TSTP Solution File: SEU716^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU716^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.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 03:29:26 EDT 2024
% Result : Theorem 9.30s 1.68s
% Output : CNFRefutation 9.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 589
% Syntax : Number of formulae : 680 ( 36 unt; 351 typ; 0 def)
% Number of atoms : 3014 ( 627 equ; 0 cnn)
% Maximal formula atoms : 932 ( 9 avg)
% Number of connectives : 12146 ( 815 ~; 907 |; 548 &;8076 @)
% ( 326 <=>;1474 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1059 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 589 ( 589 >; 0 *; 0 +; 0 <<)
% Number of symbols : 355 ( 351 usr; 241 con; 0-4 aty)
% Number of variables : 2618 ( 182 ^2313 !; 123 ?;2618 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
epred1_0: $o ).
thf(decl_293,type,
esk1_2: $i > $i > $i ).
thf(decl_294,type,
esk2_2: $i > $i > $i ).
thf(decl_295,type,
esk3_2: $i > $i > $i ).
thf(decl_296,type,
esk4_1: $i > $i ).
thf(decl_297,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_298,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_299,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_300,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_301,type,
esk9_1: $i > $i ).
thf(decl_302,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_303,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_304,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_305,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_306,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_307,type,
esk15_2: $i > $i > $i ).
thf(decl_308,type,
esk16_2: $i > $i > $i ).
thf(decl_309,type,
esk17_1: $i > $i ).
thf(decl_310,type,
esk18_1: $i > $i ).
thf(decl_311,type,
esk19_1: $i > $i ).
thf(decl_312,type,
esk20_2: $i > $i > $i ).
thf(decl_313,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_314,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_315,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_316,type,
esk24_1: $i > $i ).
thf(decl_317,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_318,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_319,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_320,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_321,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_322,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_323,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_324,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_325,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_326,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_327,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_328,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_329,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_330,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_331,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_332,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_333,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_334,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_335,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_336,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_337,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_338,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_339,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_340,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_341,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_342,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_343,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_344,type,
esk52_2: $i > $i > $i ).
thf(decl_345,type,
esk53_2: $i > $i > $i ).
thf(decl_346,type,
esk54_2: $i > $i > $i ).
thf(decl_347,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_348,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_349,type,
esk57_2: $i > $i > $i ).
thf(decl_350,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_351,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_354,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_355,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_356,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_357,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_358,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_359,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_360,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_361,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_364,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_365,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_366,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_367,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_368,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_369,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_370,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_371,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_372,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_373,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_374,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_375,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_376,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_377,type,
esk85_0: $i ).
thf(decl_378,type,
esk86_0: $i ).
thf(decl_379,type,
esk87_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(subsetTI,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
=> ! [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(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(c_0_237,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_238,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_239,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_240,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_241,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_242,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_243,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_244,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_245,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_246,plain,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuI3]) ).
thf(c_0_247,plain,
( 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_248,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_249,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_250,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_251,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_252,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_253,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_254,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_255,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_256,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_257,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_258,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_259,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X767: $i] :
( ( X6 @ X2 @ X767 )
& ! [X768: $i] :
( ( X6 @ X2 @ X768 )
=> ( X767 = X768 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_237,c_0_238]) ).
thf(c_0_260,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X769: $i] :
( ( X1 @ X769 )
& ! [X770: $i] :
( ( X1 @ X770 )
=> ( X769 = X770 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_239,c_0_238]) ).
thf(c_0_261,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_262,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_263,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_264,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X771: $i] :
( ( X1 @ X771 )
& ! [X772: $i] :
( ( X1 @ X772 )
=> ( X771 = X772 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_240,c_0_238]) ).
thf(c_0_265,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X773: $i] :
( ( X1 @ X773 )
& ! [X774: $i] :
( ( X1 @ X774 )
=> ( X773 = X774 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_241,c_0_238]) ).
thf(c_0_266,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_267,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_242]) ).
thf(c_0_268,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_243,c_0_242]) ).
thf(c_0_269,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_242]) ).
thf(c_0_270,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_271,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X775: $i] :
( ( X1 @ X775 )
& ! [X776: $i] :
( ( X1 @ X776 )
=> ( X775 = X776 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_244,c_0_238]) ).
thf(c_0_272,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_242]) ).
thf(c_0_273,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_274,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X777: $i] :
( ( X1 @ X777 )
& ! [X778: $i] :
( ( X1 @ X778 )
=> ( X777 = X778 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_245,c_0_238]) ).
thf(c_0_275,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X779: $i] :
( ( X1 @ X779 )
& ! [X780: $i] :
( ( X1 @ X780 )
=> ( X779 = X780 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_246,c_0_238]) ).
thf(c_0_276,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X781: $i] :
( ( X1 @ X781 )
& ! [X782: $i] :
( ( X1 @ X782 )
=> ( X781 = X782 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_247,c_0_238]) ).
thf(c_0_277,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X783: $i] :
( ( X1 @ X783 )
& ! [X784: $i] :
( ( X1 @ X784 )
=> ( X783 = X784 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_248,c_0_238]) ).
thf(c_0_278,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X785: $i] :
( ( X1 @ X785 )
& ! [X786: $i] :
( ( X1 @ X786 )
=> ( X785 = X786 ) ) )
<=> ? [X787: $i] :
( ( X17 @ X787 )
& ! [X788: $i] :
( ( X17 @ X788 )
=> ( X787 = X788 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_249,c_0_238]) ).
thf(c_0_279,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X789: $i] :
( ( X1 @ X789 )
& ! [X790: $i] :
( ( X1 @ X790 )
=> ( X789 = X790 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_250,c_0_238]) ).
thf(c_0_280,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X791: $i] :
( ( X1 @ X791 )
& ! [X792: $i] :
( ( X1 @ X792 )
=> ( X791 = X792 ) ) )
=> ( ? [X793: $i] :
( ( X17 @ X793 )
& ! [X794: $i] :
( ( X17 @ X794 )
=> ( X793 = X794 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_251,c_0_238]) ).
thf(c_0_281,plain,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( dsetconstr @ X5
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).
thf(c_0_282,plain,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ ( powerset @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[sepInPowerset]) ).
thf(c_0_283,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_284,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_285,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_252,c_0_253]) ).
thf(c_0_286,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_254,c_0_253]) ).
thf(c_0_287,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_255,c_0_253]) ).
thf(c_0_288,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_289,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_290,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_291,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_292,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_256,c_0_257]) ).
thf(c_0_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_257]) ).
thf(c_0_303,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_257]) ).
thf(c_0_304,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_258,c_0_253]) ).
thf(c_0_305,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_257]) ).
thf(c_0_306,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_257]) ).
thf(c_0_307,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_308,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_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,plain,
( epred1_0
<=> ! [X824: $i] :
? [X825: $i] :
( ! [X826: $i] :
( ( in @ X826 @ X825 )
=> ! [X827: $i] :
( ( in @ X827 @ X826 )
=> ( in @ X827 @ X824 ) ) )
& ! [X828: $i,X829: $i] :
( ( ( in @ X828 @ X824 )
& ( in @ X829 @ X824 ) )
=> ( ! [X830: $i] :
( ( in @ X830 @ X825 )
=> ( ( in @ X828 @ X830 )
<=> ( in @ X829 @ X830 ) ) )
=> ( X828 = X829 ) ) )
& ! [X831: $i,X832: $i] :
( ( ( in @ X831 @ X825 )
& ( in @ X832 @ X825 ) )
=> ( ! [X833: $i] :
( ( in @ X833 @ X831 )
=> ( in @ X833 @ X832 ) )
| ! [X834: $i] :
( ( in @ X834 @ X832 )
=> ( in @ X834 @ X831 ) ) ) )
& ! [X835: $i] :
( ( ! [X836: $i] :
( ( in @ X836 @ X835 )
=> ( in @ X836 @ X824 ) )
& ? [X837: $i] : ( in @ X837 @ X835 ) )
=> ? [X838: $i,X839: $i] :
( ( in @ X838 @ X825 )
& ( in @ X839 @ X835 )
& ~ ? [X840: $i] :
( ( in @ X840 @ X838 )
& ( in @ X840 @ X835 ) )
& ! [X841: $i] :
( ( in @ X841 @ X825 )
=> ( ! [X842: $i] :
( ( in @ X842 @ X841 )
=> ( in @ X842 @ X838 ) )
| ( in @ X839 @ X841 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_318,negated_conjecture,
~ ( ! [X795: $i,X796: $i] :
( ! [X797: $i] :
( ( in @ X797 @ X795 )
<=> ( in @ X797 @ X796 ) )
=> ( X795 = X796 ) )
=> ( ! [X798: $i] :
~ ( in @ X798 @ emptyset )
=> ( ! [X799: $i,X800: $i,X801: $i] :
( ( in @ X801 @ ( setadjoin @ X799 @ X800 ) )
<=> ( ( X801 = X799 )
| ( in @ X801 @ X800 ) ) )
=> ( ! [X802: $i,X803: $i] :
( ( in @ X803 @ ( powerset @ X802 ) )
<=> ! [X804: $i] :
( ( in @ X804 @ X803 )
=> ( in @ X804 @ X802 ) ) )
=> ( ! [X805: $i,X806: $i] :
( ( in @ X806 @ ( setunion @ X805 ) )
<=> ? [X807: $i] :
( ( in @ X806 @ X807 )
& ( in @ X807 @ X805 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X808: $i] :
( ( in @ X808 @ omega )
=> ( in @ ( setadjoin @ X808 @ X808 ) @ omega ) )
=> ( ! [X809: $i] :
( ( ( in @ emptyset @ X809 )
& ! [X810: $i] :
( ( ( in @ X810 @ omega )
& ( in @ X810 @ X809 ) )
=> ( in @ ( setadjoin @ X810 @ X810 ) @ X809 ) ) )
=> ! [X811: $i] :
( ( in @ X811 @ omega )
=> ( in @ X811 @ X809 ) ) )
=> ( ! [X812: $i > $i > $o,X813: $i] :
( ! [X814: $i] :
( ( in @ X814 @ X813 )
=> ? [X815: $i] :
( ( X812 @ X814 @ X815 )
& ! [X816: $i] :
( ( X812 @ X814 @ X816 )
=> ( X815 = X816 ) ) ) )
=> ? [X817: $i] :
! [X818: $i] :
( ( in @ X818 @ X817 )
<=> ? [X819: $i] :
( ( in @ X819 @ X813 )
& ( X812 @ X819 @ X818 ) ) ) )
=> ( ! [X820: $i] :
( ? [X821: $i] : ( in @ X821 @ X820 )
=> ? [X822: $i] :
( ( in @ X822 @ X820 )
& ~ ? [X823: $i] :
( ( in @ X823 @ X822 )
& ( in @ X823 @ X820 ) ) ) )
=> ( epred1_0
=> ( ! [X843: $i > $o] :
( ? [X844: $i] :
( ( X843 @ X844 )
& ! [X845: $i] :
( ( X843 @ X845 )
=> ( X844 = X845 ) ) )
=> ( X843
@ ( descr
@ ^ [Z0: $i] : ( X843 @ Z0 ) ) ) )
=> ( ! [X846: $i,X847: $i > $o,X848: $i] :
( ( in @ X848 @ X846 )
=> ( ( X847 @ X848 )
=> ( in @ X848 @ ( dsetconstr @ X846 @ X847 ) ) ) )
=> ( ! [X849: $i,X850: $i > $o,X851: $i] :
( ( in @ X851 @ ( dsetconstr @ X849 @ X850 ) )
=> ( in @ X851 @ X849 ) )
=> ( ! [X852: $i,X853: $i > $o,X854: $i] :
( ( in @ X854 @ ( dsetconstr @ X852 @ X853 ) )
=> ( X853 @ X854 ) )
=> ( ! [X855: $i > $o] :
( ? [X856: $i] :
( ( X855 @ X856 )
& ! [X857: $i] :
( ( X855 @ X857 )
=> ( X856 = X857 ) ) )
=> ? [X858: $i] :
( ( X855 @ X858 )
& ! [X859: $i] :
( ( X855 @ X859 )
=> ( X858 = X859 ) ) ) )
=> ( ! [X860: $o,X861: $i] :
( ( in @ X861 @ ( prop2set @ X860 ) )
=> X860 )
=> ( ! [X862: $i] :
( ( in @ X862 @ emptyset )
=> ! [X863: $o] : X863 )
=> ( ! [X864: $i] :
( ( in @ X864 @ emptyset )
=> ~ $true )
=> ( ! [X865: $i] :
~ ( in @ X865 @ emptyset )
=> ( ! [X866: $i > $o] :
( ? [X867: $i] :
( ( X866 @ X867 )
& ! [X868: $i] :
( ( X866 @ X868 )
=> ( X867 = X868 ) ) )
=> ? [X869: $i] : ( X866 @ X869 ) )
=> ( ! [X870: $i,X871: $i] :
( ! [X872: $i] :
( ( in @ X872 @ X870 )
=> ( in @ X872 @ X871 ) )
=> ( ! [X873: $i] :
( ( in @ X873 @ X871 )
=> ( in @ X873 @ X870 ) )
=> ( X870 = X871 ) ) )
=> ( ! [X874: $i] :
( ! [X875: $i] :
~ ( in @ X875 @ X874 )
=> ( X874 = emptyset ) )
=> ( ! [X876: $i] :
( ! [X877: $i] :
~ ( in @ X877 @ X876 )
=> ( X876 = emptyset ) )
=> ( ! [X878: $i,X879: $i > $o,X880: $i] :
( ( in @ X880 @ X878 )
=> ( ( in @ X880 @ ( dsetconstr @ X878 @ X879 ) )
<=> ( X879 @ X880 ) ) )
=> ( ! [X881: $i] :
( ( X881 != emptyset )
=> ? [X882: $i] : ( in @ X882 @ X881 ) )
=> ( ! [X883: $i,X884: $i > $o,X885: $i] :
( ( in @ X885 @ X883 )
=> ( ( X884 @ X885 )
=> ( ( dsetconstr @ X883 @ X884 )
!= emptyset ) ) )
=> ( ! [X886: $i] :
( ? [X887: $i] : ( in @ X887 @ X886 )
=> ( X886 != emptyset ) )
=> ( ! [X888: $i,X889: $i] : ( in @ X888 @ ( setadjoin @ X888 @ X889 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X890: $i,X891: $i,X892: $i] :
( ( in @ X892 @ X891 )
=> ( in @ X892 @ ( setadjoin @ X890 @ X891 ) ) )
=> ( ! [X893: $i,X894: $i,X895: $i] :
( ( in @ X895 @ ( setadjoin @ X893 @ X894 ) )
=> ! [X896: $o] :
( ( ( X895 = X893 )
=> X896 )
=> ( ( ( in @ X895 @ X894 )
=> X896 )
=> X896 ) ) )
=> ( ! [X897: $i,X898: $i,X899: $i] :
( ( in @ X899 @ ( setadjoin @ X897 @ X898 ) )
=> ( ( X899 = X897 )
| ( in @ X899 @ X898 ) ) )
=> ( ! [X900: $i] :
( ( dsetconstr @ X900
@ ^ [Z0: $i] : $true )
= X900 )
=> ( ! [X901: $i,X902: $i] :
( ! [X903: $i] :
( ( in @ X903 @ X902 )
=> ( in @ X903 @ X901 ) )
=> ( in @ X902 @ ( powerset @ X901 ) ) )
=> ( ! [X904: $i] : ( in @ emptyset @ ( powerset @ X904 ) )
=> ( ! [X905: $i] : ( in @ emptyset @ ( powerset @ X905 ) )
=> ( ! [X906: $i,X907: $i,X908: $i] :
( ( in @ X907 @ ( powerset @ X906 ) )
=> ( ( in @ X908 @ X907 )
=> ( in @ X908 @ X906 ) ) )
=> ( ! [X909: $i,X910: $i,X911: $i] :
( ( in @ X910 @ X911 )
=> ( ( in @ X911 @ X909 )
=> ( in @ X910 @ ( setunion @ X909 ) ) ) )
=> ( ! [X912: $i,X913: $i] :
( ( in @ X913 @ ( setunion @ X912 ) )
=> ! [X914: $o] :
( ! [X915: $i] :
( ( in @ X913 @ X915 )
=> ( ( in @ X915 @ X912 )
=> X914 ) )
=> X914 ) )
=> ( ! [X916: $i,X917: $i] :
( ( in @ X917 @ X916 )
=> ( in @ X917 @ ( powerset @ ( setunion @ X916 ) ) ) )
=> ( ! [X918: $i > $o] :
( ? [X919: $i] :
( ( X918 @ X919 )
& ! [X920: $i] :
( ( X918 @ X920 )
=> ( X919 = X920 ) ) )
=> ? [X921: $i] :
! [X922: $i] :
( ( X918 @ X922 )
<=> ( X922 = X921 ) ) )
=> ( ! [X923: $i] :
( ( X923 != emptyset )
=> ? [X924: $i] :
( ( in @ X924 @ X923 )
& $true ) )
=> ( ! [X925: $i,X926: $i] :
( ( in @ X925 @ ( setadjoin @ X926 @ emptyset ) )
=> ( X925 = X926 ) )
=> ( ! [X927: $i,X928: $i] :
( ( X927 != X928 )
=> ~ ( in @ X928 @ ( setadjoin @ X927 @ emptyset ) ) )
=> ( ! [X929: $i,X930: $i] :
( ( X929 = X930 )
=> ( in @ X929 @ ( setadjoin @ X930 @ emptyset ) ) )
=> ( ! [X931: $i,X932: $i] :
( ( in @ X931 @ ( setadjoin @ X932 @ emptyset ) )
=> ( in @ X932 @ ( setadjoin @ X931 @ emptyset ) ) )
=> ( ! [X933: $i,X934: $i,X935: $i] :
( ( in @ X935 @ ( setadjoin @ X933 @ ( setadjoin @ X934 @ emptyset ) ) )
=> ( ( X935 = X933 )
| ( X935 = X934 ) ) )
=> ( ! [X936: $i,X937: $i] : ( in @ X936 @ ( setadjoin @ X936 @ ( setadjoin @ X937 @ emptyset ) ) )
=> ( ! [X938: $i,X939: $i] : ( in @ X939 @ ( setadjoin @ X938 @ ( setadjoin @ X939 @ emptyset ) ) )
=> ( ! [X940: $i,X941: $i > $o] :
( ? [X942: $i] :
( ( in @ X942 @ X940 )
& ( X941 @ X942 ) )
=> ( ( ( dsetconstr @ X940 @ X941 )
= emptyset )
=> ~ $true ) )
=> ( ! [X943: $i > $o,X944: $i] :
( ( in @ X944 @ emptyset )
=> ( X943 @ X944 ) )
=> ( ! [X945: $i,X946: $i > $o] :
( ~ ! [X947: $i] :
( ( in @ X947 @ X945 )
=> ( X946 @ X947 ) )
=> ? [X948: $i] :
( ( in @ X948 @ X945 )
& ~ ( X946 @ X948 ) ) )
=> ( ! [X949: $i,X950: $i > $o] :
( ! [X951: $i] :
( ( in @ X951 @ X949 )
=> ~ ( X950 @ X951 ) )
=> ~ ? [X952: $i] :
( ( in @ X952 @ X949 )
& ( X950 @ X952 ) ) )
=> ( ! [X953: $i,X954: $i > $o] :
( ~ ? [X955: $i] :
( ( in @ X955 @ X953 )
& ( X954 @ X955 ) )
=> ! [X956: $i] :
( ( in @ X956 @ X953 )
=> ~ ( X954 @ X956 ) ) )
=> ( ! [X957: $i,X958: $i > $o] :
( ? [X959: $i] :
( ( in @ X959 @ X957 )
& ~ ( X958 @ X959 ) )
=> ~ ! [X960: $i] :
( ( in @ X960 @ X957 )
=> ( X958 @ X960 ) ) )
=> ( ! [X961: $o] :
( X961
=> ( in @ emptyset @ ( prop2set @ X961 ) ) )
=> ( ! [X962: $o] :
( X962
=> ( set2prop @ ( prop2set @ X962 ) ) )
=> ( ! [X963: $i,X964: $i > $o] :
( ~ ? [X965: $i] :
( ( in @ X965 @ X963 )
& ( X964 @ X965 ) )
=> ! [X966: $i] :
( ( in @ X966 @ X963 )
=> ~ ( X964 @ X966 ) ) )
=> ( ! [X967: $i,X968: $i > $o] :
( ~ ! [X969: $i] :
( ( in @ X969 @ X967 )
=> ( X968 @ X969 ) )
=> ? [X970: $i] :
( ( in @ X970 @ X967 )
& ~ ( X968 @ X970 ) ) )
=> ( ! [X971: $i > $o] :
( ? [X972: $i] :
( ( X971 @ X972 )
& ! [X973: $i] :
( ( X971 @ X973 )
=> ( X972 = X973 ) ) )
=> ? [X974: $i] :
( ( X971 @ X974 )
& ! [X975: $i] :
( ( X971 @ X975 )
=> ( X974 = X975 ) ) ) )
=> ( ! [X976: $i > $o] :
( ? [X977: $i] : ( X976 @ X977 )
=> ( ! [X978: $i,X979: $i] :
( ( X976 @ X978 )
=> ( ( X976 @ X979 )
=> ( X978 = X979 ) ) )
=> ? [X980: $i] :
( ( X976 @ X980 )
& ! [X981: $i] :
( ( X976 @ X981 )
=> ( X980 = X981 ) ) ) ) )
=> ( ! [X982: $i > $o] :
( ? [X983: $i] :
! [X984: $i] :
( ( X982 @ X984 )
<=> ( X984 = X983 ) )
=> ? [X985: $i] :
( ( X982 @ X985 )
& ! [X986: $i] :
( ( X982 @ X986 )
=> ( X985 = X986 ) ) ) )
=> ( ! [X987: $i,X988: $i] :
( ( X987 = X988 )
=> ! [X989: $i,X990: $i] :
( ( X989 = X990 )
=> ( ( in @ X989 @ X987 )
=> ( in @ X990 @ X988 ) ) ) )
=> ( ! [X991: $i,X992: $i] :
( ( X991 = X992 )
=> ! [X993: $i,X994: $i] :
( ( X993 = X994 )
=> ( ( in @ X993 @ X991 )
<=> ( in @ X994 @ X992 ) ) ) )
=> ( ! [X995: $i > $o] :
( ? [X996: $i] :
( ( X995 @ X996 )
& ! [X997: $i] :
( ( X995 @ X997 )
=> ( X996 = X997 ) ) )
=> ! [X998: $i,X999: $i] :
( ( X995 @ X998 )
=> ( ( X995 @ X999 )
=> ( X998 = X999 ) ) ) )
=> ( ! [X1000: $i > $o,X1001: $i > $o] :
( ! [X1002: $i,X1003: $i] :
( ( X1002 = X1003 )
=> ( ( X1000 @ X1002 )
<=> ( X1001 @ X1003 ) ) )
=> ( ? [X1004: $i] :
( ( X1000 @ X1004 )
& ! [X1005: $i] :
( ( X1000 @ X1005 )
=> ( X1004 = X1005 ) ) )
<=> ? [X1006: $i] :
( ( X1001 @ X1006 )
& ! [X1007: $i] :
( ( X1001 @ X1007 )
=> ( X1006 = X1007 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1008: $i,X1009: $i] :
( ( X1008 = X1009 )
=> ! [X1010: $i,X1011: $i] :
( ( X1010 = X1011 )
=> ( ( setadjoin @ X1008 @ X1010 )
= ( setadjoin @ X1009 @ X1011 ) ) ) )
=> ( ! [X1012: $i,X1013: $i] :
( ( X1012 = X1013 )
=> ( ( powerset @ X1012 )
= ( powerset @ X1013 ) ) )
=> ( ! [X1014: $i,X1015: $i] :
( ( X1014 = X1015 )
=> ( ( setunion @ X1014 )
= ( setunion @ X1015 ) ) )
=> ( ( omega = omega )
=> ( ! [X1016: $i > $o] :
( ? [X1017: $i] :
( ( X1016 @ X1017 )
& ! [X1018: $i] :
( ( X1016 @ X1018 )
=> ( X1017 = X1018 ) ) )
=> ! [X1019: $i,X1020: $i] :
( ( X1016 @ X1019 )
=> ( ( X1016 @ X1020 )
=> ( X1019 = X1020 ) ) ) )
=> ( ! [X1021: $i > $o,X1022: $i > $o] :
( ! [X1023: $i,X1024: $i] :
( ( X1023 = X1024 )
=> ( ( X1021 @ X1023 )
<=> ( X1022 @ X1024 ) ) )
=> ( ? [X1025: $i] :
( ( X1021 @ X1025 )
& ! [X1026: $i] :
( ( X1021 @ X1026 )
=> ( X1025 = X1026 ) ) )
=> ( ? [X1027: $i] :
( ( X1022 @ X1027 )
& ! [X1028: $i] :
( ( X1022 @ X1028 )
=> ( X1027 = X1028 ) ) )
=> ( ( descr @ X1021 )
= ( descr @ X1022 ) ) ) ) )
=> ( ! [X1029: $i,X1030: $i] :
( ( X1029 = X1030 )
=> ! [X1031: $i > $o,X1032: $i > $o] :
( ! [X1033: $i] :
( ( in @ X1033 @ X1029 )
=> ! [X1034: $i] :
( ( in @ X1034 @ X1030 )
=> ( ( X1033 = X1034 )
=> ( ( X1031 @ X1033 )
<=> ( X1032 @ X1034 ) ) ) ) )
=> ( ( dsetconstr @ X1029 @ X1031 )
= ( dsetconstr @ X1030 @ X1032 ) ) ) )
=> ( ! [X1035: $i,X1036: $i] :
( ! [X1037: $i] :
( ( in @ X1037 @ X1035 )
=> ( in @ X1037 @ X1036 ) )
=> ( subset @ X1035 @ X1036 ) )
=> ( ! [X1038: $i,X1039: $i] :
( ( X1038 = X1039 )
=> ( subset @ X1039 @ X1038 ) )
=> ( ! [X1040: $i,X1041: $i] :
( ( X1040 = X1041 )
=> ( subset @ X1040 @ X1041 ) )
=> ( ! [X1042: $i,X1043: $i] :
( ! [X1044: $i] :
( ( in @ X1044 @ X1042 )
=> ( in @ X1044 @ X1043 ) )
=> ( subset @ X1042 @ X1043 ) )
=> ( ! [X1045: $i] : ( subset @ emptyset @ X1045 )
=> ( ! [X1046: $i,X1047: $i,X1048: $i] :
( ( subset @ X1046 @ X1047 )
=> ( ( in @ X1048 @ X1046 )
=> ( in @ X1048 @ X1047 ) ) )
=> ( ! [X1049: $i,X1050: $i,X1051: $i] :
( ( subset @ X1049 @ X1050 )
=> ( ~ ( in @ X1051 @ X1050 )
=> ~ ( in @ X1051 @ X1049 ) ) )
=> ( ! [X1052: $i,X1053: $i,X1054: $i] :
( ( in @ X1054 @ X1052 )
=> ( ~ ( in @ X1054 @ X1053 )
=> ~ ( subset @ X1052 @ X1053 ) ) )
=> ( ! [X1055: $i,X1056: $i] :
( ~ ( subset @ X1055 @ X1056 )
=> ( X1055 != X1056 ) )
=> ( ! [X1057: $i,X1058: $i,X1059: $i] :
( ( in @ X1059 @ X1057 )
=> ( ~ ( in @ X1059 @ X1058 )
=> ( X1057 != X1058 ) ) )
=> ( ! [X1060: $i] : ( subset @ X1060 @ X1060 )
=> ( ! [X1061: $i,X1062: $i,X1063: $i] :
( ( subset @ X1061 @ X1062 )
=> ( ( subset @ X1062 @ X1063 )
=> ( subset @ X1061 @ X1063 ) ) )
=> ( ! [X1064: $i,X1065: $i] : ( subset @ X1065 @ ( setadjoin @ X1064 @ X1065 ) )
=> ( ! [X1066: $i,X1067: $i,X1068: $i] :
( ( subset @ X1066 @ X1068 )
=> ( subset @ X1066 @ ( setadjoin @ X1067 @ X1068 ) ) )
=> ( ! [X1069: $i,X1070: $i] :
( ( subset @ X1069 @ X1070 )
=> ( in @ X1069 @ ( powerset @ X1070 ) ) )
=> ( ! [X1071: $i,X1072: $i] :
( ( subset @ X1071 @ X1072 )
=> ( ( subset @ X1072 @ X1071 )
=> ( X1071 = X1072 ) ) )
=> ( ! [X1073: $i] :
( ( subset @ X1073 @ emptyset )
=> ( X1073 = emptyset ) )
=> ( ! [X1074: $i,X1075: $i] :
( ( subset @ X1075 @ X1074 )
=> ( in @ X1075 @ ( powerset @ X1074 ) ) )
=> ( ! [X1076: $i,X1077: $i] :
( ( in @ X1077 @ ( powerset @ X1076 ) )
=> ( subset @ X1077 @ X1076 ) )
=> ( ! [X1078: $i] : ( in @ X1078 @ ( powerset @ X1078 ) )
=> ( ! [X1079: $i,X1080: $i] :
( ( subset @ X1079 @ X1080 )
=> ( subset @ ( powerset @ X1079 ) @ ( powerset @ X1080 ) ) )
=> ( ! [X1081: $i,X1082: $i > $o] : ( in @ ( dsetconstr @ X1081 @ X1082 ) @ ( powerset @ X1081 ) )
=> ( ! [X1083: $i,X1084: $i > $o] : ( subset @ ( dsetconstr @ X1083 @ X1084 ) @ X1083 )
=> ( ! [X1085: $i,X1086: $i,X1087: $i] :
( ( in @ X1087 @ X1085 )
=> ( in @ X1087 @ ( binunion @ X1085 @ X1086 ) ) )
=> ( ! [X1088: $i,X1089: $i] : ( in @ X1089 @ ( setadjoin @ X1088 @ ( setadjoin @ X1089 @ emptyset ) ) )
=> ( ! [X1090: $i,X1091: $i,X1092: $i] :
( ( in @ X1092 @ X1091 )
=> ( in @ X1092 @ ( binunion @ X1090 @ X1091 ) ) )
=> ( ! [X1093: $i,X1094: $i,X1095: $i,X1096: $o] :
( ( in @ X1095 @ ( binunion @ X1093 @ X1094 ) )
=> ( ( ( in @ X1095 @ X1093 )
=> X1096 )
=> ( ( ( in @ X1095 @ X1094 )
=> X1096 )
=> X1096 ) ) )
=> ( ! [X1097: $i,X1098: $i,X1099: $i] :
( ( in @ X1099 @ ( binunion @ X1097 @ X1098 ) )
=> ( ( in @ X1099 @ X1097 )
| ( in @ X1099 @ X1098 ) ) )
=> ( ! [X1100: $i,X1101: $i] : ( subset @ X1100 @ ( binunion @ X1100 @ X1101 ) )
=> ( ! [X1102: $i,X1103: $i] : ( subset @ X1103 @ ( binunion @ X1102 @ X1103 ) )
=> ( ! [X1104: $i,X1105: $i,X1106: $i] :
( ( in @ X1106 @ X1104 )
=> ( ( in @ X1106 @ X1105 )
=> ( in @ X1106 @ ( binintersect @ X1104 @ X1105 ) ) ) )
=> ( ! [X1107: $i,X1108: $i,X1109: $i] :
( ( subset @ X1109 @ X1107 )
=> ( ( subset @ X1109 @ X1108 )
=> ( subset @ X1109 @ ( binintersect @ X1107 @ X1108 ) ) ) )
=> ( ! [X1110: $i,X1111: $i,X1112: $i] :
( ( in @ X1112 @ ( binintersect @ X1110 @ X1111 ) )
=> ( in @ X1112 @ X1110 ) )
=> ( ! [X1113: $i,X1114: $i] : ( subset @ ( binintersect @ X1113 @ X1114 ) @ X1113 )
=> ( ! [X1115: $i,X1116: $i] :
( ( subset @ X1115 @ X1116 )
=> ( ( binintersect @ X1115 @ X1116 )
= X1115 ) )
=> ( ! [X1117: $i,X1118: $i] :
( ( ( binintersect @ X1117 @ X1118 )
= X1118 )
=> ( subset @ X1118 @ X1117 ) )
=> ( ! [X1119: $i,X1120: $i,X1121: $i] :
( ( in @ X1121 @ ( binintersect @ X1119 @ X1120 ) )
=> ( in @ X1121 @ X1120 ) )
=> ( ! [X1122: $i,X1123: $i] :
( ~ ? [X1124: $i] :
( ( in @ X1124 @ X1122 )
& ( in @ X1124 @ X1123 ) )
=> ( ( binintersect @ X1122 @ X1123 )
= emptyset ) )
=> ( ! [X1125: $i,X1126: $i] : ( subset @ ( binintersect @ X1125 @ X1126 ) @ X1126 )
=> ( ! [X1127: $i,X1128: $i] :
( ( subset @ X1128 @ X1127 )
=> ( ( binintersect @ X1127 @ X1128 )
= X1128 ) )
=> ( ! [X1129: $i,X1130: $i] :
( ( ( binintersect @ X1129 @ X1130 )
= X1129 )
=> ( subset @ X1129 @ X1130 ) )
=> ( ! [X1131: $i,X1132: $i,X1133: $i] :
( ( binintersect @ X1131 @ ( binunion @ X1132 @ X1133 ) )
= ( binunion @ ( binintersect @ X1131 @ X1132 ) @ ( binintersect @ X1131 @ X1133 ) ) )
=> ( ! [X1134: $i,X1135: $i,X1136: $i] :
( ( in @ X1136 @ X1134 )
=> ( ~ ( in @ X1136 @ X1135 )
=> ( in @ X1136 @ ( setminus @ X1134 @ X1135 ) ) ) )
=> ( ! [X1137: $i,X1138: $i,X1139: $i] :
( ( in @ X1139 @ ( setminus @ X1137 @ X1138 ) )
=> ( in @ X1139 @ X1137 ) )
=> ( ! [X1140: $i,X1141: $i,X1142: $i] :
( ( in @ X1142 @ ( setminus @ X1140 @ X1141 ) )
=> ~ ( in @ X1142 @ X1141 ) )
=> ( ! [X1143: $i,X1144: $i] :
( ( subset @ X1143 @ X1144 )
=> ( ( setminus @ X1143 @ X1144 )
= emptyset ) )
=> ( ! [X1145: $i,X1146: $i,X1147: $i] :
( ~ ( in @ X1147 @ ( setminus @ X1145 @ X1146 ) )
=> ( ( in @ X1147 @ X1145 )
=> ( in @ X1147 @ X1146 ) ) )
=> ( ! [X1148: $i,X1149: $i,X1150: $i] :
( ~ ( in @ X1150 @ ( setminus @ X1148 @ X1149 ) )
=> ( ~ ( in @ X1150 @ X1149 )
=> ~ ( in @ X1150 @ X1148 ) ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i] :
( ~ ( in @ X1153 @ X1151 )
=> ~ ( in @ X1153 @ ( setminus @ X1151 @ X1152 ) ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ X1155 )
=> ~ ( in @ X1156 @ ( setminus @ X1154 @ X1155 ) ) )
=> ( ! [X1157: $i,X1158: $i] : ( subset @ ( setminus @ X1157 @ X1158 ) @ X1157 )
=> ( ! [X1159: $i,X1160: $i] :
( ( ( setminus @ X1159 @ X1160 )
= emptyset )
=> ( subset @ X1159 @ X1160 ) )
=> ( ! [X1161: $i,X1162: $i,X1163: $i] :
( ( in @ X1163 @ ( symdiff @ X1161 @ X1162 ) )
=> ! [X1164: $o] :
( ( ( in @ X1163 @ X1161 )
=> ( ~ ( in @ X1163 @ X1162 )
=> X1164 ) )
=> ( ( ~ ( in @ X1163 @ X1161 )
=> ( ( in @ X1163 @ X1162 )
=> X1164 ) )
=> X1164 ) ) )
=> ( ! [X1165: $i,X1166: $i,X1167: $i] :
( ( in @ X1167 @ X1165 )
=> ( ~ ( in @ X1167 @ X1166 )
=> ( in @ X1167 @ ( symdiff @ X1165 @ X1166 ) ) ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ~ ( in @ X1170 @ X1168 )
=> ( ( in @ X1170 @ X1169 )
=> ( in @ X1170 @ ( symdiff @ X1168 @ X1169 ) ) ) )
=> ( ! [X1171: $i,X1172: $i,X1173: $i] :
( ( in @ X1173 @ X1171 )
=> ( ( in @ X1173 @ X1172 )
=> ~ ( in @ X1173 @ ( symdiff @ X1171 @ X1172 ) ) ) )
=> ( ! [X1174: $i,X1175: $i,X1176: $i] :
( ~ ( in @ X1176 @ X1174 )
=> ( ~ ( in @ X1176 @ X1175 )
=> ~ ( in @ X1176 @ ( symdiff @ X1174 @ X1175 ) ) ) )
=> ( ! [X1177: $i,X1178: $i] : ( in @ X1178 @ ( setadjoin @ X1177 @ ( setadjoin @ X1178 @ emptyset ) ) )
=> ( ! [X1179: $i,X1180: $i] : ( in @ X1179 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1179 @ ( setadjoin @ X1180 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1181: $i,X1182: $i] : ( in @ X1182 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1181 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1181 @ ( setadjoin @ X1182 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1183: $i,X1184: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1183 @ ( setadjoin @ X1184 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1185: $i,X1186: $i] : ( iskpair @ ( kpair @ X1185 @ X1186 ) )
=> ( ! [X1187: $i,X1188: $i] :
( ( in @ X1188 @ X1187 )
=> ( subset @ ( setadjoin @ X1188 @ emptyset ) @ X1187 ) )
=> ( ! [X1189: $i,X1190: $i] :
( ( in @ X1190 @ X1189 )
=> ( in @ ( setadjoin @ X1190 @ emptyset ) @ ( powerset @ X1189 ) ) )
=> ( ! [X1191: $i,X1192: $i,X1193: $i] :
( ( in @ X1193 @ X1191 )
=> ( in @ ( setadjoin @ X1193 @ emptyset ) @ ( powerset @ ( binunion @ X1191 @ X1192 ) ) ) )
=> ( ! [X1194: $i,X1195: $i,X1196: $i] :
( ( in @ X1196 @ ( setadjoin @ X1194 @ ( setadjoin @ X1195 @ emptyset ) ) )
=> ( ( X1196 = X1194 )
| ( X1196 = X1195 ) ) )
=> ( ! [X1197: $i,X1198: $i,X1199: $i] :
( ( in @ X1199 @ X1197 )
=> ! [X1200: $i] :
( ( in @ X1200 @ X1198 )
=> ( subset @ ( setadjoin @ X1199 @ ( setadjoin @ X1200 @ emptyset ) ) @ ( binunion @ X1197 @ X1198 ) ) ) )
=> ( ! [X1201: $i,X1202: $i,X1203: $i] :
( ( in @ X1203 @ X1201 )
=> ! [X1204: $i] :
( ( in @ X1204 @ X1202 )
=> ( in @ ( setadjoin @ X1203 @ ( setadjoin @ X1204 @ emptyset ) ) @ ( powerset @ ( binunion @ X1201 @ X1202 ) ) ) ) )
=> ( ! [X1205: $i,X1206: $i,X1207: $i] :
( ( in @ X1207 @ X1205 )
=> ! [X1208: $i] :
( ( in @ X1208 @ X1206 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1207 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1207 @ ( setadjoin @ X1208 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1205 @ X1206 ) ) ) ) )
=> ( ! [X1209: $i,X1210: $i,X1211: $i] :
( ( in @ X1211 @ X1209 )
=> ! [X1212: $i] :
( ( in @ X1212 @ X1210 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1211 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1211 @ ( setadjoin @ X1212 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1209 @ X1210 ) ) ) ) ) )
=> ( ! [X1213: $i,X1214: $i,X1215: $i] :
( ( in @ X1215 @ X1213 )
=> ! [X1216: $i] :
( ( in @ X1216 @ X1214 )
=> ( in @ ( kpair @ X1215 @ X1216 ) @ ( powerset @ ( powerset @ ( binunion @ X1213 @ X1214 ) ) ) ) ) )
=> ( ! [X1217: $i,X1218: $i,X1219: $i] :
( ( in @ X1219 @ X1217 )
=> ! [X1220: $i] :
( ( in @ X1220 @ X1218 )
=> ( in @ ( kpair @ X1219 @ X1220 ) @ ( cartprod @ X1217 @ X1218 ) ) ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i] :
( ( in @ X1223 @ ( cartprod @ X1221 @ X1222 ) )
=> ? [X1224: $i] :
( ( in @ X1224 @ X1221 )
& ? [X1225: $i] :
( ( in @ X1225 @ X1222 )
& ( X1223
= ( kpair @ X1224 @ X1225 ) ) ) ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i] :
( ( in @ X1228 @ ( cartprod @ X1226 @ X1227 ) )
=> ( iskpair @ X1228 ) )
=> ( ! [X1229: $i,X1230: $i] :
( ( in @ X1230 @ ( setunion @ X1229 ) )
=> ? [X1231: $i] :
( ( in @ X1231 @ X1229 )
& ( in @ X1230 @ X1231 ) ) )
=> ( ! [X1232: $i] : ( subset @ ( setunion @ ( setadjoin @ X1232 @ emptyset ) ) @ X1232 )
=> ( ! [X1233: $i] : ( subset @ X1233 @ ( setunion @ ( setadjoin @ X1233 @ emptyset ) ) )
=> ( ! [X1234: $i] :
( ( setunion @ ( setadjoin @ X1234 @ emptyset ) )
= X1234 )
=> ( ! [X1235: $i,X1236: $i > $o] :
( ! [X1237: $i] :
( ( in @ X1237 @ X1235 )
=> ! [X1238: $i] :
( ( in @ X1238 @ X1235 )
=> ( ( X1236 @ X1237 )
=> ( ( X1236 @ X1238 )
=> ( X1237 = X1238 ) ) ) ) )
=> ( ? [X1239: $i] :
( ( in @ X1239 @ X1235 )
& ( X1236 @ X1239 ) )
=> ( singleton @ ( dsetconstr @ X1235 @ X1236 ) ) ) )
=> ( ! [X1240: $i,X1241: $i > $o] :
( ( singleton @ ( dsetconstr @ X1240 @ X1241 ) )
=> ? [X1242: $i] :
( ( in @ X1242 @ X1240 )
& ( X1241 @ X1242 ) ) )
=> ( ! [X1243: $i,X1244: $i > $o,X1245: $i] :
( ( in @ X1245 @ X1243 )
=> ( ( X1244 @ X1245 )
=> ( ! [X1246: $i] :
( ( in @ X1246 @ X1243 )
=> ( ( X1244 @ X1246 )
=> ( X1246 = X1245 ) ) )
=> ( singleton @ ( dsetconstr @ X1243 @ X1244 ) ) ) ) )
=> ( ! [X1247: $i,X1248: $i > $o] :
( ! [X1249: $i] :
( ( in @ X1249 @ X1247 )
=> ! [X1250: $i] :
( ( in @ X1250 @ X1247 )
=> ( ( X1248 @ X1249 )
=> ( ( X1248 @ X1250 )
=> ( X1249 = X1250 ) ) ) ) )
=> ( ? [X1251: $i] :
( ( in @ X1251 @ X1247 )
& ( X1248 @ X1251 ) )
=> ( singleton @ ( dsetconstr @ X1247 @ X1248 ) ) ) )
=> ( ! [X1252: $i,X1253: $i] :
( ( ( setadjoin @ X1252 @ emptyset )
= ( setadjoin @ X1253 @ emptyset ) )
=> ( X1252 = X1253 ) )
=> ( ! [X1254: $i,X1255: $i,X1256: $i] :
( ( in @ ( setadjoin @ X1256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1254 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1254 @ ( setadjoin @ X1255 @ emptyset ) ) @ emptyset ) ) )
=> ( X1254 = X1256 ) )
=> ( ! [X1257: $i] :
( ( iskpair @ X1257 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1257 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1257 ) ) ) )
=> ( ! [X1258: $i] :
( ( singleton @ X1258 )
=> ( in @ ( setunion @ X1258 ) @ X1258 ) )
=> ( ! [X1259: $i,X1260: $i] :
( ( kfst @ ( kpair @ X1259 @ X1260 ) )
= X1259 )
=> ( ! [X1261: $i,X1262: $i,X1263: $i] :
( ( in @ X1263 @ ( cartprod @ X1261 @ X1262 ) )
=> ( in @ ( kfst @ X1263 ) @ X1261 ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i,X1267: $i] :
( ( ( setadjoin @ ( setadjoin @ X1264 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1264 @ ( setadjoin @ X1265 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1266 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1266 @ ( setadjoin @ X1267 @ emptyset ) ) @ emptyset ) ) )
=> ( X1264 = X1266 ) )
=> ( ! [X1268: $i,X1269: $i,X1270: $i,X1271: $i] :
( ( ( kpair @ X1268 @ X1269 )
= ( kpair @ X1270 @ X1271 ) )
=> ( X1268 = X1270 ) )
=> ( ! [X1272: $i,X1273: $i] :
( ( X1272 = X1273 )
=> ( ( setadjoin @ X1272 @ ( setadjoin @ X1273 @ emptyset ) )
= ( setadjoin @ X1272 @ emptyset ) ) )
=> ( ! [X1274: $i,X1275: $i] :
( ( X1274 = X1275 )
=> ( ( setadjoin @ ( setadjoin @ X1274 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1274 @ ( setadjoin @ X1275 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1274 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1276: $i,X1277: $i,X1278: $i,X1279: $i] :
( ( ( setadjoin @ ( setadjoin @ X1276 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1276 @ ( setadjoin @ X1277 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1278 @ ( setadjoin @ X1279 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1278 = X1279 )
=> ( X1277 = X1279 ) ) )
=> ( ! [X1280: $i,X1281: $i,X1282: $i] :
( ( ( setadjoin @ X1280 @ ( setadjoin @ X1281 @ emptyset ) )
= ( setadjoin @ X1282 @ emptyset ) )
=> ( X1280 = X1281 ) )
=> ( ! [X1283: $i,X1284: $i,X1285: $i,X1286: $i] :
( ( ( setadjoin @ ( setadjoin @ X1283 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1283 @ ( setadjoin @ X1284 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1285 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1285 @ ( setadjoin @ X1286 @ emptyset ) ) @ emptyset ) ) )
=> ( X1284 = X1286 ) )
=> ( ! [X1287: $i,X1288: $i,X1289: $i,X1290: $i] :
( ( ( kpair @ X1287 @ X1288 )
= ( kpair @ X1289 @ X1290 ) )
=> ( X1288 = X1290 ) )
=> ( ! [X1291: $i] :
( ( iskpair @ X1291 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1291 )
@ ^ [Z0: $i] :
( X1291
= ( kpair @ ( kfst @ X1291 ) @ Z0 ) ) ) ) )
=> ( ! [X1292: $i,X1293: $i] :
( ( ksnd @ ( kpair @ X1292 @ X1293 ) )
= X1293 )
=> ( ! [X1294: $i] :
( ( iskpair @ X1294 )
=> ( ( kpair @ ( kfst @ X1294 ) @ ( ksnd @ X1294 ) )
= X1294 ) )
=> ( ! [X1295: $i,X1296: $i,X1297: $i] :
( ( in @ X1297 @ ( cartprod @ X1295 @ X1296 ) )
=> ( in @ ( ksnd @ X1297 ) @ X1296 ) )
=> ( ! [X1298: $i,X1299: $i,X1300: $i,X1301: $i] :
( ( in @ ( kpair @ X1300 @ X1301 ) @ ( cartprod @ X1298 @ X1299 ) )
=> ( in @ X1300 @ X1298 ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i,X1305: $i] :
( ( in @ ( kpair @ X1304 @ X1305 ) @ ( cartprod @ X1302 @ X1303 ) )
=> ( in @ X1305 @ X1303 ) )
=> ( ! [X1306: $i,X1307: $i,X1308: $i] :
( ( in @ X1308 @ X1306 )
=> ! [X1309: $i] :
( ( in @ X1309 @ X1307 )
=> ( ( kpair @ X1308 @ X1309 )
= ( kpair @ X1308 @ X1309 ) ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i] :
( ( in @ X1312 @ X1310 )
=> ! [X1313: $i] :
( ( in @ X1313 @ X1311 )
=> ( ( kfst @ ( kpair @ X1312 @ X1313 ) )
= X1312 ) ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( in @ X1316 @ X1314 )
=> ! [X1317: $i] :
( ( in @ X1317 @ X1315 )
=> ( ( ksnd @ ( kpair @ X1316 @ X1317 ) )
= X1317 ) ) )
=> ( ! [X1318: $i,X1319: $i,X1320: $i] :
( ( in @ X1320 @ ( cartprod @ X1318 @ X1319 ) )
=> ( ( kpair @ ( kfst @ X1320 ) @ ( ksnd @ X1320 ) )
= X1320 ) )
=> ( ! [X1321: $i,X1322: $i,X1323: $i > $i > $o,X1324: $i] :
( ( in @ X1324 @ X1321 )
=> ! [X1325: $i] :
( ( in @ X1325 @ X1322 )
=> ( ( X1323 @ X1324 @ X1325 )
=> ( in @ ( kpair @ X1324 @ X1325 ) @ ( dpsetconstr @ X1321 @ X1322 @ X1323 ) ) ) ) )
=> ( ! [X1326: $i,X1327: $i,X1328: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1326 @ X1327 @ X1328 ) @ ( cartprod @ X1326 @ X1327 ) )
=> ( ! [X1329: $i,X1330: $i,X1331: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1329 @ X1330 @ X1331 ) @ ( cartprod @ X1329 @ X1330 ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i > $i > $o,X1335: $i] :
( ( in @ X1335 @ X1332 )
=> ! [X1336: $i] :
( ( in @ X1336 @ X1333 )
=> ( ( in @ ( kpair @ X1335 @ X1336 ) @ ( dpsetconstr @ X1332 @ X1333 @ X1334 ) )
=> ( X1334 @ X1335 @ X1336 ) ) ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i > $i > $o,X1340: $i,X1341: $i] :
( ( in @ ( kpair @ X1340 @ X1341 ) @ ( dpsetconstr @ X1337 @ X1338 @ X1339 ) )
=> ( in @ X1340 @ X1337 ) )
=> ( ! [X1342: $i,X1343: $i,X1344: $i > $i > $o,X1345: $i,X1346: $i] :
( ( in @ ( kpair @ X1345 @ X1346 ) @ ( dpsetconstr @ X1342 @ X1343 @ X1344 ) )
=> ( in @ X1346 @ X1343 ) )
=> ( ! [X1347: $i,X1348: $i,X1349: $i > $i > $o,X1350: $i,X1351: $i] :
( ( in @ ( kpair @ X1350 @ X1351 ) @ ( dpsetconstr @ X1347 @ X1348 @ X1349 ) )
=> ( X1349 @ X1350 @ X1351 ) )
=> ( ! [X1352: $i,X1353: $i,X1354: $i] :
( ( func @ X1352 @ X1353 @ X1354 )
=> ! [X1355: $i] :
( ( in @ X1355 @ X1352 )
=> ( singleton
@ ( dsetconstr @ X1353
@ ^ [Z0: $i] : ( in @ ( kpair @ X1355 @ Z0 ) @ X1354 ) ) ) ) )
=> ( ! [X1356: $i,X1357: $i,X1358: $i] :
( ( func @ X1356 @ X1357 @ X1358 )
=> ! [X1359: $i] :
( ( in @ X1359 @ X1356 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1357
@ ^ [Z0: $i] : ( in @ ( kpair @ X1359 @ Z0 ) @ X1358 ) ) )
@ X1357 ) ) )
=> ( ! [X1360: $i,X1361: $i,X1362: $i] :
( ( func @ X1360 @ X1361 @ X1362 )
=> ! [X1363: $i] :
( ( in @ X1363 @ X1360 )
=> ( in @ ( ap @ X1360 @ X1361 @ X1362 @ X1363 ) @ X1361 ) ) )
=> ( ! [X1364: $i,X1365: $i,X1366: $i] :
( ( in @ X1366 @ ( funcSet @ X1364 @ X1365 ) )
=> ( func @ X1364 @ X1365 @ X1366 ) )
=> ( ! [X1367: $i,X1368: $i,X1369: $i] :
( ( in @ X1369 @ ( funcSet @ X1367 @ X1368 ) )
=> ! [X1370: $i] :
( ( in @ X1370 @ X1367 )
=> ( in @ ( ap @ X1367 @ X1368 @ X1369 @ X1370 ) @ X1368 ) ) )
=> ( ! [X1371: $i,X1372: $i,X1373: $i] :
( ( func @ X1371 @ X1372 @ X1373 )
=> ( in @ X1373 @ ( funcSet @ X1371 @ X1372 ) ) )
=> ( ! [X1374: $i,X1375: $i,X1376: $i > $i] :
( ! [X1377: $i] :
( ( in @ X1377 @ X1374 )
=> ( in @ ( X1376 @ X1377 ) @ X1375 ) )
=> ( func @ X1374 @ X1375
@ ( dpsetconstr @ X1374 @ X1375
@ ^ [Z0: $i] : ( $eq @ ( X1376 @ Z0 ) ) ) ) )
=> ( ! [X1378: $i,X1379: $i,X1380: $i > $i] :
( ! [X1381: $i] :
( ( in @ X1381 @ X1378 )
=> ( in @ ( X1380 @ X1381 ) @ X1379 ) )
=> ( func @ X1378 @ X1379 @ ( lam @ X1378 @ X1379 @ X1380 ) ) )
=> ( ! [X1382: $i,X1383: $i,X1384: $i > $i] :
( ! [X1385: $i] :
( ( in @ X1385 @ X1382 )
=> ( in @ ( X1384 @ X1385 ) @ X1383 ) )
=> ( in @ ( lam @ X1382 @ X1383 @ X1384 ) @ ( funcSet @ X1382 @ X1383 ) ) )
=> ( ! [X1386: $i,X1387: $i,X1388: $i] :
( ( subset @ X1388 @ ( cartprod @ X1386 @ X1387 ) )
=> ! [X1389: $i > $o] :
( ! [X1390: $i] :
( ( in @ X1390 @ X1386 )
=> ! [X1391: $i] :
( ( in @ X1391 @ X1387 )
=> ( ( in @ ( kpair @ X1390 @ X1391 ) @ X1388 )
=> ( X1389 @ ( kpair @ X1390 @ X1391 ) ) ) ) )
=> ! [X1392: $i] :
( ( in @ X1392 @ X1388 )
=> ( X1389 @ X1392 ) ) ) )
=> ( ! [X1393: $i,X1394: $i,X1395: $i] :
( ( subset @ X1395 @ ( cartprod @ X1393 @ X1394 ) )
=> ! [X1396: $i > $o] :
( ! [X1397: $i] :
( ( in @ X1397 @ X1393 )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1394 )
=> ( ( in @ ( kpair @ X1397 @ X1398 ) @ X1395 )
=> ( X1396 @ ( kpair @ X1397 @ X1398 ) ) ) ) )
=> ! [X1399: $i] :
( ( in @ X1399 @ X1395 )
=> ( X1396 @ X1399 ) ) ) )
=> ( ! [X1400: $i,X1401: $i > $o] :
( ( singleton @ ( dsetconstr @ X1400 @ X1401 ) )
=> ! [X1402: $i] :
( ( in @ X1402 @ X1400 )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1400 )
=> ( ( X1401 @ X1402 )
=> ( ( X1401 @ X1403 )
=> ( X1402 = X1403 ) ) ) ) ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i] :
( ( func @ X1404 @ X1405 @ X1406 )
=> ! [X1407: $i] :
( ( in @ X1407 @ X1404 )
=> ( in @ ( kpair @ X1407 @ ( ap @ X1404 @ X1405 @ X1406 @ X1407 ) ) @ X1406 ) ) )
=> ( ! [X1408: $i,X1409: $i,X1410: $i] :
( ( in @ X1410 @ ( funcSet @ X1408 @ X1409 ) )
=> ! [X1411: $i] :
( ( in @ X1411 @ X1408 )
=> ( in @ ( kpair @ X1411 @ ( ap @ X1408 @ X1409 @ X1410 @ X1411 ) ) @ X1410 ) ) )
=> ( ! [X1412: $i,X1413: $i,X1414: $i] :
( ( func @ X1412 @ X1413 @ X1414 )
=> ! [X1415: $i] :
( ( in @ X1415 @ X1412 )
=> ! [X1416: $i] :
( ( in @ X1416 @ X1413 )
=> ( ( in @ ( kpair @ X1415 @ X1416 ) @ X1414 )
=> ( ( ap @ X1412 @ X1413 @ X1414 @ X1415 )
= X1416 ) ) ) ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( func @ X1417 @ X1418 @ X1419 )
=> ! [X1420: $i] :
( ( func @ X1417 @ X1418 @ X1420 )
=> ( ! [X1421: $i] :
( ( in @ X1421 @ X1417 )
=> ( ( ap @ X1417 @ X1418 @ X1419 @ X1421 )
= ( ap @ X1417 @ X1418 @ X1420 @ X1421 ) ) )
=> ! [X1422: $i] :
( ( in @ X1422 @ X1417 )
=> ! [X1423: $i] :
( ( in @ X1423 @ X1418 )
=> ( ( in @ ( kpair @ X1422 @ X1423 ) @ X1420 )
=> ( in @ ( kpair @ X1422 @ X1423 ) @ X1419 ) ) ) ) ) ) )
=> ( ! [X1424: $i,X1425: $i,X1426: $i] :
( ( in @ X1426 @ ( funcSet @ X1424 @ X1425 ) )
=> ! [X1427: $i] :
( ( in @ X1427 @ X1424 )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ( ( in @ ( kpair @ X1427 @ X1428 ) @ X1426 )
=> ( ( ap @ X1424 @ X1425 @ X1426 @ X1427 )
= X1428 ) ) ) ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i] :
( ( subset @ X1431 @ ( cartprod @ X1429 @ X1430 ) )
=> ! [X1432: $i] :
( ( subset @ X1432 @ ( cartprod @ X1429 @ X1430 ) )
=> ( ! [X1433: $i] :
( ( in @ X1433 @ X1429 )
=> ! [X1434: $i] :
( ( in @ X1434 @ X1430 )
=> ( ( in @ ( kpair @ X1433 @ X1434 ) @ X1431 )
=> ( in @ ( kpair @ X1433 @ X1434 ) @ X1432 ) ) ) )
=> ( subset @ X1431 @ X1432 ) ) ) )
=> ( ! [X1435: $i,X1436: $i,X1437: $i] :
( ( subset @ X1437 @ ( cartprod @ X1435 @ X1436 ) )
=> ! [X1438: $i] :
( ( subset @ X1438 @ ( cartprod @ X1435 @ X1436 ) )
=> ( ! [X1439: $i] :
( ( in @ X1439 @ X1435 )
=> ! [X1440: $i] :
( ( in @ X1440 @ X1436 )
=> ( ( in @ ( kpair @ X1439 @ X1440 ) @ X1437 )
=> ( in @ ( kpair @ X1439 @ X1440 ) @ X1438 ) ) ) )
=> ( ! [X1441: $i] :
( ( in @ X1441 @ X1435 )
=> ! [X1442: $i] :
( ( in @ X1442 @ X1436 )
=> ( ( in @ ( kpair @ X1441 @ X1442 ) @ X1438 )
=> ( in @ ( kpair @ X1441 @ X1442 ) @ X1437 ) ) ) )
=> ( X1437 = X1438 ) ) ) ) )
=> ( ! [X1443: $i,X1444: $i,X1445: $i] :
( ( func @ X1443 @ X1444 @ X1445 )
=> ! [X1446: $i] :
( ( func @ X1443 @ X1444 @ X1446 )
=> ( ! [X1447: $i] :
( ( in @ X1447 @ X1443 )
=> ( ( ap @ X1443 @ X1444 @ X1445 @ X1447 )
= ( ap @ X1443 @ X1444 @ X1446 @ X1447 ) ) )
=> ( X1445 = X1446 ) ) ) )
=> ( ! [X1448: $i,X1449: $i,X1450: $i] :
( ( in @ X1450 @ ( funcSet @ X1448 @ X1449 ) )
=> ! [X1451: $i] :
( ( in @ X1451 @ ( funcSet @ X1448 @ X1449 ) )
=> ( ! [X1452: $i] :
( ( in @ X1452 @ X1448 )
=> ( ( ap @ X1448 @ X1449 @ X1450 @ X1452 )
= ( ap @ X1448 @ X1449 @ X1451 @ X1452 ) ) )
=> ( X1450 = X1451 ) ) ) )
=> ( ! [X1453: $i,X1454: $i,X1455: $i] :
( ( in @ X1455 @ ( funcSet @ X1453 @ X1454 ) )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1453 )
=> ( ( ap @ X1453 @ X1454 @ X1455 @ X1456 )
= ( ap @ X1453 @ X1454 @ X1455 @ X1456 ) ) ) )
=> ( ! [X1457: $i,X1458: $i,X1459: $i] :
( ( func @ X1457 @ X1458 @ X1459 )
=> ! [X1460: $i] :
( ( in @ X1460 @ X1457 )
=> ( ( ap @ X1457 @ X1458 @ X1459 @ X1460 )
= ( ap @ X1457 @ X1458 @ X1459 @ X1460 ) ) ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i > $i] :
( ! [X1464: $i] :
( ( in @ X1464 @ X1461 )
=> ( in @ ( X1463 @ X1464 ) @ X1462 ) )
=> ! [X1465: $i] :
( ( in @ X1465 @ X1461 )
=> ( ( ap @ X1461 @ X1462 @ ( lam @ X1461 @ X1462 @ X1463 ) @ X1465 )
= ( X1463 @ X1465 ) ) ) )
=> ( ! [X1466: $i,X1467: $i,X1468: $i] :
( ( func @ X1466 @ X1467 @ X1468 )
=> ( ( lam @ X1466 @ X1467 @ ( ap @ X1466 @ X1467 @ X1468 ) )
= X1468 ) )
=> ( ! [X1469: $i,X1470: $i,X1471: $i > $i] :
( ! [X1472: $i] :
( ( in @ X1472 @ X1469 )
=> ( in @ ( X1471 @ X1472 ) @ X1470 ) )
=> ( ( lam @ X1469 @ X1470 @ X1471 )
= ( lam @ X1469 @ X1470 @ X1471 ) ) )
=> ( ! [X1473: $i,X1474: $i,X1475: $i > $i] :
( ! [X1476: $i] :
( ( in @ X1476 @ X1473 )
=> ( in @ ( X1475 @ X1476 ) @ X1474 ) )
=> ! [X1477: $i] :
( ( in @ X1477 @ X1473 )
=> ( ( ap @ X1473 @ X1474 @ ( lam @ X1473 @ X1474 @ X1475 ) @ X1477 )
= ( X1475 @ X1477 ) ) ) )
=> ( ! [X1478: $i,X1479: $i,X1480: $i] :
( ( in @ X1480 @ ( funcSet @ X1478 @ X1479 ) )
=> ( ( lam @ X1478 @ X1479 @ ( ap @ X1478 @ X1479 @ X1480 ) )
= X1480 ) )
=> ( ! [X1481: $i,X1482: $o,X1483: $i] :
( ( in @ X1483 @ X1481 )
=> ! [X1484: $i] :
( ( in @ X1484 @ X1481 )
=> ( ~ X1482
=> ( in @ X1484
@ ( dsetconstr @ X1481
@ ^ [Z0: $i] :
( ( X1482
& ( Z0 = X1483 ) )
| ( ~ X1482
& ( Z0 = X1484 ) ) ) ) ) ) ) )
=> ( ! [X1485: $i,X1486: $o,X1487: $i] :
( ( in @ X1487 @ X1485 )
=> ! [X1488: $i] :
( ( in @ X1488 @ X1485 )
=> ( ~ X1486
=> ( ( dsetconstr @ X1485
@ ^ [Z0: $i] :
( ( X1486
& ( Z0 = X1487 ) )
| ( ~ X1486
& ( Z0 = X1488 ) ) ) )
= ( setadjoin @ X1488 @ emptyset ) ) ) ) )
=> ( ! [X1489: $i,X1490: $o,X1491: $i] :
( ( in @ X1491 @ X1489 )
=> ! [X1492: $i] :
( ( in @ X1492 @ X1489 )
=> ( X1490
=> ( in @ X1491
@ ( dsetconstr @ X1489
@ ^ [Z0: $i] :
( ( X1490
& ( Z0 = X1491 ) )
| ( ~ X1490
& ( Z0 = X1492 ) ) ) ) ) ) ) )
=> ( ! [X1493: $i,X1494: $o,X1495: $i] :
( ( in @ X1495 @ X1493 )
=> ! [X1496: $i] :
( ( in @ X1496 @ X1493 )
=> ( X1494
=> ( ( dsetconstr @ X1493
@ ^ [Z0: $i] :
( ( X1494
& ( Z0 = X1495 ) )
| ( ~ X1494
& ( Z0 = X1496 ) ) ) )
= ( setadjoin @ X1495 @ emptyset ) ) ) ) )
=> ( ! [X1497: $i,X1498: $o,X1499: $i] :
( ( in @ X1499 @ X1497 )
=> ! [X1500: $i] :
( ( in @ X1500 @ X1497 )
=> ( singleton
@ ( dsetconstr @ X1497
@ ^ [Z0: $i] :
( ( X1498
& ( Z0 = X1499 ) )
| ( ~ X1498
& ( Z0 = X1500 ) ) ) ) ) ) )
=> ( ! [X1501: $i,X1502: $o,X1503: $i] :
( ( in @ X1503 @ X1501 )
=> ! [X1504: $i] :
( ( in @ X1504 @ X1501 )
=> ( in @ ( if @ X1501 @ X1502 @ X1503 @ X1504 ) @ X1501 ) ) )
=> ( ! [X1505: $i] :
( ( singleton @ X1505 )
=> ! [X1506: $i] :
( ( in @ X1506 @ X1505 )
=> ( ( setunion @ X1505 )
= X1506 ) ) )
=> ( ! [X1507: $i,X1508: $o,X1509: $i] :
( ( in @ X1509 @ X1507 )
=> ! [X1510: $i] :
( ( in @ X1510 @ X1507 )
=> ( X1508
=> ( ( if @ X1507 @ X1508 @ X1509 @ X1510 )
= X1509 ) ) ) )
=> ( ! [X1511: $i,X1512: $o,X1513: $i] :
( ( in @ X1513 @ X1511 )
=> ! [X1514: $i] :
( ( in @ X1514 @ X1511 )
=> ( ~ X1512
=> ( ( if @ X1511 @ X1512 @ X1513 @ X1514 )
= X1514 ) ) ) )
=> ( ! [X1515: $i,X1516: $o,X1517: $i] :
( ( in @ X1517 @ X1515 )
=> ! [X1518: $i] :
( ( in @ X1518 @ X1515 )
=> ( in @ ( if @ X1515 @ X1516 @ X1517 @ X1518 ) @ ( setadjoin @ X1517 @ ( setadjoin @ X1518 @ emptyset ) ) ) ) )
=> ( ! [X1519: $i,X1520: $i] :
( ( in @ X1520 @ ( powerset @ X1519 ) )
=> ! [X1521: $i] :
( ( in @ X1521 @ ( powerset @ X1519 ) )
=> ( in @ ( binintersect @ X1520 @ X1521 ) @ ( powerset @ X1519 ) ) ) )
=> ( ! [X1522: $i,X1523: $i] :
( ( in @ X1523 @ ( powerset @ X1522 ) )
=> ! [X1524: $i] :
( ( in @ X1524 @ ( powerset @ X1522 ) )
=> ( in @ ( binunion @ X1523 @ X1524 ) @ ( powerset @ X1522 ) ) ) )
=> ( ! [X1525: $i,X1526: $i] :
( ( in @ X1526 @ ( powerset @ X1525 ) )
=> ( in @ ( powerset @ X1526 ) @ ( powerset @ ( powerset @ X1525 ) ) ) )
=> ( ! [X1527: $i,X1528: $i] :
( ( in @ X1528 @ ( powerset @ X1527 ) )
=> ! [X1529: $i] :
( ( in @ X1529 @ ( powerset @ X1527 ) )
=> ( in @ ( setminus @ X1528 @ X1529 ) @ ( powerset @ X1527 ) ) ) )
=> ( ! [X1530: $i,X1531: $i] :
( ( in @ X1531 @ ( powerset @ X1530 ) )
=> ( in @ ( setminus @ X1530 @ X1531 ) @ ( powerset @ X1530 ) ) )
=> ( ! [X1532: $i,X1533: $i] :
( ( in @ X1533 @ ( powerset @ X1532 ) )
=> ! [X1534: $i] :
( ( in @ X1534 @ ( powerset @ X1532 ) )
=> ( ! [X1535: $i] :
( ( in @ X1535 @ X1532 )
=> ( ( in @ X1535 @ X1533 )
=> ( in @ X1535 @ X1534 ) ) )
=> ( ! [X1536: $i] :
( ( in @ X1536 @ X1532 )
=> ( ( in @ X1536 @ X1534 )
=> ( in @ X1536 @ X1533 ) ) )
=> ( X1533 = X1534 ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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g]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_284]),c_0_285]),c_0_286]),c_0_287]),singletonsuniq]),setukpairinjL1]),c_0_288]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_289]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),c_0_294]),c_0_295]),c_0_296]),c_0_297]),c_0_298]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_299]),c_0_300]),c_0_301]),c_0_302]),c_0_303]),c_0_304]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_305]),c_0_306]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_307]),c_0_308]),c_0_309]),c_0_310]),c_0_311]),c_0_312]),c_0_313]),c_0_314]),c_0_315]),c_0_316]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),setminusT_lem]),complementT_lem]),setextT])])]),c_0_317]) ).
thf(c_0_319,negated_conjecture,
! 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$o,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i > $i > $o,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i > $i > $o,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 > $i,X2114: $i,X2115: $i,X2116: $i > $i,X2118: $i,X2119: $i,X2120: $i > $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i > $o,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i > $o,X2135: $i,X2136: $i,X2137: $i > $o,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2179: $i,X2180: $i,X2181: $i,X2182: $i,X2184: $i,X2185: $i,X2186: $i,X2187: $i,X2189: $i,X2190: $i,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i,X2196: $i,X2197: $i,X2198: $i,X2199: $i > $i,X2201: $i,X2202: $i,X2203: $i,X2204: $i,X2205: $i,X2206: $i,X2207: $i > $i,X2209: $i,X2210: $i,X2211: $i > $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $o,X2219: $i,X2220: $i,X2221: $i,X2222: $o,X2223: $i,X2224: $i,X2225: $i,X2226: $o,X2227: $i,X2228: $i,X2229: $i,X2230: $o,X2231: $i,X2232: $i,X2233: $i,X2234: $o,X2235: $i,X2236: $i,X2237: $i,X2238: $o,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $o,X2245: $i,X2246: $i,X2247: $i,X2248: $o,X2249: $i,X2250: $i,X2251: $i,X2252: $o,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2276: $i] :
( ( ~ ( in @ ( esk1_2 @ X1537 @ X1538 ) @ X1537 )
| ~ ( in @ ( esk1_2 @ X1537 @ X1538 ) @ X1538 )
| ( X1537 = X1538 ) )
& ( ( in @ ( esk1_2 @ X1537 @ X1538 ) @ X1537 )
| ( in @ ( esk1_2 @ X1537 @ X1538 ) @ X1538 )
| ( X1537 = X1538 ) )
& ~ ( in @ X1540 @ emptyset )
& ( ~ ( in @ X1543 @ ( setadjoin @ X1541 @ X1542 ) )
| ( X1543 = X1541 )
| ( in @ X1543 @ X1542 ) )
& ( ( X1543 != X1541 )
| ( in @ X1543 @ ( setadjoin @ X1541 @ X1542 ) ) )
& ( ~ ( in @ X1543 @ X1542 )
| ( in @ X1543 @ ( setadjoin @ X1541 @ X1542 ) ) )
& ( ~ ( in @ X1545 @ ( powerset @ X1544 ) )
| ~ ( in @ X1546 @ X1545 )
| ( in @ X1546 @ X1544 ) )
& ( ( in @ ( esk2_2 @ X1547 @ X1548 ) @ X1548 )
| ( in @ X1548 @ ( powerset @ X1547 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1547 @ X1548 ) @ X1547 )
| ( in @ X1548 @ ( powerset @ X1547 ) ) )
& ( ( in @ X1551 @ ( esk3_2 @ X1550 @ X1551 ) )
| ~ ( in @ X1551 @ ( setunion @ X1550 ) ) )
& ( ( in @ ( esk3_2 @ X1550 @ X1551 ) @ X1550 )
| ~ ( in @ X1551 @ ( setunion @ X1550 ) ) )
& ( ~ ( in @ X1554 @ X1555 )
| ~ ( in @ X1555 @ X1553 )
| ( in @ X1554 @ ( setunion @ X1553 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1556 @ omega )
| ( in @ ( setadjoin @ X1556 @ X1556 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1557 ) @ omega )
| ~ ( in @ emptyset @ X1557 )
| ~ ( in @ X1559 @ omega )
| ( in @ X1559 @ X1557 ) )
& ( ( in @ ( esk4_1 @ X1557 ) @ X1557 )
| ~ ( in @ emptyset @ X1557 )
| ~ ( in @ X1559 @ omega )
| ( in @ X1559 @ X1557 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1557 ) @ ( esk4_1 @ X1557 ) ) @ X1557 )
| ~ ( in @ emptyset @ X1557 )
| ~ ( in @ X1559 @ omega )
| ( in @ X1559 @ X1557 ) )
& ( ( in @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1561 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( in @ ( esk5_2 @ X1560 @ X1561 ) @ X1561 ) )
& ( ( X1560 @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1566 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( in @ ( esk5_2 @ X1560 @ X1561 ) @ X1561 ) )
& ( ~ ( in @ X1569 @ X1561 )
| ~ ( X1560 @ X1569 @ X1568 )
| ( in @ X1568 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( in @ ( esk5_2 @ X1560 @ X1561 ) @ X1561 ) )
& ( ( in @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1561 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ( X1560 @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1566 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ~ ( in @ X1569 @ X1561 )
| ~ ( X1560 @ X1569 @ X1568 )
| ( in @ X1568 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ( in @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1561 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1563
!= ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ( X1560 @ ( esk8_3 @ X1560 @ X1561 @ X1566 ) @ X1566 )
| ~ ( in @ X1566 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1563
!= ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ~ ( in @ X1569 @ X1561 )
| ~ ( X1560 @ X1569 @ X1568 )
| ( in @ X1568 @ ( esk7_2 @ X1560 @ X1561 ) )
| ( X1563
!= ( esk6_3 @ X1560 @ X1561 @ X1563 ) )
| ~ ( X1560 @ ( esk5_2 @ X1560 @ X1561 ) @ X1563 ) )
& ( ( in @ ( esk9_1 @ X1570 ) @ X1570 )
| ~ ( in @ X1571 @ X1570 ) )
& ( ~ ( in @ X1573 @ ( esk9_1 @ X1570 ) )
| ~ ( in @ X1573 @ X1570 )
| ~ ( in @ X1571 @ X1570 ) )
& epred1_0
& ( ( X1574 @ ( esk10_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 )
| ( X1574 @ ( descr @ X1574 ) ) )
& ( ( X1575
!= ( esk10_2 @ X1574 @ X1575 ) )
| ~ ( X1574 @ X1575 )
| ( X1574 @ ( descr @ X1574 ) ) )
& ( ~ ( in @ X1579 @ X1577 )
| ~ ( X1578 @ X1579 )
| ( in @ X1579 @ ( dsetconstr @ X1577 @ X1578 ) ) )
& ( ~ ( in @ X1582 @ ( dsetconstr @ X1580 @ X1581 ) )
| ( in @ X1582 @ X1580 ) )
& ( ~ ( in @ X1585 @ ( dsetconstr @ X1583 @ X1584 ) )
| ( X1584 @ X1585 ) )
& ( ( X1586 @ ( esk12_1 @ X1586 ) )
| ( X1586 @ ( esk11_2 @ X1586 @ X1587 ) )
| ~ ( X1586 @ X1587 ) )
& ( ~ ( X1586 @ X1590 )
| ( ( esk12_1 @ X1586 )
= X1590 )
| ( X1586 @ ( esk11_2 @ X1586 @ X1587 ) )
| ~ ( X1586 @ X1587 ) )
& ( ( X1586 @ ( esk12_1 @ X1586 ) )
| ( X1587
!= ( esk11_2 @ X1586 @ X1587 ) )
| ~ ( X1586 @ X1587 ) )
& ( ~ ( X1586 @ X1590 )
| ( ( esk12_1 @ X1586 )
= X1590 )
| ( X1587
!= ( esk11_2 @ X1586 @ X1587 ) )
| ~ ( X1586 @ X1587 ) )
& ( ~ ( in @ X1592 @ ( prop2set @ X1591 ) )
| X1591 )
& ( ~ ( in @ X1593 @ emptyset )
| X1594 )
& ( ~ ( in @ X1595 @ emptyset )
| ~ $true )
& ~ ( in @ X1596 @ emptyset )
& ( ( X1597 @ ( esk13_2 @ X1597 @ X1598 ) )
| ~ ( X1597 @ X1598 )
| ( X1597 @ ( esk14_1 @ X1597 ) ) )
& ( ( X1598
!= ( esk13_2 @ X1597 @ X1598 ) )
| ~ ( X1597 @ X1598 )
| ( X1597 @ ( esk14_1 @ X1597 ) ) )
& ( ( in @ ( esk16_2 @ X1601 @ X1602 ) @ X1602 )
| ( X1601 = X1602 )
| ( in @ ( esk15_2 @ X1601 @ X1602 ) @ X1601 ) )
& ( ~ ( in @ ( esk16_2 @ X1601 @ X1602 ) @ X1601 )
| ( X1601 = X1602 )
| ( in @ ( esk15_2 @ X1601 @ X1602 ) @ X1601 ) )
& ( ( in @ ( esk16_2 @ X1601 @ X1602 ) @ X1602 )
| ( X1601 = X1602 )
| ~ ( in @ ( esk15_2 @ X1601 @ X1602 ) @ X1602 ) )
& ( ~ ( in @ ( esk16_2 @ X1601 @ X1602 ) @ X1601 )
| ( X1601 = X1602 )
| ~ ( in @ ( esk15_2 @ X1601 @ X1602 ) @ X1602 ) )
& ( ( in @ ( esk17_1 @ X1605 ) @ X1605 )
| ( X1605 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1607 ) @ X1607 )
| ( X1607 = emptyset ) )
& ( ~ ( in @ X1611 @ ( dsetconstr @ X1609 @ X1610 ) )
| ( X1610 @ X1611 )
| ~ ( in @ X1611 @ X1609 ) )
& ( ~ ( X1610 @ X1611 )
| ( in @ X1611 @ ( dsetconstr @ X1609 @ X1610 ) )
| ~ ( in @ X1611 @ X1609 ) )
& ( ( X1612 = emptyset )
| ( in @ ( esk19_1 @ X1612 ) @ X1612 ) )
& ( ~ ( in @ X1616 @ X1614 )
| ~ ( X1615 @ X1616 )
| ( ( dsetconstr @ X1614 @ X1615 )
!= emptyset ) )
& ( ~ ( in @ X1618 @ X1617 )
| ( X1617 != emptyset ) )
& ( in @ X1619 @ ( setadjoin @ X1619 @ X1620 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1623 @ X1622 )
| ( in @ X1623 @ ( setadjoin @ X1621 @ X1622 ) ) )
& ( ( in @ X1626 @ X1625 )
| X1627
| ( X1626 = X1624 )
| ~ ( in @ X1626 @ ( setadjoin @ X1624 @ X1625 ) ) )
& ( ~ X1627
| X1627
| ( X1626 = X1624 )
| ~ ( in @ X1626 @ ( setadjoin @ X1624 @ X1625 ) ) )
& ( ( in @ X1626 @ X1625 )
| X1627
| ~ X1627
| ~ ( in @ X1626 @ ( setadjoin @ X1624 @ X1625 ) ) )
& ( ~ X1627
| X1627
| ~ X1627
| ~ ( in @ X1626 @ ( setadjoin @ X1624 @ X1625 ) ) )
& ( ~ ( in @ X1630 @ ( setadjoin @ X1628 @ X1629 ) )
| ( X1630 = X1628 )
| ( in @ X1630 @ X1629 ) )
& ( ( dsetconstr @ X1631
@ ^ [Z0: $i] : $true )
= X1631 )
& ( ( in @ ( esk20_2 @ X1632 @ X1633 ) @ X1633 )
| ( in @ X1633 @ ( powerset @ X1632 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1632 @ X1633 ) @ X1632 )
| ( in @ X1633 @ ( powerset @ X1632 ) ) )
& ( in @ emptyset @ ( powerset @ X1635 ) )
& ( in @ emptyset @ ( powerset @ X1636 ) )
& ( ~ ( in @ X1638 @ ( powerset @ X1637 ) )
| ~ ( in @ X1639 @ X1638 )
| ( in @ X1639 @ X1637 ) )
& ( ~ ( in @ X1641 @ X1642 )
| ~ ( in @ X1642 @ X1640 )
| ( in @ X1641 @ ( setunion @ X1640 ) ) )
& ( ( in @ X1644 @ ( esk21_3 @ X1643 @ X1644 @ X1645 ) )
| X1645
| ~ ( in @ X1644 @ ( setunion @ X1643 ) ) )
& ( ( in @ ( esk21_3 @ X1643 @ X1644 @ X1645 ) @ X1643 )
| X1645
| ~ ( in @ X1644 @ ( setunion @ X1643 ) ) )
& ( ~ X1645
| X1645
| ~ ( in @ X1644 @ ( setunion @ X1643 ) ) )
& ( ~ ( in @ X1648 @ X1647 )
| ( in @ X1648 @ ( powerset @ ( setunion @ X1647 ) ) ) )
& ( ~ ( X1649 @ X1653 )
| ( X1653
= ( esk23_1 @ X1649 ) )
| ( X1649 @ ( esk22_2 @ X1649 @ X1650 ) )
| ~ ( X1649 @ X1650 ) )
& ( ( X1654
!= ( esk23_1 @ X1649 ) )
| ( X1649 @ X1654 )
| ( X1649 @ ( esk22_2 @ X1649 @ X1650 ) )
| ~ ( X1649 @ X1650 ) )
& ( ~ ( X1649 @ X1653 )
| ( X1653
= ( esk23_1 @ X1649 ) )
| ( X1650
!= ( esk22_2 @ X1649 @ X1650 ) )
| ~ ( X1649 @ X1650 ) )
& ( ( X1654
!= ( esk23_1 @ X1649 ) )
| ( X1649 @ X1654 )
| ( X1650
!= ( esk22_2 @ X1649 @ X1650 ) )
| ~ ( X1649 @ X1650 ) )
& ( ( in @ ( esk24_1 @ X1655 ) @ X1655 )
| ( X1655 = emptyset ) )
& ( $true
| ( X1655 = emptyset ) )
& ( ~ ( in @ X1657 @ ( setadjoin @ X1658 @ emptyset ) )
| ( X1657 = X1658 ) )
& ( ( X1659 = X1660 )
| ~ ( in @ X1660 @ ( setadjoin @ X1659 @ emptyset ) ) )
& ( ( X1661 != X1662 )
| ( in @ X1661 @ ( setadjoin @ X1662 @ emptyset ) ) )
& ( ~ ( in @ X1663 @ ( setadjoin @ X1664 @ emptyset ) )
| ( in @ X1664 @ ( setadjoin @ X1663 @ emptyset ) ) )
& ( ~ ( in @ X1667 @ ( setadjoin @ X1665 @ ( setadjoin @ X1666 @ emptyset ) ) )
| ( X1667 = X1665 )
| ( X1667 = X1666 ) )
& ( in @ X1668 @ ( setadjoin @ X1668 @ ( setadjoin @ X1669 @ emptyset ) ) )
& ( in @ X1671 @ ( setadjoin @ X1670 @ ( setadjoin @ X1671 @ emptyset ) ) )
& ( ~ ( in @ X1674 @ X1672 )
| ~ ( X1673 @ X1674 )
| ( ( dsetconstr @ X1672 @ X1673 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1676 @ emptyset )
| ( X1675 @ X1676 ) )
& ( ( in @ ( esk25_2 @ X1677 @ X1678 ) @ X1677 )
| ~ ( in @ X1679 @ X1677 )
| ( X1678 @ X1679 ) )
& ( ~ ( X1678 @ ( esk25_2 @ X1677 @ X1678 ) )
| ~ ( in @ X1679 @ X1677 )
| ( X1678 @ X1679 ) )
& ( ( in @ ( esk26_2 @ X1681 @ X1682 ) @ X1681 )
| ~ ( in @ X1684 @ X1681 )
| ~ ( X1682 @ X1684 ) )
& ( ( X1682 @ ( esk26_2 @ X1681 @ X1682 ) )
| ~ ( in @ X1684 @ X1681 )
| ~ ( X1682 @ X1684 ) )
& ( ( in @ ( esk27_2 @ X1685 @ X1686 ) @ X1685 )
| ~ ( in @ X1688 @ X1685 )
| ~ ( X1686 @ X1688 ) )
& ( ( X1686 @ ( esk27_2 @ X1685 @ X1686 ) )
| ~ ( in @ X1688 @ X1685 )
| ~ ( X1686 @ X1688 ) )
& ( ( in @ ( esk28_2 @ X1689 @ X1690 ) @ X1689 )
| ~ ( in @ X1691 @ X1689 )
| ( X1690 @ X1691 ) )
& ( ~ ( X1690 @ ( esk28_2 @ X1689 @ X1690 ) )
| ~ ( in @ X1691 @ X1689 )
| ( X1690 @ X1691 ) )
& ( ~ X1693
| ( in @ emptyset @ ( prop2set @ X1693 ) ) )
& ( ~ X1694
| ( set2prop @ ( prop2set @ X1694 ) ) )
& ( ( in @ ( esk29_2 @ X1695 @ X1696 ) @ X1695 )
| ~ ( in @ X1698 @ X1695 )
| ~ ( X1696 @ X1698 ) )
& ( ( X1696 @ ( esk29_2 @ X1695 @ X1696 ) )
| ~ ( in @ X1698 @ X1695 )
| ~ ( X1696 @ X1698 ) )
& ( ( in @ ( esk30_2 @ X1699 @ X1700 ) @ X1699 )
| ~ ( in @ X1701 @ X1699 )
| ( X1700 @ X1701 ) )
& ( ~ ( X1700 @ ( esk30_2 @ X1699 @ X1700 ) )
| ~ ( in @ X1701 @ X1699 )
| ( X1700 @ X1701 ) )
& ( ( X1703 @ ( esk32_1 @ X1703 ) )
| ( X1703 @ ( esk31_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 ) )
& ( ~ ( X1703 @ X1707 )
| ( ( esk32_1 @ X1703 )
= X1707 )
| ( X1703 @ ( esk31_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 ) )
& ( ( X1703 @ ( esk32_1 @ X1703 ) )
| ( X1704
!= ( esk31_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 ) )
& ( ~ ( X1703 @ X1707 )
| ( ( esk32_1 @ X1703 )
= X1707 )
| ( X1704
!= ( esk31_2 @ X1703 @ X1704 ) )
| ~ ( X1703 @ X1704 ) )
& ( ( X1708 @ ( esk35_1 @ X1708 ) )
| ( X1708 @ ( esk33_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ~ ( X1708 @ X1713 )
| ( ( esk35_1 @ X1708 )
= X1713 )
| ( X1708 @ ( esk33_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ( X1708 @ ( esk35_1 @ X1708 ) )
| ( X1708 @ ( esk34_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ~ ( X1708 @ X1713 )
| ( ( esk35_1 @ X1708 )
= X1713 )
| ( X1708 @ ( esk34_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ( X1708 @ ( esk35_1 @ X1708 ) )
| ( ( esk33_1 @ X1708 )
!= ( esk34_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ~ ( X1708 @ X1713 )
| ( ( esk35_1 @ X1708 )
= X1713 )
| ( ( esk33_1 @ X1708 )
!= ( esk34_1 @ X1708 ) )
| ~ ( X1708 @ X1709 ) )
& ( ( X1714 @ ( esk37_1 @ X1714 ) )
| ~ ( X1714 @ ( esk36_2 @ X1714 @ X1715 ) )
| ( ( esk36_2 @ X1714 @ X1715 )
!= X1715 ) )
& ( ~ ( X1714 @ X1718 )
| ( ( esk37_1 @ X1714 )
= X1718 )
| ~ ( X1714 @ ( esk36_2 @ X1714 @ X1715 ) )
| ( ( esk36_2 @ X1714 @ X1715 )
!= X1715 ) )
& ( ( X1714 @ ( esk37_1 @ X1714 ) )
| ( X1714 @ ( esk36_2 @ X1714 @ X1715 ) )
| ( ( esk36_2 @ X1714 @ X1715 )
= X1715 ) )
& ( ~ ( X1714 @ X1718 )
| ( ( esk37_1 @ X1714 )
= X1718 )
| ( X1714 @ ( esk36_2 @ X1714 @ X1715 ) )
| ( ( esk36_2 @ X1714 @ X1715 )
= X1715 ) )
& ( ( X1719 != X1720 )
| ( X1721 != X1722 )
| ~ ( in @ X1721 @ X1719 )
| ( in @ X1722 @ X1720 ) )
& ( ~ ( in @ X1725 @ X1723 )
| ( in @ X1726 @ X1724 )
| ( X1725 != X1726 )
| ( X1723 != X1724 ) )
& ( ~ ( in @ X1726 @ X1724 )
| ( in @ X1725 @ X1723 )
| ( X1725 != X1726 )
| ( X1723 != X1724 ) )
& ( ( X1727 @ ( esk38_2 @ X1727 @ X1728 ) )
| ~ ( X1727 @ X1728 )
| ~ ( X1727 @ X1730 )
| ~ ( X1727 @ X1731 )
| ( X1730 = X1731 ) )
& ( ( X1728
!= ( esk38_2 @ X1727 @ X1728 ) )
| ~ ( X1727 @ X1728 )
| ~ ( X1727 @ X1730 )
| ~ ( X1727 @ X1731 )
| ( X1730 = X1731 ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( ( esk39_2 @ X1732 @ X1733 )
= ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ~ ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ~ ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1732 @ ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1733 @ ( esk42_2 @ X1732 @ X1733 ) )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1733 @ X1739 )
| ( ( esk42_2 @ X1732 @ X1733 )
= X1739 )
| ( X1736
!= ( esk41_3 @ X1732 @ X1733 @ X1736 ) )
| ~ ( X1732 @ X1736 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1733 @ ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ( X1732 @ ( esk44_2 @ X1732 @ X1733 ) )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( ~ ( X1732 @ X1743 )
| ( ( esk44_2 @ X1732 @ X1733 )
= X1743 )
| ( X1740
!= ( esk43_3 @ X1732 @ X1733 @ X1740 ) )
| ~ ( X1733 @ X1740 )
| ( X1732 @ ( esk39_2 @ X1732 @ X1733 ) )
| ( X1733 @ ( esk40_2 @ X1732 @ X1733 ) ) )
& ( emptyset = emptyset )
& ( ( X1744 != X1745 )
| ( X1746 != X1747 )
| ( ( setadjoin @ X1744 @ X1746 )
= ( setadjoin @ X1745 @ X1747 ) ) )
& ( ( X1748 != X1749 )
| ( ( powerset @ X1748 )
= ( powerset @ X1749 ) ) )
& ( ( X1750 != X1751 )
| ( ( setunion @ X1750 )
= ( setunion @ X1751 ) ) )
& ( omega = omega )
& ( ( X1752 @ ( esk45_2 @ X1752 @ X1753 ) )
| ~ ( X1752 @ X1753 )
| ~ ( X1752 @ X1755 )
| ~ ( X1752 @ X1756 )
| ( X1755 = X1756 ) )
& ( ( X1753
!= ( esk45_2 @ X1752 @ X1753 ) )
| ~ ( X1752 @ X1753 )
| ~ ( X1752 @ X1755 )
| ~ ( X1752 @ X1756 )
| ( X1755 = X1756 ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( ( esk46_2 @ X1757 @ X1758 )
= ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( ( esk46_2 @ X1757 @ X1758 )
= ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( ( esk46_2 @ X1757 @ X1758 )
= ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( ( esk46_2 @ X1757 @ X1758 )
= ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ~ ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ~ ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ~ ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ~ ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ~ ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ~ ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ~ ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ~ ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1757 @ ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1758 @ ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( X1763
!= ( esk49_3 @ X1757 @ X1758 @ X1763 ) )
| ~ ( X1758 @ X1763 )
| ( ( descr @ X1757 )
= ( descr @ X1758 ) )
| ( X1761
!= ( esk48_3 @ X1757 @ X1758 @ X1761 ) )
| ~ ( X1757 @ X1761 )
| ( X1757 @ ( esk46_2 @ X1757 @ X1758 ) )
| ( X1758 @ ( esk47_2 @ X1757 @ X1758 ) ) )
& ( ( in @ ( esk50_4 @ X1765 @ X1766 @ X1767 @ X1768 ) @ X1765 )
| ( ( dsetconstr @ X1765 @ X1767 )
= ( dsetconstr @ X1766 @ X1768 ) )
| ( X1765 != X1766 ) )
& ( ( in @ ( esk51_4 @ X1765 @ X1766 @ X1767 @ X1768 ) @ X1766 )
| ( ( dsetconstr @ X1765 @ X1767 )
= ( dsetconstr @ X1766 @ X1768 ) )
| ( X1765 != X1766 ) )
& ( ( ( esk50_4 @ X1765 @ X1766 @ X1767 @ X1768 )
= ( esk51_4 @ X1765 @ X1766 @ X1767 @ X1768 ) )
| ( ( dsetconstr @ X1765 @ X1767 )
= ( dsetconstr @ X1766 @ X1768 ) )
| ( X1765 != X1766 ) )
& ( ~ ( X1767 @ ( esk50_4 @ X1765 @ X1766 @ X1767 @ X1768 ) )
| ~ ( X1768 @ ( esk51_4 @ X1765 @ X1766 @ X1767 @ X1768 ) )
| ( ( dsetconstr @ X1765 @ X1767 )
= ( dsetconstr @ X1766 @ X1768 ) )
| ( X1765 != X1766 ) )
& ( ( X1767 @ ( esk50_4 @ X1765 @ X1766 @ X1767 @ X1768 ) )
| ( X1768 @ ( esk51_4 @ X1765 @ X1766 @ X1767 @ X1768 ) )
| ( ( dsetconstr @ X1765 @ X1767 )
= ( dsetconstr @ X1766 @ X1768 ) )
| ( X1765 != X1766 ) )
& ( ( in @ ( esk52_2 @ X1771 @ X1772 ) @ X1771 )
| ( subset @ X1771 @ X1772 ) )
& ( ~ ( in @ ( esk52_2 @ X1771 @ X1772 ) @ X1772 )
| ( subset @ X1771 @ X1772 ) )
& ( ( X1774 != X1775 )
| ( subset @ X1775 @ X1774 ) )
& ( ( X1776 != X1777 )
| ( subset @ X1776 @ X1777 ) )
& ( ( in @ ( esk53_2 @ X1778 @ X1779 ) @ X1778 )
| ( subset @ X1778 @ X1779 ) )
& ( ~ ( in @ ( esk53_2 @ X1778 @ X1779 ) @ X1779 )
| ( subset @ X1778 @ X1779 ) )
& ( subset @ emptyset @ X1781 )
& ( ~ ( subset @ X1782 @ X1783 )
| ~ ( in @ X1784 @ X1782 )
| ( in @ X1784 @ X1783 ) )
& ( ~ ( subset @ X1785 @ X1786 )
| ( in @ X1787 @ X1786 )
| ~ ( in @ X1787 @ X1785 ) )
& ( ~ ( in @ X1790 @ X1788 )
| ( in @ X1790 @ X1789 )
| ~ ( subset @ X1788 @ X1789 ) )
& ( ( subset @ X1791 @ X1792 )
| ( X1791 != X1792 ) )
& ( ~ ( in @ X1795 @ X1793 )
| ( in @ X1795 @ X1794 )
| ( X1793 != X1794 ) )
& ( subset @ X1796 @ X1796 )
& ( ~ ( subset @ X1797 @ X1798 )
| ~ ( subset @ X1798 @ X1799 )
| ( subset @ X1797 @ X1799 ) )
& ( subset @ X1801 @ ( setadjoin @ X1800 @ X1801 ) )
& ( ~ ( subset @ X1802 @ X1804 )
| ( subset @ X1802 @ ( setadjoin @ X1803 @ X1804 ) ) )
& ( ~ ( subset @ X1805 @ X1806 )
| ( in @ X1805 @ ( powerset @ X1806 ) ) )
& ( ~ ( subset @ X1807 @ X1808 )
| ~ ( subset @ X1808 @ X1807 )
| ( X1807 = X1808 ) )
& ( ~ ( subset @ X1809 @ emptyset )
| ( X1809 = emptyset ) )
& ( ~ ( subset @ X1811 @ X1810 )
| ( in @ X1811 @ ( powerset @ X1810 ) ) )
& ( ~ ( in @ X1813 @ ( powerset @ X1812 ) )
| ( subset @ X1813 @ X1812 ) )
& ( in @ X1814 @ ( powerset @ X1814 ) )
& ( ~ ( subset @ X1815 @ X1816 )
| ( subset @ ( powerset @ X1815 ) @ ( powerset @ X1816 ) ) )
& ( in @ ( dsetconstr @ X1817 @ X1818 ) @ ( powerset @ X1817 ) )
& ( subset @ ( dsetconstr @ X1819 @ X1820 ) @ X1819 )
& ( ~ ( in @ X1823 @ X1821 )
| ( in @ X1823 @ ( binunion @ X1821 @ X1822 ) ) )
& ( in @ X1825 @ ( setadjoin @ X1824 @ ( setadjoin @ X1825 @ emptyset ) ) )
& ( ~ ( in @ X1828 @ X1827 )
| ( in @ X1828 @ ( binunion @ X1826 @ X1827 ) ) )
& ( ( in @ X1831 @ X1830 )
| X1832
| ( in @ X1831 @ X1829 )
| ~ ( in @ X1831 @ ( binunion @ X1829 @ X1830 ) ) )
& ( ~ X1832
| X1832
| ( in @ X1831 @ X1829 )
| ~ ( in @ X1831 @ ( binunion @ X1829 @ X1830 ) ) )
& ( ( in @ X1831 @ X1830 )
| X1832
| ~ X1832
| ~ ( in @ X1831 @ ( binunion @ X1829 @ X1830 ) ) )
& ( ~ X1832
| X1832
| ~ X1832
| ~ ( in @ X1831 @ ( binunion @ X1829 @ X1830 ) ) )
& ( ~ ( in @ X1835 @ ( binunion @ X1833 @ X1834 ) )
| ( in @ X1835 @ X1833 )
| ( in @ X1835 @ X1834 ) )
& ( subset @ X1836 @ ( binunion @ X1836 @ X1837 ) )
& ( subset @ X1839 @ ( binunion @ X1838 @ X1839 ) )
& ( ~ ( in @ X1842 @ X1840 )
| ~ ( in @ X1842 @ X1841 )
| ( in @ X1842 @ ( binintersect @ X1840 @ X1841 ) ) )
& ( ~ ( subset @ X1845 @ X1843 )
| ~ ( subset @ X1845 @ X1844 )
| ( subset @ X1845 @ ( binintersect @ X1843 @ X1844 ) ) )
& ( ~ ( in @ X1848 @ ( binintersect @ X1846 @ X1847 ) )
| ( in @ X1848 @ X1846 ) )
& ( subset @ ( binintersect @ X1849 @ X1850 ) @ X1849 )
& ( ~ ( subset @ X1851 @ X1852 )
| ( ( binintersect @ X1851 @ X1852 )
= X1851 ) )
& ( ( ( binintersect @ X1853 @ X1854 )
!= X1854 )
| ( subset @ X1854 @ X1853 ) )
& ( ~ ( in @ X1857 @ ( binintersect @ X1855 @ X1856 ) )
| ( in @ X1857 @ X1856 ) )
& ( ( in @ ( esk54_2 @ X1858 @ X1859 ) @ X1858 )
| ( ( binintersect @ X1858 @ X1859 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X1858 @ X1859 ) @ X1859 )
| ( ( binintersect @ X1858 @ X1859 )
= emptyset ) )
& ( subset @ ( binintersect @ X1861 @ X1862 ) @ X1862 )
& ( ~ ( subset @ X1864 @ X1863 )
| ( ( binintersect @ X1863 @ X1864 )
= X1864 ) )
& ( ( ( binintersect @ X1865 @ X1866 )
!= X1865 )
| ( subset @ X1865 @ X1866 ) )
& ( ( binintersect @ X1867 @ ( binunion @ X1868 @ X1869 ) )
= ( binunion @ ( binintersect @ X1867 @ X1868 ) @ ( binintersect @ X1867 @ X1869 ) ) )
& ( ~ ( in @ X1872 @ X1870 )
| ( in @ X1872 @ X1871 )
| ( in @ X1872 @ ( setminus @ X1870 @ X1871 ) ) )
& ( ~ ( in @ X1875 @ ( setminus @ X1873 @ X1874 ) )
| ( in @ X1875 @ X1873 ) )
& ( ~ ( in @ X1878 @ ( setminus @ X1876 @ X1877 ) )
| ~ ( in @ X1878 @ X1877 ) )
& ( ~ ( subset @ X1879 @ X1880 )
| ( ( setminus @ X1879 @ X1880 )
= emptyset ) )
& ( ( in @ X1883 @ ( setminus @ X1881 @ X1882 ) )
| ~ ( in @ X1883 @ X1881 )
| ( in @ X1883 @ X1882 ) )
& ( ( in @ X1886 @ ( setminus @ X1884 @ X1885 ) )
| ( in @ X1886 @ X1885 )
| ~ ( in @ X1886 @ X1884 ) )
& ( ( in @ X1889 @ X1887 )
| ~ ( in @ X1889 @ ( setminus @ X1887 @ X1888 ) ) )
& ( ~ ( in @ X1892 @ X1891 )
| ~ ( in @ X1892 @ ( setminus @ X1890 @ X1891 ) ) )
& ( subset @ ( setminus @ X1893 @ X1894 ) @ X1893 )
& ( ( ( setminus @ X1895 @ X1896 )
!= emptyset )
| ( subset @ X1895 @ X1896 ) )
& ( ~ ( in @ X1899 @ X1897 )
| X1900
| ( in @ X1899 @ X1897 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ( in @ X1899 @ X1898 )
| X1900
| ( in @ X1899 @ X1897 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ X1900
| X1900
| ( in @ X1899 @ X1897 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ ( in @ X1899 @ X1897 )
| X1900
| ~ ( in @ X1899 @ X1898 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ( in @ X1899 @ X1898 )
| X1900
| ~ ( in @ X1899 @ X1898 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ X1900
| X1900
| ~ ( in @ X1899 @ X1898 )
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ ( in @ X1899 @ X1897 )
| X1900
| ~ X1900
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ( in @ X1899 @ X1898 )
| X1900
| ~ X1900
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ X1900
| X1900
| ~ X1900
| ~ ( in @ X1899 @ ( symdiff @ X1897 @ X1898 ) ) )
& ( ~ ( in @ X1903 @ X1901 )
| ( in @ X1903 @ X1902 )
| ( in @ X1903 @ ( symdiff @ X1901 @ X1902 ) ) )
& ( ( in @ X1906 @ X1904 )
| ~ ( in @ X1906 @ X1905 )
| ( in @ X1906 @ ( symdiff @ X1904 @ X1905 ) ) )
& ( ~ ( in @ X1909 @ X1907 )
| ~ ( in @ X1909 @ X1908 )
| ~ ( in @ X1909 @ ( symdiff @ X1907 @ X1908 ) ) )
& ( ( in @ X1912 @ X1910 )
| ( in @ X1912 @ X1911 )
| ~ ( in @ X1912 @ ( symdiff @ X1910 @ X1911 ) ) )
& ( in @ X1914 @ ( setadjoin @ X1913 @ ( setadjoin @ X1914 @ emptyset ) ) )
& ( in @ X1915 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1915 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1915 @ ( setadjoin @ X1916 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1918 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1917 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1917 @ ( setadjoin @ X1918 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1919 @ ( setadjoin @ X1920 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1921 @ X1922 ) )
& ( ~ ( in @ X1924 @ X1923 )
| ( subset @ ( setadjoin @ X1924 @ emptyset ) @ X1923 ) )
& ( ~ ( in @ X1926 @ X1925 )
| ( in @ ( setadjoin @ X1926 @ emptyset ) @ ( powerset @ X1925 ) ) )
& ( ~ ( in @ X1929 @ X1927 )
| ( in @ ( setadjoin @ X1929 @ emptyset ) @ ( powerset @ ( binunion @ X1927 @ X1928 ) ) ) )
& ( ~ ( in @ X1932 @ ( setadjoin @ X1930 @ ( setadjoin @ X1931 @ emptyset ) ) )
| ( X1932 = X1930 )
| ( X1932 = X1931 ) )
& ( ~ ( in @ X1935 @ X1933 )
| ~ ( in @ X1936 @ X1934 )
| ( subset @ ( setadjoin @ X1935 @ ( setadjoin @ X1936 @ emptyset ) ) @ ( binunion @ X1933 @ X1934 ) ) )
& ( ~ ( in @ X1939 @ X1937 )
| ~ ( in @ X1940 @ X1938 )
| ( in @ ( setadjoin @ X1939 @ ( setadjoin @ X1940 @ emptyset ) ) @ ( powerset @ ( binunion @ X1937 @ X1938 ) ) ) )
& ( ~ ( in @ X1943 @ X1941 )
| ~ ( in @ X1944 @ X1942 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1943 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1943 @ ( setadjoin @ X1944 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1941 @ X1942 ) ) ) )
& ( ~ ( in @ X1947 @ X1945 )
| ~ ( in @ X1948 @ X1946 )
| ( in @ ( setadjoin @ ( setadjoin @ X1947 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1947 @ ( setadjoin @ X1948 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1945 @ X1946 ) ) ) ) )
& ( ~ ( in @ X1951 @ X1949 )
| ~ ( in @ X1952 @ X1950 )
| ( in @ ( kpair @ X1951 @ X1952 ) @ ( powerset @ ( powerset @ ( binunion @ X1949 @ X1950 ) ) ) ) )
& ( ~ ( in @ X1955 @ X1953 )
| ~ ( in @ X1956 @ X1954 )
| ( in @ ( kpair @ X1955 @ X1956 ) @ ( cartprod @ X1953 @ X1954 ) ) )
& ( ( in @ ( esk55_3 @ X1957 @ X1958 @ X1959 ) @ X1957 )
| ~ ( in @ X1959 @ ( cartprod @ X1957 @ X1958 ) ) )
& ( ( in @ ( esk56_3 @ X1957 @ X1958 @ X1959 ) @ X1958 )
| ~ ( in @ X1959 @ ( cartprod @ X1957 @ X1958 ) ) )
& ( ( X1959
= ( kpair @ ( esk55_3 @ X1957 @ X1958 @ X1959 ) @ ( esk56_3 @ X1957 @ X1958 @ X1959 ) ) )
| ~ ( in @ X1959 @ ( cartprod @ X1957 @ X1958 ) ) )
& ( ~ ( in @ X1964 @ ( cartprod @ X1962 @ X1963 ) )
| ( iskpair @ X1964 ) )
& ( ( in @ ( esk57_2 @ X1965 @ X1966 ) @ X1965 )
| ~ ( in @ X1966 @ ( setunion @ X1965 ) ) )
& ( ( in @ X1966 @ ( esk57_2 @ X1965 @ X1966 ) )
| ~ ( in @ X1966 @ ( setunion @ X1965 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1968 @ emptyset ) ) @ X1968 )
& ( subset @ X1969 @ ( setunion @ ( setadjoin @ X1969 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1970 @ emptyset ) )
= X1970 )
& ( ( in @ ( esk58_2 @ X1971 @ X1972 ) @ X1971 )
| ~ ( in @ X1975 @ X1971 )
| ~ ( X1972 @ X1975 )
| ( singleton @ ( dsetconstr @ X1971 @ X1972 ) ) )
& ( ( in @ ( esk59_2 @ X1971 @ X1972 ) @ X1971 )
| ~ ( in @ X1975 @ X1971 )
| ~ ( X1972 @ X1975 )
| ( singleton @ ( dsetconstr @ X1971 @ X1972 ) ) )
& ( ( X1972 @ ( esk58_2 @ X1971 @ X1972 ) )
| ~ ( in @ X1975 @ X1971 )
| ~ ( X1972 @ X1975 )
| ( singleton @ ( dsetconstr @ X1971 @ X1972 ) ) )
& ( ( X1972 @ ( esk59_2 @ X1971 @ X1972 ) )
| ~ ( in @ X1975 @ X1971 )
| ~ ( X1972 @ X1975 )
| ( singleton @ ( dsetconstr @ X1971 @ X1972 ) ) )
& ( ( ( esk58_2 @ X1971 @ X1972 )
!= ( esk59_2 @ X1971 @ X1972 ) )
| ~ ( in @ X1975 @ X1971 )
| ~ ( X1972 @ X1975 )
| ( singleton @ ( dsetconstr @ X1971 @ X1972 ) ) )
& ( ( in @ ( esk60_2 @ X1976 @ X1977 ) @ X1976 )
| ~ ( singleton @ ( dsetconstr @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk60_2 @ X1976 @ X1977 ) )
| ~ ( singleton @ ( dsetconstr @ X1976 @ X1977 ) ) )
& ( ( in @ ( esk61_3 @ X1979 @ X1980 @ X1981 ) @ X1979 )
| ( singleton @ ( dsetconstr @ X1979 @ X1980 ) )
| ~ ( X1980 @ X1981 )
| ~ ( in @ X1981 @ X1979 ) )
& ( ( X1980 @ ( esk61_3 @ X1979 @ X1980 @ X1981 ) )
| ( singleton @ ( dsetconstr @ X1979 @ X1980 ) )
| ~ ( X1980 @ X1981 )
| ~ ( in @ X1981 @ X1979 ) )
& ( ( ( esk61_3 @ X1979 @ X1980 @ X1981 )
!= X1981 )
| ( singleton @ ( dsetconstr @ X1979 @ X1980 ) )
| ~ ( X1980 @ X1981 )
| ~ ( in @ X1981 @ X1979 ) )
& ( ( in @ ( esk62_2 @ X1983 @ X1984 ) @ X1983 )
| ~ ( in @ X1987 @ X1983 )
| ~ ( X1984 @ X1987 )
| ( singleton @ ( dsetconstr @ X1983 @ X1984 ) ) )
& ( ( in @ ( esk63_2 @ X1983 @ X1984 ) @ X1983 )
| ~ ( in @ X1987 @ X1983 )
| ~ ( X1984 @ X1987 )
| ( singleton @ ( dsetconstr @ X1983 @ X1984 ) ) )
& ( ( X1984 @ ( esk62_2 @ X1983 @ X1984 ) )
| ~ ( in @ X1987 @ X1983 )
| ~ ( X1984 @ X1987 )
| ( singleton @ ( dsetconstr @ X1983 @ X1984 ) ) )
& ( ( X1984 @ ( esk63_2 @ X1983 @ X1984 ) )
| ~ ( in @ X1987 @ X1983 )
| ~ ( X1984 @ X1987 )
| ( singleton @ ( dsetconstr @ X1983 @ X1984 ) ) )
& ( ( ( esk62_2 @ X1983 @ X1984 )
!= ( esk63_2 @ X1983 @ X1984 ) )
| ~ ( in @ X1987 @ X1983 )
| ~ ( X1984 @ X1987 )
| ( singleton @ ( dsetconstr @ X1983 @ X1984 ) ) )
& ( ( ( setadjoin @ X1988 @ emptyset )
!= ( setadjoin @ X1989 @ emptyset ) )
| ( X1988 = X1989 ) )
& ( ~ ( in @ ( setadjoin @ X1992 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1990 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1990 @ ( setadjoin @ X1991 @ emptyset ) ) @ emptyset ) ) )
| ( X1990 = X1992 ) )
& ( ~ ( iskpair @ X1993 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1993 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1993 ) ) ) )
& ( ~ ( singleton @ X1994 )
| ( in @ ( setunion @ X1994 ) @ X1994 ) )
& ( ( kfst @ ( kpair @ X1995 @ X1996 ) )
= X1995 )
& ( ~ ( in @ X1999 @ ( cartprod @ X1997 @ X1998 ) )
| ( in @ ( kfst @ X1999 ) @ X1997 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2000 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2000 @ ( setadjoin @ X2001 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2002 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2002 @ ( setadjoin @ X2003 @ emptyset ) ) @ emptyset ) ) )
| ( X2000 = X2002 ) )
& ( ( ( kpair @ X2004 @ X2005 )
!= ( kpair @ X2006 @ X2007 ) )
| ( X2004 = X2006 ) )
& ( ( X2008 != X2009 )
| ( ( setadjoin @ X2008 @ ( setadjoin @ X2009 @ emptyset ) )
= ( setadjoin @ X2008 @ emptyset ) ) )
& ( ( X2010 != X2011 )
| ( ( setadjoin @ ( setadjoin @ X2010 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2010 @ ( setadjoin @ X2011 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2010 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2012 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2012 @ ( setadjoin @ X2013 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2014 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2014 @ ( setadjoin @ X2015 @ emptyset ) ) @ emptyset ) ) )
| ( X2014 != X2015 )
| ( X2013 = X2015 ) )
& ( ( ( setadjoin @ X2016 @ ( setadjoin @ X2017 @ emptyset ) )
!= ( setadjoin @ X2018 @ emptyset ) )
| ( X2016 = X2017 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2019 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2019 @ ( setadjoin @ X2020 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2021 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2021 @ ( setadjoin @ X2022 @ emptyset ) ) @ emptyset ) ) )
| ( X2020 = X2022 ) )
& ( ( ( kpair @ X2023 @ X2024 )
!= ( kpair @ X2025 @ X2026 ) )
| ( X2024 = X2026 ) )
& ( ~ ( iskpair @ X2027 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2027 )
@ ^ [Z0: $i] :
( X2027
= ( kpair @ ( kfst @ X2027 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2028 @ X2029 ) )
= X2029 )
& ( ~ ( iskpair @ X2030 )
| ( ( kpair @ ( kfst @ X2030 ) @ ( ksnd @ X2030 ) )
= X2030 ) )
& ( ~ ( in @ X2033 @ ( cartprod @ X2031 @ X2032 ) )
| ( in @ ( ksnd @ X2033 ) @ X2032 ) )
& ( ~ ( in @ ( kpair @ X2036 @ X2037 ) @ ( cartprod @ X2034 @ X2035 ) )
| ( in @ X2036 @ X2034 ) )
& ( ~ ( in @ ( kpair @ X2040 @ X2041 ) @ ( cartprod @ X2038 @ X2039 ) )
| ( in @ X2041 @ X2039 ) )
& ( ~ ( in @ X2044 @ X2042 )
| ~ ( in @ X2045 @ X2043 )
| ( ( kpair @ X2044 @ X2045 )
= ( kpair @ X2044 @ X2045 ) ) )
& ( ~ ( in @ X2048 @ X2046 )
| ~ ( in @ X2049 @ X2047 )
| ( ( kfst @ ( kpair @ X2048 @ X2049 ) )
= X2048 ) )
& ( ~ ( in @ X2052 @ X2050 )
| ~ ( in @ X2053 @ X2051 )
| ( ( ksnd @ ( kpair @ X2052 @ X2053 ) )
= X2053 ) )
& ( ~ ( in @ X2056 @ ( cartprod @ X2054 @ X2055 ) )
| ( ( kpair @ ( kfst @ X2056 ) @ ( ksnd @ X2056 ) )
= X2056 ) )
& ( ~ ( in @ X2060 @ X2057 )
| ~ ( in @ X2061 @ X2058 )
| ~ ( X2059 @ X2060 @ X2061 )
| ( in @ ( kpair @ X2060 @ X2061 ) @ ( dpsetconstr @ X2057 @ X2058 @ X2059 ) ) )
& ( subset @ ( dpsetconstr @ X2062 @ X2063 @ X2064 ) @ ( cartprod @ X2062 @ X2063 ) )
& ( subset @ ( dpsetconstr @ X2065 @ X2066 @ X2067 ) @ ( cartprod @ X2065 @ X2066 ) )
& ( ~ ( in @ X2071 @ X2068 )
| ~ ( in @ X2072 @ X2069 )
| ~ ( in @ ( kpair @ X2071 @ X2072 ) @ ( dpsetconstr @ X2068 @ X2069 @ X2070 ) )
| ( X2070 @ X2071 @ X2072 ) )
& ( ~ ( in @ ( kpair @ X2076 @ X2077 ) @ ( dpsetconstr @ X2073 @ X2074 @ X2075 ) )
| ( in @ X2076 @ X2073 ) )
& ( ~ ( in @ ( kpair @ X2081 @ X2082 ) @ ( dpsetconstr @ X2078 @ X2079 @ X2080 ) )
| ( in @ X2082 @ X2079 ) )
& ( ~ ( in @ ( kpair @ X2086 @ X2087 ) @ ( dpsetconstr @ X2083 @ X2084 @ X2085 ) )
| ( X2085 @ X2086 @ X2087 ) )
& ( ~ ( func @ X2088 @ X2089 @ X2090 )
| ~ ( in @ X2091 @ X2088 )
| ( singleton
@ ( dsetconstr @ X2089
@ ^ [Z0: $i] : ( in @ ( kpair @ X2091 @ Z0 ) @ X2090 ) ) ) )
& ( ~ ( func @ X2092 @ X2093 @ X2094 )
| ~ ( in @ X2095 @ X2092 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2093
@ ^ [Z0: $i] : ( in @ ( kpair @ X2095 @ Z0 ) @ X2094 ) ) )
@ X2093 ) )
& ( ~ ( func @ X2096 @ X2097 @ X2098 )
| ~ ( in @ X2099 @ X2096 )
| ( in @ ( ap @ X2096 @ X2097 @ X2098 @ X2099 ) @ X2097 ) )
& ( ~ ( in @ X2102 @ ( funcSet @ X2100 @ X2101 ) )
| ( func @ X2100 @ X2101 @ X2102 ) )
& ( ~ ( in @ X2105 @ ( funcSet @ X2103 @ X2104 ) )
| ~ ( in @ X2106 @ X2103 )
| ( in @ ( ap @ X2103 @ X2104 @ X2105 @ X2106 ) @ X2104 ) )
& ( ~ ( func @ X2107 @ X2108 @ X2109 )
| ( in @ X2109 @ ( funcSet @ X2107 @ X2108 ) ) )
& ( ( in @ ( esk64_3 @ X2110 @ X2111 @ X2112 ) @ X2110 )
| ( func @ X2110 @ X2111
@ ( dpsetconstr @ X2110 @ X2111
@ ^ [Z0: $i] : ( $eq @ ( X2112 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2112 @ ( esk64_3 @ X2110 @ X2111 @ X2112 ) ) @ X2111 )
| ( func @ X2110 @ X2111
@ ( dpsetconstr @ X2110 @ X2111
@ ^ [Z0: $i] : ( $eq @ ( X2112 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2114 @ X2115 @ X2116 ) @ X2114 )
| ( func @ X2114 @ X2115 @ ( lam @ X2114 @ X2115 @ X2116 ) ) )
& ( ~ ( in @ ( X2116 @ ( esk65_3 @ X2114 @ X2115 @ X2116 ) ) @ X2115 )
| ( func @ X2114 @ X2115 @ ( lam @ X2114 @ X2115 @ X2116 ) ) )
& ( ( in @ ( esk66_3 @ X2118 @ X2119 @ X2120 ) @ X2118 )
| ( in @ ( lam @ X2118 @ X2119 @ X2120 ) @ ( funcSet @ X2118 @ X2119 ) ) )
& ( ~ ( in @ ( X2120 @ ( esk66_3 @ X2118 @ X2119 @ X2120 ) ) @ X2119 )
| ( in @ ( lam @ X2118 @ X2119 @ X2120 ) @ ( funcSet @ X2118 @ X2119 ) ) )
& ( ( in @ ( esk67_4 @ X2122 @ X2123 @ X2124 @ X2125 ) @ X2122 )
| ~ ( in @ X2128 @ X2124 )
| ( X2125 @ X2128 )
| ~ ( subset @ X2124 @ ( cartprod @ X2122 @ X2123 ) ) )
& ( ( in @ ( esk68_4 @ X2122 @ X2123 @ X2124 @ X2125 ) @ X2123 )
| ~ ( in @ X2128 @ X2124 )
| ( X2125 @ X2128 )
| ~ ( subset @ X2124 @ ( cartprod @ X2122 @ X2123 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2122 @ X2123 @ X2124 @ X2125 ) @ ( esk68_4 @ X2122 @ X2123 @ X2124 @ X2125 ) ) @ X2124 )
| ~ ( in @ X2128 @ X2124 )
| ( X2125 @ X2128 )
| ~ ( subset @ X2124 @ ( cartprod @ X2122 @ X2123 ) ) )
& ( ~ ( X2125 @ ( kpair @ ( esk67_4 @ X2122 @ X2123 @ X2124 @ X2125 ) @ ( esk68_4 @ X2122 @ X2123 @ X2124 @ X2125 ) ) )
| ~ ( in @ X2128 @ X2124 )
| ( X2125 @ X2128 )
| ~ ( subset @ X2124 @ ( cartprod @ X2122 @ X2123 ) ) )
& ( ( in @ ( esk69_4 @ X2129 @ X2130 @ X2131 @ X2132 ) @ X2129 )
| ~ ( in @ X2135 @ X2131 )
| ( X2132 @ X2135 )
| ~ ( subset @ X2131 @ ( cartprod @ X2129 @ X2130 ) ) )
& ( ( in @ ( esk70_4 @ X2129 @ X2130 @ X2131 @ X2132 ) @ X2130 )
| ~ ( in @ X2135 @ X2131 )
| ( X2132 @ X2135 )
| ~ ( subset @ X2131 @ ( cartprod @ X2129 @ X2130 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2129 @ X2130 @ X2131 @ X2132 ) @ ( esk70_4 @ X2129 @ X2130 @ X2131 @ X2132 ) ) @ X2131 )
| ~ ( in @ X2135 @ X2131 )
| ( X2132 @ X2135 )
| ~ ( subset @ X2131 @ ( cartprod @ X2129 @ X2130 ) ) )
& ( ~ ( X2132 @ ( kpair @ ( esk69_4 @ X2129 @ X2130 @ X2131 @ X2132 ) @ ( esk70_4 @ X2129 @ X2130 @ X2131 @ X2132 ) ) )
| ~ ( in @ X2135 @ X2131 )
| ( X2132 @ X2135 )
| ~ ( subset @ X2131 @ ( cartprod @ X2129 @ X2130 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2136 @ X2137 ) )
| ~ ( in @ X2138 @ X2136 )
| ~ ( in @ X2139 @ X2136 )
| ~ ( X2137 @ X2138 )
| ~ ( X2137 @ X2139 )
| ( X2138 = X2139 ) )
& ( ~ ( func @ X2140 @ X2141 @ X2142 )
| ~ ( in @ X2143 @ X2140 )
| ( in @ ( kpair @ X2143 @ ( ap @ X2140 @ X2141 @ X2142 @ X2143 ) ) @ X2142 ) )
& ( ~ ( in @ X2146 @ ( funcSet @ X2144 @ X2145 ) )
| ~ ( in @ X2147 @ X2144 )
| ( in @ ( kpair @ X2147 @ ( ap @ X2144 @ X2145 @ X2146 @ X2147 ) ) @ X2146 ) )
& ( ~ ( func @ X2148 @ X2149 @ X2150 )
| ~ ( in @ X2151 @ X2148 )
| ~ ( in @ X2152 @ X2149 )
| ~ ( in @ ( kpair @ X2151 @ X2152 ) @ X2150 )
| ( ( ap @ X2148 @ X2149 @ X2150 @ X2151 )
= X2152 ) )
& ( ( in @ ( esk71_4 @ X2153 @ X2154 @ X2155 @ X2156 ) @ X2153 )
| ~ ( in @ X2158 @ X2153 )
| ~ ( in @ X2159 @ X2154 )
| ~ ( in @ ( kpair @ X2158 @ X2159 ) @ X2156 )
| ( in @ ( kpair @ X2158 @ X2159 ) @ X2155 )
| ~ ( func @ X2153 @ X2154 @ X2156 )
| ~ ( func @ X2153 @ X2154 @ X2155 ) )
& ( ( ( ap @ X2153 @ X2154 @ X2155 @ ( esk71_4 @ X2153 @ X2154 @ X2155 @ X2156 ) )
!= ( ap @ X2153 @ X2154 @ X2156 @ ( esk71_4 @ X2153 @ X2154 @ X2155 @ X2156 ) ) )
| ~ ( in @ X2158 @ X2153 )
| ~ ( in @ X2159 @ X2154 )
| ~ ( in @ ( kpair @ X2158 @ X2159 ) @ X2156 )
| ( in @ ( kpair @ X2158 @ X2159 ) @ X2155 )
| ~ ( func @ X2153 @ X2154 @ X2156 )
| ~ ( func @ X2153 @ X2154 @ X2155 ) )
& ( ~ ( in @ X2162 @ ( funcSet @ X2160 @ X2161 ) )
| ~ ( in @ X2163 @ X2160 )
| ~ ( in @ X2164 @ X2161 )
| ~ ( in @ ( kpair @ X2163 @ X2164 ) @ X2162 )
| ( ( ap @ X2160 @ X2161 @ X2162 @ X2163 )
= X2164 ) )
& ( ( in @ ( esk72_4 @ X2165 @ X2166 @ X2167 @ X2168 ) @ X2165 )
| ( subset @ X2167 @ X2168 )
| ~ ( subset @ X2168 @ ( cartprod @ X2165 @ X2166 ) )
| ~ ( subset @ X2167 @ ( cartprod @ X2165 @ X2166 ) ) )
& ( ( in @ ( esk73_4 @ X2165 @ X2166 @ X2167 @ X2168 ) @ X2166 )
| ( subset @ X2167 @ X2168 )
| ~ ( subset @ X2168 @ ( cartprod @ X2165 @ X2166 ) )
| ~ ( subset @ X2167 @ ( cartprod @ X2165 @ X2166 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2165 @ X2166 @ X2167 @ X2168 ) @ ( esk73_4 @ X2165 @ X2166 @ X2167 @ X2168 ) ) @ X2167 )
| ( subset @ X2167 @ X2168 )
| ~ ( subset @ X2168 @ ( cartprod @ X2165 @ X2166 ) )
| ~ ( subset @ X2167 @ ( cartprod @ X2165 @ X2166 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2165 @ X2166 @ X2167 @ X2168 ) @ ( esk73_4 @ X2165 @ X2166 @ X2167 @ X2168 ) ) @ X2168 )
| ( subset @ X2167 @ X2168 )
| ~ ( subset @ X2168 @ ( cartprod @ X2165 @ X2166 ) )
| ~ ( subset @ X2167 @ ( cartprod @ X2165 @ X2166 ) ) )
& ( ( in @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ( X2173 = X2174 )
| ( in @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ( X2173 = X2174 )
| ( in @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ( X2173 = X2174 )
| ( in @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ( X2173 = X2174 )
| ( in @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ( X2173 = X2174 )
| ( in @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ( X2173 = X2174 )
| ( in @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ( X2173 = X2174 )
| ( in @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ( X2173 = X2174 )
| ( in @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ( X2173 = X2174 )
| ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ( X2173 = X2174 )
| ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ( X2173 = X2174 )
| ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ( X2173 = X2174 )
| ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2171 )
| ( X2173 = X2174 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ X2172 )
| ( X2173 = X2174 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ( X2173 = X2174 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk77_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
| ( X2173 = X2174 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2171 @ X2172 @ X2173 @ X2174 ) @ ( esk75_4 @ X2171 @ X2172 @ X2173 @ X2174 ) ) @ X2174 )
| ~ ( subset @ X2174 @ ( cartprod @ X2171 @ X2172 ) )
| ~ ( subset @ X2173 @ ( cartprod @ X2171 @ X2172 ) ) )
& ( ( in @ ( esk78_4 @ X2179 @ X2180 @ X2181 @ X2182 ) @ X2179 )
| ( X2181 = X2182 )
| ~ ( func @ X2179 @ X2180 @ X2182 )
| ~ ( func @ X2179 @ X2180 @ X2181 ) )
& ( ( ( ap @ X2179 @ X2180 @ X2181 @ ( esk78_4 @ X2179 @ X2180 @ X2181 @ X2182 ) )
!= ( ap @ X2179 @ X2180 @ X2182 @ ( esk78_4 @ X2179 @ X2180 @ X2181 @ X2182 ) ) )
| ( X2181 = X2182 )
| ~ ( func @ X2179 @ X2180 @ X2182 )
| ~ ( func @ X2179 @ X2180 @ X2181 ) )
& ( ( in @ ( esk79_4 @ X2184 @ X2185 @ X2186 @ X2187 ) @ X2184 )
| ( X2186 = X2187 )
| ~ ( in @ X2187 @ ( funcSet @ X2184 @ X2185 ) )
| ~ ( in @ X2186 @ ( funcSet @ X2184 @ X2185 ) ) )
& ( ( ( ap @ X2184 @ X2185 @ X2186 @ ( esk79_4 @ X2184 @ X2185 @ X2186 @ X2187 ) )
!= ( ap @ X2184 @ X2185 @ X2187 @ ( esk79_4 @ X2184 @ X2185 @ X2186 @ X2187 ) ) )
| ( X2186 = X2187 )
| ~ ( in @ X2187 @ ( funcSet @ X2184 @ X2185 ) )
| ~ ( in @ X2186 @ ( funcSet @ X2184 @ X2185 ) ) )
& ( ~ ( in @ X2191 @ ( funcSet @ X2189 @ X2190 ) )
| ~ ( in @ X2192 @ X2189 )
| ( ( ap @ X2189 @ X2190 @ X2191 @ X2192 )
= ( ap @ X2189 @ X2190 @ X2191 @ X2192 ) ) )
& ( ~ ( func @ X2193 @ X2194 @ X2195 )
| ~ ( in @ X2196 @ X2193 )
| ( ( ap @ X2193 @ X2194 @ X2195 @ X2196 )
= ( ap @ X2193 @ X2194 @ X2195 @ X2196 ) ) )
& ( ( in @ ( esk80_3 @ X2197 @ X2198 @ X2199 ) @ X2197 )
| ~ ( in @ X2201 @ X2197 )
| ( ( ap @ X2197 @ X2198 @ ( lam @ X2197 @ X2198 @ X2199 ) @ X2201 )
= ( X2199 @ X2201 ) ) )
& ( ~ ( in @ ( X2199 @ ( esk80_3 @ X2197 @ X2198 @ X2199 ) ) @ X2198 )
| ~ ( in @ X2201 @ X2197 )
| ( ( ap @ X2197 @ X2198 @ ( lam @ X2197 @ X2198 @ X2199 ) @ X2201 )
= ( X2199 @ X2201 ) ) )
& ( ~ ( func @ X2202 @ X2203 @ X2204 )
| ( ( lam @ X2202 @ X2203 @ ( ap @ X2202 @ X2203 @ X2204 ) )
= X2204 ) )
& ( ( in @ ( esk81_3 @ X2205 @ X2206 @ X2207 ) @ X2205 )
| ( ( lam @ X2205 @ X2206 @ X2207 )
= ( lam @ X2205 @ X2206 @ X2207 ) ) )
& ( ~ ( in @ ( X2207 @ ( esk81_3 @ X2205 @ X2206 @ X2207 ) ) @ X2206 )
| ( ( lam @ X2205 @ X2206 @ X2207 )
= ( lam @ X2205 @ X2206 @ X2207 ) ) )
& ( ( in @ ( esk82_3 @ X2209 @ X2210 @ X2211 ) @ X2209 )
| ~ ( in @ X2213 @ X2209 )
| ( ( ap @ X2209 @ X2210 @ ( lam @ X2209 @ X2210 @ X2211 ) @ X2213 )
= ( X2211 @ X2213 ) ) )
& ( ~ ( in @ ( X2211 @ ( esk82_3 @ X2209 @ X2210 @ X2211 ) ) @ X2210 )
| ~ ( in @ X2213 @ X2209 )
| ( ( ap @ X2209 @ X2210 @ ( lam @ X2209 @ X2210 @ X2211 ) @ X2213 )
= ( X2211 @ X2213 ) ) )
& ( ~ ( in @ X2216 @ ( funcSet @ X2214 @ X2215 ) )
| ( ( lam @ X2214 @ X2215 @ ( ap @ X2214 @ X2215 @ X2216 ) )
= X2216 ) )
& ( ~ ( in @ X2219 @ X2217 )
| ~ ( in @ X2220 @ X2217 )
| X2218
| ( in @ X2220
@ ( dsetconstr @ X2217
@ ^ [Z0: $i] :
( ( X2218
& ( Z0 = X2219 ) )
| ( ~ X2218
& ( Z0 = X2220 ) ) ) ) ) )
& ( ~ ( in @ X2223 @ X2221 )
| ~ ( in @ X2224 @ X2221 )
| X2222
| ( ( dsetconstr @ X2221
@ ^ [Z0: $i] :
( ( X2222
& ( Z0 = X2223 ) )
| ( ~ X2222
& ( Z0 = X2224 ) ) ) )
= ( setadjoin @ X2224 @ emptyset ) ) )
& ( ~ ( in @ X2227 @ X2225 )
| ~ ( in @ X2228 @ X2225 )
| ~ X2226
| ( in @ X2227
@ ( dsetconstr @ X2225
@ ^ [Z0: $i] :
( ( X2226
& ( Z0 = X2227 ) )
| ( ~ X2226
& ( Z0 = X2228 ) ) ) ) ) )
& ( ~ ( in @ X2231 @ X2229 )
| ~ ( in @ X2232 @ X2229 )
| ~ X2230
| ( ( dsetconstr @ X2229
@ ^ [Z0: $i] :
( ( X2230
& ( Z0 = X2231 ) )
| ( ~ X2230
& ( Z0 = X2232 ) ) ) )
= ( setadjoin @ X2231 @ emptyset ) ) )
& ( ~ ( in @ X2235 @ X2233 )
| ~ ( in @ X2236 @ X2233 )
| ( singleton
@ ( dsetconstr @ X2233
@ ^ [Z0: $i] :
( ( X2234
& ( Z0 = X2235 ) )
| ( ~ X2234
& ( Z0 = X2236 ) ) ) ) ) )
& ( ~ ( in @ X2239 @ X2237 )
| ~ ( in @ X2240 @ X2237 )
| ( in @ ( if @ X2237 @ X2238 @ X2239 @ X2240 ) @ X2237 ) )
& ( ~ ( singleton @ X2241 )
| ~ ( in @ X2242 @ X2241 )
| ( ( setunion @ X2241 )
= X2242 ) )
& ( ~ ( in @ X2245 @ X2243 )
| ~ ( in @ X2246 @ X2243 )
| ~ X2244
| ( ( if @ X2243 @ X2244 @ X2245 @ X2246 )
= X2245 ) )
& ( ~ ( in @ X2249 @ X2247 )
| ~ ( in @ X2250 @ X2247 )
| X2248
| ( ( if @ X2247 @ X2248 @ X2249 @ X2250 )
= X2250 ) )
& ( ~ ( in @ X2253 @ X2251 )
| ~ ( in @ X2254 @ X2251 )
| ( in @ ( if @ X2251 @ X2252 @ X2253 @ X2254 ) @ ( setadjoin @ X2253 @ ( setadjoin @ X2254 @ emptyset ) ) ) )
& ( ~ ( in @ X2256 @ ( powerset @ X2255 ) )
| ~ ( in @ X2257 @ ( powerset @ X2255 ) )
| ( in @ ( binintersect @ X2256 @ X2257 ) @ ( powerset @ X2255 ) ) )
& ( ~ ( in @ X2259 @ ( powerset @ X2258 ) )
| ~ ( in @ X2260 @ ( powerset @ X2258 ) )
| ( in @ ( binunion @ X2259 @ X2260 ) @ ( powerset @ X2258 ) ) )
& ( ~ ( in @ X2262 @ ( powerset @ X2261 ) )
| ( in @ ( powerset @ X2262 ) @ ( powerset @ ( powerset @ X2261 ) ) ) )
& ( ~ ( in @ X2264 @ ( powerset @ X2263 ) )
| ~ ( in @ X2265 @ ( powerset @ X2263 ) )
| ( in @ ( setminus @ X2264 @ X2265 ) @ ( powerset @ X2263 ) ) )
& ( ~ ( in @ X2267 @ ( powerset @ X2266 ) )
| ( in @ ( setminus @ X2266 @ X2267 ) @ ( powerset @ X2266 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ( X2269 = X2270 )
| ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2268 )
| ( X2269 = X2270 )
| ~ ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ( X2269 = X2270 )
| ~ ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2268 @ X2269 @ X2270 ) @ X2269 )
| ( X2269 = X2270 )
| ~ ( in @ ( esk83_3 @ X2268 @ X2269 @ X2270 ) @ X2270 )
| ~ ( in @ X2270 @ ( powerset @ X2268 ) )
| ~ ( in @ X2269 @ ( powerset @ X2268 ) ) )
& ( in @ esk86_0 @ ( powerset @ esk85_0 ) )
& ( in @ esk87_0 @ ( powerset @ esk85_0 ) )
& ( ~ ( in @ X2276 @ esk85_0 )
| ~ ( in @ X2276 @ esk86_0 )
| ( in @ X2276 @ esk87_0 ) )
& ~ ( subset @ esk86_0 @ esk87_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_318])])])])])])]) ).
thf(c_0_320,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_319]) ).
thf(c_0_321,negated_conjecture,
in @ esk86_0 @ ( powerset @ esk85_0 ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
thf(c_0_322,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk52_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
thf(c_0_323,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk87_0 )
| ~ ( in @ X2 @ esk85_0 )
| ~ ( in @ X2 @ esk86_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
thf(c_0_324,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk85_0 )
| ~ ( in @ X2 @ esk86_0 ) ),
inference(spm,[status(thm)],[c_0_320,c_0_321]) ).
thf(c_0_325,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk87_0 )
| ~ ( in @ ( esk52_2 @ X2 @ esk87_0 ) @ esk86_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_323]),c_0_324]) ).
thf(c_0_326,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk52_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
thf(c_0_327,negated_conjecture,
~ ( subset @ esk86_0 @ esk87_0 ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
thf(c_0_328,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_326]),c_0_327]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU716^1 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:16:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.51 Running higher-order theorem proving
% 0.22/0.51 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
% 9.30/1.68 # Version: 3.1.0-ho
% 9.30/1.68 # Preprocessing class: HSLMSLSSLLLCHFA.
% 9.30/1.68 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 9.30/1.68 # Starting ehoh_best5 with 300s (1) cores
% 9.30/1.68 # Starting almost_fo_3_lam with 300s (1) cores
% 9.30/1.68 # Starting new_bool_5 with 300s (1) cores
% 9.30/1.68 # Starting pre_casc_3 with 300s (1) cores
% 9.30/1.68 # Starting ho_unfolding_8 with 300s (1) cores
% 9.30/1.68 # Starting new_ho_10_cnf2 with 300s (1) cores
% 9.30/1.68 # Starting new_bool_3 with 300s (1) cores
% 9.30/1.68 # Starting new_ho_5 with 300s (1) cores
% 9.30/1.68 # ho_unfolding_8 with pid 31562 completed with status 0
% 9.30/1.68 # Result found by ho_unfolding_8
% 9.30/1.68 # Preprocessing class: HSLMSLSSLLLCHFA.
% 9.30/1.68 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 9.30/1.68 # Starting ehoh_best5 with 300s (1) cores
% 9.30/1.68 # Starting almost_fo_3_lam with 300s (1) cores
% 9.30/1.68 # Starting new_bool_5 with 300s (1) cores
% 9.30/1.68 # Starting pre_casc_3 with 300s (1) cores
% 9.30/1.68 # Starting ho_unfolding_8 with 300s (1) cores
% 9.30/1.68 # No SInE strategy applied
% 9.30/1.68 # Search class: HGHSM-FSLM32-MHFMMSBN
% 9.30/1.68 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 9.30/1.68 # Starting ho_unfolding_8 with 61s (1) cores
% 9.30/1.68 # ho_unfolding_8 with pid 31570 completed with status 0
% 9.30/1.68 # Result found by ho_unfolding_8
% 9.30/1.68 # Preprocessing class: HSLMSLSSLLLCHFA.
% 9.30/1.68 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 9.30/1.68 # Starting ehoh_best5 with 300s (1) cores
% 9.30/1.68 # Starting almost_fo_3_lam with 300s (1) cores
% 9.30/1.68 # Starting new_bool_5 with 300s (1) cores
% 9.30/1.68 # Starting pre_casc_3 with 300s (1) cores
% 9.30/1.68 # Starting ho_unfolding_8 with 300s (1) cores
% 9.30/1.68 # No SInE strategy applied
% 9.30/1.68 # Search class: HGHSM-FSLM32-MHFMMSBN
% 9.30/1.68 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 9.30/1.68 # Starting ho_unfolding_8 with 61s (1) cores
% 9.30/1.68 # Preprocessing time : 0.060 s
% 9.30/1.68 # Presaturation interreduction done
% 9.30/1.68
% 9.30/1.68 # Proof found!
% 9.30/1.68 # SZS status Theorem
% 9.30/1.68 # SZS output start CNFRefutation
% See solution above
% 9.30/1.68 # Parsed axioms : 507
% 9.30/1.68 # Removed by relevancy pruning/SinE : 0
% 9.30/1.68 # Initial clauses : 683
% 9.30/1.68 # Removed in clause preprocessing : 299
% 9.30/1.68 # Initial clauses in saturation : 384
% 9.30/1.68 # Processed clauses : 2609
% 9.30/1.68 # ...of these trivial : 22
% 9.30/1.68 # ...subsumed : 1056
% 9.30/1.68 # ...remaining for further processing : 1531
% 9.30/1.68 # Other redundant clauses eliminated : 66
% 9.30/1.68 # Clauses deleted for lack of memory : 0
% 9.30/1.68 # Backward-subsumed : 80
% 9.30/1.68 # Backward-rewritten : 19
% 9.30/1.68 # Generated clauses : 46974
% 9.30/1.68 # ...of the previous two non-redundant : 45956
% 9.30/1.68 # ...aggressively subsumed : 0
% 9.30/1.68 # Contextual simplify-reflections : 5
% 9.30/1.68 # Paramodulations : 46860
% 9.30/1.68 # Factorizations : 22
% 9.30/1.68 # NegExts : 2
% 9.30/1.68 # Equation resolutions : 74
% 9.30/1.68 # Disequality decompositions : 0
% 9.30/1.68 # Total rewrite steps : 2655
% 9.30/1.68 # ...of those cached : 2463
% 9.30/1.68 # Propositional unsat checks : 0
% 9.30/1.68 # Propositional check models : 0
% 9.30/1.68 # Propositional check unsatisfiable : 0
% 9.30/1.68 # Propositional clauses : 0
% 9.30/1.68 # Propositional clauses after purity: 0
% 9.30/1.68 # Propositional unsat core size : 0
% 9.30/1.68 # Propositional preprocessing time : 0.000
% 9.30/1.68 # Propositional encoding time : 0.000
% 9.30/1.68 # Propositional solver time : 0.000
% 9.30/1.68 # Success case prop preproc time : 0.000
% 9.30/1.68 # Success case prop encoding time : 0.000
% 9.30/1.68 # Success case prop solver time : 0.000
% 9.30/1.68 # Current number of processed clauses : 1078
% 9.30/1.68 # Positive orientable unit clauses : 52
% 9.30/1.68 # Positive unorientable unit clauses: 0
% 9.30/1.68 # Negative unit clauses : 101
% 9.30/1.68 # Non-unit-clauses : 925
% 9.30/1.68 # Current number of unprocessed clauses: 43989
% 9.30/1.68 # ...number of literals in the above : 166382
% 9.30/1.68 # Current number of archived formulas : 0
% 9.30/1.68 # Current number of archived clauses : 438
% 9.30/1.68 # Clause-clause subsumption calls (NU) : 115624
% 9.30/1.68 # Rec. Clause-clause subsumption calls : 54308
% 9.30/1.68 # Non-unit clause-clause subsumptions : 802
% 9.30/1.68 # Unit Clause-clause subsumption calls : 1851
% 9.30/1.68 # Rewrite failures with RHS unbound : 0
% 9.30/1.68 # BW rewrite match attempts : 39
% 9.30/1.68 # BW rewrite match successes : 11
% 9.30/1.68 # Condensation attempts : 0
% 9.30/1.68 # Condensation successes : 0
% 9.30/1.68 # Termbank termtop insertions : 944111
% 9.30/1.68 # Search garbage collected termcells : 23772
% 9.30/1.68
% 9.30/1.68 # -------------------------------------------------
% 9.30/1.68 # User time : 1.056 s
% 9.30/1.68 # System time : 0.052 s
% 9.30/1.68 # Total time : 1.108 s
% 9.30/1.68 # Maximum resident set size: 7620 pages
% 9.30/1.68
% 9.30/1.68 # -------------------------------------------------
% 9.30/1.68 # User time : 1.068 s
% 9.30/1.68 # System time : 0.057 s
% 9.30/1.68 # Total time : 1.125 s
% 9.30/1.68 # Maximum resident set size: 2608 pages
% 9.30/1.68 % E---3.1 exiting
% 9.30/1.68 % E exiting
%------------------------------------------------------------------------------