%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU726^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 03:29:33 EDT 2024
% Result : Theorem 11.26s 2.12s
% Output : CNFRefutation 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 609
% Syntax : Number of formulae : 708 ( 38 unt; 362 typ; 0 def)
% Number of atoms : 3216 ( 627 equ; 0 cnn)
% Maximal formula atoms : 994 ( 9 avg)
% Number of connectives : 12935 ( 894 ~; 968 |; 562 &;8604 @)
% ( 335 <=>;1572 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1104 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 594 ( 594 >; 0 *; 0 +; 0 <<)
% Number of symbols : 366 ( 362 usr; 251 con; 0-4 aty)
% Number of variables : 2738 ( 182 ^2433 !; 123 ?;2738 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
epred1_0: $o ).
thf(decl_303,type,
esk1_2: $i > $i > $i ).
thf(decl_304,type,
esk2_2: $i > $i > $i ).
thf(decl_305,type,
esk3_2: $i > $i > $i ).
thf(decl_306,type,
esk4_1: $i > $i ).
thf(decl_307,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_308,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_309,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_310,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_311,type,
esk9_1: $i > $i ).
thf(decl_312,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_313,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_314,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_315,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_316,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_317,type,
esk15_2: $i > $i > $i ).
thf(decl_318,type,
esk16_2: $i > $i > $i ).
thf(decl_319,type,
esk17_1: $i > $i ).
thf(decl_320,type,
esk18_1: $i > $i ).
thf(decl_321,type,
esk19_1: $i > $i ).
thf(decl_322,type,
esk20_2: $i > $i > $i ).
thf(decl_323,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_324,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_325,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_326,type,
esk24_1: $i > $i ).
thf(decl_327,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_328,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_329,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_330,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_331,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_332,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_333,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_334,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_335,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_336,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_337,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_338,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_339,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_340,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_341,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_342,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_343,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_344,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_345,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_346,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_347,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_348,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_349,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_350,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_351,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_352,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_353,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_354,type,
esk52_2: $i > $i > $i ).
thf(decl_355,type,
esk53_2: $i > $i > $i ).
thf(decl_356,type,
esk54_2: $i > $i > $i ).
thf(decl_357,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_358,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_359,type,
esk57_2: $i > $i > $i ).
thf(decl_360,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_361,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_364,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_366,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_367,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_368,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_369,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_370,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_371,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_372,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_373,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_374,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_375,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_376,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_377,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_378,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_379,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_380,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_381,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_382,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_383,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_384,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_385,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_386,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_387,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_388,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_389,type,
esk87_0: $i ).
thf(decl_390,type,
esk88_0: $i ).
thf(decl_391,type,
esk89_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(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(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(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(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(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(contrasubsetT3,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(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(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(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(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(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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
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(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(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(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(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(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(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(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(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(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(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(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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
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(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
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(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(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(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(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_246,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_247,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_248,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_249,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_250,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_251,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_252,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_253,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_254,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_255,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_256,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_257,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_258,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_259,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_260,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_261,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_262,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_263,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_264,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_265,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_266,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_267,plain,
( 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_268,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_246]) ).
thf(c_0_269,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_246]) ).
thf(c_0_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_282,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_283,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_247,c_0_248]) ).
thf(c_0_284,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_249,c_0_248]) ).
thf(c_0_285,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_250,c_0_248]) ).
thf(c_0_286,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_287,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_288,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_289,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_290,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_251,c_0_246]) ).
thf(c_0_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_246]) ).
thf(c_0_301,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_246]) ).
thf(c_0_302,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_252,c_0_248]) ).
thf(c_0_303,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_304,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X826: $i] :
( ( X1 @ X826 )
& ! [X827: $i] :
( ( X1 @ X827 )
=> ( X826 = X827 ) ) )
=> ( ? [X828: $i] :
( ( X17 @ X828 )
& ! [X829: $i] :
( ( X17 @ X829 )
=> ( X828 = X829 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_253,c_0_254]) ).
thf(c_0_305,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X824: $i] :
( ( X1 @ X824 )
& ! [X825: $i] :
( ( X1 @ X825 )
=> ( X824 = X825 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_255,c_0_254]) ).
thf(c_0_306,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X820: $i] :
( ( X1 @ X820 )
& ! [X821: $i] :
( ( X1 @ X821 )
=> ( X820 = X821 ) ) )
<=> ? [X822: $i] :
( ( X17 @ X822 )
& ! [X823: $i] :
( ( X17 @ X823 )
=> ( X822 = X823 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_256,c_0_254]) ).
thf(c_0_307,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X818: $i] :
( ( X1 @ X818 )
& ! [X819: $i] :
( ( X1 @ X819 )
=> ( X818 = X819 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_257,c_0_254]) ).
thf(c_0_308,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X816: $i] :
( ( X1 @ X816 )
& ! [X817: $i] :
( ( X1 @ X817 )
=> ( X816 = X817 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_258,c_0_254]) ).
thf(c_0_309,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X814: $i] :
( ( X1 @ X814 )
& ! [X815: $i] :
( ( X1 @ X815 )
=> ( X814 = X815 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_259,c_0_254]) ).
thf(c_0_310,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X812: $i] :
( ( X1 @ X812 )
& ! [X813: $i] :
( ( X1 @ X813 )
=> ( X812 = X813 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_260,c_0_254]) ).
thf(c_0_311,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_312,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_261]) ).
thf(c_0_313,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X810: $i] :
( ( X1 @ X810 )
& ! [X811: $i] :
( ( X1 @ X811 )
=> ( X810 = X811 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_262,c_0_254]) ).
thf(c_0_314,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_315,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_261]) ).
thf(c_0_316,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_263,c_0_261]) ).
thf(c_0_317,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_261]) ).
thf(c_0_318,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_319,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X808: $i] :
( ( X1 @ X808 )
& ! [X809: $i] :
( ( X1 @ X809 )
=> ( X808 = X809 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_264,c_0_254]) ).
thf(c_0_320,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X806: $i] :
( ( X1 @ X806 )
& ! [X807: $i] :
( ( X1 @ X807 )
=> ( X806 = X807 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_265,c_0_254]) ).
thf(c_0_321,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_322,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_323,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_324,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X804: $i] :
( ( X1 @ X804 )
& ! [X805: $i] :
( ( X1 @ X805 )
=> ( X804 = X805 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_266,c_0_254]) ).
thf(c_0_325,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X802: $i] :
( ( X6 @ X2 @ X802 )
& ! [X803: $i] :
( ( X6 @ X2 @ X803 )
=> ( X802 = X803 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_267,c_0_254]) ).
thf(c_0_326,plain,
( epred1_0
<=> ! [X859: $i] :
? [X860: $i] :
( ! [X861: $i] :
( ( in @ X861 @ X860 )
=> ! [X862: $i] :
( ( in @ X862 @ X861 )
=> ( in @ X862 @ X859 ) ) )
& ! [X863: $i,X864: $i] :
( ( ( in @ X863 @ X859 )
& ( in @ X864 @ X859 ) )
=> ( ! [X865: $i] :
( ( in @ X865 @ X860 )
=> ( ( in @ X863 @ X865 )
<=> ( in @ X864 @ X865 ) ) )
=> ( X863 = X864 ) ) )
& ! [X866: $i,X867: $i] :
( ( ( in @ X866 @ X860 )
& ( in @ X867 @ X860 ) )
=> ( ! [X868: $i] :
( ( in @ X868 @ X866 )
=> ( in @ X868 @ X867 ) )
| ! [X869: $i] :
( ( in @ X869 @ X867 )
=> ( in @ X869 @ X866 ) ) ) )
& ! [X870: $i] :
( ( ! [X871: $i] :
( ( in @ X871 @ X870 )
=> ( in @ X871 @ X859 ) )
& ? [X872: $i] : ( in @ X872 @ X870 ) )
=> ? [X873: $i,X874: $i] :
( ( in @ X873 @ X860 )
& ( in @ X874 @ X870 )
& ~ ? [X875: $i] :
( ( in @ X875 @ X873 )
& ( in @ X875 @ X870 ) )
& ! [X876: $i] :
( ( in @ X876 @ X860 )
=> ( ! [X877: $i] :
( ( in @ X877 @ X876 )
=> ( in @ X877 @ X873 ) )
| ( in @ X874 @ X876 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_327,negated_conjecture,
~ ( ! [X830: $i,X831: $i] :
( ! [X832: $i] :
( ( in @ X832 @ X830 )
<=> ( in @ X832 @ X831 ) )
=> ( X830 = X831 ) )
=> ( ! [X833: $i] :
~ ( in @ X833 @ emptyset )
=> ( ! [X834: $i,X835: $i,X836: $i] :
( ( in @ X836 @ ( setadjoin @ X834 @ X835 ) )
<=> ( ( X836 = X834 )
| ( in @ X836 @ X835 ) ) )
=> ( ! [X837: $i,X838: $i] :
( ( in @ X838 @ ( powerset @ X837 ) )
<=> ! [X839: $i] :
( ( in @ X839 @ X838 )
=> ( in @ X839 @ X837 ) ) )
=> ( ! [X840: $i,X841: $i] :
( ( in @ X841 @ ( setunion @ X840 ) )
<=> ? [X842: $i] :
( ( in @ X841 @ X842 )
& ( in @ X842 @ X840 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X843: $i] :
( ( in @ X843 @ omega )
=> ( in @ ( setadjoin @ X843 @ X843 ) @ omega ) )
=> ( ! [X844: $i] :
( ( ( in @ emptyset @ X844 )
& ! [X845: $i] :
( ( ( in @ X845 @ omega )
& ( in @ X845 @ X844 ) )
=> ( in @ ( setadjoin @ X845 @ X845 ) @ X844 ) ) )
=> ! [X846: $i] :
( ( in @ X846 @ omega )
=> ( in @ X846 @ X844 ) ) )
=> ( ! [X847: $i > $i > $o,X848: $i] :
( ! [X849: $i] :
( ( in @ X849 @ X848 )
=> ? [X850: $i] :
( ( X847 @ X849 @ X850 )
& ! [X851: $i] :
( ( X847 @ X849 @ X851 )
=> ( X850 = X851 ) ) ) )
=> ? [X852: $i] :
! [X853: $i] :
( ( in @ X853 @ X852 )
<=> ? [X854: $i] :
( ( in @ X854 @ X848 )
& ( X847 @ X854 @ X853 ) ) ) )
=> ( ! [X855: $i] :
( ? [X856: $i] : ( in @ X856 @ X855 )
=> ? [X857: $i] :
( ( in @ X857 @ X855 )
& ~ ? [X858: $i] :
( ( in @ X858 @ X857 )
& ( in @ X858 @ X855 ) ) ) )
=> ( epred1_0
=> ( ! [X878: $i > $o] :
( ? [X879: $i] :
( ( X878 @ X879 )
& ! [X880: $i] :
( ( X878 @ X880 )
=> ( X879 = X880 ) ) )
=> ( X878
@ ( descr
@ ^ [Z0: $i] : ( X878 @ Z0 ) ) ) )
=> ( ! [X881: $i,X882: $i > $o,X883: $i] :
( ( in @ X883 @ X881 )
=> ( ( X882 @ X883 )
=> ( in @ X883 @ ( dsetconstr @ X881 @ X882 ) ) ) )
=> ( ! [X884: $i,X885: $i > $o,X886: $i] :
( ( in @ X886 @ ( dsetconstr @ X884 @ X885 ) )
=> ( in @ X886 @ X884 ) )
=> ( ! [X887: $i,X888: $i > $o,X889: $i] :
( ( in @ X889 @ ( dsetconstr @ X887 @ X888 ) )
=> ( X888 @ X889 ) )
=> ( ! [X890: $i > $o] :
( ? [X891: $i] :
( ( X890 @ X891 )
& ! [X892: $i] :
( ( X890 @ X892 )
=> ( X891 = X892 ) ) )
=> ? [X893: $i] :
( ( X890 @ X893 )
& ! [X894: $i] :
( ( X890 @ X894 )
=> ( X893 = X894 ) ) ) )
=> ( ! [X895: $o,X896: $i] :
( ( in @ X896 @ ( prop2set @ X895 ) )
=> X895 )
=> ( ! [X897: $i] :
( ( in @ X897 @ emptyset )
=> ! [X898: $o] : X898 )
=> ( ! [X899: $i] :
( ( in @ X899 @ emptyset )
=> ~ $true )
=> ( ! [X900: $i] :
~ ( in @ X900 @ emptyset )
=> ( ! [X901: $i > $o] :
( ? [X902: $i] :
( ( X901 @ X902 )
& ! [X903: $i] :
( ( X901 @ X903 )
=> ( X902 = X903 ) ) )
=> ? [X904: $i] : ( X901 @ X904 ) )
=> ( ! [X905: $i,X906: $i] :
( ! [X907: $i] :
( ( in @ X907 @ X905 )
=> ( in @ X907 @ X906 ) )
=> ( ! [X908: $i] :
( ( in @ X908 @ X906 )
=> ( in @ X908 @ X905 ) )
=> ( X905 = X906 ) ) )
=> ( ! [X909: $i] :
( ! [X910: $i] :
~ ( in @ X910 @ X909 )
=> ( X909 = emptyset ) )
=> ( ! [X911: $i] :
( ! [X912: $i] :
~ ( in @ X912 @ X911 )
=> ( X911 = emptyset ) )
=> ( ! [X913: $i,X914: $i > $o,X915: $i] :
( ( in @ X915 @ X913 )
=> ( ( in @ X915 @ ( dsetconstr @ X913 @ X914 ) )
<=> ( X914 @ X915 ) ) )
=> ( ! [X916: $i] :
( ( X916 != emptyset )
=> ? [X917: $i] : ( in @ X917 @ X916 ) )
=> ( ! [X918: $i,X919: $i > $o,X920: $i] :
( ( in @ X920 @ X918 )
=> ( ( X919 @ X920 )
=> ( ( dsetconstr @ X918 @ X919 )
!= emptyset ) ) )
=> ( ! [X921: $i] :
( ? [X922: $i] : ( in @ X922 @ X921 )
=> ( X921 != emptyset ) )
=> ( ! [X923: $i,X924: $i] : ( in @ X923 @ ( setadjoin @ X923 @ X924 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X925: $i,X926: $i,X927: $i] :
( ( in @ X927 @ X926 )
=> ( in @ X927 @ ( setadjoin @ X925 @ X926 ) ) )
=> ( ! [X928: $i,X929: $i,X930: $i] :
( ( in @ X930 @ ( setadjoin @ X928 @ X929 ) )
=> ! [X931: $o] :
( ( ( X930 = X928 )
=> X931 )
=> ( ( ( in @ X930 @ X929 )
=> X931 )
=> X931 ) ) )
=> ( ! [X932: $i,X933: $i,X934: $i] :
( ( in @ X934 @ ( setadjoin @ X932 @ X933 ) )
=> ( ( X934 = X932 )
| ( in @ X934 @ X933 ) ) )
=> ( ! [X935: $i] :
( ( dsetconstr @ X935
@ ^ [Z0: $i] : $true )
= X935 )
=> ( ! [X936: $i,X937: $i] :
( ! [X938: $i] :
( ( in @ X938 @ X937 )
=> ( in @ X938 @ X936 ) )
=> ( in @ X937 @ ( powerset @ X936 ) ) )
=> ( ! [X939: $i] : ( in @ emptyset @ ( powerset @ X939 ) )
=> ( ! [X940: $i] : ( in @ emptyset @ ( powerset @ X940 ) )
=> ( ! [X941: $i,X942: $i,X943: $i] :
( ( in @ X942 @ ( powerset @ X941 ) )
=> ( ( in @ X943 @ X942 )
=> ( in @ X943 @ X941 ) ) )
=> ( ! [X944: $i,X945: $i,X946: $i] :
( ( in @ X945 @ X946 )
=> ( ( in @ X946 @ X944 )
=> ( in @ X945 @ ( setunion @ X944 ) ) ) )
=> ( ! [X947: $i,X948: $i] :
( ( in @ X948 @ ( setunion @ X947 ) )
=> ! [X949: $o] :
( ! [X950: $i] :
( ( in @ X948 @ X950 )
=> ( ( in @ X950 @ X947 )
=> X949 ) )
=> X949 ) )
=> ( ! [X951: $i,X952: $i] :
( ( in @ X952 @ X951 )
=> ( in @ X952 @ ( powerset @ ( setunion @ X951 ) ) ) )
=> ( ! [X953: $i > $o] :
( ? [X954: $i] :
( ( X953 @ X954 )
& ! [X955: $i] :
( ( X953 @ X955 )
=> ( X954 = X955 ) ) )
=> ? [X956: $i] :
! [X957: $i] :
( ( X953 @ X957 )
<=> ( X957 = X956 ) ) )
=> ( ! [X958: $i] :
( ( X958 != emptyset )
=> ? [X959: $i] :
( ( in @ X959 @ X958 )
& $true ) )
=> ( ! [X960: $i,X961: $i] :
( ( in @ X960 @ ( setadjoin @ X961 @ emptyset ) )
=> ( X960 = X961 ) )
=> ( ! [X962: $i,X963: $i] :
( ( X962 != X963 )
=> ~ ( in @ X963 @ ( setadjoin @ X962 @ emptyset ) ) )
=> ( ! [X964: $i,X965: $i] :
( ( X964 = X965 )
=> ( in @ X964 @ ( setadjoin @ X965 @ emptyset ) ) )
=> ( ! [X966: $i,X967: $i] :
( ( in @ X966 @ ( setadjoin @ X967 @ emptyset ) )
=> ( in @ X967 @ ( setadjoin @ X966 @ emptyset ) ) )
=> ( ! [X968: $i,X969: $i,X970: $i] :
( ( in @ X970 @ ( setadjoin @ X968 @ ( setadjoin @ X969 @ emptyset ) ) )
=> ( ( X970 = X968 )
| ( X970 = X969 ) ) )
=> ( ! [X971: $i,X972: $i] : ( in @ X971 @ ( setadjoin @ X971 @ ( setadjoin @ X972 @ emptyset ) ) )
=> ( ! [X973: $i,X974: $i] : ( in @ X974 @ ( setadjoin @ X973 @ ( setadjoin @ X974 @ emptyset ) ) )
=> ( ! [X975: $i,X976: $i > $o] :
( ? [X977: $i] :
( ( in @ X977 @ X975 )
& ( X976 @ X977 ) )
=> ( ( ( dsetconstr @ X975 @ X976 )
= emptyset )
=> ~ $true ) )
=> ( ! [X978: $i > $o,X979: $i] :
( ( in @ X979 @ emptyset )
=> ( X978 @ X979 ) )
=> ( ! [X980: $i,X981: $i > $o] :
( ~ ! [X982: $i] :
( ( in @ X982 @ X980 )
=> ( X981 @ X982 ) )
=> ? [X983: $i] :
( ( in @ X983 @ X980 )
& ~ ( X981 @ X983 ) ) )
=> ( ! [X984: $i,X985: $i > $o] :
( ! [X986: $i] :
( ( in @ X986 @ X984 )
=> ~ ( X985 @ X986 ) )
=> ~ ? [X987: $i] :
( ( in @ X987 @ X984 )
& ( X985 @ X987 ) ) )
=> ( ! [X988: $i,X989: $i > $o] :
( ~ ? [X990: $i] :
( ( in @ X990 @ X988 )
& ( X989 @ X990 ) )
=> ! [X991: $i] :
( ( in @ X991 @ X988 )
=> ~ ( X989 @ X991 ) ) )
=> ( ! [X992: $i,X993: $i > $o] :
( ? [X994: $i] :
( ( in @ X994 @ X992 )
& ~ ( X993 @ X994 ) )
=> ~ ! [X995: $i] :
( ( in @ X995 @ X992 )
=> ( X993 @ X995 ) ) )
=> ( ! [X996: $o] :
( X996
=> ( in @ emptyset @ ( prop2set @ X996 ) ) )
=> ( prop2set2propI
=> ( ! [X997: $i,X998: $i > $o] :
( ~ ? [X999: $i] :
( ( in @ X999 @ X997 )
& ( X998 @ X999 ) )
=> ! [X1000: $i] :
( ( in @ X1000 @ X997 )
=> ~ ( X998 @ X1000 ) ) )
=> ( ! [X1001: $i,X1002: $i > $o] :
( ~ ! [X1003: $i] :
( ( in @ X1003 @ X1001 )
=> ( X1002 @ X1003 ) )
=> ? [X1004: $i] :
( ( in @ X1004 @ X1001 )
& ~ ( X1002 @ X1004 ) ) )
=> ( ! [X1005: $i > $o] :
( ? [X1006: $i] :
( ( X1005 @ X1006 )
& ! [X1007: $i] :
( ( X1005 @ X1007 )
=> ( X1006 = X1007 ) ) )
=> ? [X1008: $i] :
( ( X1005 @ X1008 )
& ! [X1009: $i] :
( ( X1005 @ X1009 )
=> ( X1008 = X1009 ) ) ) )
=> ( ! [X1010: $i > $o] :
( ? [X1011: $i] : ( X1010 @ X1011 )
=> ( ! [X1012: $i,X1013: $i] :
( ( X1010 @ X1012 )
=> ( ( X1010 @ X1013 )
=> ( X1012 = X1013 ) ) )
=> ? [X1014: $i] :
( ( X1010 @ X1014 )
& ! [X1015: $i] :
( ( X1010 @ X1015 )
=> ( X1014 = X1015 ) ) ) ) )
=> ( ! [X1016: $i > $o] :
( ? [X1017: $i] :
! [X1018: $i] :
( ( X1016 @ X1018 )
<=> ( X1018 = X1017 ) )
=> ? [X1019: $i] :
( ( X1016 @ X1019 )
& ! [X1020: $i] :
( ( X1016 @ X1020 )
=> ( X1019 = X1020 ) ) ) )
=> ( ! [X1021: $i,X1022: $i] :
( ( X1021 = X1022 )
=> ! [X1023: $i,X1024: $i] :
( ( X1023 = X1024 )
=> ( ( in @ X1023 @ X1021 )
=> ( in @ X1024 @ X1022 ) ) ) )
=> ( ! [X1025: $i,X1026: $i] :
( ( X1025 = X1026 )
=> ! [X1027: $i,X1028: $i] :
( ( X1027 = X1028 )
=> ( ( in @ X1027 @ X1025 )
<=> ( in @ X1028 @ X1026 ) ) ) )
=> ( ! [X1029: $i > $o] :
( ? [X1030: $i] :
( ( X1029 @ X1030 )
& ! [X1031: $i] :
( ( X1029 @ X1031 )
=> ( X1030 = X1031 ) ) )
=> ! [X1032: $i,X1033: $i] :
( ( X1029 @ X1032 )
=> ( ( X1029 @ X1033 )
=> ( X1032 = X1033 ) ) ) )
=> ( ! [X1034: $i > $o,X1035: $i > $o] :
( ! [X1036: $i,X1037: $i] :
( ( X1036 = X1037 )
=> ( ( X1034 @ X1036 )
<=> ( X1035 @ X1037 ) ) )
=> ( ? [X1038: $i] :
( ( X1034 @ X1038 )
& ! [X1039: $i] :
( ( X1034 @ X1039 )
=> ( X1038 = X1039 ) ) )
<=> ? [X1040: $i] :
( ( X1035 @ X1040 )
& ! [X1041: $i] :
( ( X1035 @ X1041 )
=> ( X1040 = X1041 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1042: $i,X1043: $i] :
( ( X1042 = X1043 )
=> ! [X1044: $i,X1045: $i] :
( ( X1044 = X1045 )
=> ( ( setadjoin @ X1042 @ X1044 )
= ( setadjoin @ X1043 @ X1045 ) ) ) )
=> ( ! [X1046: $i,X1047: $i] :
( ( X1046 = X1047 )
=> ( ( powerset @ X1046 )
= ( powerset @ X1047 ) ) )
=> ( ! [X1048: $i,X1049: $i] :
( ( X1048 = X1049 )
=> ( ( setunion @ X1048 )
= ( setunion @ X1049 ) ) )
=> ( ( omega = omega )
=> ( ! [X1050: $i > $o] :
( ? [X1051: $i] :
( ( X1050 @ X1051 )
& ! [X1052: $i] :
( ( X1050 @ X1052 )
=> ( X1051 = X1052 ) ) )
=> ! [X1053: $i,X1054: $i] :
( ( X1050 @ X1053 )
=> ( ( X1050 @ X1054 )
=> ( X1053 = X1054 ) ) ) )
=> ( ! [X1055: $i > $o,X1056: $i > $o] :
( ! [X1057: $i,X1058: $i] :
( ( X1057 = X1058 )
=> ( ( X1055 @ X1057 )
<=> ( X1056 @ X1058 ) ) )
=> ( ? [X1059: $i] :
( ( X1055 @ X1059 )
& ! [X1060: $i] :
( ( X1055 @ X1060 )
=> ( X1059 = X1060 ) ) )
=> ( ? [X1061: $i] :
( ( X1056 @ X1061 )
& ! [X1062: $i] :
( ( X1056 @ X1062 )
=> ( X1061 = X1062 ) ) )
=> ( ( descr @ X1055 )
= ( descr @ X1056 ) ) ) ) )
=> ( ! [X1063: $i,X1064: $i] :
( ( X1063 = X1064 )
=> ! [X1065: $i > $o,X1066: $i > $o] :
( ! [X1067: $i] :
( ( in @ X1067 @ X1063 )
=> ! [X1068: $i] :
( ( in @ X1068 @ X1064 )
=> ( ( X1067 = X1068 )
=> ( ( X1065 @ X1067 )
<=> ( X1066 @ X1068 ) ) ) ) )
=> ( ( dsetconstr @ X1063 @ X1065 )
= ( dsetconstr @ X1064 @ X1066 ) ) ) )
=> ( ! [X1069: $i,X1070: $i] :
( ! [X1071: $i] :
( ( in @ X1071 @ X1069 )
=> ( in @ X1071 @ X1070 ) )
=> ( subset @ X1069 @ X1070 ) )
=> ( ! [X1072: $i,X1073: $i] :
( ( X1072 = X1073 )
=> ( subset @ X1073 @ X1072 ) )
=> ( ! [X1074: $i,X1075: $i] :
( ( X1074 = X1075 )
=> ( subset @ X1074 @ X1075 ) )
=> ( ! [X1076: $i,X1077: $i] :
( ! [X1078: $i] :
( ( in @ X1078 @ X1076 )
=> ( in @ X1078 @ X1077 ) )
=> ( subset @ X1076 @ X1077 ) )
=> ( ! [X1079: $i] : ( subset @ emptyset @ X1079 )
=> ( ! [X1080: $i,X1081: $i,X1082: $i] :
( ( subset @ X1080 @ X1081 )
=> ( ( in @ X1082 @ X1080 )
=> ( in @ X1082 @ X1081 ) ) )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ( subset @ X1083 @ X1084 )
=> ( ~ ( in @ X1085 @ X1084 )
=> ~ ( in @ X1085 @ X1083 ) ) )
=> ( ! [X1086: $i,X1087: $i,X1088: $i] :
( ( in @ X1088 @ X1086 )
=> ( ~ ( in @ X1088 @ X1087 )
=> ~ ( subset @ X1086 @ X1087 ) ) )
=> ( ! [X1089: $i,X1090: $i] :
( ~ ( subset @ X1089 @ X1090 )
=> ( X1089 != X1090 ) )
=> ( ! [X1091: $i,X1092: $i,X1093: $i] :
( ( in @ X1093 @ X1091 )
=> ( ~ ( in @ X1093 @ X1092 )
=> ( X1091 != X1092 ) ) )
=> ( ! [X1094: $i] : ( subset @ X1094 @ X1094 )
=> ( ! [X1095: $i,X1096: $i,X1097: $i] :
( ( subset @ X1095 @ X1096 )
=> ( ( subset @ X1096 @ X1097 )
=> ( subset @ X1095 @ X1097 ) ) )
=> ( ! [X1098: $i,X1099: $i] : ( subset @ X1099 @ ( setadjoin @ X1098 @ X1099 ) )
=> ( ! [X1100: $i,X1101: $i,X1102: $i] :
( ( subset @ X1100 @ X1102 )
=> ( subset @ X1100 @ ( setadjoin @ X1101 @ X1102 ) ) )
=> ( ! [X1103: $i,X1104: $i] :
( ( subset @ X1103 @ X1104 )
=> ( in @ X1103 @ ( powerset @ X1104 ) ) )
=> ( ! [X1105: $i,X1106: $i] :
( ( subset @ X1105 @ X1106 )
=> ( ( subset @ X1106 @ X1105 )
=> ( X1105 = X1106 ) ) )
=> ( ! [X1107: $i] :
( ( subset @ X1107 @ emptyset )
=> ( X1107 = emptyset ) )
=> ( ! [X1108: $i,X1109: $i] :
( ( subset @ X1109 @ X1108 )
=> ( in @ X1109 @ ( powerset @ X1108 ) ) )
=> ( ! [X1110: $i,X1111: $i] :
( ( in @ X1111 @ ( powerset @ X1110 ) )
=> ( subset @ X1111 @ X1110 ) )
=> ( ! [X1112: $i] : ( in @ X1112 @ ( powerset @ X1112 ) )
=> ( ! [X1113: $i,X1114: $i] :
( ( subset @ X1113 @ X1114 )
=> ( subset @ ( powerset @ X1113 ) @ ( powerset @ X1114 ) ) )
=> ( ! [X1115: $i,X1116: $i > $o] : ( in @ ( dsetconstr @ X1115 @ X1116 ) @ ( powerset @ X1115 ) )
=> ( ! [X1117: $i,X1118: $i > $o] : ( subset @ ( dsetconstr @ X1117 @ X1118 ) @ X1117 )
=> ( ! [X1119: $i,X1120: $i,X1121: $i] :
( ( in @ X1121 @ X1119 )
=> ( in @ X1121 @ ( binunion @ X1119 @ X1120 ) ) )
=> ( ! [X1122: $i,X1123: $i] : ( in @ X1123 @ ( setadjoin @ X1122 @ ( setadjoin @ X1123 @ emptyset ) ) )
=> ( ! [X1124: $i,X1125: $i,X1126: $i] :
( ( in @ X1126 @ X1125 )
=> ( in @ X1126 @ ( binunion @ X1124 @ X1125 ) ) )
=> ( ! [X1127: $i,X1128: $i,X1129: $i,X1130: $o] :
( ( in @ X1129 @ ( binunion @ X1127 @ X1128 ) )
=> ( ( ( in @ X1129 @ X1127 )
=> X1130 )
=> ( ( ( in @ X1129 @ X1128 )
=> X1130 )
=> X1130 ) ) )
=> ( ! [X1131: $i,X1132: $i,X1133: $i] :
( ( in @ X1133 @ ( binunion @ X1131 @ X1132 ) )
=> ( ( in @ X1133 @ X1131 )
| ( in @ X1133 @ X1132 ) ) )
=> ( ! [X1134: $i,X1135: $i] : ( subset @ X1134 @ ( binunion @ X1134 @ X1135 ) )
=> ( ! [X1136: $i,X1137: $i] : ( subset @ X1137 @ ( binunion @ X1136 @ X1137 ) )
=> ( ! [X1138: $i,X1139: $i,X1140: $i] :
( ( in @ X1140 @ X1138 )
=> ( ( in @ X1140 @ X1139 )
=> ( in @ X1140 @ ( binintersect @ X1138 @ X1139 ) ) ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i] :
( ( subset @ X1143 @ X1141 )
=> ( ( subset @ X1143 @ X1142 )
=> ( subset @ X1143 @ ( binintersect @ X1141 @ X1142 ) ) ) )
=> ( ! [X1144: $i,X1145: $i,X1146: $i] :
( ( in @ X1146 @ ( binintersect @ X1144 @ X1145 ) )
=> ( in @ X1146 @ X1144 ) )
=> ( ! [X1147: $i,X1148: $i] : ( subset @ ( binintersect @ X1147 @ X1148 ) @ X1147 )
=> ( ! [X1149: $i,X1150: $i] :
( ( subset @ X1149 @ X1150 )
=> ( ( binintersect @ X1149 @ X1150 )
= X1149 ) )
=> ( ! [X1151: $i,X1152: $i] :
( ( ( binintersect @ X1151 @ X1152 )
= X1152 )
=> ( subset @ X1152 @ X1151 ) )
=> ( ! [X1153: $i,X1154: $i,X1155: $i] :
( ( in @ X1155 @ ( binintersect @ X1153 @ X1154 ) )
=> ( in @ X1155 @ X1154 ) )
=> ( ! [X1156: $i,X1157: $i] :
( ~ ? [X1158: $i] :
( ( in @ X1158 @ X1156 )
& ( in @ X1158 @ X1157 ) )
=> ( ( binintersect @ X1156 @ X1157 )
= emptyset ) )
=> ( ! [X1159: $i,X1160: $i] : ( subset @ ( binintersect @ X1159 @ X1160 ) @ X1160 )
=> ( ! [X1161: $i,X1162: $i] :
( ( subset @ X1162 @ X1161 )
=> ( ( binintersect @ X1161 @ X1162 )
= X1162 ) )
=> ( ! [X1163: $i,X1164: $i] :
( ( ( binintersect @ X1163 @ X1164 )
= X1163 )
=> ( subset @ X1163 @ X1164 ) )
=> ( ! [X1165: $i,X1166: $i,X1167: $i] :
( ( binintersect @ X1165 @ ( binunion @ X1166 @ X1167 ) )
= ( binunion @ ( binintersect @ X1165 @ X1166 ) @ ( binintersect @ X1165 @ X1167 ) ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ( in @ X1170 @ X1168 )
=> ( ~ ( in @ X1170 @ X1169 )
=> ( in @ X1170 @ ( setminus @ X1168 @ X1169 ) ) ) )
=> ( ! [X1171: $i,X1172: $i,X1173: $i] :
( ( in @ X1173 @ ( setminus @ X1171 @ X1172 ) )
=> ( in @ X1173 @ X1171 ) )
=> ( ! [X1174: $i,X1175: $i,X1176: $i] :
( ( in @ X1176 @ ( setminus @ X1174 @ X1175 ) )
=> ~ ( in @ X1176 @ X1175 ) )
=> ( ! [X1177: $i,X1178: $i] :
( ( subset @ X1177 @ X1178 )
=> ( ( setminus @ X1177 @ X1178 )
= emptyset ) )
=> ( ! [X1179: $i,X1180: $i,X1181: $i] :
( ~ ( in @ X1181 @ ( setminus @ X1179 @ X1180 ) )
=> ( ( in @ X1181 @ X1179 )
=> ( in @ X1181 @ X1180 ) ) )
=> ( ! [X1182: $i,X1183: $i,X1184: $i] :
( ~ ( in @ X1184 @ ( setminus @ X1182 @ X1183 ) )
=> ( ~ ( in @ X1184 @ X1183 )
=> ~ ( in @ X1184 @ X1182 ) ) )
=> ( ! [X1185: $i,X1186: $i,X1187: $i] :
( ~ ( in @ X1187 @ X1185 )
=> ~ ( in @ X1187 @ ( setminus @ X1185 @ X1186 ) ) )
=> ( ! [X1188: $i,X1189: $i,X1190: $i] :
( ( in @ X1190 @ X1189 )
=> ~ ( in @ X1190 @ ( setminus @ X1188 @ X1189 ) ) )
=> ( ! [X1191: $i,X1192: $i] : ( subset @ ( setminus @ X1191 @ X1192 ) @ X1191 )
=> ( ! [X1193: $i,X1194: $i] :
( ( ( setminus @ X1193 @ X1194 )
= emptyset )
=> ( subset @ X1193 @ X1194 ) )
=> ( ! [X1195: $i,X1196: $i,X1197: $i] :
( ( in @ X1197 @ ( symdiff @ X1195 @ X1196 ) )
=> ! [X1198: $o] :
( ( ( in @ X1197 @ X1195 )
=> ( ~ ( in @ X1197 @ X1196 )
=> X1198 ) )
=> ( ( ~ ( in @ X1197 @ X1195 )
=> ( ( in @ X1197 @ X1196 )
=> X1198 ) )
=> X1198 ) ) )
=> ( ! [X1199: $i,X1200: $i,X1201: $i] :
( ( in @ X1201 @ X1199 )
=> ( ~ ( in @ X1201 @ X1200 )
=> ( in @ X1201 @ ( symdiff @ X1199 @ X1200 ) ) ) )
=> ( ! [X1202: $i,X1203: $i,X1204: $i] :
( ~ ( in @ X1204 @ X1202 )
=> ( ( in @ X1204 @ X1203 )
=> ( in @ X1204 @ ( symdiff @ X1202 @ X1203 ) ) ) )
=> ( ! [X1205: $i,X1206: $i,X1207: $i] :
( ( in @ X1207 @ X1205 )
=> ( ( in @ X1207 @ X1206 )
=> ~ ( in @ X1207 @ ( symdiff @ X1205 @ X1206 ) ) ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ~ ( in @ X1210 @ X1208 )
=> ( ~ ( in @ X1210 @ X1209 )
=> ~ ( in @ X1210 @ ( symdiff @ X1208 @ X1209 ) ) ) )
=> ( ! [X1211: $i,X1212: $i] : ( in @ X1212 @ ( setadjoin @ X1211 @ ( setadjoin @ X1212 @ emptyset ) ) )
=> ( ! [X1213: $i,X1214: $i] : ( in @ X1213 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1213 @ ( setadjoin @ X1214 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1215: $i,X1216: $i] : ( in @ X1216 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1215 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1215 @ ( setadjoin @ X1216 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1217: $i,X1218: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1217 @ ( setadjoin @ X1218 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1219: $i,X1220: $i] : ( iskpair @ ( kpair @ X1219 @ X1220 ) )
=> ( ! [X1221: $i,X1222: $i] :
( ( in @ X1222 @ X1221 )
=> ( subset @ ( setadjoin @ X1222 @ emptyset ) @ X1221 ) )
=> ( ! [X1223: $i,X1224: $i] :
( ( in @ X1224 @ X1223 )
=> ( in @ ( setadjoin @ X1224 @ emptyset ) @ ( powerset @ X1223 ) ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i] :
( ( in @ X1227 @ X1225 )
=> ( in @ ( setadjoin @ X1227 @ emptyset ) @ ( powerset @ ( binunion @ X1225 @ X1226 ) ) ) )
=> ( ! [X1228: $i,X1229: $i,X1230: $i] :
( ( in @ X1230 @ ( setadjoin @ X1228 @ ( setadjoin @ X1229 @ emptyset ) ) )
=> ( ( X1230 = X1228 )
| ( X1230 = X1229 ) ) )
=> ( ! [X1231: $i,X1232: $i,X1233: $i] :
( ( in @ X1233 @ X1231 )
=> ! [X1234: $i] :
( ( in @ X1234 @ X1232 )
=> ( subset @ ( setadjoin @ X1233 @ ( setadjoin @ X1234 @ emptyset ) ) @ ( binunion @ X1231 @ X1232 ) ) ) )
=> ( ! [X1235: $i,X1236: $i,X1237: $i] :
( ( in @ X1237 @ X1235 )
=> ! [X1238: $i] :
( ( in @ X1238 @ X1236 )
=> ( in @ ( setadjoin @ X1237 @ ( setadjoin @ X1238 @ emptyset ) ) @ ( powerset @ ( binunion @ X1235 @ X1236 ) ) ) ) )
=> ( ! [X1239: $i,X1240: $i,X1241: $i] :
( ( in @ X1241 @ X1239 )
=> ! [X1242: $i] :
( ( in @ X1242 @ X1240 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1241 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1241 @ ( setadjoin @ X1242 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1239 @ X1240 ) ) ) ) )
=> ( ! [X1243: $i,X1244: $i,X1245: $i] :
( ( in @ X1245 @ X1243 )
=> ! [X1246: $i] :
( ( in @ X1246 @ X1244 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1245 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1245 @ ( setadjoin @ X1246 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1243 @ X1244 ) ) ) ) ) )
=> ( ! [X1247: $i,X1248: $i,X1249: $i] :
( ( in @ X1249 @ X1247 )
=> ! [X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ( in @ ( kpair @ X1249 @ X1250 ) @ ( powerset @ ( powerset @ ( binunion @ X1247 @ X1248 ) ) ) ) ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i] :
( ( in @ X1253 @ X1251 )
=> ! [X1254: $i] :
( ( in @ X1254 @ X1252 )
=> ( in @ ( kpair @ X1253 @ X1254 ) @ ( cartprod @ X1251 @ X1252 ) ) ) )
=> ( ! [X1255: $i,X1256: $i,X1257: $i] :
( ( in @ X1257 @ ( cartprod @ X1255 @ X1256 ) )
=> ? [X1258: $i] :
( ( in @ X1258 @ X1255 )
& ? [X1259: $i] :
( ( in @ X1259 @ X1256 )
& ( X1257
= ( kpair @ X1258 @ X1259 ) ) ) ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i] :
( ( in @ X1262 @ ( cartprod @ X1260 @ X1261 ) )
=> ( iskpair @ X1262 ) )
=> ( ! [X1263: $i,X1264: $i] :
( ( in @ X1264 @ ( setunion @ X1263 ) )
=> ? [X1265: $i] :
( ( in @ X1265 @ X1263 )
& ( in @ X1264 @ X1265 ) ) )
=> ( ! [X1266: $i] : ( subset @ ( setunion @ ( setadjoin @ X1266 @ emptyset ) ) @ X1266 )
=> ( ! [X1267: $i] : ( subset @ X1267 @ ( setunion @ ( setadjoin @ X1267 @ emptyset ) ) )
=> ( ! [X1268: $i] :
( ( setunion @ ( setadjoin @ X1268 @ emptyset ) )
= X1268 )
=> ( ! [X1269: $i,X1270: $i > $o] :
( ! [X1271: $i] :
( ( in @ X1271 @ X1269 )
=> ! [X1272: $i] :
( ( in @ X1272 @ X1269 )
=> ( ( X1270 @ X1271 )
=> ( ( X1270 @ X1272 )
=> ( X1271 = X1272 ) ) ) ) )
=> ( ? [X1273: $i] :
( ( in @ X1273 @ X1269 )
& ( X1270 @ X1273 ) )
=> ( singleton @ ( dsetconstr @ X1269 @ X1270 ) ) ) )
=> ( ! [X1274: $i,X1275: $i > $o] :
( ( singleton @ ( dsetconstr @ X1274 @ X1275 ) )
=> ? [X1276: $i] :
( ( in @ X1276 @ X1274 )
& ( X1275 @ X1276 ) ) )
=> ( ! [X1277: $i,X1278: $i > $o,X1279: $i] :
( ( in @ X1279 @ X1277 )
=> ( ( X1278 @ X1279 )
=> ( ! [X1280: $i] :
( ( in @ X1280 @ X1277 )
=> ( ( X1278 @ X1280 )
=> ( X1280 = X1279 ) ) )
=> ( singleton @ ( dsetconstr @ X1277 @ X1278 ) ) ) ) )
=> ( ! [X1281: $i,X1282: $i > $o] :
( ! [X1283: $i] :
( ( in @ X1283 @ X1281 )
=> ! [X1284: $i] :
( ( in @ X1284 @ X1281 )
=> ( ( X1282 @ X1283 )
=> ( ( X1282 @ X1284 )
=> ( X1283 = X1284 ) ) ) ) )
=> ( ? [X1285: $i] :
( ( in @ X1285 @ X1281 )
& ( X1282 @ X1285 ) )
=> ( singleton @ ( dsetconstr @ X1281 @ X1282 ) ) ) )
=> ( ! [X1286: $i,X1287: $i] :
( ( ( setadjoin @ X1286 @ emptyset )
= ( setadjoin @ X1287 @ emptyset ) )
=> ( X1286 = X1287 ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i] :
( ( in @ ( setadjoin @ X1290 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1288 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1288 @ ( setadjoin @ X1289 @ emptyset ) ) @ emptyset ) ) )
=> ( X1288 = X1290 ) )
=> ( ! [X1291: $i] :
( ( iskpair @ X1291 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1291 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1291 ) ) ) )
=> ( ! [X1292: $i] :
( ( singleton @ X1292 )
=> ( in @ ( setunion @ X1292 ) @ X1292 ) )
=> ( ! [X1293: $i,X1294: $i] :
( ( kfst @ ( kpair @ X1293 @ X1294 ) )
= X1293 )
=> ( ! [X1295: $i,X1296: $i,X1297: $i] :
( ( in @ X1297 @ ( cartprod @ X1295 @ X1296 ) )
=> ( in @ ( kfst @ X1297 ) @ X1295 ) )
=> ( ! [X1298: $i,X1299: $i,X1300: $i,X1301: $i] :
( ( ( setadjoin @ ( setadjoin @ X1298 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1298 @ ( setadjoin @ X1299 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1300 @ ( setadjoin @ X1301 @ emptyset ) ) @ emptyset ) ) )
=> ( X1298 = X1300 ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i,X1305: $i] :
( ( ( kpair @ X1302 @ X1303 )
= ( kpair @ X1304 @ X1305 ) )
=> ( X1302 = X1304 ) )
=> ( ! [X1306: $i,X1307: $i] :
( ( X1306 = X1307 )
=> ( ( setadjoin @ X1306 @ ( setadjoin @ X1307 @ emptyset ) )
= ( setadjoin @ X1306 @ emptyset ) ) )
=> ( ! [X1308: $i,X1309: $i] :
( ( X1308 = X1309 )
=> ( ( setadjoin @ ( setadjoin @ X1308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1308 @ ( setadjoin @ X1309 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1308 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i,X1313: $i] :
( ( ( setadjoin @ ( setadjoin @ X1310 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1310 @ ( setadjoin @ X1311 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1312 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1312 @ ( setadjoin @ X1313 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1312 = X1313 )
=> ( X1311 = X1313 ) ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( ( setadjoin @ X1314 @ ( setadjoin @ X1315 @ emptyset ) )
= ( setadjoin @ X1316 @ emptyset ) )
=> ( X1314 = X1315 ) )
=> ( ! [X1317: $i,X1318: $i,X1319: $i,X1320: $i] :
( ( ( setadjoin @ ( setadjoin @ X1317 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1317 @ ( setadjoin @ X1318 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1319 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1319 @ ( setadjoin @ X1320 @ emptyset ) ) @ emptyset ) ) )
=> ( X1318 = X1320 ) )
=> ( ! [X1321: $i,X1322: $i,X1323: $i,X1324: $i] :
( ( ( kpair @ X1321 @ X1322 )
= ( kpair @ X1323 @ X1324 ) )
=> ( X1322 = X1324 ) )
=> ( ! [X1325: $i] :
( ( iskpair @ X1325 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1325 )
@ ^ [Z0: $i] :
( X1325
= ( kpair @ ( kfst @ X1325 ) @ Z0 ) ) ) ) )
=> ( ! [X1326: $i,X1327: $i] :
( ( ksnd @ ( kpair @ X1326 @ X1327 ) )
= X1327 )
=> ( ! [X1328: $i] :
( ( iskpair @ X1328 )
=> ( ( kpair @ ( kfst @ X1328 ) @ ( ksnd @ X1328 ) )
= X1328 ) )
=> ( ! [X1329: $i,X1330: $i,X1331: $i] :
( ( in @ X1331 @ ( cartprod @ X1329 @ X1330 ) )
=> ( in @ ( ksnd @ X1331 ) @ X1330 ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i,X1335: $i] :
( ( in @ ( kpair @ X1334 @ X1335 ) @ ( cartprod @ X1332 @ X1333 ) )
=> ( in @ X1334 @ X1332 ) )
=> ( ! [X1336: $i,X1337: $i,X1338: $i,X1339: $i] :
( ( in @ ( kpair @ X1338 @ X1339 ) @ ( cartprod @ X1336 @ X1337 ) )
=> ( in @ X1339 @ X1337 ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i] :
( ( in @ X1342 @ X1340 )
=> ! [X1343: $i] :
( ( in @ X1343 @ X1341 )
=> ( ( kpair @ X1342 @ X1343 )
= ( kpair @ X1342 @ X1343 ) ) ) )
=> ( ! [X1344: $i,X1345: $i,X1346: $i] :
( ( in @ X1346 @ X1344 )
=> ! [X1347: $i] :
( ( in @ X1347 @ X1345 )
=> ( ( kfst @ ( kpair @ X1346 @ X1347 ) )
= X1346 ) ) )
=> ( ! [X1348: $i,X1349: $i,X1350: $i] :
( ( in @ X1350 @ X1348 )
=> ! [X1351: $i] :
( ( in @ X1351 @ X1349 )
=> ( ( ksnd @ ( kpair @ X1350 @ X1351 ) )
= X1351 ) ) )
=> ( ! [X1352: $i,X1353: $i,X1354: $i] :
( ( in @ X1354 @ ( cartprod @ X1352 @ X1353 ) )
=> ( ( kpair @ ( kfst @ X1354 ) @ ( ksnd @ X1354 ) )
= X1354 ) )
=> ( ! [X1355: $i,X1356: $i,X1357: $i > $i > $o,X1358: $i] :
( ( in @ X1358 @ X1355 )
=> ! [X1359: $i] :
( ( in @ X1359 @ X1356 )
=> ( ( X1357 @ X1358 @ X1359 )
=> ( in @ ( kpair @ X1358 @ X1359 ) @ ( dpsetconstr @ X1355 @ X1356 @ X1357 ) ) ) ) )
=> ( ! [X1360: $i,X1361: $i,X1362: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1360 @ X1361 @ X1362 ) @ ( cartprod @ X1360 @ X1361 ) )
=> ( ! [X1363: $i,X1364: $i,X1365: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1363 @ X1364 @ X1365 ) @ ( cartprod @ X1363 @ X1364 ) )
=> ( ! [X1366: $i,X1367: $i,X1368: $i > $i > $o,X1369: $i] :
( ( in @ X1369 @ X1366 )
=> ! [X1370: $i] :
( ( in @ X1370 @ X1367 )
=> ( ( in @ ( kpair @ X1369 @ X1370 ) @ ( dpsetconstr @ X1366 @ X1367 @ X1368 ) )
=> ( X1368 @ X1369 @ X1370 ) ) ) )
=> ( ! [X1371: $i,X1372: $i,X1373: $i > $i > $o,X1374: $i,X1375: $i] :
( ( in @ ( kpair @ X1374 @ X1375 ) @ ( dpsetconstr @ X1371 @ X1372 @ X1373 ) )
=> ( in @ X1374 @ X1371 ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i > $i > $o,X1379: $i,X1380: $i] :
( ( in @ ( kpair @ X1379 @ X1380 ) @ ( dpsetconstr @ X1376 @ X1377 @ X1378 ) )
=> ( in @ X1380 @ X1377 ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i > $i > $o,X1384: $i,X1385: $i] :
( ( in @ ( kpair @ X1384 @ X1385 ) @ ( dpsetconstr @ X1381 @ X1382 @ X1383 ) )
=> ( X1383 @ X1384 @ X1385 ) )
=> ( ! [X1386: $i,X1387: $i,X1388: $i] :
( ( func @ X1386 @ X1387 @ X1388 )
=> ! [X1389: $i] :
( ( in @ X1389 @ X1386 )
=> ( singleton
@ ( dsetconstr @ X1387
@ ^ [Z0: $i] : ( in @ ( kpair @ X1389 @ Z0 ) @ X1388 ) ) ) ) )
=> ( ! [X1390: $i,X1391: $i,X1392: $i] :
( ( func @ X1390 @ X1391 @ X1392 )
=> ! [X1393: $i] :
( ( in @ X1393 @ X1390 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1391
@ ^ [Z0: $i] : ( in @ ( kpair @ X1393 @ Z0 ) @ X1392 ) ) )
@ X1391 ) ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i] :
( ( func @ X1394 @ X1395 @ X1396 )
=> ! [X1397: $i] :
( ( in @ X1397 @ X1394 )
=> ( in @ ( ap @ X1394 @ X1395 @ X1396 @ X1397 ) @ X1395 ) ) )
=> ( ! [X1398: $i,X1399: $i,X1400: $i] :
( ( in @ X1400 @ ( funcSet @ X1398 @ X1399 ) )
=> ( func @ X1398 @ X1399 @ X1400 ) )
=> ( ! [X1401: $i,X1402: $i,X1403: $i] :
( ( in @ X1403 @ ( funcSet @ X1401 @ X1402 ) )
=> ! [X1404: $i] :
( ( in @ X1404 @ X1401 )
=> ( in @ ( ap @ X1401 @ X1402 @ X1403 @ X1404 ) @ X1402 ) ) )
=> ( ! [X1405: $i,X1406: $i,X1407: $i] :
( ( func @ X1405 @ X1406 @ X1407 )
=> ( in @ X1407 @ ( funcSet @ X1405 @ X1406 ) ) )
=> ( ! [X1408: $i,X1409: $i,X1410: $i > $i] :
( ! [X1411: $i] :
( ( in @ X1411 @ X1408 )
=> ( in @ ( X1410 @ X1411 ) @ X1409 ) )
=> ( func @ X1408 @ X1409
@ ( dpsetconstr @ X1408 @ X1409
@ ^ [Z0: $i] : ( $eq @ ( X1410 @ Z0 ) ) ) ) )
=> ( ! [X1412: $i,X1413: $i,X1414: $i > $i] :
( ! [X1415: $i] :
( ( in @ X1415 @ X1412 )
=> ( in @ ( X1414 @ X1415 ) @ X1413 ) )
=> ( func @ X1412 @ X1413 @ ( lam @ X1412 @ X1413 @ X1414 ) ) )
=> ( ! [X1416: $i,X1417: $i,X1418: $i > $i] :
( ! [X1419: $i] :
( ( in @ X1419 @ X1416 )
=> ( in @ ( X1418 @ X1419 ) @ X1417 ) )
=> ( in @ ( lam @ X1416 @ X1417 @ X1418 ) @ ( funcSet @ X1416 @ X1417 ) ) )
=> ( ! [X1420: $i,X1421: $i,X1422: $i] :
( ( subset @ X1422 @ ( cartprod @ X1420 @ X1421 ) )
=> ! [X1423: $i > $o] :
( ! [X1424: $i] :
( ( in @ X1424 @ X1420 )
=> ! [X1425: $i] :
( ( in @ X1425 @ X1421 )
=> ( ( in @ ( kpair @ X1424 @ X1425 ) @ X1422 )
=> ( X1423 @ ( kpair @ X1424 @ X1425 ) ) ) ) )
=> ! [X1426: $i] :
( ( in @ X1426 @ X1422 )
=> ( X1423 @ X1426 ) ) ) )
=> ( ! [X1427: $i,X1428: $i,X1429: $i] :
( ( subset @ X1429 @ ( cartprod @ X1427 @ X1428 ) )
=> ! [X1430: $i > $o] :
( ! [X1431: $i] :
( ( in @ X1431 @ X1427 )
=> ! [X1432: $i] :
( ( in @ X1432 @ X1428 )
=> ( ( in @ ( kpair @ X1431 @ X1432 ) @ X1429 )
=> ( X1430 @ ( kpair @ X1431 @ X1432 ) ) ) ) )
=> ! [X1433: $i] :
( ( in @ X1433 @ X1429 )
=> ( X1430 @ X1433 ) ) ) )
=> ( ! [X1434: $i,X1435: $i > $o] :
( ( singleton @ ( dsetconstr @ X1434 @ X1435 ) )
=> ! [X1436: $i] :
( ( in @ X1436 @ X1434 )
=> ! [X1437: $i] :
( ( in @ X1437 @ X1434 )
=> ( ( X1435 @ X1436 )
=> ( ( X1435 @ X1437 )
=> ( X1436 = X1437 ) ) ) ) ) )
=> ( ! [X1438: $i,X1439: $i,X1440: $i] :
( ( func @ X1438 @ X1439 @ X1440 )
=> ! [X1441: $i] :
( ( in @ X1441 @ X1438 )
=> ( in @ ( kpair @ X1441 @ ( ap @ X1438 @ X1439 @ X1440 @ X1441 ) ) @ X1440 ) ) )
=> ( ! [X1442: $i,X1443: $i,X1444: $i] :
( ( in @ X1444 @ ( funcSet @ X1442 @ X1443 ) )
=> ! [X1445: $i] :
( ( in @ X1445 @ X1442 )
=> ( in @ ( kpair @ X1445 @ ( ap @ X1442 @ X1443 @ X1444 @ X1445 ) ) @ X1444 ) ) )
=> ( ! [X1446: $i,X1447: $i,X1448: $i] :
( ( func @ X1446 @ X1447 @ X1448 )
=> ! [X1449: $i] :
( ( in @ X1449 @ X1446 )
=> ! [X1450: $i] :
( ( in @ X1450 @ X1447 )
=> ( ( in @ ( kpair @ X1449 @ X1450 ) @ X1448 )
=> ( ( ap @ X1446 @ X1447 @ X1448 @ X1449 )
= X1450 ) ) ) ) )
=> ( ! [X1451: $i,X1452: $i,X1453: $i] :
( ( func @ X1451 @ X1452 @ X1453 )
=> ! [X1454: $i] :
( ( func @ X1451 @ X1452 @ X1454 )
=> ( ! [X1455: $i] :
( ( in @ X1455 @ X1451 )
=> ( ( ap @ X1451 @ X1452 @ X1453 @ X1455 )
= ( ap @ X1451 @ X1452 @ X1454 @ X1455 ) ) )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1451 )
=> ! [X1457: $i] :
( ( in @ X1457 @ X1452 )
=> ( ( in @ ( kpair @ X1456 @ X1457 ) @ X1454 )
=> ( in @ ( kpair @ X1456 @ X1457 ) @ X1453 ) ) ) ) ) ) )
=> ( ! [X1458: $i,X1459: $i,X1460: $i] :
( ( in @ X1460 @ ( funcSet @ X1458 @ X1459 ) )
=> ! [X1461: $i] :
( ( in @ X1461 @ X1458 )
=> ! [X1462: $i] :
( ( in @ X1462 @ X1459 )
=> ( ( in @ ( kpair @ X1461 @ X1462 ) @ X1460 )
=> ( ( ap @ X1458 @ X1459 @ X1460 @ X1461 )
= X1462 ) ) ) ) )
=> ( ! [X1463: $i,X1464: $i,X1465: $i] :
( ( subset @ X1465 @ ( cartprod @ X1463 @ X1464 ) )
=> ! [X1466: $i] :
( ( subset @ X1466 @ ( cartprod @ X1463 @ X1464 ) )
=> ( ! [X1467: $i] :
( ( in @ X1467 @ X1463 )
=> ! [X1468: $i] :
( ( in @ X1468 @ X1464 )
=> ( ( in @ ( kpair @ X1467 @ X1468 ) @ X1465 )
=> ( in @ ( kpair @ X1467 @ X1468 ) @ X1466 ) ) ) )
=> ( subset @ X1465 @ X1466 ) ) ) )
=> ( ! [X1469: $i,X1470: $i,X1471: $i] :
( ( subset @ X1471 @ ( cartprod @ X1469 @ X1470 ) )
=> ! [X1472: $i] :
( ( subset @ X1472 @ ( cartprod @ X1469 @ X1470 ) )
=> ( ! [X1473: $i] :
( ( in @ X1473 @ X1469 )
=> ! [X1474: $i] :
( ( in @ X1474 @ X1470 )
=> ( ( in @ ( kpair @ X1473 @ X1474 ) @ X1471 )
=> ( in @ ( kpair @ X1473 @ X1474 ) @ X1472 ) ) ) )
=> ( ! [X1475: $i] :
( ( in @ X1475 @ X1469 )
=> ! [X1476: $i] :
( ( in @ X1476 @ X1470 )
=> ( ( in @ ( kpair @ X1475 @ X1476 ) @ X1472 )
=> ( in @ ( kpair @ X1475 @ X1476 ) @ X1471 ) ) ) )
=> ( X1471 = X1472 ) ) ) ) )
=> ( ! [X1477: $i,X1478: $i,X1479: $i] :
( ( func @ X1477 @ X1478 @ X1479 )
=> ! [X1480: $i] :
( ( func @ X1477 @ X1478 @ X1480 )
=> ( ! [X1481: $i] :
( ( in @ X1481 @ X1477 )
=> ( ( ap @ X1477 @ X1478 @ X1479 @ X1481 )
= ( ap @ X1477 @ X1478 @ X1480 @ X1481 ) ) )
=> ( X1479 = X1480 ) ) ) )
=> ( ! [X1482: $i,X1483: $i,X1484: $i] :
( ( in @ X1484 @ ( funcSet @ X1482 @ X1483 ) )
=> ! [X1485: $i] :
( ( in @ X1485 @ ( funcSet @ X1482 @ X1483 ) )
=> ( ! [X1486: $i] :
( ( in @ X1486 @ X1482 )
=> ( ( ap @ X1482 @ X1483 @ X1484 @ X1486 )
= ( ap @ X1482 @ X1483 @ X1485 @ X1486 ) ) )
=> ( X1484 = X1485 ) ) ) )
=> ( ! [X1487: $i,X1488: $i,X1489: $i] :
( ( in @ X1489 @ ( funcSet @ X1487 @ X1488 ) )
=> ! [X1490: $i] :
( ( in @ X1490 @ X1487 )
=> ( ( ap @ X1487 @ X1488 @ X1489 @ X1490 )
= ( ap @ X1487 @ X1488 @ X1489 @ X1490 ) ) ) )
=> ( ! [X1491: $i,X1492: $i,X1493: $i] :
( ( func @ X1491 @ X1492 @ X1493 )
=> ! [X1494: $i] :
( ( in @ X1494 @ X1491 )
=> ( ( ap @ X1491 @ X1492 @ X1493 @ X1494 )
= ( ap @ X1491 @ X1492 @ X1493 @ X1494 ) ) ) )
=> ( ! [X1495: $i,X1496: $i,X1497: $i > $i] :
( ! [X1498: $i] :
( ( in @ X1498 @ X1495 )
=> ( in @ ( X1497 @ X1498 ) @ X1496 ) )
=> ! [X1499: $i] :
( ( in @ X1499 @ X1495 )
=> ( ( ap @ X1495 @ X1496 @ ( lam @ X1495 @ X1496 @ X1497 ) @ X1499 )
= ( X1497 @ X1499 ) ) ) )
=> ( ! [X1500: $i,X1501: $i,X1502: $i] :
( ( func @ X1500 @ X1501 @ X1502 )
=> ( ( lam @ X1500 @ X1501 @ ( ap @ X1500 @ X1501 @ X1502 ) )
= X1502 ) )
=> ( ! [X1503: $i,X1504: $i,X1505: $i > $i] :
( ! [X1506: $i] :
( ( in @ X1506 @ X1503 )
=> ( in @ ( X1505 @ X1506 ) @ X1504 ) )
=> ( ( lam @ X1503 @ X1504 @ X1505 )
= ( lam @ X1503 @ X1504 @ X1505 ) ) )
=> ( ! [X1507: $i,X1508: $i,X1509: $i > $i] :
( ! [X1510: $i] :
( ( in @ X1510 @ X1507 )
=> ( in @ ( X1509 @ X1510 ) @ X1508 ) )
=> ! [X1511: $i] :
( ( in @ X1511 @ X1507 )
=> ( ( ap @ X1507 @ X1508 @ ( lam @ X1507 @ X1508 @ X1509 ) @ X1511 )
= ( X1509 @ X1511 ) ) ) )
=> ( ! [X1512: $i,X1513: $i,X1514: $i] :
( ( in @ X1514 @ ( funcSet @ X1512 @ X1513 ) )
=> ( ( lam @ X1512 @ X1513 @ ( ap @ X1512 @ X1513 @ X1514 ) )
= X1514 ) )
=> ( ! [X1515: $i,X1516: $o,X1517: $i] :
( ( in @ X1517 @ X1515 )
=> ! [X1518: $i] :
( ( in @ X1518 @ X1515 )
=> ( ~ X1516
=> ( in @ X1518
@ ( dsetconstr @ X1515
@ ^ [Z0: $i] :
( ( X1516
& ( Z0 = X1517 ) )
| ( ~ X1516
& ( Z0 = X1518 ) ) ) ) ) ) ) )
=> ( ! [X1519: $i,X1520: $o,X1521: $i] :
( ( in @ X1521 @ X1519 )
=> ! [X1522: $i] :
( ( in @ X1522 @ X1519 )
=> ( ~ X1520
=> ( ( dsetconstr @ X1519
@ ^ [Z0: $i] :
( ( X1520
& ( Z0 = X1521 ) )
| ( ~ X1520
& ( Z0 = X1522 ) ) ) )
= ( setadjoin @ X1522 @ emptyset ) ) ) ) )
=> ( ! [X1523: $i,X1524: $o,X1525: $i] :
( ( in @ X1525 @ X1523 )
=> ! [X1526: $i] :
( ( in @ X1526 @ X1523 )
=> ( X1524
=> ( in @ X1525
@ ( dsetconstr @ X1523
@ ^ [Z0: $i] :
( ( X1524
& ( Z0 = X1525 ) )
| ( ~ X1524
& ( Z0 = X1526 ) ) ) ) ) ) ) )
=> ( ! [X1527: $i,X1528: $o,X1529: $i] :
( ( in @ X1529 @ X1527 )
=> ! [X1530: $i] :
( ( in @ X1530 @ X1527 )
=> ( X1528
=> ( ( dsetconstr @ X1527
@ ^ [Z0: $i] :
( ( X1528
& ( Z0 = X1529 ) )
| ( ~ X1528
& ( Z0 = X1530 ) ) ) )
= ( setadjoin @ X1529 @ emptyset ) ) ) ) )
=> ( ! [X1531: $i,X1532: $o,X1533: $i] :
( ( in @ X1533 @ X1531 )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1531 )
=> ( singleton
@ ( dsetconstr @ X1531
@ ^ [Z0: $i] :
( ( X1532
& ( Z0 = X1533 ) )
| ( ~ X1532
& ( Z0 = X1534 ) ) ) ) ) ) )
=> ( ! [X1535: $i,X1536: $o,X1537: $i] :
( ( in @ X1537 @ X1535 )
=> ! [X1538: $i] :
( ( in @ X1538 @ X1535 )
=> ( in @ ( if @ X1535 @ X1536 @ X1537 @ X1538 ) @ X1535 ) ) )
=> ( ! [X1539: $i] :
( ( singleton @ X1539 )
=> ! [X1540: $i] :
( ( in @ X1540 @ X1539 )
=> ( ( setunion @ X1539 )
= X1540 ) ) )
=> ( ! [X1541: $i,X1542: $o,X1543: $i] :
( ( in @ X1543 @ X1541 )
=> ! [X1544: $i] :
( ( in @ X1544 @ X1541 )
=> ( X1542
=> ( ( if @ X1541 @ X1542 @ X1543 @ X1544 )
= X1543 ) ) ) )
=> ( ! [X1545: $i,X1546: $o,X1547: $i] :
( ( in @ X1547 @ X1545 )
=> ! [X1548: $i] :
( ( in @ X1548 @ X1545 )
=> ( ~ X1546
=> ( ( if @ X1545 @ X1546 @ X1547 @ X1548 )
= X1548 ) ) ) )
=> ( ! [X1549: $i,X1550: $o,X1551: $i] :
( ( in @ X1551 @ X1549 )
=> ! [X1552: $i] :
( ( in @ X1552 @ X1549 )
=> ( in @ ( if @ X1549 @ X1550 @ X1551 @ X1552 ) @ ( setadjoin @ X1551 @ ( setadjoin @ X1552 @ emptyset ) ) ) ) )
=> ( ! [X1553: $i,X1554: $i] :
( ( in @ X1554 @ ( powerset @ X1553 ) )
=> ! [X1555: $i] :
( ( in @ X1555 @ ( powerset @ X1553 ) )
=> ( in @ ( binintersect @ X1554 @ X1555 ) @ ( powerset @ X1553 ) ) ) )
=> ( ! [X1556: $i,X1557: $i] :
( ( in @ X1557 @ ( powerset @ X1556 ) )
=> ! [X1558: $i] :
( ( in @ X1558 @ ( powerset @ X1556 ) )
=> ( in @ ( binunion @ X1557 @ X1558 ) @ ( powerset @ X1556 ) ) ) )
=> ( ! [X1559: $i,X1560: $i] :
( ( in @ X1560 @ ( powerset @ X1559 ) )
=> ( in @ ( powerset @ X1560 ) @ ( powerset @ ( powerset @ X1559 ) ) ) )
=> ( ! [X1561: $i,X1562: $i] :
( ( in @ X1562 @ ( powerset @ X1561 ) )
=> ! [X1563: $i] :
( ( in @ X1563 @ ( powerset @ X1561 ) )
=> ( in @ ( setminus @ X1562 @ X1563 ) @ ( powerset @ X1561 ) ) ) )
=> ( ! [X1564: $i,X1565: $i] :
( ( in @ X1565 @ ( powerset @ X1564 ) )
=> ( in @ ( setminus @ X1564 @ X1565 ) @ ( powerset @ X1564 ) ) )
=> ( ! [X1566: $i,X1567: $i] :
( ( in @ X1567 @ ( powerset @ X1566 ) )
=> ! [X1568: $i] :
( ( in @ X1568 @ ( powerset @ X1566 ) )
=> ( ! [X1569: $i] :
( ( in @ X1569 @ X1566 )
=> ( ( in @ X1569 @ X1567 )
=> ( in @ X1569 @ X1568 ) ) )
=> ( ! [X1570: $i] :
( ( in @ X1570 @ X1566 )
=> ( ( in @ X1570 @ X1568 )
=> ( in @ X1570 @ X1567 ) ) )
=> ( X1567 = X1568 ) ) ) ) )
=> ( ! [X1571: $i,X1572: $i] :
( ( in @ X1572 @ ( powerset @ X1571 ) )
=> ! [X1573: $i] :
( ( in @ X1573 @ ( powerset @ X1571 ) )
=> ( ! [X1574: $i] :
( ( in @ X1574 @ X1571 )
=> ( ( in @ X1574 @ X1572 )
=> ( in @ X1574 @ X1573 ) ) )
=> ( subset @ X1572 @ X1573 ) ) ) )
=> ( ! [X1575: $i,X1576: $i] :
( ( in @ X1576 @ ( powerset @ X1575 ) )
=> ! [X1577: $i] :
( ( in @ X1577 @ ( powerset @ X1575 ) )
=> ( ! [X1578: $i] :
( ( in @ X1578 @ X1575 )
=> ( ( in @ X1578 @ X1576 )
=> ( in @ X1578 @ X1577 ) ) )
=> ( in @ X1576 @ ( powerset @ X1577 ) ) ) ) )
=> ( ! [X1579: $i,X1580: $i] :
( ( in @ X1580 @ ( powerset @ X1579 ) )
=> ! [X1581: $i] :
( ( in @ X1581 @ ( powerset @ X1579 ) )
=> ! [X1582: $i] :
( ( in @ X1582 @ X1579 )
=> ( ( in @ X1580 @ ( powerset @ X1581 ) )
=> ( ( in @ X1582 @ X1580 )
=> ( in @ X1582 @ X1581 ) ) ) ) ) )
=> ( ! [X1583: $i,X1584: $i] :
( ( in @ X1584 @ ( powerset @ X1583 ) )
=> ! [X1585: $i] :
( ( in @ X1585 @ X1583 )
=> ( ( in @ X1585 @ X1584 )
=> ~ ( in @ X1585 @ ( setminus @ X1583 @ X1584 ) ) ) ) )
=> ( ! [X1586: $i,X1587: $i] :
( ( in @ X1587 @ ( powerset @ X1586 ) )
=> ! [X1588: $i] :
( ( in @ X1588 @ X1586 )
=> ( ~ ( in @ X1588 @ ( setminus @ X1586 @ X1587 ) )
=> ( in @ X1588 @ X1587 ) ) ) )
=> ( ! [X1589: $i,X1590: $i] :
( ( in @ X1590 @ ( powerset @ X1589 ) )
=> ! [X1591: $i] :
( ( in @ X1591 @ ( powerset @ X1589 ) )
=> ! [X1592: $i] :
( ( in @ X1592 @ X1589 )
=> ( ~ ( in @ X1592 @ X1590 )
=> ~ ( in @ X1592 @ ( binintersect @ X1590 @ X1591 ) ) ) ) ) )
=> ( ! [X1593: $i,X1594: $i] :
( ( in @ X1594 @ ( powerset @ X1593 ) )
=> ! [X1595: $i] :
( ( in @ X1595 @ ( powerset @ X1593 ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ X1593 )
=> ( ~ ( in @ X1596 @ X1595 )
=> ~ ( in @ X1596 @ ( binintersect @ X1594 @ X1595 ) ) ) ) ) )
=> ( ! [X1597: $i,X1598: $i] :
( ( in @ X1598 @ ( powerset @ X1597 ) )
=> ! [X1599: $i] :
( ( in @ X1599 @ ( powerset @ X1597 ) )
=> ! [X1600: $i] :
( ( in @ X1600 @ X1597 )
=> ( ( subset @ X1598 @ ( setminus @ X1597 @ X1599 ) )
=> ( ( in @ X1600 @ X1599 )
=> ~ ( in @ X1600 @ X1598 ) ) ) ) ) )
=> ( ! [X1601: $i,X1602: $i] :
( ( in @ X1602 @ ( powerset @ X1601 ) )
=> ! [X1603: $i] :
( ( in @ X1603 @ ( powerset @ X1601 ) )
=> ! [X1604: $i] :
( ( in @ X1604 @ X1601 )
=> ( ( subset @ X1602 @ X1603 )
=> ( ~ ( in @ X1604 @ X1603 )
=> ~ ( in @ X1604 @ X1602 ) ) ) ) ) )
=> ( ! [X1605: $i,X1606: $i] :
( ( in @ X1606 @ ( powerset @ X1605 ) )
=> ! [X1607: $i] :
( ( in @ X1607 @ ( powerset @ X1605 ) )
=> ( ( subset @ X1606 @ X1607 )
=> ( subset @ ( setminus @ X1605 @ X1607 ) @ ( setminus @ X1605 @ X1606 ) ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[contrasubsetT3]),iftrueorfalse]),contrasubsetT2]),c_0_268]),c_0_269]),funcext]),setadjoinSub2]),funcext2]),ap2apEq1]),subset2powerset]),ap2apEq2]),c_0_270]),setextsub]),c_0_271]),c_0_272]),subsetemptysetimpeq]),c_0_273]),c_0_274]),powersetI1]),c_0_275]),c_0_276]),powersetE1]),c_0_277]),inPowerset]),c_0_278]),c_0_279]),ifp]),powersetsubset]),theeq]),iftrue]),iffalse]),c_0_280]),binintersectSubset4]),binintersectT_lem]),binunionT_lem]),c_0_281]),powersetT_lem]),setminusT_lem]),binunionIL]),complementT_lem]),setextT]),upairset2IR]),subsetTI]),powersetTI1]),powersetTE1]),complementTI1]),binunionIR]),complementTE1]),binintersectTELcontra]),binunionEcases]),binintersectTERcontra]),contrasubsetT]),binunionE]),contrasubsetT1]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),notequalI2]),ubforcartprodlem3]),subsetRefl]),cartprodpairin]),subsetTrans]),setadjoinSub]),cartprodmempair1]),cartprodmempair]),setunionE2]),c_0_282]),c_0_283]),c_0_284]),c_0_285]),singletonsuniq]),setukpairinjL1]),c_0_286]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_287]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_288]),c_0_289]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),c_0_294]),c_0_295]),c_0_296]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_297]),c_0_298]),c_0_299]),c_0_300]),c_0_301]),c_0_302]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_303]),c_0_304]),c_0_305]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_306]),c_0_307]),in__Cong]),inCongP]),c_0_308]),c_0_309]),c_0_310]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_311]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_312]),c_0_313]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_314]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_315]),c_0_316]),c_0_317]),c_0_318]),noeltsimpempty]),emptyI]),setext]),c_0_319]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),c_0_324]),wellorderingAx]),foundationAx]),c_0_325]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_326]) ).
thf(c_0_328,negated_conjecture,
! [X1608: $i,X1609: $i,X1611: $i,X1612: $i,X1613: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1619: $i,X1621: $i,X1622: $i,X1624: $i,X1625: $i,X1626: $i,X1627: $i,X1628: $i,X1630: $i,X1631: $i > $i > $o,X1632: $i,X1634: $i,X1637: $i,X1639: $i,X1640: $i,X1641: $i,X1642: $i,X1644: $i,X1645: $i > $o,X1646: $i,X1648: $i,X1649: $i > $o,X1650: $i,X1651: $i,X1652: $i > $o,X1653: $i,X1654: $i,X1655: $i > $o,X1656: $i,X1657: $i > $o,X1658: $i,X1661: $i,X1662: $o,X1663: $i,X1664: $i,X1665: $o,X1666: $i,X1667: $i,X1668: $i > $o,X1669: $i,X1672: $i,X1673: $i,X1676: $i,X1678: $i,X1680: $i,X1681: $i > $o,X1682: $i,X1683: $i,X1685: $i,X1686: $i > $o,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $o,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $i,X1716: $o,X1718: $i,X1719: $i,X1720: $i > $o,X1721: $i,X1724: $i,X1725: $i,X1726: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i > $o,X1745: $i,X1746: $i > $o,X1747: $i,X1748: $i,X1749: $i > $o,X1750: $i,X1752: $i,X1753: $i > $o,X1755: $i,X1756: $i,X1757: $i > $o,X1759: $i,X1760: $i,X1761: $i > $o,X1762: $i,X1764: $o,X1765: $i,X1766: $i > $o,X1768: $i,X1769: $i,X1770: $i > $o,X1771: $i,X1773: $i > $o,X1774: $i,X1777: $i,X1778: $i > $o,X1779: $i,X1783: $i,X1784: $i > $o,X1785: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i > $o,X1798: $i,X1800: $i,X1801: $i,X1802: $i > $o,X1803: $i > $o,X1806: $i,X1809: $i,X1810: $i,X1813: $i,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i > $o,X1823: $i,X1825: $i,X1826: $i,X1827: $i > $o,X1828: $i > $o,X1831: $i,X1833: $i,X1835: $i,X1836: $i,X1837: $i > $o,X1838: $i > $o,X1841: $i,X1842: $i,X1844: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $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: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i > $o,X1889: $i,X1890: $i > $o,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $o,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,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $i,X1943: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i,X1950: $i,X1951: $i,X1952: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $o,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,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i > $o,X2045: $i,X2046: $i,X2047: $i > $o,X2049: $i,X2050: $i > $o,X2051: $i,X2053: $i,X2054: $i > $o,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i > $i > $o,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i > $i > $o,X2135: $i,X2136: $i,X2137: $i > $i > $o,X2138: $i,X2139: $i,X2140: $i > $i > $o,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i > $i > $o,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i > $i > $o,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i > $i > $o,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i > $i,X2184: $i,X2185: $i,X2186: $i > $i,X2188: $i,X2189: $i,X2190: $i > $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i > $o,X2198: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i > $o,X2205: $i,X2206: $i,X2207: $i > $o,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2249: $i,X2250: $i,X2251: $i,X2252: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i > $i,X2271: $i,X2272: $i,X2273: $i,X2274: $i,X2275: $i,X2276: $i,X2277: $i > $i,X2279: $i,X2280: $i,X2281: $i > $i,X2283: $i,X2284: $i,X2285: $i,X2286: $i,X2287: $i,X2288: $o,X2289: $i,X2290: $i,X2291: $i,X2292: $o,X2293: $i,X2294: $i,X2295: $i,X2296: $o,X2297: $i,X2298: $i,X2299: $i,X2300: $o,X2301: $i,X2302: $i,X2303: $i,X2304: $o,X2305: $i,X2306: $i,X2307: $i,X2308: $o,X2309: $i,X2310: $i,X2311: $i,X2312: $i,X2313: $i,X2314: $o,X2315: $i,X2316: $i,X2317: $i,X2318: $o,X2319: $i,X2320: $i,X2321: $i,X2322: $o,X2323: $i,X2324: $i,X2325: $i,X2326: $i,X2327: $i,X2328: $i,X2329: $i,X2330: $i,X2331: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $i,X2338: $i,X2339: $i,X2340: $i,X2343: $i,X2344: $i,X2345: $i,X2347: $i,X2348: $i,X2349: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,X2363: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2368: $i,X2369: $i,X2370: $i,X2371: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2376: $i,X2377: $i,X2378: $i,X2379: $i] :
( ( ~ ( in @ ( esk1_2 @ X1608 @ X1609 ) @ X1608 )
| ~ ( in @ ( esk1_2 @ X1608 @ X1609 ) @ X1609 )
| ( X1608 = X1609 ) )
& ( ( in @ ( esk1_2 @ X1608 @ X1609 ) @ X1608 )
| ( in @ ( esk1_2 @ X1608 @ X1609 ) @ X1609 )
| ( X1608 = X1609 ) )
& ~ ( in @ X1611 @ emptyset )
& ( ~ ( in @ X1614 @ ( setadjoin @ X1612 @ X1613 ) )
| ( X1614 = X1612 )
| ( in @ X1614 @ X1613 ) )
& ( ( X1614 != X1612 )
| ( in @ X1614 @ ( setadjoin @ X1612 @ X1613 ) ) )
& ( ~ ( in @ X1614 @ X1613 )
| ( in @ X1614 @ ( setadjoin @ X1612 @ X1613 ) ) )
& ( ~ ( in @ X1616 @ ( powerset @ X1615 ) )
| ~ ( in @ X1617 @ X1616 )
| ( in @ X1617 @ X1615 ) )
& ( ( in @ ( esk2_2 @ X1618 @ X1619 ) @ X1619 )
| ( in @ X1619 @ ( powerset @ X1618 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1618 @ X1619 ) @ X1618 )
| ( in @ X1619 @ ( powerset @ X1618 ) ) )
& ( ( in @ X1622 @ ( esk3_2 @ X1621 @ X1622 ) )
| ~ ( in @ X1622 @ ( setunion @ X1621 ) ) )
& ( ( in @ ( esk3_2 @ X1621 @ X1622 ) @ X1621 )
| ~ ( in @ X1622 @ ( setunion @ X1621 ) ) )
& ( ~ ( in @ X1625 @ X1626 )
| ~ ( in @ X1626 @ X1624 )
| ( in @ X1625 @ ( setunion @ X1624 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1627 @ omega )
| ( in @ ( setadjoin @ X1627 @ X1627 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1628 ) @ omega )
| ~ ( in @ emptyset @ X1628 )
| ~ ( in @ X1630 @ omega )
| ( in @ X1630 @ X1628 ) )
& ( ( in @ ( esk4_1 @ X1628 ) @ X1628 )
| ~ ( in @ emptyset @ X1628 )
| ~ ( in @ X1630 @ omega )
| ( in @ X1630 @ X1628 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1628 ) @ ( esk4_1 @ X1628 ) ) @ X1628 )
| ~ ( in @ emptyset @ X1628 )
| ~ ( in @ X1630 @ omega )
| ( in @ X1630 @ X1628 ) )
& ( ( in @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1632 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( in @ ( esk5_2 @ X1631 @ X1632 ) @ X1632 ) )
& ( ( X1631 @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1637 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( in @ ( esk5_2 @ X1631 @ X1632 ) @ X1632 ) )
& ( ~ ( in @ X1640 @ X1632 )
| ~ ( X1631 @ X1640 @ X1639 )
| ( in @ X1639 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( in @ ( esk5_2 @ X1631 @ X1632 ) @ X1632 ) )
& ( ( in @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1632 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ( X1631 @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1637 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ~ ( in @ X1640 @ X1632 )
| ~ ( X1631 @ X1640 @ X1639 )
| ( in @ X1639 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ( in @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1632 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1634
!= ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ( X1631 @ ( esk8_3 @ X1631 @ X1632 @ X1637 ) @ X1637 )
| ~ ( in @ X1637 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1634
!= ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ~ ( in @ X1640 @ X1632 )
| ~ ( X1631 @ X1640 @ X1639 )
| ( in @ X1639 @ ( esk7_2 @ X1631 @ X1632 ) )
| ( X1634
!= ( esk6_3 @ X1631 @ X1632 @ X1634 ) )
| ~ ( X1631 @ ( esk5_2 @ X1631 @ X1632 ) @ X1634 ) )
& ( ( in @ ( esk9_1 @ X1641 ) @ X1641 )
| ~ ( in @ X1642 @ X1641 ) )
& ( ~ ( in @ X1644 @ ( esk9_1 @ X1641 ) )
| ~ ( in @ X1644 @ X1641 )
| ~ ( in @ X1642 @ X1641 ) )
& epred1_0
& ( ( X1645 @ ( esk10_2 @ X1645 @ X1646 ) )
| ~ ( X1645 @ X1646 )
| ( X1645 @ ( descr @ X1645 ) ) )
& ( ( X1646
!= ( esk10_2 @ X1645 @ X1646 ) )
| ~ ( X1645 @ X1646 )
| ( X1645 @ ( descr @ X1645 ) ) )
& ( ~ ( in @ X1650 @ X1648 )
| ~ ( X1649 @ X1650 )
| ( in @ X1650 @ ( dsetconstr @ X1648 @ X1649 ) ) )
& ( ~ ( in @ X1653 @ ( dsetconstr @ X1651 @ X1652 ) )
| ( in @ X1653 @ X1651 ) )
& ( ~ ( in @ X1656 @ ( dsetconstr @ X1654 @ X1655 ) )
| ( X1655 @ X1656 ) )
& ( ( X1657 @ ( esk12_1 @ X1657 ) )
| ( X1657 @ ( esk11_2 @ X1657 @ X1658 ) )
| ~ ( X1657 @ X1658 ) )
& ( ~ ( X1657 @ X1661 )
| ( ( esk12_1 @ X1657 )
= X1661 )
| ( X1657 @ ( esk11_2 @ X1657 @ X1658 ) )
| ~ ( X1657 @ X1658 ) )
& ( ( X1657 @ ( esk12_1 @ X1657 ) )
| ( X1658
!= ( esk11_2 @ X1657 @ X1658 ) )
| ~ ( X1657 @ X1658 ) )
& ( ~ ( X1657 @ X1661 )
| ( ( esk12_1 @ X1657 )
= X1661 )
| ( X1658
!= ( esk11_2 @ X1657 @ X1658 ) )
| ~ ( X1657 @ X1658 ) )
& ( ~ ( in @ X1663 @ ( prop2set @ X1662 ) )
| X1662 )
& ( ~ ( in @ X1664 @ emptyset )
| X1665 )
& ( ~ ( in @ X1666 @ emptyset )
| ~ $true )
& ~ ( in @ X1667 @ emptyset )
& ( ( X1668 @ ( esk13_2 @ X1668 @ X1669 ) )
| ~ ( X1668 @ X1669 )
| ( X1668 @ ( esk14_1 @ X1668 ) ) )
& ( ( X1669
!= ( esk13_2 @ X1668 @ X1669 ) )
| ~ ( X1668 @ X1669 )
| ( X1668 @ ( esk14_1 @ X1668 ) ) )
& ( ( in @ ( esk16_2 @ X1672 @ X1673 ) @ X1673 )
| ( X1672 = X1673 )
| ( in @ ( esk15_2 @ X1672 @ X1673 ) @ X1672 ) )
& ( ~ ( in @ ( esk16_2 @ X1672 @ X1673 ) @ X1672 )
| ( X1672 = X1673 )
| ( in @ ( esk15_2 @ X1672 @ X1673 ) @ X1672 ) )
& ( ( in @ ( esk16_2 @ X1672 @ X1673 ) @ X1673 )
| ( X1672 = X1673 )
| ~ ( in @ ( esk15_2 @ X1672 @ X1673 ) @ X1673 ) )
& ( ~ ( in @ ( esk16_2 @ X1672 @ X1673 ) @ X1672 )
| ( X1672 = X1673 )
| ~ ( in @ ( esk15_2 @ X1672 @ X1673 ) @ X1673 ) )
& ( ( in @ ( esk17_1 @ X1676 ) @ X1676 )
| ( X1676 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1678 ) @ X1678 )
| ( X1678 = emptyset ) )
& ( ~ ( in @ X1682 @ ( dsetconstr @ X1680 @ X1681 ) )
| ( X1681 @ X1682 )
| ~ ( in @ X1682 @ X1680 ) )
& ( ~ ( X1681 @ X1682 )
| ( in @ X1682 @ ( dsetconstr @ X1680 @ X1681 ) )
| ~ ( in @ X1682 @ X1680 ) )
& ( ( X1683 = emptyset )
| ( in @ ( esk19_1 @ X1683 ) @ X1683 ) )
& ( ~ ( in @ X1687 @ X1685 )
| ~ ( X1686 @ X1687 )
| ( ( dsetconstr @ X1685 @ X1686 )
!= emptyset ) )
& ( ~ ( in @ X1689 @ X1688 )
| ( X1688 != emptyset ) )
& ( in @ X1690 @ ( setadjoin @ X1690 @ X1691 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1694 @ X1693 )
| ( in @ X1694 @ ( setadjoin @ X1692 @ X1693 ) ) )
& ( ( in @ X1697 @ X1696 )
| X1698
| ( X1697 = X1695 )
| ~ ( in @ X1697 @ ( setadjoin @ X1695 @ X1696 ) ) )
& ( ~ X1698
| X1698
| ( X1697 = X1695 )
| ~ ( in @ X1697 @ ( setadjoin @ X1695 @ X1696 ) ) )
& ( ( in @ X1697 @ X1696 )
| X1698
| ~ X1698
| ~ ( in @ X1697 @ ( setadjoin @ X1695 @ X1696 ) ) )
& ( ~ X1698
| X1698
| ~ X1698
| ~ ( in @ X1697 @ ( setadjoin @ X1695 @ X1696 ) ) )
& ( ~ ( in @ X1701 @ ( setadjoin @ X1699 @ X1700 ) )
| ( X1701 = X1699 )
| ( in @ X1701 @ X1700 ) )
& ( ( dsetconstr @ X1702
@ ^ [Z0: $i] : $true )
= X1702 )
& ( ( in @ ( esk20_2 @ X1703 @ X1704 ) @ X1704 )
| ( in @ X1704 @ ( powerset @ X1703 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1703 @ X1704 ) @ X1703 )
| ( in @ X1704 @ ( powerset @ X1703 ) ) )
& ( in @ emptyset @ ( powerset @ X1706 ) )
& ( in @ emptyset @ ( powerset @ X1707 ) )
& ( ~ ( in @ X1709 @ ( powerset @ X1708 ) )
| ~ ( in @ X1710 @ X1709 )
| ( in @ X1710 @ X1708 ) )
& ( ~ ( in @ X1712 @ X1713 )
| ~ ( in @ X1713 @ X1711 )
| ( in @ X1712 @ ( setunion @ X1711 ) ) )
& ( ( in @ X1715 @ ( esk21_3 @ X1714 @ X1715 @ X1716 ) )
| X1716
| ~ ( in @ X1715 @ ( setunion @ X1714 ) ) )
& ( ( in @ ( esk21_3 @ X1714 @ X1715 @ X1716 ) @ X1714 )
| X1716
| ~ ( in @ X1715 @ ( setunion @ X1714 ) ) )
& ( ~ X1716
| X1716
| ~ ( in @ X1715 @ ( setunion @ X1714 ) ) )
& ( ~ ( in @ X1719 @ X1718 )
| ( in @ X1719 @ ( powerset @ ( setunion @ X1718 ) ) ) )
& ( ~ ( X1720 @ X1724 )
| ( X1724
= ( esk23_1 @ X1720 ) )
| ( X1720 @ ( esk22_2 @ X1720 @ X1721 ) )
| ~ ( X1720 @ X1721 ) )
& ( ( X1725
!= ( esk23_1 @ X1720 ) )
| ( X1720 @ X1725 )
| ( X1720 @ ( esk22_2 @ X1720 @ X1721 ) )
| ~ ( X1720 @ X1721 ) )
& ( ~ ( X1720 @ X1724 )
| ( X1724
= ( esk23_1 @ X1720 ) )
| ( X1721
!= ( esk22_2 @ X1720 @ X1721 ) )
| ~ ( X1720 @ X1721 ) )
& ( ( X1725
!= ( esk23_1 @ X1720 ) )
| ( X1720 @ X1725 )
| ( X1721
!= ( esk22_2 @ X1720 @ X1721 ) )
| ~ ( X1720 @ X1721 ) )
& ( ( in @ ( esk24_1 @ X1726 ) @ X1726 )
| ( X1726 = emptyset ) )
& ( $true
| ( X1726 = emptyset ) )
& ( ~ ( in @ X1728 @ ( setadjoin @ X1729 @ emptyset ) )
| ( X1728 = X1729 ) )
& ( ( X1730 = X1731 )
| ~ ( in @ X1731 @ ( setadjoin @ X1730 @ emptyset ) ) )
& ( ( X1732 != X1733 )
| ( in @ X1732 @ ( setadjoin @ X1733 @ emptyset ) ) )
& ( ~ ( in @ X1734 @ ( setadjoin @ X1735 @ emptyset ) )
| ( in @ X1735 @ ( setadjoin @ X1734 @ emptyset ) ) )
& ( ~ ( in @ X1738 @ ( setadjoin @ X1736 @ ( setadjoin @ X1737 @ emptyset ) ) )
| ( X1738 = X1736 )
| ( X1738 = X1737 ) )
& ( in @ X1739 @ ( setadjoin @ X1739 @ ( setadjoin @ X1740 @ emptyset ) ) )
& ( in @ X1742 @ ( setadjoin @ X1741 @ ( setadjoin @ X1742 @ emptyset ) ) )
& ( ~ ( in @ X1745 @ X1743 )
| ~ ( X1744 @ X1745 )
| ( ( dsetconstr @ X1743 @ X1744 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1747 @ emptyset )
| ( X1746 @ X1747 ) )
& ( ( in @ ( esk25_2 @ X1748 @ X1749 ) @ X1748 )
| ~ ( in @ X1750 @ X1748 )
| ( X1749 @ X1750 ) )
& ( ~ ( X1749 @ ( esk25_2 @ X1748 @ X1749 ) )
| ~ ( in @ X1750 @ X1748 )
| ( X1749 @ X1750 ) )
& ( ( in @ ( esk26_2 @ X1752 @ X1753 ) @ X1752 )
| ~ ( in @ X1755 @ X1752 )
| ~ ( X1753 @ X1755 ) )
& ( ( X1753 @ ( esk26_2 @ X1752 @ X1753 ) )
| ~ ( in @ X1755 @ X1752 )
| ~ ( X1753 @ X1755 ) )
& ( ( in @ ( esk27_2 @ X1756 @ X1757 ) @ X1756 )
| ~ ( in @ X1759 @ X1756 )
| ~ ( X1757 @ X1759 ) )
& ( ( X1757 @ ( esk27_2 @ X1756 @ X1757 ) )
| ~ ( in @ X1759 @ X1756 )
| ~ ( X1757 @ X1759 ) )
& ( ( in @ ( esk28_2 @ X1760 @ X1761 ) @ X1760 )
| ~ ( in @ X1762 @ X1760 )
| ( X1761 @ X1762 ) )
& ( ~ ( X1761 @ ( esk28_2 @ X1760 @ X1761 ) )
| ~ ( in @ X1762 @ X1760 )
| ( X1761 @ X1762 ) )
& ( ~ X1764
| ( in @ emptyset @ ( prop2set @ X1764 ) ) )
& prop2set2propI
& ( ( in @ ( esk29_2 @ X1765 @ X1766 ) @ X1765 )
| ~ ( in @ X1768 @ X1765 )
| ~ ( X1766 @ X1768 ) )
& ( ( X1766 @ ( esk29_2 @ X1765 @ X1766 ) )
| ~ ( in @ X1768 @ X1765 )
| ~ ( X1766 @ X1768 ) )
& ( ( in @ ( esk30_2 @ X1769 @ X1770 ) @ X1769 )
| ~ ( in @ X1771 @ X1769 )
| ( X1770 @ X1771 ) )
& ( ~ ( X1770 @ ( esk30_2 @ X1769 @ X1770 ) )
| ~ ( in @ X1771 @ X1769 )
| ( X1770 @ X1771 ) )
& ( ( X1773 @ ( esk32_1 @ X1773 ) )
| ( X1773 @ ( esk31_2 @ X1773 @ X1774 ) )
| ~ ( X1773 @ X1774 ) )
& ( ~ ( X1773 @ X1777 )
| ( ( esk32_1 @ X1773 )
= X1777 )
| ( X1773 @ ( esk31_2 @ X1773 @ X1774 ) )
| ~ ( X1773 @ X1774 ) )
& ( ( X1773 @ ( esk32_1 @ X1773 ) )
| ( X1774
!= ( esk31_2 @ X1773 @ X1774 ) )
| ~ ( X1773 @ X1774 ) )
& ( ~ ( X1773 @ X1777 )
| ( ( esk32_1 @ X1773 )
= X1777 )
| ( X1774
!= ( esk31_2 @ X1773 @ X1774 ) )
| ~ ( X1773 @ X1774 ) )
& ( ( X1778 @ ( esk35_1 @ X1778 ) )
| ( X1778 @ ( esk33_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ~ ( X1778 @ X1783 )
| ( ( esk35_1 @ X1778 )
= X1783 )
| ( X1778 @ ( esk33_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ( X1778 @ ( esk35_1 @ X1778 ) )
| ( X1778 @ ( esk34_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ~ ( X1778 @ X1783 )
| ( ( esk35_1 @ X1778 )
= X1783 )
| ( X1778 @ ( esk34_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ( X1778 @ ( esk35_1 @ X1778 ) )
| ( ( esk33_1 @ X1778 )
!= ( esk34_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ~ ( X1778 @ X1783 )
| ( ( esk35_1 @ X1778 )
= X1783 )
| ( ( esk33_1 @ X1778 )
!= ( esk34_1 @ X1778 ) )
| ~ ( X1778 @ X1779 ) )
& ( ( X1784 @ ( esk37_1 @ X1784 ) )
| ~ ( X1784 @ ( esk36_2 @ X1784 @ X1785 ) )
| ( ( esk36_2 @ X1784 @ X1785 )
!= X1785 ) )
& ( ~ ( X1784 @ X1788 )
| ( ( esk37_1 @ X1784 )
= X1788 )
| ~ ( X1784 @ ( esk36_2 @ X1784 @ X1785 ) )
| ( ( esk36_2 @ X1784 @ X1785 )
!= X1785 ) )
& ( ( X1784 @ ( esk37_1 @ X1784 ) )
| ( X1784 @ ( esk36_2 @ X1784 @ X1785 ) )
| ( ( esk36_2 @ X1784 @ X1785 )
= X1785 ) )
& ( ~ ( X1784 @ X1788 )
| ( ( esk37_1 @ X1784 )
= X1788 )
| ( X1784 @ ( esk36_2 @ X1784 @ X1785 ) )
| ( ( esk36_2 @ X1784 @ X1785 )
= X1785 ) )
& ( ( X1789 != X1790 )
| ( X1791 != X1792 )
| ~ ( in @ X1791 @ X1789 )
| ( in @ X1792 @ X1790 ) )
& ( ~ ( in @ X1795 @ X1793 )
| ( in @ X1796 @ X1794 )
| ( X1795 != X1796 )
| ( X1793 != X1794 ) )
& ( ~ ( in @ X1796 @ X1794 )
| ( in @ X1795 @ X1793 )
| ( X1795 != X1796 )
| ( X1793 != X1794 ) )
& ( ( X1797 @ ( esk38_2 @ X1797 @ X1798 ) )
| ~ ( X1797 @ X1798 )
| ~ ( X1797 @ X1800 )
| ~ ( X1797 @ X1801 )
| ( X1800 = X1801 ) )
& ( ( X1798
!= ( esk38_2 @ X1797 @ X1798 ) )
| ~ ( X1797 @ X1798 )
| ~ ( X1797 @ X1800 )
| ~ ( X1797 @ X1801 )
| ( X1800 = X1801 ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( ( esk39_2 @ X1802 @ X1803 )
= ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ~ ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ~ ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1802 @ ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1803 @ ( esk42_2 @ X1802 @ X1803 ) )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1803 @ X1809 )
| ( ( esk42_2 @ X1802 @ X1803 )
= X1809 )
| ( X1806
!= ( esk41_3 @ X1802 @ X1803 @ X1806 ) )
| ~ ( X1802 @ X1806 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1803 @ ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ( X1802 @ ( esk44_2 @ X1802 @ X1803 ) )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( ~ ( X1802 @ X1813 )
| ( ( esk44_2 @ X1802 @ X1803 )
= X1813 )
| ( X1810
!= ( esk43_3 @ X1802 @ X1803 @ X1810 ) )
| ~ ( X1803 @ X1810 )
| ( X1802 @ ( esk39_2 @ X1802 @ X1803 ) )
| ( X1803 @ ( esk40_2 @ X1802 @ X1803 ) ) )
& ( emptyset = emptyset )
& ( ( X1814 != X1815 )
| ( X1816 != X1817 )
| ( ( setadjoin @ X1814 @ X1816 )
= ( setadjoin @ X1815 @ X1817 ) ) )
& ( ( X1818 != X1819 )
| ( ( powerset @ X1818 )
= ( powerset @ X1819 ) ) )
& ( ( X1820 != X1821 )
| ( ( setunion @ X1820 )
= ( setunion @ X1821 ) ) )
& ( omega = omega )
& ( ( X1822 @ ( esk45_2 @ X1822 @ X1823 ) )
| ~ ( X1822 @ X1823 )
| ~ ( X1822 @ X1825 )
| ~ ( X1822 @ X1826 )
| ( X1825 = X1826 ) )
& ( ( X1823
!= ( esk45_2 @ X1822 @ X1823 ) )
| ~ ( X1822 @ X1823 )
| ~ ( X1822 @ X1825 )
| ~ ( X1822 @ X1826 )
| ( X1825 = X1826 ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( ( esk46_2 @ X1827 @ X1828 )
= ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( ( esk46_2 @ X1827 @ X1828 )
= ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( ( esk46_2 @ X1827 @ X1828 )
= ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( ( esk46_2 @ X1827 @ X1828 )
= ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ~ ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ~ ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ~ ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ~ ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ~ ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ~ ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ~ ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ~ ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1827 @ ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1828 @ ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( X1833
!= ( esk49_3 @ X1827 @ X1828 @ X1833 ) )
| ~ ( X1828 @ X1833 )
| ( ( descr @ X1827 )
= ( descr @ X1828 ) )
| ( X1831
!= ( esk48_3 @ X1827 @ X1828 @ X1831 ) )
| ~ ( X1827 @ X1831 )
| ( X1827 @ ( esk46_2 @ X1827 @ X1828 ) )
| ( X1828 @ ( esk47_2 @ X1827 @ X1828 ) ) )
& ( ( in @ ( esk50_4 @ X1835 @ X1836 @ X1837 @ X1838 ) @ X1835 )
| ( ( dsetconstr @ X1835 @ X1837 )
= ( dsetconstr @ X1836 @ X1838 ) )
| ( X1835 != X1836 ) )
& ( ( in @ ( esk51_4 @ X1835 @ X1836 @ X1837 @ X1838 ) @ X1836 )
| ( ( dsetconstr @ X1835 @ X1837 )
= ( dsetconstr @ X1836 @ X1838 ) )
| ( X1835 != X1836 ) )
& ( ( ( esk50_4 @ X1835 @ X1836 @ X1837 @ X1838 )
= ( esk51_4 @ X1835 @ X1836 @ X1837 @ X1838 ) )
| ( ( dsetconstr @ X1835 @ X1837 )
= ( dsetconstr @ X1836 @ X1838 ) )
| ( X1835 != X1836 ) )
& ( ~ ( X1837 @ ( esk50_4 @ X1835 @ X1836 @ X1837 @ X1838 ) )
| ~ ( X1838 @ ( esk51_4 @ X1835 @ X1836 @ X1837 @ X1838 ) )
| ( ( dsetconstr @ X1835 @ X1837 )
= ( dsetconstr @ X1836 @ X1838 ) )
| ( X1835 != X1836 ) )
& ( ( X1837 @ ( esk50_4 @ X1835 @ X1836 @ X1837 @ X1838 ) )
| ( X1838 @ ( esk51_4 @ X1835 @ X1836 @ X1837 @ X1838 ) )
| ( ( dsetconstr @ X1835 @ X1837 )
= ( dsetconstr @ X1836 @ X1838 ) )
| ( X1835 != X1836 ) )
& ( ( in @ ( esk52_2 @ X1841 @ X1842 ) @ X1841 )
| ( subset @ X1841 @ X1842 ) )
& ( ~ ( in @ ( esk52_2 @ X1841 @ X1842 ) @ X1842 )
| ( subset @ X1841 @ X1842 ) )
& ( ( X1844 != X1845 )
| ( subset @ X1845 @ X1844 ) )
& ( ( X1846 != X1847 )
| ( subset @ X1846 @ X1847 ) )
& ( ( in @ ( esk53_2 @ X1848 @ X1849 ) @ X1848 )
| ( subset @ X1848 @ X1849 ) )
& ( ~ ( in @ ( esk53_2 @ X1848 @ X1849 ) @ X1849 )
| ( subset @ X1848 @ X1849 ) )
& ( subset @ emptyset @ X1851 )
& ( ~ ( subset @ X1852 @ X1853 )
| ~ ( in @ X1854 @ X1852 )
| ( in @ X1854 @ X1853 ) )
& ( ~ ( subset @ X1855 @ X1856 )
| ( in @ X1857 @ X1856 )
| ~ ( in @ X1857 @ X1855 ) )
& ( ~ ( in @ X1860 @ X1858 )
| ( in @ X1860 @ X1859 )
| ~ ( subset @ X1858 @ X1859 ) )
& ( ( subset @ X1861 @ X1862 )
| ( X1861 != X1862 ) )
& ( ~ ( in @ X1865 @ X1863 )
| ( in @ X1865 @ X1864 )
| ( X1863 != X1864 ) )
& ( subset @ X1866 @ X1866 )
& ( ~ ( subset @ X1867 @ X1868 )
| ~ ( subset @ X1868 @ X1869 )
| ( subset @ X1867 @ X1869 ) )
& ( subset @ X1871 @ ( setadjoin @ X1870 @ X1871 ) )
& ( ~ ( subset @ X1872 @ X1874 )
| ( subset @ X1872 @ ( setadjoin @ X1873 @ X1874 ) ) )
& ( ~ ( subset @ X1875 @ X1876 )
| ( in @ X1875 @ ( powerset @ X1876 ) ) )
& ( ~ ( subset @ X1877 @ X1878 )
| ~ ( subset @ X1878 @ X1877 )
| ( X1877 = X1878 ) )
& ( ~ ( subset @ X1879 @ emptyset )
| ( X1879 = emptyset ) )
& ( ~ ( subset @ X1881 @ X1880 )
| ( in @ X1881 @ ( powerset @ X1880 ) ) )
& ( ~ ( in @ X1883 @ ( powerset @ X1882 ) )
| ( subset @ X1883 @ X1882 ) )
& ( in @ X1884 @ ( powerset @ X1884 ) )
& ( ~ ( subset @ X1885 @ X1886 )
| ( subset @ ( powerset @ X1885 ) @ ( powerset @ X1886 ) ) )
& ( in @ ( dsetconstr @ X1887 @ X1888 ) @ ( powerset @ X1887 ) )
& ( subset @ ( dsetconstr @ X1889 @ X1890 ) @ X1889 )
& ( ~ ( in @ X1893 @ X1891 )
| ( in @ X1893 @ ( binunion @ X1891 @ X1892 ) ) )
& ( in @ X1895 @ ( setadjoin @ X1894 @ ( setadjoin @ X1895 @ emptyset ) ) )
& ( ~ ( in @ X1898 @ X1897 )
| ( in @ X1898 @ ( binunion @ X1896 @ X1897 ) ) )
& ( ( in @ X1901 @ X1900 )
| X1902
| ( in @ X1901 @ X1899 )
| ~ ( in @ X1901 @ ( binunion @ X1899 @ X1900 ) ) )
& ( ~ X1902
| X1902
| ( in @ X1901 @ X1899 )
| ~ ( in @ X1901 @ ( binunion @ X1899 @ X1900 ) ) )
& ( ( in @ X1901 @ X1900 )
| X1902
| ~ X1902
| ~ ( in @ X1901 @ ( binunion @ X1899 @ X1900 ) ) )
& ( ~ X1902
| X1902
| ~ X1902
| ~ ( in @ X1901 @ ( binunion @ X1899 @ X1900 ) ) )
& ( ~ ( in @ X1905 @ ( binunion @ X1903 @ X1904 ) )
| ( in @ X1905 @ X1903 )
| ( in @ X1905 @ X1904 ) )
& ( subset @ X1906 @ ( binunion @ X1906 @ X1907 ) )
& ( subset @ X1909 @ ( binunion @ X1908 @ X1909 ) )
& ( ~ ( in @ X1912 @ X1910 )
| ~ ( in @ X1912 @ X1911 )
| ( in @ X1912 @ ( binintersect @ X1910 @ X1911 ) ) )
& ( ~ ( subset @ X1915 @ X1913 )
| ~ ( subset @ X1915 @ X1914 )
| ( subset @ X1915 @ ( binintersect @ X1913 @ X1914 ) ) )
& ( ~ ( in @ X1918 @ ( binintersect @ X1916 @ X1917 ) )
| ( in @ X1918 @ X1916 ) )
& ( subset @ ( binintersect @ X1919 @ X1920 ) @ X1919 )
& ( ~ ( subset @ X1921 @ X1922 )
| ( ( binintersect @ X1921 @ X1922 )
= X1921 ) )
& ( ( ( binintersect @ X1923 @ X1924 )
!= X1924 )
| ( subset @ X1924 @ X1923 ) )
& ( ~ ( in @ X1927 @ ( binintersect @ X1925 @ X1926 ) )
| ( in @ X1927 @ X1926 ) )
& ( ( in @ ( esk54_2 @ X1928 @ X1929 ) @ X1928 )
| ( ( binintersect @ X1928 @ X1929 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1928 @ X1929 ) @ X1929 )
| ( ( binintersect @ X1928 @ X1929 )
= emptyset ) )
& ( subset @ ( binintersect @ X1931 @ X1932 ) @ X1932 )
& ( ~ ( subset @ X1934 @ X1933 )
| ( ( binintersect @ X1933 @ X1934 )
= X1934 ) )
& ( ( ( binintersect @ X1935 @ X1936 )
!= X1935 )
| ( subset @ X1935 @ X1936 ) )
& ( ( binintersect @ X1937 @ ( binunion @ X1938 @ X1939 ) )
= ( binunion @ ( binintersect @ X1937 @ X1938 ) @ ( binintersect @ X1937 @ X1939 ) ) )
& ( ~ ( in @ X1942 @ X1940 )
| ( in @ X1942 @ X1941 )
| ( in @ X1942 @ ( setminus @ X1940 @ X1941 ) ) )
& ( ~ ( in @ X1945 @ ( setminus @ X1943 @ X1944 ) )
| ( in @ X1945 @ X1943 ) )
& ( ~ ( in @ X1948 @ ( setminus @ X1946 @ X1947 ) )
| ~ ( in @ X1948 @ X1947 ) )
& ( ~ ( subset @ X1949 @ X1950 )
| ( ( setminus @ X1949 @ X1950 )
= emptyset ) )
& ( ( in @ X1953 @ ( setminus @ X1951 @ X1952 ) )
| ~ ( in @ X1953 @ X1951 )
| ( in @ X1953 @ X1952 ) )
& ( ( in @ X1956 @ ( setminus @ X1954 @ X1955 ) )
| ( in @ X1956 @ X1955 )
| ~ ( in @ X1956 @ X1954 ) )
& ( ( in @ X1959 @ X1957 )
| ~ ( in @ X1959 @ ( setminus @ X1957 @ X1958 ) ) )
& ( ~ ( in @ X1962 @ X1961 )
| ~ ( in @ X1962 @ ( setminus @ X1960 @ X1961 ) ) )
& ( subset @ ( setminus @ X1963 @ X1964 ) @ X1963 )
& ( ( ( setminus @ X1965 @ X1966 )
!= emptyset )
| ( subset @ X1965 @ X1966 ) )
& ( ~ ( in @ X1969 @ X1967 )
| X1970
| ( in @ X1969 @ X1967 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ( in @ X1969 @ X1968 )
| X1970
| ( in @ X1969 @ X1967 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ X1970
| X1970
| ( in @ X1969 @ X1967 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ ( in @ X1969 @ X1967 )
| X1970
| ~ ( in @ X1969 @ X1968 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ( in @ X1969 @ X1968 )
| X1970
| ~ ( in @ X1969 @ X1968 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ X1970
| X1970
| ~ ( in @ X1969 @ X1968 )
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ ( in @ X1969 @ X1967 )
| X1970
| ~ X1970
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ( in @ X1969 @ X1968 )
| X1970
| ~ X1970
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ X1970
| X1970
| ~ X1970
| ~ ( in @ X1969 @ ( symdiff @ X1967 @ X1968 ) ) )
& ( ~ ( in @ X1973 @ X1971 )
| ( in @ X1973 @ X1972 )
| ( in @ X1973 @ ( symdiff @ X1971 @ X1972 ) ) )
& ( ( in @ X1976 @ X1974 )
| ~ ( in @ X1976 @ X1975 )
| ( in @ X1976 @ ( symdiff @ X1974 @ X1975 ) ) )
& ( ~ ( in @ X1979 @ X1977 )
| ~ ( in @ X1979 @ X1978 )
| ~ ( in @ X1979 @ ( symdiff @ X1977 @ X1978 ) ) )
& ( ( in @ X1982 @ X1980 )
| ( in @ X1982 @ X1981 )
| ~ ( in @ X1982 @ ( symdiff @ X1980 @ X1981 ) ) )
& ( in @ X1984 @ ( setadjoin @ X1983 @ ( setadjoin @ X1984 @ emptyset ) ) )
& ( in @ X1985 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1985 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1985 @ ( setadjoin @ X1986 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1988 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1987 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1987 @ ( setadjoin @ X1988 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1989 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1989 @ ( setadjoin @ X1990 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1991 @ X1992 ) )
& ( ~ ( in @ X1994 @ X1993 )
| ( subset @ ( setadjoin @ X1994 @ emptyset ) @ X1993 ) )
& ( ~ ( in @ X1996 @ X1995 )
| ( in @ ( setadjoin @ X1996 @ emptyset ) @ ( powerset @ X1995 ) ) )
& ( ~ ( in @ X1999 @ X1997 )
| ( in @ ( setadjoin @ X1999 @ emptyset ) @ ( powerset @ ( binunion @ X1997 @ X1998 ) ) ) )
& ( ~ ( in @ X2002 @ ( setadjoin @ X2000 @ ( setadjoin @ X2001 @ emptyset ) ) )
| ( X2002 = X2000 )
| ( X2002 = X2001 ) )
& ( ~ ( in @ X2005 @ X2003 )
| ~ ( in @ X2006 @ X2004 )
| ( subset @ ( setadjoin @ X2005 @ ( setadjoin @ X2006 @ emptyset ) ) @ ( binunion @ X2003 @ X2004 ) ) )
& ( ~ ( in @ X2009 @ X2007 )
| ~ ( in @ X2010 @ X2008 )
| ( in @ ( setadjoin @ X2009 @ ( setadjoin @ X2010 @ emptyset ) ) @ ( powerset @ ( binunion @ X2007 @ X2008 ) ) ) )
& ( ~ ( in @ X2013 @ X2011 )
| ~ ( in @ X2014 @ X2012 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2013 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2013 @ ( setadjoin @ X2014 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2011 @ X2012 ) ) ) )
& ( ~ ( in @ X2017 @ X2015 )
| ~ ( in @ X2018 @ X2016 )
| ( in @ ( setadjoin @ ( setadjoin @ X2017 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2017 @ ( setadjoin @ X2018 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2015 @ X2016 ) ) ) ) )
& ( ~ ( in @ X2021 @ X2019 )
| ~ ( in @ X2022 @ X2020 )
| ( in @ ( kpair @ X2021 @ X2022 ) @ ( powerset @ ( powerset @ ( binunion @ X2019 @ X2020 ) ) ) ) )
& ( ~ ( in @ X2025 @ X2023 )
| ~ ( in @ X2026 @ X2024 )
| ( in @ ( kpair @ X2025 @ X2026 ) @ ( cartprod @ X2023 @ X2024 ) ) )
& ( ( in @ ( esk55_3 @ X2027 @ X2028 @ X2029 ) @ X2027 )
| ~ ( in @ X2029 @ ( cartprod @ X2027 @ X2028 ) ) )
& ( ( in @ ( esk56_3 @ X2027 @ X2028 @ X2029 ) @ X2028 )
| ~ ( in @ X2029 @ ( cartprod @ X2027 @ X2028 ) ) )
& ( ( X2029
= ( kpair @ ( esk55_3 @ X2027 @ X2028 @ X2029 ) @ ( esk56_3 @ X2027 @ X2028 @ X2029 ) ) )
| ~ ( in @ X2029 @ ( cartprod @ X2027 @ X2028 ) ) )
& ( ~ ( in @ X2034 @ ( cartprod @ X2032 @ X2033 ) )
| ( iskpair @ X2034 ) )
& ( ( in @ ( esk57_2 @ X2035 @ X2036 ) @ X2035 )
| ~ ( in @ X2036 @ ( setunion @ X2035 ) ) )
& ( ( in @ X2036 @ ( esk57_2 @ X2035 @ X2036 ) )
| ~ ( in @ X2036 @ ( setunion @ X2035 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2038 @ emptyset ) ) @ X2038 )
& ( subset @ X2039 @ ( setunion @ ( setadjoin @ X2039 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2040 @ emptyset ) )
= X2040 )
& ( ( in @ ( esk58_2 @ X2041 @ X2042 ) @ X2041 )
| ~ ( in @ X2045 @ X2041 )
| ~ ( X2042 @ X2045 )
| ( singleton @ ( dsetconstr @ X2041 @ X2042 ) ) )
& ( ( in @ ( esk59_2 @ X2041 @ X2042 ) @ X2041 )
| ~ ( in @ X2045 @ X2041 )
| ~ ( X2042 @ X2045 )
| ( singleton @ ( dsetconstr @ X2041 @ X2042 ) ) )
& ( ( X2042 @ ( esk58_2 @ X2041 @ X2042 ) )
| ~ ( in @ X2045 @ X2041 )
| ~ ( X2042 @ X2045 )
| ( singleton @ ( dsetconstr @ X2041 @ X2042 ) ) )
& ( ( X2042 @ ( esk59_2 @ X2041 @ X2042 ) )
| ~ ( in @ X2045 @ X2041 )
| ~ ( X2042 @ X2045 )
| ( singleton @ ( dsetconstr @ X2041 @ X2042 ) ) )
& ( ( ( esk58_2 @ X2041 @ X2042 )
!= ( esk59_2 @ X2041 @ X2042 ) )
| ~ ( in @ X2045 @ X2041 )
| ~ ( X2042 @ X2045 )
| ( singleton @ ( dsetconstr @ X2041 @ X2042 ) ) )
& ( ( in @ ( esk60_2 @ X2046 @ X2047 ) @ X2046 )
| ~ ( singleton @ ( dsetconstr @ X2046 @ X2047 ) ) )
& ( ( X2047 @ ( esk60_2 @ X2046 @ X2047 ) )
| ~ ( singleton @ ( dsetconstr @ X2046 @ X2047 ) ) )
& ( ( in @ ( esk61_3 @ X2049 @ X2050 @ X2051 ) @ X2049 )
| ( singleton @ ( dsetconstr @ X2049 @ X2050 ) )
| ~ ( X2050 @ X2051 )
| ~ ( in @ X2051 @ X2049 ) )
& ( ( X2050 @ ( esk61_3 @ X2049 @ X2050 @ X2051 ) )
| ( singleton @ ( dsetconstr @ X2049 @ X2050 ) )
| ~ ( X2050 @ X2051 )
| ~ ( in @ X2051 @ X2049 ) )
& ( ( ( esk61_3 @ X2049 @ X2050 @ X2051 )
!= X2051 )
| ( singleton @ ( dsetconstr @ X2049 @ X2050 ) )
| ~ ( X2050 @ X2051 )
| ~ ( in @ X2051 @ X2049 ) )
& ( ( in @ ( esk62_2 @ X2053 @ X2054 ) @ X2053 )
| ~ ( in @ X2057 @ X2053 )
| ~ ( X2054 @ X2057 )
| ( singleton @ ( dsetconstr @ X2053 @ X2054 ) ) )
& ( ( in @ ( esk63_2 @ X2053 @ X2054 ) @ X2053 )
| ~ ( in @ X2057 @ X2053 )
| ~ ( X2054 @ X2057 )
| ( singleton @ ( dsetconstr @ X2053 @ X2054 ) ) )
& ( ( X2054 @ ( esk62_2 @ X2053 @ X2054 ) )
| ~ ( in @ X2057 @ X2053 )
| ~ ( X2054 @ X2057 )
| ( singleton @ ( dsetconstr @ X2053 @ X2054 ) ) )
& ( ( X2054 @ ( esk63_2 @ X2053 @ X2054 ) )
| ~ ( in @ X2057 @ X2053 )
| ~ ( X2054 @ X2057 )
| ( singleton @ ( dsetconstr @ X2053 @ X2054 ) ) )
& ( ( ( esk62_2 @ X2053 @ X2054 )
!= ( esk63_2 @ X2053 @ X2054 ) )
| ~ ( in @ X2057 @ X2053 )
| ~ ( X2054 @ X2057 )
| ( singleton @ ( dsetconstr @ X2053 @ X2054 ) ) )
& ( ( ( setadjoin @ X2058 @ emptyset )
!= ( setadjoin @ X2059 @ emptyset ) )
| ( X2058 = X2059 ) )
& ( ~ ( in @ ( setadjoin @ X2062 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2060 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2060 @ ( setadjoin @ X2061 @ emptyset ) ) @ emptyset ) ) )
| ( X2060 = X2062 ) )
& ( ~ ( iskpair @ X2063 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2063 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2063 ) ) ) )
& ( ~ ( singleton @ X2064 )
| ( in @ ( setunion @ X2064 ) @ X2064 ) )
& ( ( kfst @ ( kpair @ X2065 @ X2066 ) )
= X2065 )
& ( ~ ( in @ X2069 @ ( cartprod @ X2067 @ X2068 ) )
| ( in @ ( kfst @ X2069 ) @ X2067 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2070 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2070 @ ( setadjoin @ X2071 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2072 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2072 @ ( setadjoin @ X2073 @ emptyset ) ) @ emptyset ) ) )
| ( X2070 = X2072 ) )
& ( ( ( kpair @ X2074 @ X2075 )
!= ( kpair @ X2076 @ X2077 ) )
| ( X2074 = X2076 ) )
& ( ( X2078 != X2079 )
| ( ( setadjoin @ X2078 @ ( setadjoin @ X2079 @ emptyset ) )
= ( setadjoin @ X2078 @ emptyset ) ) )
& ( ( X2080 != X2081 )
| ( ( setadjoin @ ( setadjoin @ X2080 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2080 @ ( setadjoin @ X2081 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2080 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2082 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2082 @ ( setadjoin @ X2083 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2084 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2084 @ ( setadjoin @ X2085 @ emptyset ) ) @ emptyset ) ) )
| ( X2084 != X2085 )
| ( X2083 = X2085 ) )
& ( ( ( setadjoin @ X2086 @ ( setadjoin @ X2087 @ emptyset ) )
!= ( setadjoin @ X2088 @ emptyset ) )
| ( X2086 = X2087 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2089 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2089 @ ( setadjoin @ X2090 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2091 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2091 @ ( setadjoin @ X2092 @ emptyset ) ) @ emptyset ) ) )
| ( X2090 = X2092 ) )
& ( ( ( kpair @ X2093 @ X2094 )
!= ( kpair @ X2095 @ X2096 ) )
| ( X2094 = X2096 ) )
& ( ~ ( iskpair @ X2097 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2097 )
@ ^ [Z0: $i] :
( X2097
= ( kpair @ ( kfst @ X2097 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2098 @ X2099 ) )
= X2099 )
& ( ~ ( iskpair @ X2100 )
| ( ( kpair @ ( kfst @ X2100 ) @ ( ksnd @ X2100 ) )
= X2100 ) )
& ( ~ ( in @ X2103 @ ( cartprod @ X2101 @ X2102 ) )
| ( in @ ( ksnd @ X2103 ) @ X2102 ) )
& ( ~ ( in @ ( kpair @ X2106 @ X2107 ) @ ( cartprod @ X2104 @ X2105 ) )
| ( in @ X2106 @ X2104 ) )
& ( ~ ( in @ ( kpair @ X2110 @ X2111 ) @ ( cartprod @ X2108 @ X2109 ) )
| ( in @ X2111 @ X2109 ) )
& ( ~ ( in @ X2114 @ X2112 )
| ~ ( in @ X2115 @ X2113 )
| ( ( kpair @ X2114 @ X2115 )
= ( kpair @ X2114 @ X2115 ) ) )
& ( ~ ( in @ X2118 @ X2116 )
| ~ ( in @ X2119 @ X2117 )
| ( ( kfst @ ( kpair @ X2118 @ X2119 ) )
= X2118 ) )
& ( ~ ( in @ X2122 @ X2120 )
| ~ ( in @ X2123 @ X2121 )
| ( ( ksnd @ ( kpair @ X2122 @ X2123 ) )
= X2123 ) )
& ( ~ ( in @ X2126 @ ( cartprod @ X2124 @ X2125 ) )
| ( ( kpair @ ( kfst @ X2126 ) @ ( ksnd @ X2126 ) )
= X2126 ) )
& ( ~ ( in @ X2130 @ X2127 )
| ~ ( in @ X2131 @ X2128 )
| ~ ( X2129 @ X2130 @ X2131 )
| ( in @ ( kpair @ X2130 @ X2131 ) @ ( dpsetconstr @ X2127 @ X2128 @ X2129 ) ) )
& ( subset @ ( dpsetconstr @ X2132 @ X2133 @ X2134 ) @ ( cartprod @ X2132 @ X2133 ) )
& ( subset @ ( dpsetconstr @ X2135 @ X2136 @ X2137 ) @ ( cartprod @ X2135 @ X2136 ) )
& ( ~ ( in @ X2141 @ X2138 )
| ~ ( in @ X2142 @ X2139 )
| ~ ( in @ ( kpair @ X2141 @ X2142 ) @ ( dpsetconstr @ X2138 @ X2139 @ X2140 ) )
| ( X2140 @ X2141 @ X2142 ) )
& ( ~ ( in @ ( kpair @ X2146 @ X2147 ) @ ( dpsetconstr @ X2143 @ X2144 @ X2145 ) )
| ( in @ X2146 @ X2143 ) )
& ( ~ ( in @ ( kpair @ X2151 @ X2152 ) @ ( dpsetconstr @ X2148 @ X2149 @ X2150 ) )
| ( in @ X2152 @ X2149 ) )
& ( ~ ( in @ ( kpair @ X2156 @ X2157 ) @ ( dpsetconstr @ X2153 @ X2154 @ X2155 ) )
| ( X2155 @ X2156 @ X2157 ) )
& ( ~ ( func @ X2158 @ X2159 @ X2160 )
| ~ ( in @ X2161 @ X2158 )
| ( singleton
@ ( dsetconstr @ X2159
@ ^ [Z0: $i] : ( in @ ( kpair @ X2161 @ Z0 ) @ X2160 ) ) ) )
& ( ~ ( func @ X2162 @ X2163 @ X2164 )
| ~ ( in @ X2165 @ X2162 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2163
@ ^ [Z0: $i] : ( in @ ( kpair @ X2165 @ Z0 ) @ X2164 ) ) )
@ X2163 ) )
& ( ~ ( func @ X2166 @ X2167 @ X2168 )
| ~ ( in @ X2169 @ X2166 )
| ( in @ ( ap @ X2166 @ X2167 @ X2168 @ X2169 ) @ X2167 ) )
& ( ~ ( in @ X2172 @ ( funcSet @ X2170 @ X2171 ) )
| ( func @ X2170 @ X2171 @ X2172 ) )
& ( ~ ( in @ X2175 @ ( funcSet @ X2173 @ X2174 ) )
| ~ ( in @ X2176 @ X2173 )
| ( in @ ( ap @ X2173 @ X2174 @ X2175 @ X2176 ) @ X2174 ) )
& ( ~ ( func @ X2177 @ X2178 @ X2179 )
| ( in @ X2179 @ ( funcSet @ X2177 @ X2178 ) ) )
& ( ( in @ ( esk64_3 @ X2180 @ X2181 @ X2182 ) @ X2180 )
| ( func @ X2180 @ X2181
@ ( dpsetconstr @ X2180 @ X2181
@ ^ [Z0: $i] : ( $eq @ ( X2182 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2182 @ ( esk64_3 @ X2180 @ X2181 @ X2182 ) ) @ X2181 )
| ( func @ X2180 @ X2181
@ ( dpsetconstr @ X2180 @ X2181
@ ^ [Z0: $i] : ( $eq @ ( X2182 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2184 @ X2185 @ X2186 ) @ X2184 )
| ( func @ X2184 @ X2185 @ ( lam @ X2184 @ X2185 @ X2186 ) ) )
& ( ~ ( in @ ( X2186 @ ( esk65_3 @ X2184 @ X2185 @ X2186 ) ) @ X2185 )
| ( func @ X2184 @ X2185 @ ( lam @ X2184 @ X2185 @ X2186 ) ) )
& ( ( in @ ( esk66_3 @ X2188 @ X2189 @ X2190 ) @ X2188 )
| ( in @ ( lam @ X2188 @ X2189 @ X2190 ) @ ( funcSet @ X2188 @ X2189 ) ) )
& ( ~ ( in @ ( X2190 @ ( esk66_3 @ X2188 @ X2189 @ X2190 ) ) @ X2189 )
| ( in @ ( lam @ X2188 @ X2189 @ X2190 ) @ ( funcSet @ X2188 @ X2189 ) ) )
& ( ( in @ ( esk67_4 @ X2192 @ X2193 @ X2194 @ X2195 ) @ X2192 )
| ~ ( in @ X2198 @ X2194 )
| ( X2195 @ X2198 )
| ~ ( subset @ X2194 @ ( cartprod @ X2192 @ X2193 ) ) )
& ( ( in @ ( esk68_4 @ X2192 @ X2193 @ X2194 @ X2195 ) @ X2193 )
| ~ ( in @ X2198 @ X2194 )
| ( X2195 @ X2198 )
| ~ ( subset @ X2194 @ ( cartprod @ X2192 @ X2193 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2192 @ X2193 @ X2194 @ X2195 ) @ ( esk68_4 @ X2192 @ X2193 @ X2194 @ X2195 ) ) @ X2194 )
| ~ ( in @ X2198 @ X2194 )
| ( X2195 @ X2198 )
| ~ ( subset @ X2194 @ ( cartprod @ X2192 @ X2193 ) ) )
& ( ~ ( X2195 @ ( kpair @ ( esk67_4 @ X2192 @ X2193 @ X2194 @ X2195 ) @ ( esk68_4 @ X2192 @ X2193 @ X2194 @ X2195 ) ) )
| ~ ( in @ X2198 @ X2194 )
| ( X2195 @ X2198 )
| ~ ( subset @ X2194 @ ( cartprod @ X2192 @ X2193 ) ) )
& ( ( in @ ( esk69_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2199 )
| ~ ( in @ X2205 @ X2201 )
| ( X2202 @ X2205 )
| ~ ( subset @ X2201 @ ( cartprod @ X2199 @ X2200 ) ) )
& ( ( in @ ( esk70_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ X2200 )
| ~ ( in @ X2205 @ X2201 )
| ( X2202 @ X2205 )
| ~ ( subset @ X2201 @ ( cartprod @ X2199 @ X2200 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk70_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) @ X2201 )
| ~ ( in @ X2205 @ X2201 )
| ( X2202 @ X2205 )
| ~ ( subset @ X2201 @ ( cartprod @ X2199 @ X2200 ) ) )
& ( ~ ( X2202 @ ( kpair @ ( esk69_4 @ X2199 @ X2200 @ X2201 @ X2202 ) @ ( esk70_4 @ X2199 @ X2200 @ X2201 @ X2202 ) ) )
| ~ ( in @ X2205 @ X2201 )
| ( X2202 @ X2205 )
| ~ ( subset @ X2201 @ ( cartprod @ X2199 @ X2200 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2206 @ X2207 ) )
| ~ ( in @ X2208 @ X2206 )
| ~ ( in @ X2209 @ X2206 )
| ~ ( X2207 @ X2208 )
| ~ ( X2207 @ X2209 )
| ( X2208 = X2209 ) )
& ( ~ ( func @ X2210 @ X2211 @ X2212 )
| ~ ( in @ X2213 @ X2210 )
| ( in @ ( kpair @ X2213 @ ( ap @ X2210 @ X2211 @ X2212 @ X2213 ) ) @ X2212 ) )
& ( ~ ( in @ X2216 @ ( funcSet @ X2214 @ X2215 ) )
| ~ ( in @ X2217 @ X2214 )
| ( in @ ( kpair @ X2217 @ ( ap @ X2214 @ X2215 @ X2216 @ X2217 ) ) @ X2216 ) )
& ( ~ ( func @ X2218 @ X2219 @ X2220 )
| ~ ( in @ X2221 @ X2218 )
| ~ ( in @ X2222 @ X2219 )
| ~ ( in @ ( kpair @ X2221 @ X2222 ) @ X2220 )
| ( ( ap @ X2218 @ X2219 @ X2220 @ X2221 )
= X2222 ) )
& ( ( in @ ( esk71_4 @ X2223 @ X2224 @ X2225 @ X2226 ) @ X2223 )
| ~ ( in @ X2228 @ X2223 )
| ~ ( in @ X2229 @ X2224 )
| ~ ( in @ ( kpair @ X2228 @ X2229 ) @ X2226 )
| ( in @ ( kpair @ X2228 @ X2229 ) @ X2225 )
| ~ ( func @ X2223 @ X2224 @ X2226 )
| ~ ( func @ X2223 @ X2224 @ X2225 ) )
& ( ( ( ap @ X2223 @ X2224 @ X2225 @ ( esk71_4 @ X2223 @ X2224 @ X2225 @ X2226 ) )
!= ( ap @ X2223 @ X2224 @ X2226 @ ( esk71_4 @ X2223 @ X2224 @ X2225 @ X2226 ) ) )
| ~ ( in @ X2228 @ X2223 )
| ~ ( in @ X2229 @ X2224 )
| ~ ( in @ ( kpair @ X2228 @ X2229 ) @ X2226 )
| ( in @ ( kpair @ X2228 @ X2229 ) @ X2225 )
| ~ ( func @ X2223 @ X2224 @ X2226 )
| ~ ( func @ X2223 @ X2224 @ X2225 ) )
& ( ~ ( in @ X2232 @ ( funcSet @ X2230 @ X2231 ) )
| ~ ( in @ X2233 @ X2230 )
| ~ ( in @ X2234 @ X2231 )
| ~ ( in @ ( kpair @ X2233 @ X2234 ) @ X2232 )
| ( ( ap @ X2230 @ X2231 @ X2232 @ X2233 )
= X2234 ) )
& ( ( in @ ( esk72_4 @ X2235 @ X2236 @ X2237 @ X2238 ) @ X2235 )
| ( subset @ X2237 @ X2238 )
| ~ ( subset @ X2238 @ ( cartprod @ X2235 @ X2236 ) )
| ~ ( subset @ X2237 @ ( cartprod @ X2235 @ X2236 ) ) )
& ( ( in @ ( esk73_4 @ X2235 @ X2236 @ X2237 @ X2238 ) @ X2236 )
| ( subset @ X2237 @ X2238 )
| ~ ( subset @ X2238 @ ( cartprod @ X2235 @ X2236 ) )
| ~ ( subset @ X2237 @ ( cartprod @ X2235 @ X2236 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2235 @ X2236 @ X2237 @ X2238 ) @ ( esk73_4 @ X2235 @ X2236 @ X2237 @ X2238 ) ) @ X2237 )
| ( subset @ X2237 @ X2238 )
| ~ ( subset @ X2238 @ ( cartprod @ X2235 @ X2236 ) )
| ~ ( subset @ X2237 @ ( cartprod @ X2235 @ X2236 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2235 @ X2236 @ X2237 @ X2238 ) @ ( esk73_4 @ X2235 @ X2236 @ X2237 @ X2238 ) ) @ X2238 )
| ( subset @ X2237 @ X2238 )
| ~ ( subset @ X2238 @ ( cartprod @ X2235 @ X2236 ) )
| ~ ( subset @ X2237 @ ( cartprod @ X2235 @ X2236 ) ) )
& ( ( in @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ( X2243 = X2244 )
| ( in @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ( X2243 = X2244 )
| ( in @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ( X2243 = X2244 )
| ( in @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ( X2243 = X2244 )
| ( in @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ( X2243 = X2244 )
| ( in @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ( X2243 = X2244 )
| ( in @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ( X2243 = X2244 )
| ( in @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ( X2243 = X2244 )
| ( in @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ( X2243 = X2244 )
| ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ( X2243 = X2244 )
| ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ( X2243 = X2244 )
| ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ( X2243 = X2244 )
| ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2241 )
| ( X2243 = X2244 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ X2242 )
| ( X2243 = X2244 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ( X2243 = X2244 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk77_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2243 )
| ( X2243 = X2244 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2241 @ X2242 @ X2243 @ X2244 ) @ ( esk75_4 @ X2241 @ X2242 @ X2243 @ X2244 ) ) @ X2244 )
| ~ ( subset @ X2244 @ ( cartprod @ X2241 @ X2242 ) )
| ~ ( subset @ X2243 @ ( cartprod @ X2241 @ X2242 ) ) )
& ( ( in @ ( esk78_4 @ X2249 @ X2250 @ X2251 @ X2252 ) @ X2249 )
| ( X2251 = X2252 )
| ~ ( func @ X2249 @ X2250 @ X2252 )
| ~ ( func @ X2249 @ X2250 @ X2251 ) )
& ( ( ( ap @ X2249 @ X2250 @ X2251 @ ( esk78_4 @ X2249 @ X2250 @ X2251 @ X2252 ) )
!= ( ap @ X2249 @ X2250 @ X2252 @ ( esk78_4 @ X2249 @ X2250 @ X2251 @ X2252 ) ) )
| ( X2251 = X2252 )
| ~ ( func @ X2249 @ X2250 @ X2252 )
| ~ ( func @ X2249 @ X2250 @ X2251 ) )
& ( ( in @ ( esk79_4 @ X2254 @ X2255 @ X2256 @ X2257 ) @ X2254 )
| ( X2256 = X2257 )
| ~ ( in @ X2257 @ ( funcSet @ X2254 @ X2255 ) )
| ~ ( in @ X2256 @ ( funcSet @ X2254 @ X2255 ) ) )
& ( ( ( ap @ X2254 @ X2255 @ X2256 @ ( esk79_4 @ X2254 @ X2255 @ X2256 @ X2257 ) )
!= ( ap @ X2254 @ X2255 @ X2257 @ ( esk79_4 @ X2254 @ X2255 @ X2256 @ X2257 ) ) )
| ( X2256 = X2257 )
| ~ ( in @ X2257 @ ( funcSet @ X2254 @ X2255 ) )
| ~ ( in @ X2256 @ ( funcSet @ X2254 @ X2255 ) ) )
& ( ~ ( in @ X2261 @ ( funcSet @ X2259 @ X2260 ) )
| ~ ( in @ X2262 @ X2259 )
| ( ( ap @ X2259 @ X2260 @ X2261 @ X2262 )
= ( ap @ X2259 @ X2260 @ X2261 @ X2262 ) ) )
& ( ~ ( func @ X2263 @ X2264 @ X2265 )
| ~ ( in @ X2266 @ X2263 )
| ( ( ap @ X2263 @ X2264 @ X2265 @ X2266 )
= ( ap @ X2263 @ X2264 @ X2265 @ X2266 ) ) )
& ( ( in @ ( esk80_3 @ X2267 @ X2268 @ X2269 ) @ X2267 )
| ~ ( in @ X2271 @ X2267 )
| ( ( ap @ X2267 @ X2268 @ ( lam @ X2267 @ X2268 @ X2269 ) @ X2271 )
= ( X2269 @ X2271 ) ) )
& ( ~ ( in @ ( X2269 @ ( esk80_3 @ X2267 @ X2268 @ X2269 ) ) @ X2268 )
| ~ ( in @ X2271 @ X2267 )
| ( ( ap @ X2267 @ X2268 @ ( lam @ X2267 @ X2268 @ X2269 ) @ X2271 )
= ( X2269 @ X2271 ) ) )
& ( ~ ( func @ X2272 @ X2273 @ X2274 )
| ( ( lam @ X2272 @ X2273 @ ( ap @ X2272 @ X2273 @ X2274 ) )
= X2274 ) )
& ( ( in @ ( esk81_3 @ X2275 @ X2276 @ X2277 ) @ X2275 )
| ( ( lam @ X2275 @ X2276 @ X2277 )
= ( lam @ X2275 @ X2276 @ X2277 ) ) )
& ( ~ ( in @ ( X2277 @ ( esk81_3 @ X2275 @ X2276 @ X2277 ) ) @ X2276 )
| ( ( lam @ X2275 @ X2276 @ X2277 )
= ( lam @ X2275 @ X2276 @ X2277 ) ) )
& ( ( in @ ( esk82_3 @ X2279 @ X2280 @ X2281 ) @ X2279 )
| ~ ( in @ X2283 @ X2279 )
| ( ( ap @ X2279 @ X2280 @ ( lam @ X2279 @ X2280 @ X2281 ) @ X2283 )
= ( X2281 @ X2283 ) ) )
& ( ~ ( in @ ( X2281 @ ( esk82_3 @ X2279 @ X2280 @ X2281 ) ) @ X2280 )
| ~ ( in @ X2283 @ X2279 )
| ( ( ap @ X2279 @ X2280 @ ( lam @ X2279 @ X2280 @ X2281 ) @ X2283 )
= ( X2281 @ X2283 ) ) )
& ( ~ ( in @ X2286 @ ( funcSet @ X2284 @ X2285 ) )
| ( ( lam @ X2284 @ X2285 @ ( ap @ X2284 @ X2285 @ X2286 ) )
= X2286 ) )
& ( ~ ( in @ X2289 @ X2287 )
| ~ ( in @ X2290 @ X2287 )
| X2288
| ( in @ X2290
@ ( dsetconstr @ X2287
@ ^ [Z0: $i] :
( ( X2288
& ( Z0 = X2289 ) )
| ( ~ X2288
& ( Z0 = X2290 ) ) ) ) ) )
& ( ~ ( in @ X2293 @ X2291 )
| ~ ( in @ X2294 @ X2291 )
| X2292
| ( ( dsetconstr @ X2291
@ ^ [Z0: $i] :
( ( X2292
& ( Z0 = X2293 ) )
| ( ~ X2292
& ( Z0 = X2294 ) ) ) )
= ( setadjoin @ X2294 @ emptyset ) ) )
& ( ~ ( in @ X2297 @ X2295 )
| ~ ( in @ X2298 @ X2295 )
| ~ X2296
| ( in @ X2297
@ ( dsetconstr @ X2295
@ ^ [Z0: $i] :
( ( X2296
& ( Z0 = X2297 ) )
| ( ~ X2296
& ( Z0 = X2298 ) ) ) ) ) )
& ( ~ ( in @ X2301 @ X2299 )
| ~ ( in @ X2302 @ X2299 )
| ~ X2300
| ( ( dsetconstr @ X2299
@ ^ [Z0: $i] :
( ( X2300
& ( Z0 = X2301 ) )
| ( ~ X2300
& ( Z0 = X2302 ) ) ) )
= ( setadjoin @ X2301 @ emptyset ) ) )
& ( ~ ( in @ X2305 @ X2303 )
| ~ ( in @ X2306 @ X2303 )
| ( singleton
@ ( dsetconstr @ X2303
@ ^ [Z0: $i] :
( ( X2304
& ( Z0 = X2305 ) )
| ( ~ X2304
& ( Z0 = X2306 ) ) ) ) ) )
& ( ~ ( in @ X2309 @ X2307 )
| ~ ( in @ X2310 @ X2307 )
| ( in @ ( if @ X2307 @ X2308 @ X2309 @ X2310 ) @ X2307 ) )
& ( ~ ( singleton @ X2311 )
| ~ ( in @ X2312 @ X2311 )
| ( ( setunion @ X2311 )
= X2312 ) )
& ( ~ ( in @ X2315 @ X2313 )
| ~ ( in @ X2316 @ X2313 )
| ~ X2314
| ( ( if @ X2313 @ X2314 @ X2315 @ X2316 )
= X2315 ) )
& ( ~ ( in @ X2319 @ X2317 )
| ~ ( in @ X2320 @ X2317 )
| X2318
| ( ( if @ X2317 @ X2318 @ X2319 @ X2320 )
= X2320 ) )
& ( ~ ( in @ X2323 @ X2321 )
| ~ ( in @ X2324 @ X2321 )
| ( in @ ( if @ X2321 @ X2322 @ X2323 @ X2324 ) @ ( setadjoin @ X2323 @ ( setadjoin @ X2324 @ emptyset ) ) ) )
& ( ~ ( in @ X2326 @ ( powerset @ X2325 ) )
| ~ ( in @ X2327 @ ( powerset @ X2325 ) )
| ( in @ ( binintersect @ X2326 @ X2327 ) @ ( powerset @ X2325 ) ) )
& ( ~ ( in @ X2329 @ ( powerset @ X2328 ) )
| ~ ( in @ X2330 @ ( powerset @ X2328 ) )
| ( in @ ( binunion @ X2329 @ X2330 ) @ ( powerset @ X2328 ) ) )
& ( ~ ( in @ X2332 @ ( powerset @ X2331 ) )
| ( in @ ( powerset @ X2332 ) @ ( powerset @ ( powerset @ X2331 ) ) ) )
& ( ~ ( in @ X2334 @ ( powerset @ X2333 ) )
| ~ ( in @ X2335 @ ( powerset @ X2333 ) )
| ( in @ ( setminus @ X2334 @ X2335 ) @ ( powerset @ X2333 ) ) )
& ( ~ ( in @ X2337 @ ( powerset @ X2336 ) )
| ( in @ ( setminus @ X2336 @ X2337 ) @ ( powerset @ X2336 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ( X2339 = X2340 )
| ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2338 )
| ( X2339 = X2340 )
| ~ ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ( X2339 = X2340 )
| ~ ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2338 @ X2339 @ X2340 ) @ X2339 )
| ( X2339 = X2340 )
| ~ ( in @ ( esk83_3 @ X2338 @ X2339 @ X2340 ) @ X2340 )
| ~ ( in @ X2340 @ ( powerset @ X2338 ) )
| ~ ( in @ X2339 @ ( powerset @ X2338 ) ) )
& ( ( in @ ( esk85_3 @ X2343 @ X2344 @ X2345 ) @ X2343 )
| ( subset @ X2344 @ X2345 )
| ~ ( in @ X2345 @ ( powerset @ X2343 ) )
| ~ ( in @ X2344 @ ( powerset @ X2343 ) ) )
& ( ( in @ ( esk85_3 @ X2343 @ X2344 @ X2345 ) @ X2344 )
| ( subset @ X2344 @ X2345 )
| ~ ( in @ X2345 @ ( powerset @ X2343 ) )
| ~ ( in @ X2344 @ ( powerset @ X2343 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2343 @ X2344 @ X2345 ) @ X2345 )
| ( subset @ X2344 @ X2345 )
| ~ ( in @ X2345 @ ( powerset @ X2343 ) )
| ~ ( in @ X2344 @ ( powerset @ X2343 ) ) )
& ( ( in @ ( esk86_3 @ X2347 @ X2348 @ X2349 ) @ X2347 )
| ( in @ X2348 @ ( powerset @ X2349 ) )
| ~ ( in @ X2349 @ ( powerset @ X2347 ) )
| ~ ( in @ X2348 @ ( powerset @ X2347 ) ) )
& ( ( in @ ( esk86_3 @ X2347 @ X2348 @ X2349 ) @ X2348 )
| ( in @ X2348 @ ( powerset @ X2349 ) )
| ~ ( in @ X2349 @ ( powerset @ X2347 ) )
| ~ ( in @ X2348 @ ( powerset @ X2347 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2347 @ X2348 @ X2349 ) @ X2349 )
| ( in @ X2348 @ ( powerset @ X2349 ) )
| ~ ( in @ X2349 @ ( powerset @ X2347 ) )
| ~ ( in @ X2348 @ ( powerset @ X2347 ) ) )
& ( ~ ( in @ X2352 @ ( powerset @ X2351 ) )
| ~ ( in @ X2353 @ ( powerset @ X2351 ) )
| ~ ( in @ X2354 @ X2351 )
| ~ ( in @ X2352 @ ( powerset @ X2353 ) )
| ~ ( in @ X2354 @ X2352 )
| ( in @ X2354 @ X2353 ) )
& ( ~ ( in @ X2356 @ ( powerset @ X2355 ) )
| ~ ( in @ X2357 @ X2355 )
| ~ ( in @ X2357 @ X2356 )
| ~ ( in @ X2357 @ ( setminus @ X2355 @ X2356 ) ) )
& ( ~ ( in @ X2359 @ ( powerset @ X2358 ) )
| ~ ( in @ X2360 @ X2358 )
| ( in @ X2360 @ ( setminus @ X2358 @ X2359 ) )
| ( in @ X2360 @ X2359 ) )
& ( ~ ( in @ X2362 @ ( powerset @ X2361 ) )
| ~ ( in @ X2363 @ ( powerset @ X2361 ) )
| ~ ( in @ X2364 @ X2361 )
| ( in @ X2364 @ X2362 )
| ~ ( in @ X2364 @ ( binintersect @ X2362 @ X2363 ) ) )
& ( ~ ( in @ X2366 @ ( powerset @ X2365 ) )
| ~ ( in @ X2367 @ ( powerset @ X2365 ) )
| ~ ( in @ X2368 @ X2365 )
| ( in @ X2368 @ X2367 )
| ~ ( in @ X2368 @ ( binintersect @ X2366 @ X2367 ) ) )
& ( ~ ( in @ X2370 @ ( powerset @ X2369 ) )
| ~ ( in @ X2371 @ ( powerset @ X2369 ) )
| ~ ( in @ X2372 @ X2369 )
| ~ ( subset @ X2370 @ ( setminus @ X2369 @ X2371 ) )
| ~ ( in @ X2372 @ X2371 )
| ~ ( in @ X2372 @ X2370 ) )
& ( ~ ( in @ X2374 @ ( powerset @ X2373 ) )
| ~ ( in @ X2375 @ ( powerset @ X2373 ) )
| ~ ( in @ X2376 @ X2373 )
| ~ ( subset @ X2374 @ X2375 )
| ( in @ X2376 @ X2375 )
| ~ ( in @ X2376 @ X2374 ) )
& ( ~ ( in @ X2378 @ ( powerset @ X2377 ) )
| ~ ( in @ X2379 @ ( powerset @ X2377 ) )
| ~ ( subset @ X2378 @ X2379 )
| ( subset @ ( setminus @ X2377 @ X2379 ) @ ( setminus @ X2377 @ X2378 ) ) )
& ( in @ esk88_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk89_0 @ ( powerset @ esk87_0 ) )
& ( subset @ ( setminus @ esk87_0 @ esk89_0 ) @ ( setminus @ esk87_0 @ esk88_0 ) )
& ~ ( subset @ esk88_0 @ esk89_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_327])])])])])])]) ).
thf(c_0_329,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) )
| ~ ( in @ X5 @ X3 )
| ~ ( subset @ X2 @ ( setminus @ X3 @ X4 ) )
| ~ ( in @ X5 @ X4 )
| ~ ( in @ X5 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_330,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_331,negated_conjecture,
! [X3: $i,X5: $i,X4: $i,X2: $i] :
( ~ ( subset @ X2 @ ( setminus @ X3 @ X4 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X5 @ X4 )
| ~ ( in @ X5 @ X2 ) ),
inference(csr,[status(thm)],[c_0_329,c_0_330]) ).
thf(c_0_332,negated_conjecture,
subset @ ( setminus @ esk87_0 @ esk89_0 ) @ ( setminus @ esk87_0 @ esk88_0 ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_333,negated_conjecture,
in @ esk88_0 @ ( powerset @ esk87_0 ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_334,negated_conjecture,
! [X2: $i] :
( ~ ( in @ ( setminus @ esk87_0 @ esk89_0 ) @ ( powerset @ esk87_0 ) )
| ~ ( in @ X2 @ ( setminus @ esk87_0 @ esk89_0 ) )
| ~ ( in @ X2 @ esk88_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_332]),c_0_333])]) ).
thf(c_0_335,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_336,negated_conjecture,
! [X3: $i,X2: $i] : ( subset @ ( setminus @ X2 @ X3 ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_337,negated_conjecture,
! [X2: $i] :
( ~ ( in @ X2 @ ( setminus @ esk87_0 @ esk89_0 ) )
| ~ ( in @ X2 @ esk88_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_335]),c_0_336])]) ).
thf(c_0_338,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ ( setminus @ X3 @ X4 ) )
| ( in @ X2 @ X4 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_339,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk87_0 )
| ~ ( in @ X2 @ esk88_0 ) ),
inference(spm,[status(thm)],[c_0_330,c_0_333]) ).
thf(c_0_340,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk53_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_341,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk89_0 )
| ~ ( in @ X2 @ esk88_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_338]),c_0_339]) ).
thf(c_0_342,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk89_0 )
| ~ ( in @ ( esk53_2 @ X2 @ esk89_0 ) @ esk88_0 ) ),
inference(spm,[status(thm)],[c_0_340,c_0_341]) ).
thf(c_0_343,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk53_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_344,negated_conjecture,
~ ( subset @ esk88_0 @ esk89_0 ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
thf(c_0_345,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_343]),c_0_344]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU726^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 18:05:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 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
% 11.26/2.12 # Version: 3.1.0-ho
% 11.26/2.12 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.26/2.12 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.26/2.12 # Starting ehoh_best5 with 300s (1) cores
% 11.26/2.12 # Starting almost_fo_3_lam with 300s (1) cores
% 11.26/2.12 # Starting new_bool_5 with 300s (1) cores
% 11.26/2.12 # Starting pre_casc_3 with 300s (1) cores
% 11.26/2.12 # Starting ho_unfolding_8 with 300s (1) cores
% 11.26/2.12 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.26/2.12 # Starting new_bool_3 with 300s (1) cores
% 11.26/2.12 # Starting new_ho_5 with 300s (1) cores
% 11.26/2.12 # new_ho_5 with pid 25139 completed with status 8
% 11.26/2.12 # new_bool_3 with pid 25138 completed with status 0
% 11.26/2.12 # Result found by new_bool_3
% 11.26/2.12 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.26/2.12 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.26/2.12 # Starting ehoh_best5 with 300s (1) cores
% 11.26/2.12 # Starting almost_fo_3_lam with 300s (1) cores
% 11.26/2.12 # Starting new_bool_5 with 300s (1) cores
% 11.26/2.12 # Starting pre_casc_3 with 300s (1) cores
% 11.26/2.12 # Starting ho_unfolding_8 with 300s (1) cores
% 11.26/2.12 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.26/2.12 # Starting new_bool_3 with 300s (1) cores
% 11.26/2.12 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.26/2.12 # Search class: HGHSM-FSLM32-MHFMMSBN
% 11.26/2.12 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 11.26/2.12 # Starting ho_unfolding_8 with 61s (1) cores
% 11.26/2.12 # ho_unfolding_8 with pid 25201 completed with status 0
% 11.26/2.12 # Result found by ho_unfolding_8
% 11.26/2.12 # Preprocessing class: HSLMSLSSLLLCHFA.
% 11.26/2.12 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 11.26/2.12 # Starting ehoh_best5 with 300s (1) cores
% 11.26/2.12 # Starting almost_fo_3_lam with 300s (1) cores
% 11.26/2.12 # Starting new_bool_5 with 300s (1) cores
% 11.26/2.12 # Starting pre_casc_3 with 300s (1) cores
% 11.26/2.12 # Starting ho_unfolding_8 with 300s (1) cores
% 11.26/2.12 # Starting new_ho_10_cnf2 with 300s (1) cores
% 11.26/2.12 # Starting new_bool_3 with 300s (1) cores
% 11.26/2.12 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.26/2.12 # Search class: HGHSM-FSLM32-MHFMMSBN
% 11.26/2.12 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 11.26/2.12 # Starting ho_unfolding_8 with 61s (1) cores
% 11.26/2.12 # Preprocessing time : 0.062 s
% 11.26/2.12 # Presaturation interreduction done
% 11.26/2.12
% 11.26/2.12 # Proof found!
% 11.26/2.12 # SZS status Theorem
% 11.26/2.12 # SZS output start CNFRefutation
% See solution above
% 11.26/2.12 # Parsed axioms : 527
% 11.26/2.12 # Removed by relevancy pruning/SinE : 281
% 11.26/2.12 # Initial clauses : 427
% 11.26/2.12 # Removed in clause preprocessing : 29
% 11.26/2.12 # Initial clauses in saturation : 398
% 11.26/2.12 # Processed clauses : 3186
% 11.26/2.12 # ...of these trivial : 26
% 11.26/2.12 # ...subsumed : 1394
% 11.26/2.12 # ...remaining for further processing : 1766
% 11.26/2.12 # Other redundant clauses eliminated : 66
% 11.26/2.12 # Clauses deleted for lack of memory : 0
% 11.26/2.12 # Backward-subsumed : 95
% 11.26/2.12 # Backward-rewritten : 17
% 11.26/2.12 # Generated clauses : 71279
% 11.26/2.12 # ...of the previous two non-redundant : 69415
% 11.26/2.12 # ...aggressively subsumed : 0
% 11.26/2.12 # Contextual simplify-reflections : 5
% 11.26/2.12 # Paramodulations : 71165
% 11.26/2.12 # Factorizations : 22
% 11.26/2.12 # NegExts : 2
% 11.26/2.12 # Equation resolutions : 74
% 11.26/2.12 # Disequality decompositions : 0
% 11.26/2.12 # Total rewrite steps : 5656
% 11.26/2.12 # ...of those cached : 5437
% 11.26/2.12 # Propositional unsat checks : 0
% 11.26/2.12 # Propositional check models : 0
% 11.26/2.12 # Propositional check unsatisfiable : 0
% 11.26/2.12 # Propositional clauses : 0
% 11.26/2.12 # Propositional clauses after purity: 0
% 11.26/2.12 # Propositional unsat core size : 0
% 11.26/2.12 # Propositional preprocessing time : 0.000
% 11.26/2.12 # Propositional encoding time : 0.000
% 11.26/2.12 # Propositional solver time : 0.000
% 11.26/2.12 # Success case prop preproc time : 0.000
% 11.26/2.12 # Success case prop encoding time : 0.000
% 11.26/2.12 # Success case prop solver time : 0.000
% 11.26/2.12 # Current number of processed clauses : 1292
% 11.26/2.12 # Positive orientable unit clauses : 54
% 11.26/2.12 # Positive unorientable unit clauses: 0
% 11.26/2.12 # Negative unit clauses : 53
% 11.26/2.12 # Non-unit-clauses : 1185
% 11.26/2.12 # Current number of unprocessed clauses: 66848
% 11.26/2.12 # ...number of literals in the above : 255142
% 11.26/2.12 # Current number of archived formulas : 0
% 11.26/2.12 # Current number of archived clauses : 459
% 11.26/2.12 # Clause-clause subsumption calls (NU) : 152992
% 11.26/2.12 # Rec. Clause-clause subsumption calls : 77550
% 11.26/2.12 # Non-unit clause-clause subsumptions : 977
% 11.26/2.12 # Unit Clause-clause subsumption calls : 2154
% 11.26/2.12 # Rewrite failures with RHS unbound : 0
% 11.26/2.12 # BW rewrite match attempts : 48
% 11.26/2.12 # BW rewrite match successes : 12
% 11.26/2.12 # Condensation attempts : 0
% 11.26/2.12 # Condensation successes : 0
% 11.26/2.12 # Termbank termtop insertions : 1384141
% 11.26/2.12 # Search garbage collected termcells : 25103
% 11.26/2.12
% 11.26/2.12 # -------------------------------------------------
% 11.26/2.12 # User time : 1.475 s
% 11.26/2.12 # System time : 0.072 s
% 11.26/2.12 # Total time : 1.547 s
% 11.26/2.12 # Maximum resident set size: 8056 pages
% 11.26/2.12
% 11.26/2.12 # -------------------------------------------------
% 11.26/2.12 # User time : 1.592 s
% 11.26/2.12 # System time : 0.115 s
% 11.26/2.12 # Total time : 1.707 s
% 11.26/2.12 # Maximum resident set size: 2616 pages
% 11.26/2.12 % E---3.1 exiting
% 11.26/2.12 % E exiting
%------------------------------------------------------------------------------