i > $o] :
( ( singleton @ ( dsetconstr @ X1227 @ X1228 ) )
=> ? [X1229: $i] :
( ( in @ X1229 @ X1227 )
& ( X1228 @ X1229 ) ) )
=> ( ! [X1230: $i,X1231: $i > $o,X1232: $i] :
( ( in @ X1232 @ X1230 )
=> ( ( X1231 @ X1232 )
=> ( ! [X1233: $i] :
( ( in @ X1233 @ X1230 )
=> ( ( X1231 @ X1233 )
=> ( X1233 = X1232 ) ) )
=> ( singleton @ ( dsetconstr @ X1230 @ X1231 ) ) ) ) )
=> ( ! [X1234: $i,X1235: $i > $o] :
( ! [X1236: $i] :
( ( in @ X1236 @ X1234 )
=> ! [X1237: $i] :
( ( in @ X1237 @ X1234 )
=> ( ( X1235 @ X1236 )
=> ( ( X1235 @ X1237 )
=> ( X1236 = X1237 ) ) ) ) )
=> ( ? [X1238: $i] :
( ( in @ X1238 @ X1234 )
& ( X1235 @ X1238 ) )
=> ( singleton @ ( dsetconstr @ X1234 @ X1235 ) ) ) )
=> ( ! [X1239: $i,X1240: $i] :
( ( ( setadjoin @ X1239 @ emptyset )
= ( setadjoin @ X1240 @ emptyset ) )
=> ( X1239 = X1240 ) )
=> ( ! [X1241: $i,X1242: $i,X1243: $i] :
( ( in @ ( setadjoin @ X1243 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1241 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1241 @ ( setadjoin @ X1242 @ emptyset ) ) @ emptyset ) ) )
=> ( X1241 = X1243 ) )
=> ( ! [X1244: $i] :
( ( iskpair @ X1244 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1244 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1244 ) ) ) )
=> ( ! [X1245: $i] :
( ( singleton @ X1245 )
=> ( in @ ( setunion @ X1245 ) @ X1245 ) )
=> ( ! [X1246: $i,X1247: $i] :
( ( kfst @ ( kpair @ X1246 @ X1247 ) )
= X1246 )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ ( cartprod @ X1248 @ X1249 ) )
=> ( in @ ( kfst @ X1250 ) @ X1248 ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i,X1254: $i] :
( ( ( setadjoin @ ( setadjoin @ X1251 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1251 @ ( setadjoin @ X1252 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1253 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1253 @ ( setadjoin @ X1254 @ emptyset ) ) @ emptyset ) ) )
=> ( X1251 = X1253 ) )
=> ( ! [X1255: $i,X1256: $i,X1257: $i,X1258: $i] :
( ( ( kpair @ X1255 @ X1256 )
= ( kpair @ X1257 @ X1258 ) )
=> ( X1255 = X1257 ) )
=> ( ! [X1259: $i,X1260: $i] :
( ( X1259 = X1260 )
=> ( ( setadjoin @ X1259 @ ( setadjoin @ X1260 @ emptyset ) )
= ( setadjoin @ X1259 @ emptyset ) ) )
=> ( ! [X1261: $i,X1262: $i] :
( ( X1261 = X1262 )
=> ( ( setadjoin @ ( setadjoin @ X1261 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1261 @ ( setadjoin @ X1262 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1261 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1263: $i,X1264: $i,X1265: $i,X1266: $i] :
( ( ( setadjoin @ ( setadjoin @ X1263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1263 @ ( setadjoin @ X1264 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1265 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1265 @ ( setadjoin @ X1266 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1265 = X1266 )
=> ( X1264 = X1266 ) ) )
=> ( ! [X1267: $i,X1268: $i,X1269: $i] :
( ( ( setadjoin @ X1267 @ ( setadjoin @ X1268 @ emptyset ) )
= ( setadjoin @ X1269 @ emptyset ) )
=> ( X1267 = X1268 ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i,X1273: $i] :
( ( ( setadjoin @ ( setadjoin @ X1270 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1270 @ ( setadjoin @ X1271 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1272 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1272 @ ( setadjoin @ X1273 @ emptyset ) ) @ emptyset ) ) )
=> ( X1271 = X1273 ) )
=> ( ! [X1274: $i,X1275: $i,X1276: $i,X1277: $i] :
( ( ( kpair @ X1274 @ X1275 )
= ( kpair @ X1276 @ X1277 ) )
=> ( X1275 = X1277 ) )
=> ( ! [X1278: $i] :
( ( iskpair @ X1278 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1278 )
@ ^ [Z0: $i] :
( X1278
= ( kpair @ ( kfst @ X1278 ) @ Z0 ) ) ) ) )
=> ( ! [X1279: $i,X1280: $i] :
( ( ksnd @ ( kpair @ X1279 @ X1280 ) )
= X1280 )
=> ( ! [X1281: $i] :
( ( iskpair @ X1281 )
=> ( ( kpair @ ( kfst @ X1281 ) @ ( ksnd @ X1281 ) )
= X1281 ) )
=> ( ! [X1282: $i,X1283: $i,X1284: $i] :
( ( in @ X1284 @ ( cartprod @ X1282 @ X1283 ) )
=> ( in @ ( ksnd @ X1284 ) @ X1283 ) )
=> ( ! [X1285: $i,X1286: $i,X1287: $i,X1288: $i] :
( ( in @ ( kpair @ X1287 @ X1288 ) @ ( cartprod @ X1285 @ X1286 ) )
=> ( in @ X1287 @ X1285 ) )
=> ( ! [X1289: $i,X1290: $i,X1291: $i,X1292: $i] :
( ( in @ ( kpair @ X1291 @ X1292 ) @ ( cartprod @ X1289 @ X1290 ) )
=> ( in @ X1292 @ X1290 ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i] :
( ( in @ X1295 @ X1293 )
=> ! [X1296: $i] :
( ( in @ X1296 @ X1294 )
=> ( ( kpair @ X1295 @ X1296 )
= ( kpair @ X1295 @ X1296 ) ) ) )
=> ( ! [X1297: $i,X1298: $i,X1299: $i] :
( ( in @ X1299 @ X1297 )
=> ! [X1300: $i] :
( ( in @ X1300 @ X1298 )
=> ( ( kfst @ ( kpair @ X1299 @ X1300 ) )
= X1299 ) ) )
=> ( ! [X1301: $i,X1302: $i,X1303: $i] :
( ( in @ X1303 @ X1301 )
=> ! [X1304: $i] :
( ( in @ X1304 @ X1302 )
=> ( ( ksnd @ ( kpair @ X1303 @ X1304 ) )
= X1304 ) ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( in @ X1307 @ ( cartprod @ X1305 @ X1306 ) )
=> ( ( kpair @ ( kfst @ X1307 ) @ ( ksnd @ X1307 ) )
= X1307 ) )
=> ( ! [X1308: $i,X1309: $i,X1310: $i > $i > $o,X1311: $i] :
( ( in @ X1311 @ X1308 )
=> ! [X1312: $i] :
( ( in @ X1312 @ X1309 )
=> ( ( X1310 @ X1311 @ X1312 )
=> ( in @ ( kpair @ X1311 @ X1312 ) @ ( dpsetconstr @ X1308 @ X1309 @ X1310 ) ) ) ) )
=> ( ! [X1313: $i,X1314: $i,X1315: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1313 @ X1314 @ X1315 ) @ ( cartprod @ X1313 @ X1314 ) )
=> ( ! [X1316: $i,X1317: $i,X1318: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1316 @ X1317 @ X1318 ) @ ( cartprod @ X1316 @ X1317 ) )
=> ( ! [X1319: $i,X1320: $i,X1321: $i > $i > $o,X1322: $i] :
( ( in @ X1322 @ X1319 )
=> ! [X1323: $i] :
( ( in @ X1323 @ X1320 )
=> ( ( in @ ( kpair @ X1322 @ X1323 ) @ ( dpsetconstr @ X1319 @ X1320 @ X1321 ) )
=> ( X1321 @ X1322 @ X1323 ) ) ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i > $i > $o,X1327: $i,X1328: $i] :
( ( in @ ( kpair @ X1327 @ X1328 ) @ ( dpsetconstr @ X1324 @ X1325 @ X1326 ) )
=> ( in @ X1327 @ X1324 ) )
=> ( ! [X1329: $i,X1330: $i,X1331: $i > $i > $o,X1332: $i,X1333: $i] :
( ( in @ ( kpair @ X1332 @ X1333 ) @ ( dpsetconstr @ X1329 @ X1330 @ X1331 ) )
=> ( in @ X1333 @ X1330 ) )
=> ( ! [X1334: $i,X1335: $i,X1336: $i > $i > $o,X1337: $i,X1338: $i] :
( ( in @ ( kpair @ X1337 @ X1338 ) @ ( dpsetconstr @ X1334 @ X1335 @ X1336 ) )
=> ( X1336 @ X1337 @ X1338 ) )
=> ( ! [X1339: $i,X1340: $i,X1341: $i] :
( ( func @ X1339 @ X1340 @ X1341 )
=> ! [X1342: $i] :
( ( in @ X1342 @ X1339 )
=> ( singleton
@ ( dsetconstr @ X1340
@ ^ [Z0: $i] : ( in @ ( kpair @ X1342 @ Z0 ) @ X1341 ) ) ) ) )
=> ( ! [X1343: $i,X1344: $i,X1345: $i] :
( ( func @ X1343 @ X1344 @ X1345 )
=> ! [X1346: $i] :
( ( in @ X1346 @ X1343 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1344
@ ^ [Z0: $i] : ( in @ ( kpair @ X1346 @ Z0 ) @ X1345 ) ) )
@ X1344 ) ) )
=> ( ! [X1347: $i,X1348: $i,X1349: $i] :
( ( func @ X1347 @ X1348 @ X1349 )
=> ! [X1350: $i] :
( ( in @ X1350 @ X1347 )
=> ( in @ ( ap @ X1347 @ X1348 @ X1349 @ X1350 ) @ X1348 ) ) )
=> ( ! [X1351: $i,X1352: $i,X1353: $i] :
( ( in @ X1353 @ ( funcSet @ X1351 @ X1352 ) )
=> ( func @ X1351 @ X1352 @ X1353 ) )
=> ( ! [X1354: $i,X1355: $i,X1356: $i] :
( ( in @ X1356 @ ( funcSet @ X1354 @ X1355 ) )
=> ! [X1357: $i] :
( ( in @ X1357 @ X1354 )
=> ( in @ ( ap @ X1354 @ X1355 @ X1356 @ X1357 ) @ X1355 ) ) )
=> ( ! [X1358: $i,X1359: $i,X1360: $i] :
( ( func @ X1358 @ X1359 @ X1360 )
=> ( in @ X1360 @ ( funcSet @ X1358 @ X1359 ) ) )
=> ( ! [X1361: $i,X1362: $i,X1363: $i > $i] :
( ! [X1364: $i] :
( ( in @ X1364 @ X1361 )
=> ( in @ ( X1363 @ X1364 ) @ X1362 ) )
=> ( func @ X1361 @ X1362
@ ( dpsetconstr @ X1361 @ X1362
@ ^ [Z0: $i] : ( $eq @ ( X1363 @ Z0 ) ) ) ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i > $i] :
( ! [X1368: $i] :
( ( in @ X1368 @ X1365 )
=> ( in @ ( X1367 @ X1368 ) @ X1366 ) )
=> ( func @ X1365 @ X1366 @ ( lam @ X1365 @ X1366 @ X1367 ) ) )
=> ( ! [X1369: $i,X1370: $i,X1371: $i > $i] :
( ! [X1372: $i] :
( ( in @ X1372 @ X1369 )
=> ( in @ ( X1371 @ X1372 ) @ X1370 ) )
=> ( in @ ( lam @ X1369 @ X1370 @ X1371 ) @ ( funcSet @ X1369 @ X1370 ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( subset @ X1375 @ ( cartprod @ X1373 @ X1374 ) )
=> ! [X1376: $i > $o] :
( ! [X1377: $i] :
( ( in @ X1377 @ X1373 )
=> ! [X1378: $i] :
( ( in @ X1378 @ X1374 )
=> ( ( in @ ( kpair @ X1377 @ X1378 ) @ X1375 )
=> ( X1376 @ ( kpair @ X1377 @ X1378 ) ) ) ) )
=> ! [X1379: $i] :
( ( in @ X1379 @ X1375 )
=> ( X1376 @ X1379 ) ) ) )
=> ( ! [X1380: $i,X1381: $i,X1382: $i] :
( ( subset @ X1382 @ ( cartprod @ X1380 @ X1381 ) )
=> ! [X1383: $i > $o] :
( ! [X1384: $i] :
( ( in @ X1384 @ X1380 )
=> ! [X1385: $i] :
( ( in @ X1385 @ X1381 )
=> ( ( in @ ( kpair @ X1384 @ X1385 ) @ X1382 )
=> ( X1383 @ ( kpair @ X1384 @ X1385 ) ) ) ) )
=> ! [X1386: $i] :
( ( in @ X1386 @ X1382 )
=> ( X1383 @ X1386 ) ) ) )
=> ( ! [X1387: $i,X1388: $i > $o] :
( ( singleton @ ( dsetconstr @ X1387 @ X1388 ) )
=> ! [X1389: $i] :
( ( in @ X1389 @ X1387 )
=> ! [X1390: $i] :
( ( in @ X1390 @ X1387 )
=> ( ( X1388 @ X1389 )
=> ( ( X1388 @ X1390 )
=> ( X1389 = X1390 ) ) ) ) ) )
=> ( ! [X1391: $i,X1392: $i,X1393: $i] :
( ( func @ X1391 @ X1392 @ X1393 )
=> ! [X1394: $i] :
( ( in @ X1394 @ X1391 )
=> ( in @ ( kpair @ X1394 @ ( ap @ X1391 @ X1392 @ X1393 @ X1394 ) ) @ X1393 ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i] :
( ( in @ X1397 @ ( funcSet @ X1395 @ X1396 ) )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1395 )
=> ( in @ ( kpair @ X1398 @ ( ap @ X1395 @ X1396 @ X1397 @ X1398 ) ) @ X1397 ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( func @ X1399 @ X1400 @ X1401 )
=> ! [X1402: $i] :
( ( in @ X1402 @ X1399 )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1400 )
=> ( ( in @ ( kpair @ X1402 @ X1403 ) @ X1401 )
=> ( ( ap @ X1399 @ X1400 @ X1401 @ X1402 )
= X1403 ) ) ) ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i] :
( ( func @ X1404 @ X1405 @ X1406 )
=> ! [X1407: $i] :
( ( func @ X1404 @ X1405 @ X1407 )
=> ( ! [X1408: $i] :
( ( in @ X1408 @ X1404 )
=> ( ( ap @ X1404 @ X1405 @ X1406 @ X1408 )
= ( ap @ X1404 @ X1405 @ X1407 @ X1408 ) ) )
=> ! [X1409: $i] :
( ( in @ X1409 @ X1404 )
=> ! [X1410: $i] :
( ( in @ X1410 @ X1405 )
=> ( ( in @ ( kpair @ X1409 @ X1410 ) @ X1407 )
=> ( in @ ( kpair @ X1409 @ X1410 ) @ X1406 ) ) ) ) ) ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i] :
( ( in @ X1413 @ ( funcSet @ X1411 @ X1412 ) )
=> ! [X1414: $i] :
( ( in @ X1414 @ X1411 )
=> ! [X1415: $i] :
( ( in @ X1415 @ X1412 )
=> ( ( in @ ( kpair @ X1414 @ X1415 ) @ X1413 )
=> ( ( ap @ X1411 @ X1412 @ X1413 @ X1414 )
= X1415 ) ) ) ) )
=> ( ! [X1416: $i,X1417: $i,X1418: $i] :
( ( subset @ X1418 @ ( cartprod @ X1416 @ X1417 ) )
=> ! [X1419: $i] :
( ( subset @ X1419 @ ( cartprod @ X1416 @ X1417 ) )
=> ( ! [X1420: $i] :
( ( in @ X1420 @ X1416 )
=> ! [X1421: $i] :
( ( in @ X1421 @ X1417 )
=> ( ( in @ ( kpair @ X1420 @ X1421 ) @ X1418 )
=> ( in @ ( kpair @ X1420 @ X1421 ) @ X1419 ) ) ) )
=> ( subset @ X1418 @ X1419 ) ) ) )
=> ( ! [X1422: $i,X1423: $i,X1424: $i] :
( ( subset @ X1424 @ ( cartprod @ X1422 @ X1423 ) )
=> ! [X1425: $i] :
( ( subset @ X1425 @ ( cartprod @ X1422 @ X1423 ) )
=> ( ! [X1426: $i] :
( ( in @ X1426 @ X1422 )
=> ! [X1427: $i] :
( ( in @ X1427 @ X1423 )
=> ( ( in @ ( kpair @ X1426 @ X1427 ) @ X1424 )
=> ( in @ ( kpair @ X1426 @ X1427 ) @ X1425 ) ) ) )
=> ( ! [X1428: $i] :
( ( in @ X1428 @ X1422 )
=> ! [X1429: $i] :
( ( in @ X1429 @ X1423 )
=> ( ( in @ ( kpair @ X1428 @ X1429 ) @ X1425 )
=> ( in @ ( kpair @ X1428 @ X1429 ) @ X1424 ) ) ) )
=> ( X1424 = X1425 ) ) ) ) )
=> ( ! [X1430: $i,X1431: $i,X1432: $i] :
( ( func @ X1430 @ X1431 @ X1432 )
=> ! [X1433: $i] :
( ( func @ X1430 @ X1431 @ X1433 )
=> ( ! [X1434: $i] :
( ( in @ X1434 @ X1430 )
=> ( ( ap @ X1430 @ X1431 @ X1432 @ X1434 )
= ( ap @ X1430 @ X1431 @ X1433 @ X1434 ) ) )
=> ( X1432 = X1433 ) ) ) )
=> ( ! [X1435: $i,X1436: $i,X1437: $i] :
( ( in @ X1437 @ ( funcSet @ X1435 @ X1436 ) )
=> ! [X1438: $i] :
( ( in @ X1438 @ ( funcSet @ X1435 @ X1436 ) )
=> ( ! [X1439: $i] :
( ( in @ X1439 @ X1435 )
=> ( ( ap @ X1435 @ X1436 @ X1437 @ X1439 )
= ( ap @ X1435 @ X1436 @ X1438 @ X1439 ) ) )
=> ( X1437 = X1438 ) ) ) )
=> ( ! [X1440: $i,X1441: $i,X1442: $i] :
( ( in @ X1442 @ ( funcSet @ X1440 @ X1441 ) )
=> ! [X1443: $i] :
( ( in @ X1443 @ X1440 )
=> ( ( ap @ X1440 @ X1441 @ X1442 @ X1443 )
= ( ap @ X1440 @ X1441 @ X1442 @ X1443 ) ) ) )
=> ( ! [X1444: $i,X1445: $i,X1446: $i] :
( ( func @ X1444 @ X1445 @ X1446 )
=> ! [X1447: $i] :
( ( in @ X1447 @ X1444 )
=> ( ( ap @ X1444 @ X1445 @ X1446 @ X1447 )
= ( ap @ X1444 @ X1445 @ X1446 @ X1447 ) ) ) )
=> ( ! [X1448: $i,X1449: $i,X1450: $i > $i] :
( ! [X1451: $i] :
( ( in @ X1451 @ X1448 )
=> ( in @ ( X1450 @ X1451 ) @ X1449 ) )
=> ! [X1452: $i] :
( ( in @ X1452 @ X1448 )
=> ( ( ap @ X1448 @ X1449 @ ( lam @ X1448 @ X1449 @ X1450 ) @ X1452 )
= ( X1450 @ X1452 ) ) ) )
=> ( ! [X1453: $i,X1454: $i,X1455: $i] :
( ( func @ X1453 @ X1454 @ X1455 )
=> ( ( lam @ X1453 @ X1454 @ ( ap @ X1453 @ X1454 @ X1455 ) )
= X1455 ) )
=> ( ! [X1456: $i,X1457: $i,X1458: $i > $i] :
( ! [X1459: $i] :
( ( in @ X1459 @ X1456 )
=> ( in @ ( X1458 @ X1459 ) @ X1457 ) )
=> ( ( lam @ X1456 @ X1457 @ X1458 )
= ( lam @ X1456 @ X1457 @ X1458 ) ) )
=> ( ! [X1460: $i,X1461: $i,X1462: $i > $i] :
( ! [X1463: $i] :
( ( in @ X1463 @ X1460 )
=> ( in @ ( X1462 @ X1463 ) @ X1461 ) )
=> ! [X1464: $i] :
( ( in @ X1464 @ X1460 )
=> ( ( ap @ X1460 @ X1461 @ ( lam @ X1460 @ X1461 @ X1462 ) @ X1464 )
= ( X1462 @ X1464 ) ) ) )
=> ( ! [X1465: $i,X1466: $i,X1467: $i] :
( ( in @ X1467 @ ( funcSet @ X1465 @ X1466 ) )
=> ( ( lam @ X1465 @ X1466 @ ( ap @ X1465 @ X1466 @ X1467 ) )
= X1467 ) )
=> ( ! [X1468: $i,X1469: $o,X1470: $i] :
( ( in @ X1470 @ X1468 )
=> ! [X1471: $i] :
( ( in @ X1471 @ X1468 )
=> ( ~ X1469
=> ( in @ X1471
@ ( dsetconstr @ X1468
@ ^ [Z0: $i] :
( ( X1469
& ( Z0 = X1470 ) )
| ( ~ X1469
& ( Z0 = X1471 ) ) ) ) ) ) ) )
=> ( ! [X1472: $i,X1473: $o,X1474: $i] :
( ( in @ X1474 @ X1472 )
=> ! [X1475: $i] :
( ( in @ X1475 @ X1472 )
=> ( ~ X1473
=> ( ( dsetconstr @ X1472
@ ^ [Z0: $i] :
( ( X1473
& ( Z0 = X1474 ) )
| ( ~ X1473
& ( Z0 = X1475 ) ) ) )
= ( setadjoin @ X1475 @ emptyset ) ) ) ) )
=> ( ! [X1476: $i,X1477: $o,X1478: $i] :
( ( in @ X1478 @ X1476 )
=> ! [X1479: $i] :
( ( in @ X1479 @ X1476 )
=> ( X1477
=> ( in @ X1478
@ ( dsetconstr @ X1476
@ ^ [Z0: $i] :
( ( X1477
& ( Z0 = X1478 ) )
| ( ~ X1477
& ( Z0 = X1479 ) ) ) ) ) ) ) )
=> ( ! [X1480: $i,X1481: $o,X1482: $i] :
( ( in @ X1482 @ X1480 )
=> ! [X1483: $i] :
( ( in @ X1483 @ X1480 )
=> ( X1481
=> ( ( dsetconstr @ X1480
@ ^ [Z0: $i] :
( ( X1481
& ( Z0 = X1482 ) )
| ( ~ X1481
& ( Z0 = X1483 ) ) ) )
= ( setadjoin @ X1482 @ emptyset ) ) ) ) )
=> ( ! [X1484: $i,X1485: $o,X1486: $i] :
( ( in @ X1486 @ X1484 )
=> ! [X1487: $i] :
( ( in @ X1487 @ X1484 )
=> ( singleton
@ ( dsetconstr @ X1484
@ ^ [Z0: $i] :
( ( X1485
& ( Z0 = X1486 ) )
| ( ~ X1485
& ( Z0 = X1487 ) ) ) ) ) ) )
=> ( ! [X1488: $i,X1489: $o,X1490: $i] :
( ( in @ X1490 @ X1488 )
=> ! [X1491: $i] :
( ( in @ X1491 @ X1488 )
=> ( in @ ( if @ X1488 @ X1489 @ X1490 @ X1491 ) @ X1488 ) ) )
=> ( ! [X1492: $i] :
( ( singleton @ X1492 )
=> ! [X1493: $i] :
( ( in @ X1493 @ X1492 )
=> ( ( setunion @ X1492 )
= X1493 ) ) )
=> ( ! [X1494: $i,X1495: $o,X1496: $i] :
( ( in @ X1496 @ X1494 )
=> ! [X1497: $i] :
( ( in @ X1497 @ X1494 )
=> ( X1495
=> ( ( if @ X1494 @ X1495 @ X1496 @ X1497 )
= X1496 ) ) ) )
=> ( ! [X1498: $i,X1499: $o,X1500: $i] :
( ( in @ X1500 @ X1498 )
=> ! [X1501: $i] :
( ( in @ X1501 @ X1498 )
=> ( ~ X1499
=> ( ( if @ X1498 @ X1499 @ X1500 @ X1501 )
= X1501 ) ) ) )
=> ( ! [X1502: $i,X1503: $o,X1504: $i] :
( ( in @ X1504 @ X1502 )
=> ! [X1505: $i] :
( ( in @ X1505 @ X1502 )
=> ( in @ ( if @ X1502 @ X1503 @ X1504 @ X1505 ) @ ( setadjoin @ X1504 @ ( setadjoin @ X1505 @ emptyset ) ) ) ) )
=> ( ! [X1506: $i,X1507: $i] :
( ( in @ X1507 @ ( powerset @ X1506 ) )
=> ! [X1508: $i] :
( ( in @ X1508 @ ( powerset @ X1506 ) )
=> ( in @ ( binintersect @ X1507 @ X1508 ) @ ( powerset @ X1506 ) ) ) )
=> ( ! [X1509: $i,X1510: $i] :
( ( in @ X1510 @ ( powerset @ X1509 ) )
=> ! [X1511: $i] :
( ( in @ X1511 @ ( powerset @ X1509 ) )
=> ( in @ ( binunion @ X1510 @ X1511 ) @ ( powerset @ X1509 ) ) ) )
=> ( ! [X1512: $i,X1513: $i] :
( ( in @ X1513 @ ( powerset @ X1512 ) )
=> ( in @ ( powerset @ X1513 ) @ ( powerset @ ( powerset @ X1512 ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setminusT_lem]),subsetemptysetimpeq]),c_0_255]),powersetT_lem]),ap2p]),notsubsetI]),funcinfuncset]),c_0_256]),c_0_257]),notequalI1]),c_0_258]),c_0_259]),notequalI2]),c_0_260]),c_0_261]),subsetRefl]),funcGraphProp1]),funcGraphProp3]),subsetTrans]),funcGraphProp2]),funcextLem]),setadjoinSub]),funcGraphProp4]),c_0_262]),setadjoinSub2]),c_0_263]),funcext]),subset2powerset]),funcext2]),ap2apEq1]),ap2apEq2]),setextsub]),c_0_264]),binintersectSubset2]),c_0_265]),c_0_266]),c_0_267]),powersetI1]),c_0_268]),c_0_269]),powersetE1]),c_0_270]),c_0_271]),inPowerset]),c_0_272]),ifp]),theeq]),iftrue]),powersetsubset]),iffalse]),iftrueorfalse]),c_0_273]),binintersectT_lem]),binunionT_lem]),c_0_274]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),ubforcartprodlem3]),cartprodpairin]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),subsetI2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),emptysetsubset]),upairset2E]),upairsubunion]),subsetE]),subsetE2]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_275]),c_0_276]),c_0_277]),c_0_278]),singletonsuniq]),setukpairinjL1]),c_0_279]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_280]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_281]),c_0_282]),c_0_283]),c_0_284]),c_0_285]),c_0_286]),c_0_287]),c_0_288]),c_0_289]),app]),infuncsetfunc]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_290]),c_0_291]),c_0_292]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_293]),c_0_294]),in__Cong]),inCongP]),c_0_295]),c_0_296]),c_0_297]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_298]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_299]),c_0_300]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_301]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_302]),c_0_303]),c_0_304]),c_0_305]),noeltsimpempty]),emptyI]),setext]),c_0_306]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_307]),c_0_308]),c_0_309]),c_0_310]),c_0_311]),wellorderingAx]),foundationAx]),c_0_312]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_313]) ).
thf(c_0_315,negated_conjecture,
! [X1514: $i,X1515: $i,X1517: $i,X1518: $i,X1519: $i,X1520: $i,X1521: $i,X1522: $i,X1523: $i,X1524: $i,X1525: $i,X1527: $i,X1528: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $i,X1536: $i,X1537: $i > $i > $o,X1538: $i,X1540: $i,X1543: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1550: $i,X1551: $i > $o,X1552: $i,X1554: $i,X1555: $i > $o,X1556: $i,X1557: $i,X1558: $i > $o,X1559: $i,X1560: $i,X1561: $i > $o,X1562: $i,X1563: $i > $o,X1564: $i,X1567: $i,X1568: $o,X1569: $i,X1570: $i,X1571: $o,X1572: $i,X1573: $i,X1574: $i > $o,X1575: $i,X1578: $i,X1579: $i,X1582: $i,X1584: $i,X1586: $i,X1587: $i > $o,X1588: $i,X1589: $i,X1591: $i,X1592: $i > $o,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $o,X1605: $i,X1606: $i,X1607: $i,X1608: $i,X1609: $i,X1610: $i,X1612: $i,X1613: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $o,X1624: $i,X1625: $i,X1626: $i > $o,X1627: $i,X1630: $i,X1631: $i,X1632: $i,X1634: $i,X1635: $i,X1636: $i,X1637: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1643: $i,X1644: $i,X1645: $i,X1646: $i,X1647: $i,X1648: $i,X1649: $i,X1650: $i > $o,X1651: $i,X1652: $i > $o,X1653: $i,X1654: $i,X1655: $i > $o,X1656: $i,X1658: $i,X1659: $i > $o,X1661: $i,X1662: $i,X1663: $i > $o,X1665: $i,X1666: $i,X1667: $i > $o,X1668: $i,X1670: $o,X1671: $i,X1672: $i > $o,X1674: $i,X1675: $i,X1676: $i > $o,X1677: $i,X1679: $i > $o,X1680: $i,X1683: $i,X1684: $i > $o,X1685: $i,X1689: $i,X1690: $i > $o,X1691: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i > $o,X1704: $i,X1706: $i,X1707: $i,X1708: $i > $o,X1709: $i > $o,X1712: $i,X1715: $i,X1716: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1724: $i,X1725: $i,X1726: $i,X1727: $i,X1728: $i > $o,X1729: $i,X1731: $i,X1732: $i,X1733: $i > $o,X1734: $i > $o,X1737: $i,X1739: $i,X1741: $i,X1742: $i,X1743: $i > $o,X1744: $i > $o,X1747: $i,X1748: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i,X1772: $i,X1773: $i,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i > $o,X1795: $i,X1796: $i > $o,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $o,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $o,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $i,X1929: $i,X1930: $i,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i > $o,X1951: $i,X1952: $i,X1953: $i > $o,X1955: $i,X1956: $i > $o,X1957: $i,X1959: $i,X1960: $i > $o,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i,X1988: $i,X1989: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i > $i > $o,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i > $i > $o,X2041: $i,X2042: $i,X2043: $i > $i > $o,X2044: $i,X2045: $i,X2046: $i > $i > $o,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i > $i > $o,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i > $i > $o,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i > $i > $o,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i > $i,X2090: $i,X2091: $i,X2092: $i > $i,X2094: $i,X2095: $i,X2096: $i > $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i > $o,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i > $o,X2111: $i,X2112: $i,X2113: $i > $o,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i > $i,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2183: $i > $i,X2185: $i,X2186: $i,X2187: $i > $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $o,X2195: $i,X2196: $i,X2197: $i,X2198: $o,X2199: $i,X2200: $i,X2201: $i,X2202: $o,X2203: $i,X2204: $i,X2205: $i,X2206: $o,X2207: $i,X2208: $i,X2209: $i,X2210: $o,X2211: $i,X2212: $i,X2213: $i,X2214: $o,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $o,X2221: $i,X2222: $i,X2223: $i,X2224: $o,X2225: $i,X2226: $i,X2227: $i,X2228: $o,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i] :
( ( ~ ( in @ ( esk1_2 @ X1514 @ X1515 ) @ X1514 )
| ~ ( in @ ( esk1_2 @ X1514 @ X1515 ) @ X1515 )
| ( X1514 = X1515 ) )
& ( ( in @ ( esk1_2 @ X1514 @ X1515 ) @ X1514 )
| ( in @ ( esk1_2 @ X1514 @ X1515 ) @ X1515 )
| ( X1514 = X1515 ) )
& ~ ( in @ X1517 @ emptyset )
& ( ~ ( in @ X1520 @ ( setadjoin @ X1518 @ X1519 ) )
| ( X1520 = X1518 )
| ( in @ X1520 @ X1519 ) )
& ( ( X1520 != X1518 )
| ( in @ X1520 @ ( setadjoin @ X1518 @ X1519 ) ) )
& ( ~ ( in @ X1520 @ X1519 )
| ( in @ X1520 @ ( setadjoin @ X1518 @ X1519 ) ) )
& ( ~ ( in @ X1522 @ ( powerset @ X1521 ) )
| ~ ( in @ X1523 @ X1522 )
| ( in @ X1523 @ X1521 ) )
& ( ( in @ ( esk2_2 @ X1524 @ X1525 ) @ X1525 )
| ( in @ X1525 @ ( powerset @ X1524 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1524 @ X1525 ) @ X1524 )
| ( in @ X1525 @ ( powerset @ X1524 ) ) )
& ( ( in @ X1528 @ ( esk3_2 @ X1527 @ X1528 ) )
| ~ ( in @ X1528 @ ( setunion @ X1527 ) ) )
& ( ( in @ ( esk3_2 @ X1527 @ X1528 ) @ X1527 )
| ~ ( in @ X1528 @ ( setunion @ X1527 ) ) )
& ( ~ ( in @ X1531 @ X1532 )
| ~ ( in @ X1532 @ X1530 )
| ( in @ X1531 @ ( setunion @ X1530 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1533 @ omega )
| ( in @ ( setadjoin @ X1533 @ X1533 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1534 ) @ omega )
| ~ ( in @ emptyset @ X1534 )
| ~ ( in @ X1536 @ omega )
| ( in @ X1536 @ X1534 ) )
& ( ( in @ ( esk4_1 @ X1534 ) @ X1534 )
| ~ ( in @ emptyset @ X1534 )
| ~ ( in @ X1536 @ omega )
| ( in @ X1536 @ X1534 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1534 ) @ ( esk4_1 @ X1534 ) ) @ X1534 )
| ~ ( in @ emptyset @ X1534 )
| ~ ( in @ X1536 @ omega )
| ( in @ X1536 @ X1534 ) )
& ( ( in @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1538 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( in @ ( esk5_2 @ X1537 @ X1538 ) @ X1538 ) )
& ( ( X1537 @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1543 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( in @ ( esk5_2 @ X1537 @ X1538 ) @ X1538 ) )
& ( ~ ( in @ X1546 @ X1538 )
| ~ ( X1537 @ X1546 @ X1545 )
| ( in @ X1545 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( in @ ( esk5_2 @ X1537 @ X1538 ) @ X1538 ) )
& ( ( in @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1538 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ( X1537 @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1543 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ~ ( in @ X1546 @ X1538 )
| ~ ( X1537 @ X1546 @ X1545 )
| ( in @ X1545 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ( in @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1538 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1540
!= ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ( X1537 @ ( esk8_3 @ X1537 @ X1538 @ X1543 ) @ X1543 )
| ~ ( in @ X1543 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1540
!= ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ~ ( in @ X1546 @ X1538 )
| ~ ( X1537 @ X1546 @ X1545 )
| ( in @ X1545 @ ( esk7_2 @ X1537 @ X1538 ) )
| ( X1540
!= ( esk6_3 @ X1537 @ X1538 @ X1540 ) )
| ~ ( X1537 @ ( esk5_2 @ X1537 @ X1538 ) @ X1540 ) )
& ( ( in @ ( esk9_1 @ X1547 ) @ X1547 )
| ~ ( in @ X1548 @ X1547 ) )
& ( ~ ( in @ X1550 @ ( esk9_1 @ X1547 ) )
| ~ ( in @ X1550 @ X1547 )
| ~ ( in @ X1548 @ X1547 ) )
& epred1_0
& ( ( X1551 @ ( esk10_2 @ X1551 @ X1552 ) )
| ~ ( X1551 @ X1552 )
| ( X1551 @ ( descr @ X1551 ) ) )
& ( ( X1552
!= ( esk10_2 @ X1551 @ X1552 ) )
| ~ ( X1551 @ X1552 )
| ( X1551 @ ( descr @ X1551 ) ) )
& ( ~ ( in @ X1556 @ X1554 )
| ~ ( X1555 @ X1556 )
| ( in @ X1556 @ ( dsetconstr @ X1554 @ X1555 ) ) )
& ( ~ ( in @ X1559 @ ( dsetconstr @ X1557 @ X1558 ) )
| ( in @ X1559 @ X1557 ) )
& ( ~ ( in @ X1562 @ ( dsetconstr @ X1560 @ X1561 ) )
| ( X1561 @ X1562 ) )
& ( ( X1563 @ ( esk12_1 @ X1563 ) )
| ( X1563 @ ( esk11_2 @ X1563 @ X1564 ) )
| ~ ( X1563 @ X1564 ) )
& ( ~ ( X1563 @ X1567 )
| ( ( esk12_1 @ X1563 )
= X1567 )
| ( X1563 @ ( esk11_2 @ X1563 @ X1564 ) )
| ~ ( X1563 @ X1564 ) )
& ( ( X1563 @ ( esk12_1 @ X1563 ) )
| ( X1564
!= ( esk11_2 @ X1563 @ X1564 ) )
| ~ ( X1563 @ X1564 ) )
& ( ~ ( X1563 @ X1567 )
| ( ( esk12_1 @ X1563 )
= X1567 )
| ( X1564
!= ( esk11_2 @ X1563 @ X1564 ) )
| ~ ( X1563 @ X1564 ) )
& ( ~ ( in @ X1569 @ ( prop2set @ X1568 ) )
| X1568 )
& ( ~ ( in @ X1570 @ emptyset )
| X1571 )
& ( ~ ( in @ X1572 @ emptyset )
| ~ $true )
& ~ ( in @ X1573 @ emptyset )
& ( ( X1574 @ ( esk13_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 )
| ( X1574 @ ( esk14_1 @ X1574 ) ) )
& ( ( X1575
!= ( esk13_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 )
| ( X1574 @ ( esk14_1 @ X1574 ) ) )
& ( ( in @ ( esk16_2 @ X1578 @ X1579 ) @ X1579 )
| ( X1578 = X1579 )
| ( in @ ( esk15_2 @ X1578 @ X1579 ) @ X1578 ) )
& ( ~ ( in @ ( esk16_2 @ X1578 @ X1579 ) @ X1578 )
| ( X1578 = X1579 )
| ( in @ ( esk15_2 @ X1578 @ X1579 ) @ X1578 ) )
& ( ( in @ ( esk16_2 @ X1578 @ X1579 ) @ X1579 )
| ( X1578 = X1579 )
| ~ ( in @ ( esk15_2 @ X1578 @ X1579 ) @ X1579 ) )
& ( ~ ( in @ ( esk16_2 @ X1578 @ X1579 ) @ X1578 )
| ( X1578 = X1579 )
| ~ ( in @ ( esk15_2 @ X1578 @ X1579 ) @ X1579 ) )
& ( ( in @ ( esk17_1 @ X1582 ) @ X1582 )
| ( X1582 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1584 ) @ X1584 )
| ( X1584 = emptyset ) )
& ( ~ ( in @ X1588 @ ( dsetconstr @ X1586 @ X1587 ) )
| ( X1587 @ X1588 )
| ~ ( in @ X1588 @ X1586 ) )
& ( ~ ( X1587 @ X1588 )
| ( in @ X1588 @ ( dsetconstr @ X1586 @ X1587 ) )
| ~ ( in @ X1588 @ X1586 ) )
& ( ( X1589 = emptyset )
| ( in @ ( esk19_1 @ X1589 ) @ X1589 ) )
& ( ~ ( in @ X1593 @ X1591 )
| ~ ( X1592 @ X1593 )
| ( ( dsetconstr @ X1591 @ X1592 )
!= emptyset ) )
& ( ~ ( in @ X1595 @ X1594 )
| ( X1594 != emptyset ) )
& ( in @ X1596 @ ( setadjoin @ X1596 @ X1597 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1600 @ X1599 )
| ( in @ X1600 @ ( setadjoin @ X1598 @ X1599 ) ) )
& ( ( in @ X1603 @ X1602 )
| X1604
| ( X1603 = X1601 )
| ~ ( in @ X1603 @ ( setadjoin @ X1601 @ X1602 ) ) )
& ( ~ X1604
| X1604
| ( X1603 = X1601 )
| ~ ( in @ X1603 @ ( setadjoin @ X1601 @ X1602 ) ) )
& ( ( in @ X1603 @ X1602 )
| X1604
| ~ X1604
| ~ ( in @ X1603 @ ( setadjoin @ X1601 @ X1602 ) ) )
& ( ~ X1604
| X1604
| ~ X1604
| ~ ( in @ X1603 @ ( setadjoin @ X1601 @ X1602 ) ) )
& ( ~ ( in @ X1607 @ ( setadjoin @ X1605 @ X1606 ) )
| ( X1607 = X1605 )
| ( in @ X1607 @ X1606 ) )
& ( ( dsetconstr @ X1608
@ ^ [Z0: $i] : $true )
= X1608 )
& ( ( in @ ( esk20_2 @ X1609 @ X1610 ) @ X1610 )
| ( in @ X1610 @ ( powerset @ X1609 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1609 @ X1610 ) @ X1609 )
| ( in @ X1610 @ ( powerset @ X1609 ) ) )
& ( in @ emptyset @ ( powerset @ X1612 ) )
& ( in @ emptyset @ ( powerset @ X1613 ) )
& ( ~ ( in @ X1615 @ ( powerset @ X1614 ) )
| ~ ( in @ X1616 @ X1615 )
| ( in @ X1616 @ X1614 ) )
& ( ~ ( in @ X1618 @ X1619 )
| ~ ( in @ X1619 @ X1617 )
| ( in @ X1618 @ ( setunion @ X1617 ) ) )
& ( ( in @ X1621 @ ( esk21_3 @ X1620 @ X1621 @ X1622 ) )
| X1622
| ~ ( in @ X1621 @ ( setunion @ X1620 ) ) )
& ( ( in @ ( esk21_3 @ X1620 @ X1621 @ X1622 ) @ X1620 )
| X1622
| ~ ( in @ X1621 @ ( setunion @ X1620 ) ) )
& ( ~ X1622
| X1622
| ~ ( in @ X1621 @ ( setunion @ X1620 ) ) )
& ( ~ ( in @ X1625 @ X1624 )
| ( in @ X1625 @ ( powerset @ ( setunion @ X1624 ) ) ) )
& ( ~ ( X1626 @ X1630 )
| ( X1630
= ( esk23_1 @ X1626 ) )
| ( X1626 @ ( esk22_2 @ X1626 @ X1627 ) )
| ~ ( X1626 @ X1627 ) )
& ( ( X1631
!= ( esk23_1 @ X1626 ) )
| ( X1626 @ X1631 )
| ( X1626 @ ( esk22_2 @ X1626 @ X1627 ) )
| ~ ( X1626 @ X1627 ) )
& ( ~ ( X1626 @ X1630 )
| ( X1630
= ( esk23_1 @ X1626 ) )
| ( X1627
!= ( esk22_2 @ X1626 @ X1627 ) )
| ~ ( X1626 @ X1627 ) )
& ( ( X1631
!= ( esk23_1 @ X1626 ) )
| ( X1626 @ X1631 )
| ( X1627
!= ( esk22_2 @ X1626 @ X1627 ) )
| ~ ( X1626 @ X1627 ) )
& ( ( in @ ( esk24_1 @ X1632 ) @ X1632 )
| ( X1632 = emptyset ) )
& ( $true
| ( X1632 = emptyset ) )
& ( ~ ( in @ X1634 @ ( setadjoin @ X1635 @ emptyset ) )
| ( X1634 = X1635 ) )
& ( ( X1636 = X1637 )
| ~ ( in @ X1637 @ ( setadjoin @ X1636 @ emptyset ) ) )
& ( ( X1638 != X1639 )
| ( in @ X1638 @ ( setadjoin @ X1639 @ emptyset ) ) )
& ( ~ ( in @ X1640 @ ( setadjoin @ X1641 @ emptyset ) )
| ( in @ X1641 @ ( setadjoin @ X1640 @ emptyset ) ) )
& ( ~ ( in @ X1644 @ ( setadjoin @ X1642 @ ( setadjoin @ X1643 @ emptyset ) ) )
| ( X1644 = X1642 )
| ( X1644 = X1643 ) )
& ( in @ X1645 @ ( setadjoin @ X1645 @ ( setadjoin @ X1646 @ emptyset ) ) )
& ( in @ X1648 @ ( setadjoin @ X1647 @ ( setadjoin @ X1648 @ emptyset ) ) )
& ( ~ ( in @ X1651 @ X1649 )
| ~ ( X1650 @ X1651 )
| ( ( dsetconstr @ X1649 @ X1650 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1653 @ emptyset )
| ( X1652 @ X1653 ) )
& ( ( in @ ( esk25_2 @ X1654 @ X1655 ) @ X1654 )
| ~ ( in @ X1656 @ X1654 )
| ( X1655 @ X1656 ) )
& ( ~ ( X1655 @ ( esk25_2 @ X1654 @ X1655 ) )
| ~ ( in @ X1656 @ X1654 )
| ( X1655 @ X1656 ) )
& ( ( in @ ( esk26_2 @ X1658 @ X1659 ) @ X1658 )
| ~ ( in @ X1661 @ X1658 )
| ~ ( X1659 @ X1661 ) )
& ( ( X1659 @ ( esk26_2 @ X1658 @ X1659 ) )
| ~ ( in @ X1661 @ X1658 )
| ~ ( X1659 @ X1661 ) )
& ( ( in @ ( esk27_2 @ X1662 @ X1663 ) @ X1662 )
| ~ ( in @ X1665 @ X1662 )
| ~ ( X1663 @ X1665 ) )
& ( ( X1663 @ ( esk27_2 @ X1662 @ X1663 ) )
| ~ ( in @ X1665 @ X1662 )
| ~ ( X1663 @ X1665 ) )
& ( ( in @ ( esk28_2 @ X1666 @ X1667 ) @ X1666 )
| ~ ( in @ X1668 @ X1666 )
| ( X1667 @ X1668 ) )
& ( ~ ( X1667 @ ( esk28_2 @ X1666 @ X1667 ) )
| ~ ( in @ X1668 @ X1666 )
| ( X1667 @ X1668 ) )
& ( ~ X1670
| ( in @ emptyset @ ( prop2set @ X1670 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X1671 @ X1672 ) @ X1671 )
| ~ ( in @ X1674 @ X1671 )
| ~ ( X1672 @ X1674 ) )
& ( ( X1672 @ ( esk29_2 @ X1671 @ X1672 ) )
| ~ ( in @ X1674 @ X1671 )
| ~ ( X1672 @ X1674 ) )
& ( ( in @ ( esk30_2 @ X1675 @ X1676 ) @ X1675 )
| ~ ( in @ X1677 @ X1675 )
| ( X1676 @ X1677 ) )
& ( ~ ( X1676 @ ( esk30_2 @ X1675 @ X1676 ) )
| ~ ( in @ X1677 @ X1675 )
| ( X1676 @ X1677 ) )
& ( ( X1679 @ ( esk32_1 @ X1679 ) )
| ( X1679 @ ( esk31_2 @ X1679 @ X1680 ) )
| ~ ( X1679 @ X1680 ) )
& ( ~ ( X1679 @ X1683 )
| ( ( esk32_1 @ X1679 )
= X1683 )
| ( X1679 @ ( esk31_2 @ X1679 @ X1680 ) )
| ~ ( X1679 @ X1680 ) )
& ( ( X1679 @ ( esk32_1 @ X1679 ) )
| ( X1680
!= ( esk31_2 @ X1679 @ X1680 ) )
| ~ ( X1679 @ X1680 ) )
& ( ~ ( X1679 @ X1683 )
| ( ( esk32_1 @ X1679 )
= X1683 )
| ( X1680
!= ( esk31_2 @ X1679 @ X1680 ) )
| ~ ( X1679 @ X1680 ) )
& ( ( X1684 @ ( esk35_1 @ X1684 ) )
| ( X1684 @ ( esk33_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ~ ( X1684 @ X1689 )
| ( ( esk35_1 @ X1684 )
= X1689 )
| ( X1684 @ ( esk33_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ( X1684 @ ( esk35_1 @ X1684 ) )
| ( X1684 @ ( esk34_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ~ ( X1684 @ X1689 )
| ( ( esk35_1 @ X1684 )
= X1689 )
| ( X1684 @ ( esk34_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ( X1684 @ ( esk35_1 @ X1684 ) )
| ( ( esk33_1 @ X1684 )
!= ( esk34_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ~ ( X1684 @ X1689 )
| ( ( esk35_1 @ X1684 )
= X1689 )
| ( ( esk33_1 @ X1684 )
!= ( esk34_1 @ X1684 ) )
| ~ ( X1684 @ X1685 ) )
& ( ( X1690 @ ( esk37_1 @ X1690 ) )
| ~ ( X1690 @ ( esk36_2 @ X1690 @ X1691 ) )
| ( ( esk36_2 @ X1690 @ X1691 )
!= X1691 ) )
& ( ~ ( X1690 @ X1694 )
| ( ( esk37_1 @ X1690 )
= X1694 )
| ~ ( X1690 @ ( esk36_2 @ X1690 @ X1691 ) )
| ( ( esk36_2 @ X1690 @ X1691 )
!= X1691 ) )
& ( ( X1690 @ ( esk37_1 @ X1690 ) )
| ( X1690 @ ( esk36_2 @ X1690 @ X1691 ) )
| ( ( esk36_2 @ X1690 @ X1691 )
= X1691 ) )
& ( ~ ( X1690 @ X1694 )
| ( ( esk37_1 @ X1690 )
= X1694 )
| ( X1690 @ ( esk36_2 @ X1690 @ X1691 ) )
| ( ( esk36_2 @ X1690 @ X1691 )
= X1691 ) )
& ( ( X1695 != X1696 )
| ( X1697 != X1698 )
| ~ ( in @ X1697 @ X1695 )
| ( in @ X1698 @ X1696 ) )
& ( ~ ( in @ X1701 @ X1699 )
| ( in @ X1702 @ X1700 )
| ( X1701 != X1702 )
| ( X1699 != X1700 ) )
& ( ~ ( in @ X1702 @ X1700 )
| ( in @ X1701 @ X1699 )
| ( X1701 != X1702 )
| ( X1699 != X1700 ) )
& ( ( X1703 @ ( esk38_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 )
| ~ ( X1703 @ X1706 )
| ~ ( X1703 @ X1707 )
| ( X1706 = X1707 ) )
& ( ( X1704
!= ( esk38_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 )
| ~ ( X1703 @ X1706 )
| ~ ( X1703 @ X1707 )
| ( X1706 = X1707 ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( ( esk39_2 @ X1708 @ X1709 )
= ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ~ ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ~ ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1708 @ ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1709 @ ( esk42_2 @ X1708 @ X1709 ) )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1709 @ X1715 )
| ( ( esk42_2 @ X1708 @ X1709 )
= X1715 )
| ( X1712
!= ( esk41_3 @ X1708 @ X1709 @ X1712 ) )
| ~ ( X1708 @ X1712 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1709 @ ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ( X1708 @ ( esk44_2 @ X1708 @ X1709 ) )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( ~ ( X1708 @ X1719 )
| ( ( esk44_2 @ X1708 @ X1709 )
= X1719 )
| ( X1716
!= ( esk43_3 @ X1708 @ X1709 @ X1716 ) )
| ~ ( X1709 @ X1716 )
| ( X1708 @ ( esk39_2 @ X1708 @ X1709 ) )
| ( X1709 @ ( esk40_2 @ X1708 @ X1709 ) ) )
& ( emptyset = emptyset )
& ( ( X1720 != X1721 )
| ( X1722 != X1723 )
| ( ( setadjoin @ X1720 @ X1722 )
= ( setadjoin @ X1721 @ X1723 ) ) )
& ( ( X1724 != X1725 )
| ( ( powerset @ X1724 )
= ( powerset @ X1725 ) ) )
& ( ( X1726 != X1727 )
| ( ( setunion @ X1726 )
= ( setunion @ X1727 ) ) )
& ( omega = omega )
& ( ( X1728 @ ( esk45_2 @ X1728 @ X1729 ) )
| ~ ( X1728 @ X1729 )
| ~ ( X1728 @ X1731 )
| ~ ( X1728 @ X1732 )
| ( X1731 = X1732 ) )
& ( ( X1729
!= ( esk45_2 @ X1728 @ X1729 ) )
| ~ ( X1728 @ X1729 )
| ~ ( X1728 @ X1731 )
| ~ ( X1728 @ X1732 )
| ( X1731 = X1732 ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( ( esk46_2 @ X1733 @ X1734 )
= ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( ( esk46_2 @ X1733 @ X1734 )
= ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( ( esk46_2 @ X1733 @ X1734 )
= ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( ( esk46_2 @ X1733 @ X1734 )
= ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ~ ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ~ ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ~ ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ~ ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ~ ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ~ ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ~ ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ~ ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1733 @ ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1734 @ ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( X1739
!= ( esk49_3 @ X1733 @ X1734 @ X1739 ) )
| ~ ( X1734 @ X1739 )
| ( ( descr @ X1733 )
= ( descr @ X1734 ) )
| ( X1737
!= ( esk48_3 @ X1733 @ X1734 @ X1737 ) )
| ~ ( X1733 @ X1737 )
| ( X1733 @ ( esk46_2 @ X1733 @ X1734 ) )
| ( X1734 @ ( esk47_2 @ X1733 @ X1734 ) ) )
& ( ( in @ ( esk50_4 @ X1741 @ X1742 @ X1743 @ X1744 ) @ X1741 )
| ( ( dsetconstr @ X1741 @ X1743 )
= ( dsetconstr @ X1742 @ X1744 ) )
| ( X1741 != X1742 ) )
& ( ( in @ ( esk51_4 @ X1741 @ X1742 @ X1743 @ X1744 ) @ X1742 )
| ( ( dsetconstr @ X1741 @ X1743 )
= ( dsetconstr @ X1742 @ X1744 ) )
| ( X1741 != X1742 ) )
& ( ( ( esk50_4 @ X1741 @ X1742 @ X1743 @ X1744 )
= ( esk51_4 @ X1741 @ X1742 @ X1743 @ X1744 ) )
| ( ( dsetconstr @ X1741 @ X1743 )
= ( dsetconstr @ X1742 @ X1744 ) )
| ( X1741 != X1742 ) )
& ( ~ ( X1743 @ ( esk50_4 @ X1741 @ X1742 @ X1743 @ X1744 ) )
| ~ ( X1744 @ ( esk51_4 @ X1741 @ X1742 @ X1743 @ X1744 ) )
| ( ( dsetconstr @ X1741 @ X1743 )
= ( dsetconstr @ X1742 @ X1744 ) )
| ( X1741 != X1742 ) )
& ( ( X1743 @ ( esk50_4 @ X1741 @ X1742 @ X1743 @ X1744 ) )
| ( X1744 @ ( esk51_4 @ X1741 @ X1742 @ X1743 @ X1744 ) )
| ( ( dsetconstr @ X1741 @ X1743 )
= ( dsetconstr @ X1742 @ X1744 ) )
| ( X1741 != X1742 ) )
& ( ( in @ ( esk52_2 @ X1747 @ X1748 ) @ X1747 )
| ( subset @ X1747 @ X1748 ) )
& ( ~ ( in @ ( esk52_2 @ X1747 @ X1748 ) @ X1748 )
| ( subset @ X1747 @ X1748 ) )
& ( ( X1750 != X1751 )
| ( subset @ X1751 @ X1750 ) )
& ( ( X1752 != X1753 )
| ( subset @ X1752 @ X1753 ) )
& ( ( in @ ( esk53_2 @ X1754 @ X1755 ) @ X1754 )
| ( subset @ X1754 @ X1755 ) )
& ( ~ ( in @ ( esk53_2 @ X1754 @ X1755 ) @ X1755 )
| ( subset @ X1754 @ X1755 ) )
& ( subset @ emptyset @ X1757 )
& ( ~ ( subset @ X1758 @ X1759 )
| ~ ( in @ X1760 @ X1758 )
| ( in @ X1760 @ X1759 ) )
& ( ~ ( subset @ X1761 @ X1762 )
| ( in @ X1763 @ X1762 )
| ~ ( in @ X1763 @ X1761 ) )
& ( ~ ( in @ X1766 @ X1764 )
| ( in @ X1766 @ X1765 )
| ~ ( subset @ X1764 @ X1765 ) )
& ( ( subset @ X1767 @ X1768 )
| ( X1767 != X1768 ) )
& ( ~ ( in @ X1771 @ X1769 )
| ( in @ X1771 @ X1770 )
| ( X1769 != X1770 ) )
& ( subset @ X1772 @ X1772 )
& ( ~ ( subset @ X1773 @ X1774 )
| ~ ( subset @ X1774 @ X1775 )
| ( subset @ X1773 @ X1775 ) )
& ( subset @ X1777 @ ( setadjoin @ X1776 @ X1777 ) )
& ( ~ ( subset @ X1778 @ X1780 )
| ( subset @ X1778 @ ( setadjoin @ X1779 @ X1780 ) ) )
& ( ~ ( subset @ X1781 @ X1782 )
| ( in @ X1781 @ ( powerset @ X1782 ) ) )
& ( ~ ( subset @ X1783 @ X1784 )
| ~ ( subset @ X1784 @ X1783 )
| ( X1783 = X1784 ) )
& ( ~ ( subset @ X1785 @ emptyset )
| ( X1785 = emptyset ) )
& ( ~ ( subset @ X1787 @ X1786 )
| ( in @ X1787 @ ( powerset @ X1786 ) ) )
& ( ~ ( in @ X1789 @ ( powerset @ X1788 ) )
| ( subset @ X1789 @ X1788 ) )
& ( in @ X1790 @ ( powerset @ X1790 ) )
& ( ~ ( subset @ X1791 @ X1792 )
| ( subset @ ( powerset @ X1791 ) @ ( powerset @ X1792 ) ) )
& ( in @ ( dsetconstr @ X1793 @ X1794 ) @ ( powerset @ X1793 ) )
& ( subset @ ( dsetconstr @ X1795 @ X1796 ) @ X1795 )
& ( ~ ( in @ X1799 @ X1797 )
| ( in @ X1799 @ ( binunion @ X1797 @ X1798 ) ) )
& ( in @ X1801 @ ( setadjoin @ X1800 @ ( setadjoin @ X1801 @ emptyset ) ) )
& ( ~ ( in @ X1804 @ X1803 )
| ( in @ X1804 @ ( binunion @ X1802 @ X1803 ) ) )
& ( ( in @ X1807 @ X1806 )
| X1808
| ( in @ X1807 @ X1805 )
| ~ ( in @ X1807 @ ( binunion @ X1805 @ X1806 ) ) )
& ( ~ X1808
| X1808
| ( in @ X1807 @ X1805 )
| ~ ( in @ X1807 @ ( binunion @ X1805 @ X1806 ) ) )
& ( ( in @ X1807 @ X1806 )
| X1808
| ~ X1808
| ~ ( in @ X1807 @ ( binunion @ X1805 @ X1806 ) ) )
& ( ~ X1808
| X1808
| ~ X1808
| ~ ( in @ X1807 @ ( binunion @ X1805 @ X1806 ) ) )
& ( ~ ( in @ X1811 @ ( binunion @ X1809 @ X1810 ) )
| ( in @ X1811 @ X1809 )
| ( in @ X1811 @ X1810 ) )
& ( subset @ X1812 @ ( binunion @ X1812 @ X1813 ) )
& ( subset @ X1815 @ ( binunion @ X1814 @ X1815 ) )
& ( ~ ( in @ X1818 @ X1816 )
| ~ ( in @ X1818 @ X1817 )
| ( in @ X1818 @ ( binintersect @ X1816 @ X1817 ) ) )
& ( ~ ( subset @ X1821 @ X1819 )
| ~ ( subset @ X1821 @ X1820 )
| ( subset @ X1821 @ ( binintersect @ X1819 @ X1820 ) ) )
& ( ~ ( in @ X1824 @ ( binintersect @ X1822 @ X1823 ) )
| ( in @ X1824 @ X1822 ) )
& ( subset @ ( binintersect @ X1825 @ X1826 ) @ X1825 )
& ( ~ ( subset @ X1827 @ X1828 )
| ( ( binintersect @ X1827 @ X1828 )
= X1827 ) )
& ( ( ( binintersect @ X1829 @ X1830 )
!= X1830 )
| ( subset @ X1830 @ X1829 ) )
& ( ~ ( in @ X1833 @ ( binintersect @ X1831 @ X1832 ) )
| ( in @ X1833 @ X1832 ) )
& ( ( in @ ( esk54_2 @ X1834 @ X1835 ) @ X1834 )
| ( ( binintersect @ X1834 @ X1835 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1834 @ X1835 ) @ X1835 )
| ( ( binintersect @ X1834 @ X1835 )
= emptyset ) )
& ( subset @ ( binintersect @ X1837 @ X1838 ) @ X1838 )
& ( ~ ( subset @ X1840 @ X1839 )
| ( ( binintersect @ X1839 @ X1840 )
= X1840 ) )
& ( ( ( binintersect @ X1841 @ X1842 )
!= X1841 )
| ( subset @ X1841 @ X1842 ) )
& ( ( binintersect @ X1843 @ ( binunion @ X1844 @ X1845 ) )
= ( binunion @ ( binintersect @ X1843 @ X1844 ) @ ( binintersect @ X1843 @ X1845 ) ) )
& ( ~ ( in @ X1848 @ X1846 )
| ( in @ X1848 @ X1847 )
| ( in @ X1848 @ ( setminus @ X1846 @ X1847 ) ) )
& ( ~ ( in @ X1851 @ ( setminus @ X1849 @ X1850 ) )
| ( in @ X1851 @ X1849 ) )
& ( ~ ( in @ X1854 @ ( setminus @ X1852 @ X1853 ) )
| ~ ( in @ X1854 @ X1853 ) )
& ( ~ ( subset @ X1855 @ X1856 )
| ( ( setminus @ X1855 @ X1856 )
= emptyset ) )
& ( ( in @ X1859 @ ( setminus @ X1857 @ X1858 ) )
| ~ ( in @ X1859 @ X1857 )
| ( in @ X1859 @ X1858 ) )
& ( ( in @ X1862 @ ( setminus @ X1860 @ X1861 ) )
| ( in @ X1862 @ X1861 )
| ~ ( in @ X1862 @ X1860 ) )
& ( ( in @ X1865 @ X1863 )
| ~ ( in @ X1865 @ ( setminus @ X1863 @ X1864 ) ) )
& ( ~ ( in @ X1868 @ X1867 )
| ~ ( in @ X1868 @ ( setminus @ X1866 @ X1867 ) ) )
& ( subset @ ( setminus @ X1869 @ X1870 ) @ X1869 )
& ( ( ( setminus @ X1871 @ X1872 )
!= emptyset )
| ( subset @ X1871 @ X1872 ) )
& ( ~ ( in @ X1875 @ X1873 )
| X1876
| ( in @ X1875 @ X1873 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ( in @ X1875 @ X1874 )
| X1876
| ( in @ X1875 @ X1873 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ X1876
| X1876
| ( in @ X1875 @ X1873 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ ( in @ X1875 @ X1873 )
| X1876
| ~ ( in @ X1875 @ X1874 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ( in @ X1875 @ X1874 )
| X1876
| ~ ( in @ X1875 @ X1874 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ X1876
| X1876
| ~ ( in @ X1875 @ X1874 )
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ ( in @ X1875 @ X1873 )
| X1876
| ~ X1876
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ( in @ X1875 @ X1874 )
| X1876
| ~ X1876
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ X1876
| X1876
| ~ X1876
| ~ ( in @ X1875 @ ( symdiff @ X1873 @ X1874 ) ) )
& ( ~ ( in @ X1879 @ X1877 )
| ( in @ X1879 @ X1878 )
| ( in @ X1879 @ ( symdiff @ X1877 @ X1878 ) ) )
& ( ( in @ X1882 @ X1880 )
| ~ ( in @ X1882 @ X1881 )
| ( in @ X1882 @ ( symdiff @ X1880 @ X1881 ) ) )
& ( ~ ( in @ X1885 @ X1883 )
| ~ ( in @ X1885 @ X1884 )
| ~ ( in @ X1885 @ ( symdiff @ X1883 @ X1884 ) ) )
& ( ( in @ X1888 @ X1886 )
| ( in @ X1888 @ X1887 )
| ~ ( in @ X1888 @ ( symdiff @ X1886 @ X1887 ) ) )
& ( in @ X1890 @ ( setadjoin @ X1889 @ ( setadjoin @ X1890 @ emptyset ) ) )
& ( in @ X1891 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1891 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1891 @ ( setadjoin @ X1892 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1894 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1893 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1893 @ ( setadjoin @ X1894 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1895 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1895 @ ( setadjoin @ X1896 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1897 @ X1898 ) )
& ( ~ ( in @ X1900 @ X1899 )
| ( subset @ ( setadjoin @ X1900 @ emptyset ) @ X1899 ) )
& ( ~ ( in @ X1902 @ X1901 )
| ( in @ ( setadjoin @ X1902 @ emptyset ) @ ( powerset @ X1901 ) ) )
& ( ~ ( in @ X1905 @ X1903 )
| ( in @ ( setadjoin @ X1905 @ emptyset ) @ ( powerset @ ( binunion @ X1903 @ X1904 ) ) ) )
& ( ~ ( in @ X1908 @ ( setadjoin @ X1906 @ ( setadjoin @ X1907 @ emptyset ) ) )
| ( X1908 = X1906 )
| ( X1908 = X1907 ) )
& ( ~ ( in @ X1911 @ X1909 )
| ~ ( in @ X1912 @ X1910 )
| ( subset @ ( setadjoin @ X1911 @ ( setadjoin @ X1912 @ emptyset ) ) @ ( binunion @ X1909 @ X1910 ) ) )
& ( ~ ( in @ X1915 @ X1913 )
| ~ ( in @ X1916 @ X1914 )
| ( in @ ( setadjoin @ X1915 @ ( setadjoin @ X1916 @ emptyset ) ) @ ( powerset @ ( binunion @ X1913 @ X1914 ) ) ) )
& ( ~ ( in @ X1919 @ X1917 )
| ~ ( in @ X1920 @ X1918 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1919 @ ( setadjoin @ X1920 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1917 @ X1918 ) ) ) )
& ( ~ ( in @ X1923 @ X1921 )
| ~ ( in @ X1924 @ X1922 )
| ( in @ ( setadjoin @ ( setadjoin @ X1923 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1923 @ ( setadjoin @ X1924 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1921 @ X1922 ) ) ) ) )
& ( ~ ( in @ X1927 @ X1925 )
| ~ ( in @ X1928 @ X1926 )
| ( in @ ( kpair @ X1927 @ X1928 ) @ ( powerset @ ( powerset @ ( binunion @ X1925 @ X1926 ) ) ) ) )
& ( ~ ( in @ X1931 @ X1929 )
| ~ ( in @ X1932 @ X1930 )
| ( in @ ( kpair @ X1931 @ X1932 ) @ ( cartprod @ X1929 @ X1930 ) ) )
& ( ( in @ ( esk55_3 @ X1933 @ X1934 @ X1935 ) @ X1933 )
| ~ ( in @ X1935 @ ( cartprod @ X1933 @ X1934 ) ) )
& ( ( in @ ( esk56_3 @ X1933 @ X1934 @ X1935 ) @ X1934 )
| ~ ( in @ X1935 @ ( cartprod @ X1933 @ X1934 ) ) )
& ( ( X1935
= ( kpair @ ( esk55_3 @ X1933 @ X1934 @ X1935 ) @ ( esk56_3 @ X1933 @ X1934 @ X1935 ) ) )
| ~ ( in @ X1935 @ ( cartprod @ X1933 @ X1934 ) ) )
& ( ~ ( in @ X1940 @ ( cartprod @ X1938 @ X1939 ) )
| ( iskpair @ X1940 ) )
& ( ( in @ ( esk57_2 @ X1941 @ X1942 ) @ X1941 )
| ~ ( in @ X1942 @ ( setunion @ X1941 ) ) )
& ( ( in @ X1942 @ ( esk57_2 @ X1941 @ X1942 ) )
| ~ ( in @ X1942 @ ( setunion @ X1941 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1944 @ emptyset ) ) @ X1944 )
& ( subset @ X1945 @ ( setunion @ ( setadjoin @ X1945 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1946 @ emptyset ) )
= X1946 )
& ( ( in @ ( esk58_2 @ X1947 @ X1948 ) @ X1947 )
| ~ ( in @ X1951 @ X1947 )
| ~ ( X1948 @ X1951 )
| ( singleton @ ( dsetconstr @ X1947 @ X1948 ) ) )
& ( ( in @ ( esk59_2 @ X1947 @ X1948 ) @ X1947 )
| ~ ( in @ X1951 @ X1947 )
| ~ ( X1948 @ X1951 )
| ( singleton @ ( dsetconstr @ X1947 @ X1948 ) ) )
& ( ( X1948 @ ( esk58_2 @ X1947 @ X1948 ) )
| ~ ( in @ X1951 @ X1947 )
| ~ ( X1948 @ X1951 )
| ( singleton @ ( dsetconstr @ X1947 @ X1948 ) ) )
& ( ( X1948 @ ( esk59_2 @ X1947 @ X1948 ) )
| ~ ( in @ X1951 @ X1947 )
| ~ ( X1948 @ X1951 )
| ( singleton @ ( dsetconstr @ X1947 @ X1948 ) ) )
& ( ( ( esk58_2 @ X1947 @ X1948 )
!= ( esk59_2 @ X1947 @ X1948 ) )
| ~ ( in @ X1951 @ X1947 )
| ~ ( X1948 @ X1951 )
| ( singleton @ ( dsetconstr @ X1947 @ X1948 ) ) )
& ( ( in @ ( esk60_2 @ X1952 @ X1953 ) @ X1952 )
| ~ ( singleton @ ( dsetconstr @ X1952 @ X1953 ) ) )
& ( ( X1953 @ ( esk60_2 @ X1952 @ X1953 ) )
| ~ ( singleton @ ( dsetconstr @ X1952 @ X1953 ) ) )
& ( ( in @ ( esk61_3 @ X1955 @ X1956 @ X1957 ) @ X1955 )
| ( singleton @ ( dsetconstr @ X1955 @ X1956 ) )
| ~ ( X1956 @ X1957 )
| ~ ( in @ X1957 @ X1955 ) )
& ( ( X1956 @ ( esk61_3 @ X1955 @ X1956 @ X1957 ) )
| ( singleton @ ( dsetconstr @ X1955 @ X1956 ) )
| ~ ( X1956 @ X1957 )
| ~ ( in @ X1957 @ X1955 ) )
& ( ( ( esk61_3 @ X1955 @ X1956 @ X1957 )
!= X1957 )
| ( singleton @ ( dsetconstr @ X1955 @ X1956 ) )
| ~ ( X1956 @ X1957 )
| ~ ( in @ X1957 @ X1955 ) )
& ( ( in @ ( esk62_2 @ X1959 @ X1960 ) @ X1959 )
| ~ ( in @ X1963 @ X1959 )
| ~ ( X1960 @ X1963 )
| ( singleton @ ( dsetconstr @ X1959 @ X1960 ) ) )
& ( ( in @ ( esk63_2 @ X1959 @ X1960 ) @ X1959 )
| ~ ( in @ X1963 @ X1959 )
| ~ ( X1960 @ X1963 )
| ( singleton @ ( dsetconstr @ X1959 @ X1960 ) ) )
& ( ( X1960 @ ( esk62_2 @ X1959 @ X1960 ) )
| ~ ( in @ X1963 @ X1959 )
| ~ ( X1960 @ X1963 )
| ( singleton @ ( dsetconstr @ X1959 @ X1960 ) ) )
& ( ( X1960 @ ( esk63_2 @ X1959 @ X1960 ) )
| ~ ( in @ X1963 @ X1959 )
| ~ ( X1960 @ X1963 )
| ( singleton @ ( dsetconstr @ X1959 @ X1960 ) ) )
& ( ( ( esk62_2 @ X1959 @ X1960 )
!= ( esk63_2 @ X1959 @ X1960 ) )
| ~ ( in @ X1963 @ X1959 )
| ~ ( X1960 @ X1963 )
| ( singleton @ ( dsetconstr @ X1959 @ X1960 ) ) )
& ( ( ( setadjoin @ X1964 @ emptyset )
!= ( setadjoin @ X1965 @ emptyset ) )
| ( X1964 = X1965 ) )
& ( ~ ( in @ ( setadjoin @ X1968 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1966 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1966 @ ( setadjoin @ X1967 @ emptyset ) ) @ emptyset ) ) )
| ( X1966 = X1968 ) )
& ( ~ ( iskpair @ X1969 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1969 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1969 ) ) ) )
& ( ~ ( singleton @ X1970 )
| ( in @ ( setunion @ X1970 ) @ X1970 ) )
& ( ( kfst @ ( kpair @ X1971 @ X1972 ) )
= X1971 )
& ( ~ ( in @ X1975 @ ( cartprod @ X1973 @ X1974 ) )
| ( in @ ( kfst @ X1975 ) @ X1973 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1976 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1976 @ ( setadjoin @ X1977 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1978 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1978 @ ( setadjoin @ X1979 @ emptyset ) ) @ emptyset ) ) )
| ( X1976 = X1978 ) )
& ( ( ( kpair @ X1980 @ X1981 )
!= ( kpair @ X1982 @ X1983 ) )
| ( X1980 = X1982 ) )
& ( ( X1984 != X1985 )
| ( ( setadjoin @ X1984 @ ( setadjoin @ X1985 @ emptyset ) )
= ( setadjoin @ X1984 @ emptyset ) ) )
& ( ( X1986 != X1987 )
| ( ( setadjoin @ ( setadjoin @ X1986 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1986 @ ( setadjoin @ X1987 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1986 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1988 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1988 @ ( setadjoin @ X1989 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1990 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1990 @ ( setadjoin @ X1991 @ emptyset ) ) @ emptyset ) ) )
| ( X1990 != X1991 )
| ( X1989 = X1991 ) )
& ( ( ( setadjoin @ X1992 @ ( setadjoin @ X1993 @ emptyset ) )
!= ( setadjoin @ X1994 @ emptyset ) )
| ( X1992 = X1993 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1995 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1995 @ ( setadjoin @ X1996 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1997 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1997 @ ( setadjoin @ X1998 @ emptyset ) ) @ emptyset ) ) )
| ( X1996 = X1998 ) )
& ( ( ( kpair @ X1999 @ X2000 )
!= ( kpair @ X2001 @ X2002 ) )
| ( X2000 = X2002 ) )
& ( ~ ( iskpair @ X2003 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2003 )
@ ^ [Z0: $i] :
( X2003
= ( kpair @ ( kfst @ X2003 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2004 @ X2005 ) )
= X2005 )
& ( ~ ( iskpair @ X2006 )
| ( ( kpair @ ( kfst @ X2006 ) @ ( ksnd @ X2006 ) )
= X2006 ) )
& ( ~ ( in @ X2009 @ ( cartprod @ X2007 @ X2008 ) )
| ( in @ ( ksnd @ X2009 ) @ X2008 ) )
& ( ~ ( in @ ( kpair @ X2012 @ X2013 ) @ ( cartprod @ X2010 @ X2011 ) )
| ( in @ X2012 @ X2010 ) )
& ( ~ ( in @ ( kpair @ X2016 @ X2017 ) @ ( cartprod @ X2014 @ X2015 ) )
| ( in @ X2017 @ X2015 ) )
& ( ~ ( in @ X2020 @ X2018 )
| ~ ( in @ X2021 @ X2019 )
| ( ( kpair @ X2020 @ X2021 )
= ( kpair @ X2020 @ X2021 ) ) )
& ( ~ ( in @ X2024 @ X2022 )
| ~ ( in @ X2025 @ X2023 )
| ( ( kfst @ ( kpair @ X2024 @ X2025 ) )
= X2024 ) )
& ( ~ ( in @ X2028 @ X2026 )
| ~ ( in @ X2029 @ X2027 )
| ( ( ksnd @ ( kpair @ X2028 @ X2029 ) )
= X2029 ) )
& ( ~ ( in @ X2032 @ ( cartprod @ X2030 @ X2031 ) )
| ( ( kpair @ ( kfst @ X2032 ) @ ( ksnd @ X2032 ) )
= X2032 ) )
& ( ~ ( in @ X2036 @ X2033 )
| ~ ( in @ X2037 @ X2034 )
| ~ ( X2035 @ X2036 @ X2037 )
| ( in @ ( kpair @ X2036 @ X2037 ) @ ( dpsetconstr @ X2033 @ X2034 @ X2035 ) ) )
& ( subset @ ( dpsetconstr @ X2038 @ X2039 @ X2040 ) @ ( cartprod @ X2038 @ X2039 ) )
& ( subset @ ( dpsetconstr @ X2041 @ X2042 @ X2043 ) @ ( cartprod @ X2041 @ X2042 ) )
& ( ~ ( in @ X2047 @ X2044 )
| ~ ( in @ X2048 @ X2045 )
| ~ ( in @ ( kpair @ X2047 @ X2048 ) @ ( dpsetconstr @ X2044 @ X2045 @ X2046 ) )
| ( X2046 @ X2047 @ X2048 ) )
& ( ~ ( in @ ( kpair @ X2052 @ X2053 ) @ ( dpsetconstr @ X2049 @ X2050 @ X2051 ) )
| ( in @ X2052 @ X2049 ) )
& ( ~ ( in @ ( kpair @ X2057 @ X2058 ) @ ( dpsetconstr @ X2054 @ X2055 @ X2056 ) )
| ( in @ X2058 @ X2055 ) )
& ( ~ ( in @ ( kpair @ X2062 @ X2063 ) @ ( dpsetconstr @ X2059 @ X2060 @ X2061 ) )
| ( X2061 @ X2062 @ X2063 ) )
& ( ~ ( func @ X2064 @ X2065 @ X2066 )
| ~ ( in @ X2067 @ X2064 )
| ( singleton
@ ( dsetconstr @ X2065
@ ^ [Z0: $i] : ( in @ ( kpair @ X2067 @ Z0 ) @ X2066 ) ) ) )
& ( ~ ( func @ X2068 @ X2069 @ X2070 )
| ~ ( in @ X2071 @ X2068 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2069
@ ^ [Z0: $i] : ( in @ ( kpair @ X2071 @ Z0 ) @ X2070 ) ) )
@ X2069 ) )
& ( ~ ( func @ X2072 @ X2073 @ X2074 )
| ~ ( in @ X2075 @ X2072 )
| ( in @ ( ap @ X2072 @ X2073 @ X2074 @ X2075 ) @ X2073 ) )
& ( ~ ( in @ X2078 @ ( funcSet @ X2076 @ X2077 ) )
| ( func @ X2076 @ X2077 @ X2078 ) )
& ( ~ ( in @ X2081 @ ( funcSet @ X2079 @ X2080 ) )
| ~ ( in @ X2082 @ X2079 )
| ( in @ ( ap @ X2079 @ X2080 @ X2081 @ X2082 ) @ X2080 ) )
& ( ~ ( func @ X2083 @ X2084 @ X2085 )
| ( in @ X2085 @ ( funcSet @ X2083 @ X2084 ) ) )
& ( ( in @ ( esk64_3 @ X2086 @ X2087 @ X2088 ) @ X2086 )
| ( func @ X2086 @ X2087
@ ( dpsetconstr @ X2086 @ X2087
@ ^ [Z0: $i] : ( $eq @ ( X2088 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2088 @ ( esk64_3 @ X2086 @ X2087 @ X2088 ) ) @ X2087 )
| ( func @ X2086 @ X2087
@ ( dpsetconstr @ X2086 @ X2087
@ ^ [Z0: $i] : ( $eq @ ( X2088 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2090 @ X2091 @ X2092 ) @ X2090 )
| ( func @ X2090 @ X2091 @ ( lam @ X2090 @ X2091 @ X2092 ) ) )
& ( ~ ( in @ ( X2092 @ ( esk65_3 @ X2090 @ X2091 @ X2092 ) ) @ X2091 )
| ( func @ X2090 @ X2091 @ ( lam @ X2090 @ X2091 @ X2092 ) ) )
& ( ( in @ ( esk66_3 @ X2094 @ X2095 @ X2096 ) @ X2094 )
| ( in @ ( lam @ X2094 @ X2095 @ X2096 ) @ ( funcSet @ X2094 @ X2095 ) ) )
& ( ~ ( in @ ( X2096 @ ( esk66_3 @ X2094 @ X2095 @ X2096 ) ) @ X2095 )
| ( in @ ( lam @ X2094 @ X2095 @ X2096 ) @ ( funcSet @ X2094 @ X2095 ) ) )
& ( ( in @ ( esk67_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ X2098 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( subset @ X2100 @ ( cartprod @ X2098 @ X2099 ) ) )
& ( ( in @ ( esk68_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ X2099 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( subset @ X2100 @ ( cartprod @ X2098 @ X2099 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ ( esk68_4 @ X2098 @ X2099 @ X2100 @ X2101 ) ) @ X2100 )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( subset @ X2100 @ ( cartprod @ X2098 @ X2099 ) ) )
& ( ~ ( X2101 @ ( kpair @ ( esk67_4 @ X2098 @ X2099 @ X2100 @ X2101 ) @ ( esk68_4 @ X2098 @ X2099 @ X2100 @ X2101 ) ) )
| ~ ( in @ X2104 @ X2100 )
| ( X2101 @ X2104 )
| ~ ( subset @ X2100 @ ( cartprod @ X2098 @ X2099 ) ) )
& ( ( in @ ( esk69_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2105 )
| ~ ( in @ X2111 @ X2107 )
| ( X2108 @ X2111 )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( esk70_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ X2106 )
| ~ ( in @ X2111 @ X2107 )
| ( X2108 @ X2111 )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk70_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) @ X2107 )
| ~ ( in @ X2111 @ X2107 )
| ( X2108 @ X2111 )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( X2108 @ ( kpair @ ( esk69_4 @ X2105 @ X2106 @ X2107 @ X2108 ) @ ( esk70_4 @ X2105 @ X2106 @ X2107 @ X2108 ) ) )
| ~ ( in @ X2111 @ X2107 )
| ( X2108 @ X2111 )
| ~ ( subset @ X2107 @ ( cartprod @ X2105 @ X2106 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2112 @ X2113 ) )
| ~ ( in @ X2114 @ X2112 )
| ~ ( in @ X2115 @ X2112 )
| ~ ( X2113 @ X2114 )
| ~ ( X2113 @ X2115 )
| ( X2114 = X2115 ) )
& ( ~ ( func @ X2116 @ X2117 @ X2118 )
| ~ ( in @ X2119 @ X2116 )
| ( in @ ( kpair @ X2119 @ ( ap @ X2116 @ X2117 @ X2118 @ X2119 ) ) @ X2118 ) )
& ( ~ ( in @ X2122 @ ( funcSet @ X2120 @ X2121 ) )
| ~ ( in @ X2123 @ X2120 )
| ( in @ ( kpair @ X2123 @ ( ap @ X2120 @ X2121 @ X2122 @ X2123 ) ) @ X2122 ) )
& ( ~ ( func @ X2124 @ X2125 @ X2126 )
| ~ ( in @ X2127 @ X2124 )
| ~ ( in @ X2128 @ X2125 )
| ~ ( in @ ( kpair @ X2127 @ X2128 ) @ X2126 )
| ( ( ap @ X2124 @ X2125 @ X2126 @ X2127 )
= X2128 ) )
& ( ( in @ ( esk71_4 @ X2129 @ X2130 @ X2131 @ X2132 ) @ X2129 )
| ~ ( in @ X2134 @ X2129 )
| ~ ( in @ X2135 @ X2130 )
| ~ ( in @ ( kpair @ X2134 @ X2135 ) @ X2132 )
| ( in @ ( kpair @ X2134 @ X2135 ) @ X2131 )
| ~ ( func @ X2129 @ X2130 @ X2132 )
| ~ ( func @ X2129 @ X2130 @ X2131 ) )
& ( ( ( ap @ X2129 @ X2130 @ X2131 @ ( esk71_4 @ X2129 @ X2130 @ X2131 @ X2132 ) )
!= ( ap @ X2129 @ X2130 @ X2132 @ ( esk71_4 @ X2129 @ X2130 @ X2131 @ X2132 ) ) )
| ~ ( in @ X2134 @ X2129 )
| ~ ( in @ X2135 @ X2130 )
| ~ ( in @ ( kpair @ X2134 @ X2135 ) @ X2132 )
| ( in @ ( kpair @ X2134 @ X2135 ) @ X2131 )
| ~ ( func @ X2129 @ X2130 @ X2132 )
| ~ ( func @ X2129 @ X2130 @ X2131 ) )
& ( ~ ( in @ X2138 @ ( funcSet @ X2136 @ X2137 ) )
| ~ ( in @ X2139 @ X2136 )
| ~ ( in @ X2140 @ X2137 )
| ~ ( in @ ( kpair @ X2139 @ X2140 ) @ X2138 )
| ( ( ap @ X2136 @ X2137 @ X2138 @ X2139 )
= X2140 ) )
& ( ( in @ ( esk72_4 @ X2141 @ X2142 @ X2143 @ X2144 ) @ X2141 )
| ( subset @ X2143 @ X2144 )
| ~ ( subset @ X2144 @ ( cartprod @ X2141 @ X2142 ) )
| ~ ( subset @ X2143 @ ( cartprod @ X2141 @ X2142 ) ) )
& ( ( in @ ( esk73_4 @ X2141 @ X2142 @ X2143 @ X2144 ) @ X2142 )
| ( subset @ X2143 @ X2144 )
| ~ ( subset @ X2144 @ ( cartprod @ X2141 @ X2142 ) )
| ~ ( subset @ X2143 @ ( cartprod @ X2141 @ X2142 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2141 @ X2142 @ X2143 @ X2144 ) @ ( esk73_4 @ X2141 @ X2142 @ X2143 @ X2144 ) ) @ X2143 )
| ( subset @ X2143 @ X2144 )
| ~ ( subset @ X2144 @ ( cartprod @ X2141 @ X2142 ) )
| ~ ( subset @ X2143 @ ( cartprod @ X2141 @ X2142 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2141 @ X2142 @ X2143 @ X2144 ) @ ( esk73_4 @ X2141 @ X2142 @ X2143 @ X2144 ) ) @ X2144 )
| ( subset @ X2143 @ X2144 )
| ~ ( subset @ X2144 @ ( cartprod @ X2141 @ X2142 ) )
| ~ ( subset @ X2143 @ ( cartprod @ X2141 @ X2142 ) ) )
& ( ( in @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ( X2149 = X2150 )
| ( in @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ( X2149 = X2150 )
| ( in @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ( X2149 = X2150 )
| ( in @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ( X2149 = X2150 )
| ( in @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ( X2149 = X2150 )
| ( in @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ( X2149 = X2150 )
| ( in @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ( X2149 = X2150 )
| ( in @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ( X2149 = X2150 )
| ( in @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ( X2149 = X2150 )
| ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ( X2149 = X2150 )
| ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ( X2149 = X2150 )
| ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ( X2149 = X2150 )
| ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
| ( X2149 = X2150 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2148 )
| ( X2149 = X2150 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ( X2149 = X2150 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk77_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2149 )
| ( X2149 = X2150 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ ( esk75_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) @ X2150 )
| ~ ( subset @ X2150 @ ( cartprod @ X2147 @ X2148 ) )
| ~ ( subset @ X2149 @ ( cartprod @ X2147 @ X2148 ) ) )
& ( ( in @ ( esk78_4 @ X2155 @ X2156 @ X2157 @ X2158 ) @ X2155 )
| ( X2157 = X2158 )
| ~ ( func @ X2155 @ X2156 @ X2158 )
| ~ ( func @ X2155 @ X2156 @ X2157 ) )
& ( ( ( ap @ X2155 @ X2156 @ X2157 @ ( esk78_4 @ X2155 @ X2156 @ X2157 @ X2158 ) )
!= ( ap @ X2155 @ X2156 @ X2158 @ ( esk78_4 @ X2155 @ X2156 @ X2157 @ X2158 ) ) )
| ( X2157 = X2158 )
| ~ ( func @ X2155 @ X2156 @ X2158 )
| ~ ( func @ X2155 @ X2156 @ X2157 ) )
& ( ( in @ ( esk79_4 @ X2160 @ X2161 @ X2162 @ X2163 ) @ X2160 )
| ( X2162 = X2163 )
| ~ ( in @ X2163 @ ( funcSet @ X2160 @ X2161 ) )
| ~ ( in @ X2162 @ ( funcSet @ X2160 @ X2161 ) ) )
& ( ( ( ap @ X2160 @ X2161 @ X2162 @ ( esk79_4 @ X2160 @ X2161 @ X2162 @ X2163 ) )
!= ( ap @ X2160 @ X2161 @ X2163 @ ( esk79_4 @ X2160 @ X2161 @ X2162 @ X2163 ) ) )
| ( X2162 = X2163 )
| ~ ( in @ X2163 @ ( funcSet @ X2160 @ X2161 ) )
| ~ ( in @ X2162 @ ( funcSet @ X2160 @ X2161 ) ) )
& ( ~ ( in @ X2167 @ ( funcSet @ X2165 @ X2166 ) )
| ~ ( in @ X2168 @ X2165 )
| ( ( ap @ X2165 @ X2166 @ X2167 @ X2168 )
= ( ap @ X2165 @ X2166 @ X2167 @ X2168 ) ) )
& ( ~ ( func @ X2169 @ X2170 @ X2171 )
| ~ ( in @ X2172 @ X2169 )
| ( ( ap @ X2169 @ X2170 @ X2171 @ X2172 )
= ( ap @ X2169 @ X2170 @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk80_3 @ X2173 @ X2174 @ X2175 ) @ X2173 )
| ~ ( in @ X2177 @ X2173 )
| ( ( ap @ X2173 @ X2174 @ ( lam @ X2173 @ X2174 @ X2175 ) @ X2177 )
= ( X2175 @ X2177 ) ) )
& ( ~ ( in @ ( X2175 @ ( esk80_3 @ X2173 @ X2174 @ X2175 ) ) @ X2174 )
| ~ ( in @ X2177 @ X2173 )
| ( ( ap @ X2173 @ X2174 @ ( lam @ X2173 @ X2174 @ X2175 ) @ X2177 )
= ( X2175 @ X2177 ) ) )
& ( ~ ( func @ X2178 @ X2179 @ X2180 )
| ( ( lam @ X2178 @ X2179 @ ( ap @ X2178 @ X2179 @ X2180 ) )
= X2180 ) )
& ( ( in @ ( esk81_3 @ X2181 @ X2182 @ X2183 ) @ X2181 )
| ( ( lam @ X2181 @ X2182 @ X2183 )
= ( lam @ X2181 @ X2182 @ X2183 ) ) )
& ( ~ ( in @ ( X2183 @ ( esk81_3 @ X2181 @ X2182 @ X2183 ) ) @ X2182 )
| ( ( lam @ X2181 @ X2182 @ X2183 )
= ( lam @ X2181 @ X2182 @ X2183 ) ) )
& ( ( in @ ( esk82_3 @ X2185 @ X2186 @ X2187 ) @ X2185 )
| ~ ( in @ X2189 @ X2185 )
| ( ( ap @ X2185 @ X2186 @ ( lam @ X2185 @ X2186 @ X2187 ) @ X2189 )
= ( X2187 @ X2189 ) ) )
& ( ~ ( in @ ( X2187 @ ( esk82_3 @ X2185 @ X2186 @ X2187 ) ) @ X2186 )
| ~ ( in @ X2189 @ X2185 )
| ( ( ap @ X2185 @ X2186 @ ( lam @ X2185 @ X2186 @ X2187 ) @ X2189 )
= ( X2187 @ X2189 ) ) )
& ( ~ ( in @ X2192 @ ( funcSet @ X2190 @ X2191 ) )
| ( ( lam @ X2190 @ X2191 @ ( ap @ X2190 @ X2191 @ X2192 ) )
= X2192 ) )
& ( ~ ( in @ X2195 @ X2193 )
| ~ ( in @ X2196 @ X2193 )
| X2194
| ( in @ X2196
@ ( dsetconstr @ X2193
@ ^ [Z0: $i] :
( ( X2194
& ( Z0 = X2195 ) )
| ( ~ X2194
& ( Z0 = X2196 ) ) ) ) ) )
& ( ~ ( in @ X2199 @ X2197 )
| ~ ( in @ X2200 @ X2197 )
| X2198
| ( ( dsetconstr @ X2197
@ ^ [Z0: $i] :
( ( X2198
& ( Z0 = X2199 ) )
| ( ~ X2198
& ( Z0 = X2200 ) ) ) )
= ( setadjoin @ X2200 @ emptyset ) ) )
& ( ~ ( in @ X2203 @ X2201 )
| ~ ( in @ X2204 @ X2201 )
| ~ X2202
| ( in @ X2203
@ ( dsetconstr @ X2201
@ ^ [Z0: $i] :
( ( X2202
& ( Z0 = X2203 ) )
| ( ~ X2202
& ( Z0 = X2204 ) ) ) ) ) )
& ( ~ ( in @ X2207 @ X2205 )
| ~ ( in @ X2208 @ X2205 )
| ~ X2206
| ( ( dsetconstr @ X2205
@ ^ [Z0: $i] :
( ( X2206
& ( Z0 = X2207 ) )
| ( ~ X2206
& ( Z0 = X2208 ) ) ) )
= ( setadjoin @ X2207 @ emptyset ) ) )
& ( ~ ( in @ X2211 @ X2209 )
| ~ ( in @ X2212 @ X2209 )
| ( singleton
@ ( dsetconstr @ X2209
@ ^ [Z0: $i] :
( ( X2210
& ( Z0 = X2211 ) )
| ( ~ X2210
& ( Z0 = X2212 ) ) ) ) ) )
& ( ~ ( in @ X2215 @ X2213 )
| ~ ( in @ X2216 @ X2213 )
| ( in @ ( if @ X2213 @ X2214 @ X2215 @ X2216 ) @ X2213 ) )
& ( ~ ( singleton @ X2217 )
| ~ ( in @ X2218 @ X2217 )
| ( ( setunion @ X2217 )
= X2218 ) )
& ( ~ ( in @ X2221 @ X2219 )
| ~ ( in @ X2222 @ X2219 )
| ~ X2220
| ( ( if @ X2219 @ X2220 @ X2221 @ X2222 )
= X2221 ) )
& ( ~ ( in @ X2225 @ X2223 )
| ~ ( in @ X2226 @ X2223 )
| X2224
| ( ( if @ X2223 @ X2224 @ X2225 @ X2226 )
= X2226 ) )
& ( ~ ( in @ X2229 @ X2227 )
| ~ ( in @ X2230 @ X2227 )
| ( in @ ( if @ X2227 @ X2228 @ X2229 @ X2230 ) @ ( setadjoin @ X2229 @ ( setadjoin @ X2230 @ emptyset ) ) ) )
& ( ~ ( in @ X2232 @ ( powerset @ X2231 ) )
| ~ ( in @ X2233 @ ( powerset @ X2231 ) )
| ( in @ ( binintersect @ X2232 @ X2233 ) @ ( powerset @ X2231 ) ) )
& ( ~ ( in @ X2235 @ ( powerset @ X2234 ) )
| ~ ( in @ X2236 @ ( powerset @ X2234 ) )
| ( in @ ( binunion @ X2235 @ X2236 ) @ ( powerset @ X2234 ) ) )
& ( ~ ( in @ X2238 @ ( powerset @ X2237 ) )
| ( in @ ( powerset @ X2238 ) @ ( powerset @ ( powerset @ X2237 ) ) ) )
& ( in @ esk84_0 @ ( powerset @ esk83_0 ) )
& ( in @ esk85_0 @ ( powerset @ esk83_0 ) )
& ~ ( in @ ( setminus @ esk84_0 @ esk85_0 ) @ ( powerset @ esk83_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_314])])])])])])]) ).
thf(c_0_316,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_317,negated_conjecture,
in @ esk84_0 @ ( powerset @ esk83_0 ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_318,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( subset @ X2 @ X4 )
| ~ ( subset @ X2 @ X3 )
| ~ ( subset @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_319,negated_conjecture,
subset @ esk84_0 @ esk83_0,
inference(spm,[status(thm)],[c_0_316,c_0_317]) ).
thf(c_0_320,negated_conjecture,
~ ( in @ ( setminus @ esk84_0 @ esk85_0 ) @ ( powerset @ esk83_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_321,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_322,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk83_0 )
| ~ ( subset @ X2 @ esk84_0 ) ),
inference(spm,[status(thm)],[c_0_318,c_0_319]) ).
thf(c_0_323,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( setminus @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
thf(c_0_324,negated_conjecture,
~ ( subset @ ( setminus @ esk84_0 @ esk85_0 ) @ esk83_0 ),
inference(spm,[status(thm)],[c_0_320,c_0_321]) ).
thf(c_0_325,negated_conjecture,
! [X2: $i] : ( subset @ ( setminus @ esk84_0 @ X2 ) @ esk83_0 ),
inference(spm,[status(thm)],[c_0_322,c_0_323]) ).
thf(c_0_326,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_324,c_0_325])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU713^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 17:45:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.50 Running higher-order theorem proving
% 0.21/0.50 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
% 11.76/2.42 # Version: 3.1.0-ho
% 11.76/2.42 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.76/2.42 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.76/2.42 # Starting ehoh_best5 with 300s (1) cores
% 11.76/2.42 # Starting almost_fo_3_lam with 300s (1) cores
% 11.76/2.42 # Starting new_bool_5 with 300s (1) cores
% 11.76/2.42 # Starting pre_casc_3 with 300s (1) cores
% 11.76/2.42 # Starting ho_unfolding_8 with 300s (1) cores
% 11.76/2.42 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.76/2.42 # Starting new_bool_3 with 300s (1) cores
% 11.76/2.42 # Starting new_ho_5 with 300s (1) cores
% 11.76/2.42 # pre_casc_3 with pid 24136 completed with status 8
% 11.76/2.42 # new_ho_5 with pid 24140 completed with status 8
% 11.76/2.42 # new_bool_3 with pid 24139 completed with status 0
% 11.76/2.42 # Result found by new_bool_3
% 11.76/2.42 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.76/2.42 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.76/2.42 # Starting ehoh_best5 with 300s (1) cores
% 11.76/2.42 # Starting almost_fo_3_lam with 300s (1) cores
% 11.76/2.42 # Starting new_bool_5 with 300s (1) cores
% 11.76/2.42 # Starting pre_casc_3 with 300s (1) cores
% 11.76/2.42 # Starting ho_unfolding_8 with 300s (1) cores
% 11.76/2.42 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.76/2.42 # Starting new_bool_3 with 300s (1) cores
% 11.76/2.42 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.76/2.42 # Search class: HGHSM-FSLM32-MHFMMSBN
% 11.76/2.42 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 11.76/2.42 # Starting ho_unfolding_8 with 61s (1) cores
% 11.76/2.42 # ho_unfolding_8 with pid 24160 completed with status 0
% 11.76/2.42 # Result found by ho_unfolding_8
% 11.76/2.42 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.76/2.42 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.76/2.42 # Starting ehoh_best5 with 300s (1) cores
% 11.76/2.42 # Starting almost_fo_3_lam with 300s (1) cores
% 11.76/2.42 # Starting new_bool_5 with 300s (1) cores
% 11.76/2.42 # Starting pre_casc_3 with 300s (1) cores
% 11.76/2.42 # Starting ho_unfolding_8 with 300s (1) cores
% 11.76/2.42 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.76/2.42 # Starting new_bool_3 with 300s (1) cores
% 11.76/2.42 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.76/2.42 # Search class: HGHSM-FSLM32-MHFMMSBN
% 11.76/2.42 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 11.76/2.42 # Starting ho_unfolding_8 with 61s (1) cores
% 11.76/2.42 # Preprocessing time : 0.102 s
% 11.76/2.42 # Presaturation interreduction done
% 11.76/2.42
% 11.76/2.42 # Proof found!
% 11.76/2.42 # SZS status Theorem
% 11.76/2.42 # SZS output start CNFRefutation
% See solution above
% 11.76/2.42 # Parsed axioms : 501
% 11.76/2.42 # Removed by relevancy pruning/SinE : 268
% 11.76/2.42 # Initial clauses : 401
% 11.76/2.42 # Removed in clause preprocessing : 29
% 11.76/2.42 # Initial clauses in saturation : 372
% 11.76/2.42 # Processed clauses : 2778
% 11.76/2.42 # ...of these trivial : 24
% 11.76/2.42 # ...subsumed : 1166
% 11.76/2.42 # ...remaining for further processing : 1588
% 11.76/2.42 # Other redundant clauses eliminated : 67
% 11.76/2.42 # Clauses deleted for lack of memory : 0
% 11.76/2.42 # Backward-subsumed : 82
% 11.76/2.42 # Backward-rewritten : 17
% 11.76/2.42 # Generated clauses : 54307
% 11.76/2.42 # ...of the previous two non-redundant : 52521
% 11.76/2.42 # ...aggressively subsumed : 0
% 11.76/2.42 # Contextual simplify-reflections : 0
% 11.76/2.42 # Paramodulations : 54192
% 11.76/2.42 # Factorizations : 22
% 11.76/2.42 # NegExts : 2
% 11.76/2.42 # Equation resolutions : 75
% 11.76/2.42 # Disequality decompositions : 0
% 11.76/2.42 # Total rewrite steps : 5368
% 11.76/2.42 # ...of those cached : 5157
% 11.76/2.42 # Propositional unsat checks : 0
% 11.76/2.42 # Propositional check models : 0
% 11.76/2.42 # Propositional check unsatisfiable : 0
% 11.76/2.42 # Propositional clauses : 0
% 11.76/2.42 # Propositional clauses after purity: 0
% 11.76/2.42 # Propositional unsat core size : 0
% 11.76/2.42 # Propositional preprocessing time : 0.000
% 11.76/2.42 # Propositional encoding time : 0.000
% 11.76/2.42 # Propositional solver time : 0.000
% 11.76/2.42 # Success case prop preproc time : 0.000
% 11.76/2.42 # Success case prop encoding time : 0.000
% 11.76/2.42 # Success case prop solver time : 0.000
% 11.76/2.42 # Current number of processed clauses : 1147
% 11.76/2.42 # Positive orientable unit clauses : 58
% 11.76/2.42 # Positive unorientable unit clauses: 0
% 11.76/2.42 # Negative unit clauses : 60
% 11.76/2.42 # Non-unit-clauses : 1029
% 11.76/2.42 # Current number of unprocessed clauses: 50352
% 11.76/2.42 # ...number of literals in the above : 191134
% 11.76/2.42 # Current number of archived formulas : 0
% 11.76/2.42 # Current number of archived clauses : 426
% 11.76/2.42 # Clause-clause subsumption calls (NU) : 97710
% 11.76/2.42 # Rec. Clause-clause subsumption calls : 46315
% 11.76/2.42 # Non-unit clause-clause subsumptions : 794
% 11.76/2.42 # Unit Clause-clause subsumption calls : 2052
% 11.76/2.42 # Rewrite failures with RHS unbound : 0
% 11.76/2.42 # BW rewrite match attempts : 45
% 11.76/2.42 # BW rewrite match successes : 12
% 11.76/2.42 # Condensation attempts : 0
% 11.76/2.42 # Condensation successes : 0
% 11.76/2.42 # Termbank termtop insertions : 1056763
% 11.76/2.42 # Search garbage collected termcells : 23245
% 11.76/2.42
% 11.76/2.42 # -------------------------------------------------
% 11.76/2.42 # User time : 1.754 s
% 11.76/2.42 # System time : 0.063 s
% 11.76/2.42 # Total time : 1.817 s
% 11.76/2.42 # Maximum resident set size: 7588 pages
% 11.76/2.42
% 11.76/2.42 # -------------------------------------------------
% 11.76/2.42 # User time : 1.973 s
% 11.76/2.42 # System time : 0.146 s
% 11.76/2.42 # Total time : 2.120 s
% 11.76/2.42 # Maximum resident set size: 2616 pages
% 11.76/2.42 % E---3.1 exiting
% 11.76/2.42 % E exiting
%------------------------------------------------------------------------------