%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU763^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 03:30:01 EDT 2024
% Result : Theorem 2.37s 0.92s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 663
% Syntax : Number of formulae : 721 ( 4 unt; 383 typ; 0 def)
% Number of atoms : 3575 ( 463 equ; 0 cnn)
% Maximal formula atoms : 1127 ( 10 avg)
% Number of connectives : 13955 ( 891 ~; 894 |; 520 &;9474 @)
% ( 366 <=>;1810 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1224 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 509 ( 509 >; 0 *; 0 +; 0 <<)
% Number of symbols : 387 ( 383 usr; 288 con; 0-4 aty)
% Number of variables : 2931 ( 156 ^2695 !; 80 ?;2931 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
binunionTE: $o ).
thf(decl_323,type,
binunionTEcontra: $o ).
thf(decl_324,type,
demorgan2a1: $o ).
thf(decl_325,type,
complementUnionInPowersetComplement: $o ).
thf(decl_326,type,
demorgan2a2: $o ).
thf(decl_327,type,
demorgan1a: $o ).
thf(decl_328,type,
demorgan1b: $o ).
thf(decl_329,type,
demorgan1: $o ).
thf(decl_330,type,
demorgan2a: $o ).
thf(decl_331,type,
demorgan2b2: $o ).
thf(decl_332,type,
demorgan2b: $o ).
thf(decl_333,type,
demorgan2: $o ).
thf(decl_334,type,
woz13rule0: $o ).
thf(decl_335,type,
woz13rule1: $o ).
thf(decl_336,type,
woz13rule2: $o ).
thf(decl_337,type,
woz13rule3: $o ).
thf(decl_338,type,
woz13rule4: $o ).
thf(decl_339,type,
epred1_0: $o ).
thf(decl_340,type,
esk1_2: $i > $i > $i ).
thf(decl_341,type,
esk2_2: $i > $i > $i ).
thf(decl_342,type,
esk3_2: $i > $i > $i ).
thf(decl_343,type,
esk4_1: $i > $i ).
thf(decl_344,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_345,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_346,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_347,type,
esk8_1: $i > $i ).
thf(decl_348,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_349,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_350,type,
esk11_2: $i > $i > $i ).
thf(decl_351,type,
esk12_2: $i > $i > $i ).
thf(decl_352,type,
esk13_1: $i > $i ).
thf(decl_353,type,
esk14_1: $i > $i ).
thf(decl_354,type,
esk15_1: $i > $i ).
thf(decl_355,type,
esk16_2: $i > $i > $i ).
thf(decl_356,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_357,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_358,type,
esk19_1: $i > $i ).
thf(decl_359,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_360,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_361,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_362,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_363,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_364,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_365,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_366,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_367,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_368,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_369,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_370,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_371,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_372,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_373,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_374,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_375,type,
esk36_2: $i > $i > $i ).
thf(decl_376,type,
esk37_2: $i > $i > $i ).
thf(decl_377,type,
esk38_2: $i > $i > $i ).
thf(decl_378,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_379,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_380,type,
esk41_2: $i > $i > $i ).
thf(decl_381,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_382,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_383,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_384,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_385,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_386,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_387,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_388,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_389,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_390,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_391,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_392,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_393,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_394,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_395,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_396,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_397,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_398,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_399,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_400,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_401,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_402,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_403,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_404,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_405,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_406,type,
esk67_3: $i > $i > $i > $i ).
thf(decl_407,type,
esk68_3: $i > $i > $i > $i ).
thf(decl_408,type,
esk69_3: $i > $i > $i > $i ).
thf(decl_409,type,
esk70_3: $i > $i > $i > $i ).
thf(decl_410,type,
esk71_0: $i ).
thf(decl_411,type,
esk72_0: $i ).
thf(decl_412,type,
esk73_0: $i ).
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(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(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(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(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(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(woz1_1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_1) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(woz13rule4,axiom,
( woz13rule4
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X51: $i] :
( ( in @ X51 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X49 )
=> ( ( subset @ X48 @ X51 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ ( binintersect @ X49 @ X51 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule4) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(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(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(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(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(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(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(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(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
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(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(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(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(intersectInPowersetIntersectUnions,axiom,
( intersectInPowersetIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(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(inComplementUnionImpNotIn1,axiom,
( inComplementUnionImpNotIn1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inComplementUnionImpInComplement1,axiom,
( inComplementUnionImpInComplement1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
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(binunionTE,axiom,
( binunionTE
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X50: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ( ( ( in @ X2 @ X21 )
=> X50 )
=> ( ( ( in @ X2 @ X48 )
=> X50 )
=> X50 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionTEcontra,axiom,
( binunionTEcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(demorgan2a1,axiom,
( demorgan2a1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1) ).
thf(complementUnionInPowersetComplement,axiom,
( complementUnionInPowersetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) @ ( powerset @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementUnionInPowersetComplement) ).
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(demorgan2a2,axiom,
( demorgan2a2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a2) ).
thf(demorgan1a,axiom,
( demorgan1a
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(demorgan1b,axiom,
( demorgan1b
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(demorgan1,axiom,
( demorgan1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) )
= ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
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(demorgan2a,axiom,
( demorgan2a
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
=> ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a) ).
thf(demorgan2b2,axiom,
( demorgan2b2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( ( in @ X2 @ ( setminus @ X4 @ X48 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
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(demorgan2b,axiom,
( demorgan2b
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b) ).
thf(demorgan2,axiom,
( demorgan2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( setminus @ X4 @ ( binunion @ X21 @ X48 ) )
= ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).
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(woz13rule0,axiom,
( woz13rule0
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule0) ).
thf(woz13rule1,axiom,
( woz13rule1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X49 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1) ).
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(woz13rule2,axiom,
( woz13rule2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X48 @ X49 )
=> ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule2) ).
thf(woz13rule3,axiom,
( woz13rule3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( ( subset @ X21 @ X49 )
=> ( subset @ X21 @ ( binintersect @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule3) ).
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(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(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(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
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(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
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(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
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(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
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(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,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_307,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_308,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_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,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_318,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_319,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_320,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_321,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_322,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_323,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_324,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_325,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_326,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_327,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_328,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_329,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_330,plain,
( epred1_0
<=> ! [X970: $i] :
? [X971: $i] :
( ! [X972: $i] :
( ( in @ X972 @ X971 )
=> ! [X973: $i] :
( ( in @ X973 @ X972 )
=> ( in @ X973 @ X970 ) ) )
& ! [X974: $i,X975: $i] :
( ( ( in @ X974 @ X970 )
& ( in @ X975 @ X970 ) )
=> ( ! [X976: $i] :
( ( in @ X976 @ X971 )
=> ( ( in @ X974 @ X976 )
<=> ( in @ X975 @ X976 ) ) )
=> ( X974 = X975 ) ) )
& ! [X977: $i,X978: $i] :
( ( ( in @ X977 @ X971 )
& ( in @ X978 @ X971 ) )
=> ( ! [X979: $i] :
( ( in @ X979 @ X977 )
=> ( in @ X979 @ X978 ) )
| ! [X980: $i] :
( ( in @ X980 @ X978 )
=> ( in @ X980 @ X977 ) ) ) )
& ! [X981: $i] :
( ( ! [X982: $i] :
( ( in @ X982 @ X981 )
=> ( in @ X982 @ X970 ) )
& ? [X983: $i] : ( in @ X983 @ X981 ) )
=> ? [X984: $i,X985: $i] :
( ( in @ X984 @ X971 )
& ( in @ X985 @ X981 )
& ~ ? [X986: $i] :
( ( in @ X986 @ X984 )
& ( in @ X986 @ X981 ) )
& ! [X987: $i] :
( ( in @ X987 @ X971 )
=> ( ! [X988: $i] :
( ( in @ X988 @ X987 )
=> ( in @ X988 @ X984 ) )
| ( in @ X985 @ X987 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_331,negated_conjecture,
~ ( ! [X943: $i,X944: $i] :
( ! [X945: $i] :
( ( in @ X945 @ X943 )
<=> ( in @ X945 @ X944 ) )
=> ( X943 = X944 ) )
=> ( ! [X946: $i] :
~ ( in @ X946 @ emptyset )
=> ( ! [X947: $i,X948: $i,X949: $i] :
( ( in @ X949 @ ( setadjoin @ X947 @ X948 ) )
<=> ( ( X949 = X947 )
| ( in @ X949 @ X948 ) ) )
=> ( ! [X950: $i,X951: $i] :
( ( in @ X951 @ ( powerset @ X950 ) )
<=> ! [X952: $i] :
( ( in @ X952 @ X951 )
=> ( in @ X952 @ X950 ) ) )
=> ( ! [X953: $i,X954: $i] :
( ( in @ X954 @ ( setunion @ X953 ) )
<=> ? [X955: $i] :
( ( in @ X954 @ X955 )
& ( in @ X955 @ X953 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X956: $i] :
( ( in @ X956 @ omega )
=> ( in @ ( setadjoin @ X956 @ X956 ) @ omega ) )
=> ( ! [X957: $i] :
( ( ( in @ emptyset @ X957 )
& ! [X958: $i] :
( ( ( in @ X958 @ omega )
& ( in @ X958 @ X957 ) )
=> ( in @ ( setadjoin @ X958 @ X958 ) @ X957 ) ) )
=> ! [X959: $i] :
( ( in @ X959 @ omega )
=> ( in @ X959 @ X957 ) ) )
=> ( ! [X960: $i > $i > $o,X961: $i] :
( ! [X962: $i] :
( ( in @ X962 @ X961 )
=> ( exu @ ( X960 @ X962 ) ) )
=> ? [X963: $i] :
! [X964: $i] :
( ( in @ X964 @ X963 )
<=> ? [X965: $i] :
( ( in @ X965 @ X961 )
& ( X960 @ X965 @ X964 ) ) ) )
=> ( ! [X966: $i] :
( ? [X967: $i] : ( in @ X967 @ X966 )
=> ? [X968: $i] :
( ( in @ X968 @ X966 )
& ~ ? [X969: $i] :
( ( in @ X969 @ X968 )
& ( in @ X969 @ X966 ) ) ) )
=> ( epred1_0
=> ( ! [X989: $i > $o] :
( ( exu @ X989 )
=> ( X989
@ ( descr
@ ^ [Z0: $i] : ( X989 @ Z0 ) ) ) )
=> ( ! [X990: $i,X991: $i > $o,X992: $i] :
( ( in @ X992 @ X990 )
=> ( ( X991 @ X992 )
=> ( in @ X992 @ ( dsetconstr @ X990 @ X991 ) ) ) )
=> ( ! [X993: $i,X994: $i > $o,X995: $i] :
( ( in @ X995 @ ( dsetconstr @ X993 @ X994 ) )
=> ( in @ X995 @ X993 ) )
=> ( ! [X996: $i,X997: $i > $o,X998: $i] :
( ( in @ X998 @ ( dsetconstr @ X996 @ X997 ) )
=> ( X997 @ X998 ) )
=> ( ! [X999: $i > $o] :
( ( exu @ X999 )
=> ? [X1000: $i] :
( ( X999 @ X1000 )
& ! [X1001: $i] :
( ( X999 @ X1001 )
=> ( X1000 = X1001 ) ) ) )
=> ( ! [X1002: $o,X1003: $i] :
( ( in @ X1003 @ ( prop2set @ X1002 ) )
=> X1002 )
=> ( ! [X1004: $i] :
( ( in @ X1004 @ emptyset )
=> ! [X1005: $o] : X1005 )
=> ( ! [X1006: $i] :
( ( in @ X1006 @ emptyset )
=> ~ $true )
=> ( ! [X1007: $i] :
~ ( in @ X1007 @ emptyset )
=> ( ! [X1008: $i > $o] :
( ( exu @ X1008 )
=> ? [X1009: $i] : ( X1008 @ X1009 ) )
=> ( ! [X1010: $i,X1011: $i] :
( ! [X1012: $i] :
( ( in @ X1012 @ X1010 )
=> ( in @ X1012 @ X1011 ) )
=> ( ! [X1013: $i] :
( ( in @ X1013 @ X1011 )
=> ( in @ X1013 @ X1010 ) )
=> ( X1010 = X1011 ) ) )
=> ( ! [X1014: $i] :
( ! [X1015: $i] :
~ ( in @ X1015 @ X1014 )
=> ( X1014 = emptyset ) )
=> ( ! [X1016: $i] :
( ! [X1017: $i] :
~ ( in @ X1017 @ X1016 )
=> ( X1016 = emptyset ) )
=> ( ! [X1018: $i,X1019: $i > $o,X1020: $i] :
( ( in @ X1020 @ X1018 )
=> ( ( in @ X1020 @ ( dsetconstr @ X1018 @ X1019 ) )
<=> ( X1019 @ X1020 ) ) )
=> ( ! [X1021: $i] :
( ( nonempty @ X1021 )
=> ? [X1022: $i] : ( in @ X1022 @ X1021 ) )
=> ( ! [X1023: $i,X1024: $i > $o,X1025: $i] :
( ( in @ X1025 @ X1023 )
=> ( ( X1024 @ X1025 )
=> ( nonempty @ ( dsetconstr @ X1023 @ X1024 ) ) ) )
=> ( ! [X1026: $i] :
( ? [X1027: $i] : ( in @ X1027 @ X1026 )
=> ( nonempty @ X1026 ) )
=> ( ! [X1028: $i,X1029: $i] : ( in @ X1028 @ ( setadjoin @ X1028 @ X1029 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1030: $i,X1031: $i,X1032: $i] :
( ( in @ X1032 @ X1031 )
=> ( in @ X1032 @ ( setadjoin @ X1030 @ X1031 ) ) )
=> ( ! [X1033: $i,X1034: $i,X1035: $i] :
( ( in @ X1035 @ ( setadjoin @ X1033 @ X1034 ) )
=> ! [X1036: $o] :
( ( ( X1035 = X1033 )
=> X1036 )
=> ( ( ( in @ X1035 @ X1034 )
=> X1036 )
=> X1036 ) ) )
=> ( ! [X1037: $i,X1038: $i,X1039: $i] :
( ( in @ X1039 @ ( setadjoin @ X1037 @ X1038 ) )
=> ( ( X1039 = X1037 )
| ( in @ X1039 @ X1038 ) ) )
=> ( ! [X1040: $i] :
( ( dsetconstr @ X1040
@ ^ [Z0: $i] : $true )
= X1040 )
=> ( ! [X1041: $i,X1042: $i] :
( ! [X1043: $i] :
( ( in @ X1043 @ X1042 )
=> ( in @ X1043 @ X1041 ) )
=> ( in @ X1042 @ ( powerset @ X1041 ) ) )
=> ( ! [X1044: $i] : ( in @ emptyset @ ( powerset @ X1044 ) )
=> ( ! [X1045: $i] : ( in @ emptyset @ ( powerset @ X1045 ) )
=> ( ! [X1046: $i,X1047: $i,X1048: $i] :
( ( in @ X1047 @ ( powerset @ X1046 ) )
=> ( ( in @ X1048 @ X1047 )
=> ( in @ X1048 @ X1046 ) ) )
=> ( ! [X1049: $i,X1050: $i,X1051: $i] :
( ( in @ X1050 @ X1051 )
=> ( ( in @ X1051 @ X1049 )
=> ( in @ X1050 @ ( setunion @ X1049 ) ) ) )
=> ( ! [X1052: $i,X1053: $i] :
( ( in @ X1053 @ ( setunion @ X1052 ) )
=> ! [X1054: $o] :
( ! [X1055: $i] :
( ( in @ X1053 @ X1055 )
=> ( ( in @ X1055 @ X1052 )
=> X1054 ) )
=> X1054 ) )
=> ( ! [X1056: $i,X1057: $i] :
( ( in @ X1057 @ X1056 )
=> ( in @ X1057 @ ( powerset @ ( setunion @ X1056 ) ) ) )
=> ( ! [X1058: $i > $o] :
( ( exu @ X1058 )
=> ? [X1059: $i] :
! [X1060: $i] :
( ( X1058 @ X1060 )
<=> ( X1060 = X1059 ) ) )
=> ( ! [X1061: $i] :
( ( nonempty @ X1061 )
=> ? [X1062: $i] :
( ( in @ X1062 @ X1061 )
& $true ) )
=> ( ! [X1063: $i,X1064: $i] :
( ( in @ X1063 @ ( setadjoin @ X1064 @ emptyset ) )
=> ( X1063 = X1064 ) )
=> ( ! [X1065: $i,X1066: $i] :
( ( X1065 != X1066 )
=> ~ ( in @ X1066 @ ( setadjoin @ X1065 @ emptyset ) ) )
=> ( ! [X1067: $i,X1068: $i] :
( ( X1067 = X1068 )
=> ( in @ X1067 @ ( setadjoin @ X1068 @ emptyset ) ) )
=> ( ! [X1069: $i,X1070: $i] :
( ( in @ X1069 @ ( setadjoin @ X1070 @ emptyset ) )
=> ( in @ X1070 @ ( setadjoin @ X1069 @ emptyset ) ) )
=> ( ! [X1071: $i,X1072: $i,X1073: $i] :
( ( in @ X1073 @ ( setadjoin @ X1071 @ ( setadjoin @ X1072 @ emptyset ) ) )
=> ( ( X1073 = X1071 )
| ( X1073 = X1072 ) ) )
=> ( ! [X1074: $i,X1075: $i] : ( in @ X1074 @ ( setadjoin @ X1074 @ ( setadjoin @ X1075 @ emptyset ) ) )
=> ( ! [X1076: $i,X1077: $i] : ( in @ X1077 @ ( setadjoin @ X1076 @ ( setadjoin @ X1077 @ emptyset ) ) )
=> ( ! [X1078: $i,X1079: $i > $o] :
( ? [X1080: $i] :
( ( in @ X1080 @ X1078 )
& ( X1079 @ X1080 ) )
=> ( ( ( dsetconstr @ X1078 @ X1079 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1081: $i > $o,X1082: $i] :
( ( in @ X1082 @ emptyset )
=> ( X1081 @ X1082 ) )
=> ( ! [X1083: $i,X1084: $i > $o] :
( ~ ! [X1085: $i] :
( ( in @ X1085 @ X1083 )
=> ( X1084 @ X1085 ) )
=> ? [X1086: $i] :
( ( in @ X1086 @ X1083 )
& ~ ( X1084 @ X1086 ) ) )
=> ( ! [X1087: $i,X1088: $i > $o] :
( ! [X1089: $i] :
( ( in @ X1089 @ X1087 )
=> ~ ( X1088 @ X1089 ) )
=> ~ ? [X1090: $i] :
( ( in @ X1090 @ X1087 )
& ( X1088 @ X1090 ) ) )
=> ( ! [X1091: $i,X1092: $i > $o] :
( ~ ? [X1093: $i] :
( ( in @ X1093 @ X1091 )
& ( X1092 @ X1093 ) )
=> ! [X1094: $i] :
( ( in @ X1094 @ X1091 )
=> ~ ( X1092 @ X1094 ) ) )
=> ( ! [X1095: $i,X1096: $i > $o] :
( ? [X1097: $i] :
( ( in @ X1097 @ X1095 )
& ~ ( X1096 @ X1097 ) )
=> ~ ! [X1098: $i] :
( ( in @ X1098 @ X1095 )
=> ( X1096 @ X1098 ) ) )
=> ( ! [X1099: $o] :
( X1099
=> ( in @ emptyset @ ( prop2set @ X1099 ) ) )
=> ( prop2set2propI
=> ( ! [X1100: $i,X1101: $i > $o] :
( ~ ? [X1102: $i] :
( ( in @ X1102 @ X1100 )
& ( X1101 @ X1102 ) )
=> ! [X1103: $i] :
( ( in @ X1103 @ X1100 )
=> ~ ( X1101 @ X1103 ) ) )
=> ( ! [X1104: $i,X1105: $i > $o] :
( ~ ! [X1106: $i] :
( ( in @ X1106 @ X1104 )
=> ( X1105 @ X1106 ) )
=> ? [X1107: $i] :
( ( in @ X1107 @ X1104 )
& ~ ( X1105 @ X1107 ) ) )
=> ( ! [X1108: $i > $o] :
( ? [X1109: $i] :
( ( X1108 @ X1109 )
& ! [X1110: $i] :
( ( X1108 @ X1110 )
=> ( X1109 = X1110 ) ) )
=> ( exu @ X1108 ) )
=> ( ! [X1111: $i > $o] :
( ? [X1112: $i] : ( X1111 @ X1112 )
=> ( ! [X1113: $i,X1114: $i] :
( ( X1111 @ X1113 )
=> ( ( X1111 @ X1114 )
=> ( X1113 = X1114 ) ) )
=> ( exu @ X1111 ) ) )
=> ( ! [X1115: $i > $o] :
( ? [X1116: $i] :
! [X1117: $i] :
( ( X1115 @ X1117 )
<=> ( X1117 = X1116 ) )
=> ( exu @ X1115 ) )
=> ( ! [X1118: $i,X1119: $i] :
( ( X1118 = X1119 )
=> ! [X1120: $i,X1121: $i] :
( ( X1120 = X1121 )
=> ( ( in @ X1120 @ X1118 )
=> ( in @ X1121 @ X1119 ) ) ) )
=> ( ! [X1122: $i,X1123: $i] :
( ( X1122 = X1123 )
=> ! [X1124: $i,X1125: $i] :
( ( X1124 = X1125 )
=> ( ( in @ X1124 @ X1122 )
<=> ( in @ X1125 @ X1123 ) ) ) )
=> ( ! [X1126: $i > $o] :
( ( exu @ X1126 )
=> ! [X1127: $i,X1128: $i] :
( ( X1126 @ X1127 )
=> ( ( X1126 @ X1128 )
=> ( X1127 = X1128 ) ) ) )
=> ( ! [X1129: $i > $o,X1130: $i > $o] :
( ! [X1131: $i,X1132: $i] :
( ( X1131 = X1132 )
=> ( ( X1129 @ X1131 )
<=> ( X1130 @ X1132 ) ) )
=> ( ( exu @ X1129 )
<=> ( exu @ X1130 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1133: $i,X1134: $i] :
( ( X1133 = X1134 )
=> ! [X1135: $i,X1136: $i] :
( ( X1135 = X1136 )
=> ( ( setadjoin @ X1133 @ X1135 )
= ( setadjoin @ X1134 @ X1136 ) ) ) )
=> ( ! [X1137: $i,X1138: $i] :
( ( X1137 = X1138 )
=> ( ( powerset @ X1137 )
= ( powerset @ X1138 ) ) )
=> ( ! [X1139: $i,X1140: $i] :
( ( X1139 = X1140 )
=> ( ( setunion @ X1139 )
= ( setunion @ X1140 ) ) )
=> ( ( omega = omega )
=> ( ! [X1141: $i > $o] :
( ( exu @ X1141 )
=> ! [X1142: $i,X1143: $i] :
( ( X1141 @ X1142 )
=> ( ( X1141 @ X1143 )
=> ( X1142 = X1143 ) ) ) )
=> ( ! [X1144: $i > $o,X1145: $i > $o] :
( ! [X1146: $i,X1147: $i] :
( ( X1146 = X1147 )
=> ( ( X1144 @ X1146 )
<=> ( X1145 @ X1147 ) ) )
=> ( ( exu @ X1144 )
=> ( ( exu @ X1145 )
=> ( ( descr @ X1144 )
= ( descr @ X1145 ) ) ) ) )
=> ( ! [X1148: $i,X1149: $i] :
( ( X1148 = X1149 )
=> ! [X1150: $i > $o,X1151: $i > $o] :
( ! [X1152: $i] :
( ( in @ X1152 @ X1148 )
=> ! [X1153: $i] :
( ( in @ X1153 @ X1149 )
=> ( ( X1152 = X1153 )
=> ( ( X1150 @ X1152 )
<=> ( X1151 @ X1153 ) ) ) ) )
=> ( ( dsetconstr @ X1148 @ X1150 )
= ( dsetconstr @ X1149 @ X1151 ) ) ) )
=> ( ! [X1154: $i,X1155: $i] :
( ! [X1156: $i] :
( ( in @ X1156 @ X1154 )
=> ( in @ X1156 @ X1155 ) )
=> ( subset @ X1154 @ X1155 ) )
=> ( ! [X1157: $i,X1158: $i] :
( ( X1157 = X1158 )
=> ( subset @ X1158 @ X1157 ) )
=> ( ! [X1159: $i,X1160: $i] :
( ( X1159 = X1160 )
=> ( subset @ X1159 @ X1160 ) )
=> ( ! [X1161: $i,X1162: $i] :
( ! [X1163: $i] :
( ( in @ X1163 @ X1161 )
=> ( in @ X1163 @ X1162 ) )
=> ( subset @ X1161 @ X1162 ) )
=> ( ! [X1164: $i] : ( subset @ emptyset @ X1164 )
=> ( ! [X1165: $i,X1166: $i,X1167: $i] :
( ( subset @ X1165 @ X1166 )
=> ( ( in @ X1167 @ X1165 )
=> ( in @ X1167 @ X1166 ) ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ( subset @ X1168 @ X1169 )
=> ( ~ ( in @ X1170 @ X1169 )
=> ~ ( in @ X1170 @ X1168 ) ) )
=> ( ! [X1171: $i,X1172: $i,X1173: $i] :
( ( in @ X1173 @ X1171 )
=> ( ~ ( in @ X1173 @ X1172 )
=> ~ ( subset @ X1171 @ X1172 ) ) )
=> ( ! [X1174: $i,X1175: $i] :
( ~ ( subset @ X1174 @ X1175 )
=> ( X1174 != X1175 ) )
=> ( ! [X1176: $i,X1177: $i,X1178: $i] :
( ( in @ X1178 @ X1176 )
=> ( ~ ( in @ X1178 @ X1177 )
=> ( X1176 != X1177 ) ) )
=> ( ! [X1179: $i] : ( subset @ X1179 @ X1179 )
=> ( ! [X1180: $i,X1181: $i,X1182: $i] :
( ( subset @ X1180 @ X1181 )
=> ( ( subset @ X1181 @ X1182 )
=> ( subset @ X1180 @ X1182 ) ) )
=> ( ! [X1183: $i,X1184: $i] : ( subset @ X1184 @ ( setadjoin @ X1183 @ X1184 ) )
=> ( ! [X1185: $i,X1186: $i,X1187: $i] :
( ( subset @ X1185 @ X1187 )
=> ( subset @ X1185 @ ( setadjoin @ X1186 @ X1187 ) ) )
=> ( ! [X1188: $i,X1189: $i] :
( ( subset @ X1188 @ X1189 )
=> ( in @ X1188 @ ( powerset @ X1189 ) ) )
=> ( ! [X1190: $i,X1191: $i] :
( ( subset @ X1190 @ X1191 )
=> ( ( subset @ X1191 @ X1190 )
=> ( X1190 = X1191 ) ) )
=> ( ! [X1192: $i] :
( ( subset @ X1192 @ emptyset )
=> ( X1192 = emptyset ) )
=> ( ! [X1193: $i,X1194: $i] :
( ( subset @ X1194 @ X1193 )
=> ( in @ X1194 @ ( powerset @ X1193 ) ) )
=> ( ! [X1195: $i,X1196: $i] :
( ( in @ X1196 @ ( powerset @ X1195 ) )
=> ( subset @ X1196 @ X1195 ) )
=> ( ! [X1197: $i] : ( in @ X1197 @ ( powerset @ X1197 ) )
=> ( ! [X1198: $i,X1199: $i] :
( ( subset @ X1198 @ X1199 )
=> ( subset @ ( powerset @ X1198 ) @ ( powerset @ X1199 ) ) )
=> ( ! [X1200: $i,X1201: $i > $o] : ( in @ ( dsetconstr @ X1200 @ X1201 ) @ ( powerset @ X1200 ) )
=> ( ! [X1202: $i,X1203: $i > $o] : ( subset @ ( dsetconstr @ X1202 @ X1203 ) @ X1202 )
=> ( ! [X1204: $i,X1205: $i,X1206: $i] :
( ( in @ X1206 @ X1204 )
=> ( in @ X1206 @ ( binunion @ X1204 @ X1205 ) ) )
=> ( ! [X1207: $i,X1208: $i] : ( in @ X1208 @ ( setadjoin @ X1207 @ ( setadjoin @ X1208 @ emptyset ) ) )
=> ( ! [X1209: $i,X1210: $i,X1211: $i] :
( ( in @ X1211 @ X1210 )
=> ( in @ X1211 @ ( binunion @ X1209 @ X1210 ) ) )
=> ( ! [X1212: $i,X1213: $i,X1214: $i,X1215: $o] :
( ( in @ X1214 @ ( binunion @ X1212 @ X1213 ) )
=> ( ( ( in @ X1214 @ X1212 )
=> X1215 )
=> ( ( ( in @ X1214 @ X1213 )
=> X1215 )
=> X1215 ) ) )
=> ( ! [X1216: $i,X1217: $i,X1218: $i] :
( ( in @ X1218 @ ( binunion @ X1216 @ X1217 ) )
=> ( ( in @ X1218 @ X1216 )
| ( in @ X1218 @ X1217 ) ) )
=> ( ! [X1219: $i,X1220: $i] : ( subset @ X1219 @ ( binunion @ X1219 @ X1220 ) )
=> ( ! [X1221: $i,X1222: $i] : ( subset @ X1222 @ ( binunion @ X1221 @ X1222 ) )
=> ( ! [X1223: $i,X1224: $i,X1225: $i] :
( ( in @ X1225 @ X1223 )
=> ( ( in @ X1225 @ X1224 )
=> ( in @ X1225 @ ( binintersect @ X1223 @ X1224 ) ) ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i] :
( ( subset @ X1228 @ X1226 )
=> ( ( subset @ X1228 @ X1227 )
=> ( subset @ X1228 @ ( binintersect @ X1226 @ X1227 ) ) ) )
=> ( ! [X1229: $i,X1230: $i,X1231: $i] :
( ( in @ X1231 @ ( binintersect @ X1229 @ X1230 ) )
=> ( in @ X1231 @ X1229 ) )
=> ( ! [X1232: $i,X1233: $i] : ( subset @ ( binintersect @ X1232 @ X1233 ) @ X1232 )
=> ( ! [X1234: $i,X1235: $i] :
( ( subset @ X1234 @ X1235 )
=> ( ( binintersect @ X1234 @ X1235 )
= X1234 ) )
=> ( ! [X1236: $i,X1237: $i] :
( ( ( binintersect @ X1236 @ X1237 )
= X1237 )
=> ( subset @ X1237 @ X1236 ) )
=> ( ! [X1238: $i,X1239: $i,X1240: $i] :
( ( in @ X1240 @ ( binintersect @ X1238 @ X1239 ) )
=> ( in @ X1240 @ X1239 ) )
=> ( ! [X1241: $i,X1242: $i] :
( ~ ? [X1243: $i] :
( ( in @ X1243 @ X1241 )
& ( in @ X1243 @ X1242 ) )
=> ( ( binintersect @ X1241 @ X1242 )
= emptyset ) )
=> ( ! [X1244: $i,X1245: $i] : ( subset @ ( binintersect @ X1244 @ X1245 ) @ X1245 )
=> ( ! [X1246: $i,X1247: $i] :
( ( subset @ X1247 @ X1246 )
=> ( ( binintersect @ X1246 @ X1247 )
= X1247 ) )
=> ( ! [X1248: $i,X1249: $i] :
( ( ( binintersect @ X1248 @ X1249 )
= X1248 )
=> ( subset @ X1248 @ X1249 ) )
=> ( ! [X1250: $i,X1251: $i,X1252: $i] :
( ( binintersect @ X1250 @ ( binunion @ X1251 @ X1252 ) )
= ( binunion @ ( binintersect @ X1250 @ X1251 ) @ ( binintersect @ X1250 @ X1252 ) ) )
=> ( ! [X1253: $i,X1254: $i,X1255: $i] :
( ( in @ X1255 @ X1253 )
=> ( ~ ( in @ X1255 @ X1254 )
=> ( in @ X1255 @ ( setminus @ X1253 @ X1254 ) ) ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i] :
( ( in @ X1258 @ ( setminus @ X1256 @ X1257 ) )
=> ( in @ X1258 @ X1256 ) )
=> ( ! [X1259: $i,X1260: $i,X1261: $i] :
( ( in @ X1261 @ ( setminus @ X1259 @ X1260 ) )
=> ~ ( in @ X1261 @ X1260 ) )
=> ( ! [X1262: $i,X1263: $i] :
( ( subset @ X1262 @ X1263 )
=> ( ( setminus @ X1262 @ X1263 )
= emptyset ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i] :
( ~ ( in @ X1266 @ ( setminus @ X1264 @ X1265 ) )
=> ( ( in @ X1266 @ X1264 )
=> ( in @ X1266 @ X1265 ) ) )
=> ( ! [X1267: $i,X1268: $i,X1269: $i] :
( ~ ( in @ X1269 @ ( setminus @ X1267 @ X1268 ) )
=> ( ~ ( in @ X1269 @ X1268 )
=> ~ ( in @ X1269 @ X1267 ) ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i] :
( ~ ( in @ X1272 @ X1270 )
=> ~ ( in @ X1272 @ ( setminus @ X1270 @ X1271 ) ) )
=> ( ! [X1273: $i,X1274: $i,X1275: $i] :
( ( in @ X1275 @ X1274 )
=> ~ ( in @ X1275 @ ( setminus @ X1273 @ X1274 ) ) )
=> ( ! [X1276: $i,X1277: $i] : ( subset @ ( setminus @ X1276 @ X1277 ) @ X1276 )
=> ( ! [X1278: $i,X1279: $i] :
( ( ( setminus @ X1278 @ X1279 )
= emptyset )
=> ( subset @ X1278 @ X1279 ) )
=> ( ! [X1280: $i,X1281: $i,X1282: $i] :
( ( in @ X1282 @ ( symdiff @ X1280 @ X1281 ) )
=> ! [X1283: $o] :
( ( ( in @ X1282 @ X1280 )
=> ( ~ ( in @ X1282 @ X1281 )
=> X1283 ) )
=> ( ( ~ ( in @ X1282 @ X1280 )
=> ( ( in @ X1282 @ X1281 )
=> X1283 ) )
=> X1283 ) ) )
=> ( ! [X1284: $i,X1285: $i,X1286: $i] :
( ( in @ X1286 @ X1284 )
=> ( ~ ( in @ X1286 @ X1285 )
=> ( in @ X1286 @ ( symdiff @ X1284 @ X1285 ) ) ) )
=> ( ! [X1287: $i,X1288: $i,X1289: $i] :
( ~ ( in @ X1289 @ X1287 )
=> ( ( in @ X1289 @ X1288 )
=> ( in @ X1289 @ ( symdiff @ X1287 @ X1288 ) ) ) )
=> ( ! [X1290: $i,X1291: $i,X1292: $i] :
( ( in @ X1292 @ X1290 )
=> ( ( in @ X1292 @ X1291 )
=> ~ ( in @ X1292 @ ( symdiff @ X1290 @ X1291 ) ) ) )
=> ( ! [X1293: $i,X1294: $i,X1295: $i] :
( ~ ( in @ X1295 @ X1293 )
=> ( ~ ( in @ X1295 @ X1294 )
=> ~ ( in @ X1295 @ ( symdiff @ X1293 @ X1294 ) ) ) )
=> ( ! [X1296: $i,X1297: $i] : ( in @ X1297 @ ( setadjoin @ X1296 @ ( setadjoin @ X1297 @ emptyset ) ) )
=> ( ! [X1298: $i,X1299: $i] : ( in @ X1298 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1298 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1298 @ ( setadjoin @ X1299 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1300: $i,X1301: $i] : ( in @ X1301 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1300 @ ( setadjoin @ X1301 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1302: $i,X1303: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1302 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1302 @ ( setadjoin @ X1303 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1304: $i,X1305: $i] : ( iskpair @ ( kpair @ X1304 @ X1305 ) )
=> ( ! [X1306: $i,X1307: $i] :
( ( in @ X1307 @ X1306 )
=> ( subset @ ( setadjoin @ X1307 @ emptyset ) @ X1306 ) )
=> ( ! [X1308: $i,X1309: $i] :
( ( in @ X1309 @ X1308 )
=> ( in @ ( setadjoin @ X1309 @ emptyset ) @ ( powerset @ X1308 ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i] :
( ( in @ X1312 @ X1310 )
=> ( in @ ( setadjoin @ X1312 @ emptyset ) @ ( powerset @ ( binunion @ X1310 @ X1311 ) ) ) )
=> ( ! [X1313: $i,X1314: $i,X1315: $i] :
( ( in @ X1315 @ ( setadjoin @ X1313 @ ( setadjoin @ X1314 @ emptyset ) ) )
=> ( ( X1315 = X1313 )
| ( X1315 = X1314 ) ) )
=> ( ! [X1316: $i,X1317: $i,X1318: $i] :
( ( in @ X1318 @ X1316 )
=> ! [X1319: $i] :
( ( in @ X1319 @ X1317 )
=> ( subset @ ( setadjoin @ X1318 @ ( setadjoin @ X1319 @ emptyset ) ) @ ( binunion @ X1316 @ X1317 ) ) ) )
=> ( ! [X1320: $i,X1321: $i,X1322: $i] :
( ( in @ X1322 @ X1320 )
=> ! [X1323: $i] :
( ( in @ X1323 @ X1321 )
=> ( in @ ( setadjoin @ X1322 @ ( setadjoin @ X1323 @ emptyset ) ) @ ( powerset @ ( binunion @ X1320 @ X1321 ) ) ) ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i] :
( ( in @ X1326 @ X1324 )
=> ! [X1327: $i] :
( ( in @ X1327 @ X1325 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1326 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1326 @ ( setadjoin @ X1327 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1324 @ X1325 ) ) ) ) )
=> ( ! [X1328: $i,X1329: $i,X1330: $i] :
( ( in @ X1330 @ X1328 )
=> ! [X1331: $i] :
( ( in @ X1331 @ X1329 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1330 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1330 @ ( setadjoin @ X1331 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1328 @ X1329 ) ) ) ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( in @ X1334 @ X1332 )
=> ! [X1335: $i] :
( ( in @ X1335 @ X1333 )
=> ( in @ ( kpair @ X1334 @ X1335 ) @ ( powerset @ ( powerset @ ( binunion @ X1332 @ X1333 ) ) ) ) ) )
=> ( ! [X1336: $i,X1337: $i,X1338: $i] :
( ( in @ X1338 @ X1336 )
=> ! [X1339: $i] :
( ( in @ X1339 @ X1337 )
=> ( in @ ( kpair @ X1338 @ X1339 ) @ ( cartprod @ X1336 @ X1337 ) ) ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i] :
( ( in @ X1342 @ ( cartprod @ X1340 @ X1341 ) )
=> ? [X1343: $i] :
( ( in @ X1343 @ X1340 )
& ? [X1344: $i] :
( ( in @ X1344 @ X1341 )
& ( X1342
= ( kpair @ X1343 @ X1344 ) ) ) ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i] :
( ( in @ X1347 @ ( cartprod @ X1345 @ X1346 ) )
=> ( iskpair @ X1347 ) )
=> ( ! [X1348: $i,X1349: $i] :
( ( in @ X1349 @ ( setunion @ X1348 ) )
=> ? [X1350: $i] :
( ( in @ X1350 @ X1348 )
& ( in @ X1349 @ X1350 ) ) )
=> ( ! [X1351: $i] : ( subset @ ( setunion @ ( setadjoin @ X1351 @ emptyset ) ) @ X1351 )
=> ( ! [X1352: $i] : ( subset @ X1352 @ ( setunion @ ( setadjoin @ X1352 @ emptyset ) ) )
=> ( ! [X1353: $i] :
( ( setunion @ ( setadjoin @ X1353 @ emptyset ) )
= X1353 )
=> ( ! [X1354: $i,X1355: $i > $o] :
( ! [X1356: $i] :
( ( in @ X1356 @ X1354 )
=> ! [X1357: $i] :
( ( in @ X1357 @ X1354 )
=> ( ( X1355 @ X1356 )
=> ( ( X1355 @ X1357 )
=> ( X1356 = X1357 ) ) ) ) )
=> ( ? [X1358: $i] :
( ( in @ X1358 @ X1354 )
& ( X1355 @ X1358 ) )
=> ( singleton @ ( dsetconstr @ X1354 @ X1355 ) ) ) )
=> ( ! [X1359: $i,X1360: $i > $o] :
( ( ex1 @ X1359 @ X1360 )
=> ? [X1361: $i] :
( ( in @ X1361 @ X1359 )
& ( X1360 @ X1361 ) ) )
=> ( ! [X1362: $i,X1363: $i > $o,X1364: $i] :
( ( in @ X1364 @ X1362 )
=> ( ( X1363 @ X1364 )
=> ( ! [X1365: $i] :
( ( in @ X1365 @ X1362 )
=> ( ( X1363 @ X1365 )
=> ( X1365 = X1364 ) ) )
=> ( ex1 @ X1362 @ X1363 ) ) ) )
=> ( ! [X1366: $i,X1367: $i > $o] :
( ! [X1368: $i] :
( ( in @ X1368 @ X1366 )
=> ! [X1369: $i] :
( ( in @ X1369 @ X1366 )
=> ( ( X1367 @ X1368 )
=> ( ( X1367 @ X1369 )
=> ( X1368 = X1369 ) ) ) ) )
=> ( ? [X1370: $i] :
( ( in @ X1370 @ X1366 )
& ( X1367 @ X1370 ) )
=> ( ex1 @ X1366 @ X1367 ) ) )
=> ( ! [X1371: $i,X1372: $i] :
( ( ( setadjoin @ X1371 @ emptyset )
= ( setadjoin @ X1372 @ emptyset ) )
=> ( X1371 = X1372 ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( in @ ( setadjoin @ X1375 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1373 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1373 @ ( setadjoin @ X1374 @ emptyset ) ) @ emptyset ) ) )
=> ( X1373 = X1375 ) )
=> ( ! [X1376: $i] :
( ( iskpair @ X1376 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1376 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1376 ) ) ) )
=> ( ! [X1377: $i] :
( ( singleton @ X1377 )
=> ( in @ ( setunion @ X1377 ) @ X1377 ) )
=> ( ! [X1378: $i,X1379: $i] :
( ( kfst @ ( kpair @ X1378 @ X1379 ) )
= X1378 )
=> ( ! [X1380: $i,X1381: $i,X1382: $i] :
( ( in @ X1382 @ ( cartprod @ X1380 @ X1381 ) )
=> ( in @ ( kfst @ X1382 ) @ X1380 ) )
=> ( ! [X1383: $i,X1384: $i,X1385: $i,X1386: $i] :
( ( ( setadjoin @ ( setadjoin @ X1383 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1383 @ ( setadjoin @ X1384 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1385 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1385 @ ( setadjoin @ X1386 @ emptyset ) ) @ emptyset ) ) )
=> ( X1383 = X1385 ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i,X1390: $i] :
( ( ( kpair @ X1387 @ X1388 )
= ( kpair @ X1389 @ X1390 ) )
=> ( X1387 = X1389 ) )
=> ( ! [X1391: $i,X1392: $i] :
( ( X1391 = X1392 )
=> ( ( setadjoin @ X1391 @ ( setadjoin @ X1392 @ emptyset ) )
= ( setadjoin @ X1391 @ emptyset ) ) )
=> ( ! [X1393: $i,X1394: $i] :
( ( X1393 = X1394 )
=> ( ( setadjoin @ ( setadjoin @ X1393 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1393 @ ( setadjoin @ X1394 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1393 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i,X1398: $i] :
( ( ( setadjoin @ ( setadjoin @ X1395 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1395 @ ( setadjoin @ X1396 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1397 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1397 @ ( setadjoin @ X1398 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1397 = X1398 )
=> ( X1396 = X1398 ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i] :
( ( ( setadjoin @ X1399 @ ( setadjoin @ X1400 @ emptyset ) )
= ( setadjoin @ X1401 @ emptyset ) )
=> ( X1399 = X1400 ) )
=> ( ! [X1402: $i,X1403: $i,X1404: $i,X1405: $i] :
( ( ( setadjoin @ ( setadjoin @ X1402 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1402 @ ( setadjoin @ X1403 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1404 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1404 @ ( setadjoin @ X1405 @ emptyset ) ) @ emptyset ) ) )
=> ( X1403 = X1405 ) )
=> ( ! [X1406: $i,X1407: $i,X1408: $i,X1409: $i] :
( ( ( kpair @ X1406 @ X1407 )
= ( kpair @ X1408 @ X1409 ) )
=> ( X1407 = X1409 ) )
=> ( ! [X1410: $i] :
( ( iskpair @ X1410 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1410 )
@ ^ [Z0: $i] :
( X1410
= ( kpair @ ( kfst @ X1410 ) @ Z0 ) ) ) ) )
=> ( ! [X1411: $i,X1412: $i] :
( ( ksnd @ ( kpair @ X1411 @ X1412 ) )
= X1412 )
=> ( ! [X1413: $i] :
( ( iskpair @ X1413 )
=> ( ( kpair @ ( kfst @ X1413 ) @ ( ksnd @ X1413 ) )
= X1413 ) )
=> ( ! [X1414: $i,X1415: $i,X1416: $i] :
( ( in @ X1416 @ ( cartprod @ X1414 @ X1415 ) )
=> ( in @ ( ksnd @ X1416 ) @ X1415 ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i,X1420: $i] :
( ( in @ ( kpair @ X1419 @ X1420 ) @ ( cartprod @ X1417 @ X1418 ) )
=> ( in @ X1419 @ X1417 ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i,X1424: $i] :
( ( in @ ( kpair @ X1423 @ X1424 ) @ ( cartprod @ X1421 @ X1422 ) )
=> ( in @ X1424 @ X1422 ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i] :
( ( in @ X1427 @ X1425 )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1426 )
=> ( ( kpair @ X1427 @ X1428 )
= ( kpair @ X1427 @ X1428 ) ) ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i] :
( ( in @ X1431 @ X1429 )
=> ! [X1432: $i] :
( ( in @ X1432 @ X1430 )
=> ( ( kfst @ ( kpair @ X1431 @ X1432 ) )
= X1431 ) ) )
=> ( ! [X1433: $i,X1434: $i,X1435: $i] :
( ( in @ X1435 @ X1433 )
=> ! [X1436: $i] :
( ( in @ X1436 @ X1434 )
=> ( ( ksnd @ ( kpair @ X1435 @ X1436 ) )
= X1436 ) ) )
=> ( ! [X1437: $i,X1438: $i,X1439: $i] :
( ( in @ X1439 @ ( cartprod @ X1437 @ X1438 ) )
=> ( ( kpair @ ( kfst @ X1439 ) @ ( ksnd @ X1439 ) )
= X1439 ) )
=> ( ! [X1440: $i,X1441: $i,X1442: $i > $i > $o,X1443: $i] :
( ( in @ X1443 @ X1440 )
=> ! [X1444: $i] :
( ( in @ X1444 @ X1441 )
=> ( ( X1442 @ X1443 @ X1444 )
=> ( in @ ( kpair @ X1443 @ X1444 ) @ ( dpsetconstr @ X1440 @ X1441 @ X1442 ) ) ) ) )
=> ( ! [X1445: $i,X1446: $i,X1447: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1445 @ X1446 @ X1447 ) @ ( cartprod @ X1445 @ X1446 ) )
=> ( ! [X1448: $i,X1449: $i,X1450: $i > $i > $o] : ( breln @ X1448 @ X1449 @ ( dpsetconstr @ X1448 @ X1449 @ X1450 ) )
=> ( ! [X1451: $i,X1452: $i,X1453: $i > $i > $o,X1454: $i] :
( ( in @ X1454 @ X1451 )
=> ! [X1455: $i] :
( ( in @ X1455 @ X1452 )
=> ( ( in @ ( kpair @ X1454 @ X1455 ) @ ( dpsetconstr @ X1451 @ X1452 @ X1453 ) )
=> ( X1453 @ X1454 @ X1455 ) ) ) )
=> ( ! [X1456: $i,X1457: $i,X1458: $i > $i > $o,X1459: $i,X1460: $i] :
( ( in @ ( kpair @ X1459 @ X1460 ) @ ( dpsetconstr @ X1456 @ X1457 @ X1458 ) )
=> ( in @ X1459 @ X1456 ) )
=> ( ! [X1461: $i,X1462: $i,X1463: $i > $i > $o,X1464: $i,X1465: $i] :
( ( in @ ( kpair @ X1464 @ X1465 ) @ ( dpsetconstr @ X1461 @ X1462 @ X1463 ) )
=> ( in @ X1465 @ X1462 ) )
=> ( ! [X1466: $i,X1467: $i,X1468: $i > $i > $o,X1469: $i,X1470: $i] :
( ( in @ ( kpair @ X1469 @ X1470 ) @ ( dpsetconstr @ X1466 @ X1467 @ X1468 ) )
=> ( X1468 @ X1469 @ X1470 ) )
=> ( ! [X1471: $i,X1472: $i,X1473: $i] :
( ( func @ X1471 @ X1472 @ X1473 )
=> ! [X1474: $i] :
( ( in @ X1474 @ X1471 )
=> ( singleton
@ ( dsetconstr @ X1472
@ ^ [Z0: $i] : ( in @ ( kpair @ X1474 @ Z0 ) @ X1473 ) ) ) ) )
=> ( ! [X1475: $i,X1476: $i,X1477: $i] :
( ( func @ X1475 @ X1476 @ X1477 )
=> ! [X1478: $i] :
( ( in @ X1478 @ X1475 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1476
@ ^ [Z0: $i] : ( in @ ( kpair @ X1478 @ Z0 ) @ X1477 ) ) )
@ X1476 ) ) )
=> ( ! [X1479: $i,X1480: $i,X1481: $i] :
( ( func @ X1479 @ X1480 @ X1481 )
=> ! [X1482: $i] :
( ( in @ X1482 @ X1479 )
=> ( in @ ( ap @ X1479 @ X1480 @ X1481 @ X1482 ) @ X1480 ) ) )
=> ( ! [X1483: $i,X1484: $i,X1485: $i] :
( ( in @ X1485 @ ( funcSet @ X1483 @ X1484 ) )
=> ( func @ X1483 @ X1484 @ X1485 ) )
=> ( ! [X1486: $i,X1487: $i,X1488: $i] :
( ( in @ X1488 @ ( funcSet @ X1486 @ X1487 ) )
=> ! [X1489: $i] :
( ( in @ X1489 @ X1486 )
=> ( in @ ( ap @ X1486 @ X1487 @ X1488 @ X1489 ) @ X1487 ) ) )
=> ( ! [X1490: $i,X1491: $i,X1492: $i] :
( ( func @ X1490 @ X1491 @ X1492 )
=> ( in @ X1492 @ ( funcSet @ X1490 @ X1491 ) ) )
=> ( ! [X1493: $i,X1494: $i,X1495: $i > $i] :
( ! [X1496: $i] :
( ( in @ X1496 @ X1493 )
=> ( in @ ( X1495 @ X1496 ) @ X1494 ) )
=> ( func @ X1493 @ X1494
@ ( dpsetconstr @ X1493 @ X1494
@ ^ [Z0: $i] : ( $eq @ ( X1495 @ Z0 ) ) ) ) )
=> ( ! [X1497: $i,X1498: $i,X1499: $i > $i] :
( ! [X1500: $i] :
( ( in @ X1500 @ X1497 )
=> ( in @ ( X1499 @ X1500 ) @ X1498 ) )
=> ( func @ X1497 @ X1498 @ ( lam @ X1497 @ X1498 @ X1499 ) ) )
=> ( ! [X1501: $i,X1502: $i,X1503: $i > $i] :
( ! [X1504: $i] :
( ( in @ X1504 @ X1501 )
=> ( in @ ( X1503 @ X1504 ) @ X1502 ) )
=> ( in @ ( lam @ X1501 @ X1502 @ X1503 ) @ ( funcSet @ X1501 @ X1502 ) ) )
=> ( ! [X1505: $i,X1506: $i,X1507: $i] :
( ( breln @ X1505 @ X1506 @ X1507 )
=> ! [X1508: $i > $o] :
( ! [X1509: $i] :
( ( in @ X1509 @ X1505 )
=> ! [X1510: $i] :
( ( in @ X1510 @ X1506 )
=> ( ( in @ ( kpair @ X1509 @ X1510 ) @ X1507 )
=> ( X1508 @ ( kpair @ X1509 @ X1510 ) ) ) ) )
=> ! [X1511: $i] :
( ( in @ X1511 @ X1507 )
=> ( X1508 @ X1511 ) ) ) )
=> ( ! [X1512: $i,X1513: $i,X1514: $i] :
( ( breln @ X1512 @ X1513 @ X1514 )
=> ! [X1515: $i > $o] :
( ! [X1516: $i] :
( ( in @ X1516 @ X1512 )
=> ! [X1517: $i] :
( ( in @ X1517 @ X1513 )
=> ( ( in @ ( kpair @ X1516 @ X1517 ) @ X1514 )
=> ( X1515 @ ( kpair @ X1516 @ X1517 ) ) ) ) )
=> ! [X1518: $i] :
( ( in @ X1518 @ X1514 )
=> ( X1515 @ X1518 ) ) ) )
=> ( ! [X1519: $i,X1520: $i > $o] :
( ( ex1 @ X1519 @ X1520 )
=> ! [X1521: $i] :
( ( in @ X1521 @ X1519 )
=> ! [X1522: $i] :
( ( in @ X1522 @ X1519 )
=> ( ( X1520 @ X1521 )
=> ( ( X1520 @ X1522 )
=> ( X1521 = X1522 ) ) ) ) ) )
=> ( ! [X1523: $i,X1524: $i,X1525: $i] :
( ( func @ X1523 @ X1524 @ X1525 )
=> ! [X1526: $i] :
( ( in @ X1526 @ X1523 )
=> ( in @ ( kpair @ X1526 @ ( ap @ X1523 @ X1524 @ X1525 @ X1526 ) ) @ X1525 ) ) )
=> ( ! [X1527: $i,X1528: $i,X1529: $i] :
( ( in @ X1529 @ ( funcSet @ X1527 @ X1528 ) )
=> ! [X1530: $i] :
( ( in @ X1530 @ X1527 )
=> ( in @ ( kpair @ X1530 @ ( ap @ X1527 @ X1528 @ X1529 @ X1530 ) ) @ X1529 ) ) )
=> ( ! [X1531: $i,X1532: $i,X1533: $i] :
( ( func @ X1531 @ X1532 @ X1533 )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1531 )
=> ! [X1535: $i] :
( ( in @ X1535 @ X1532 )
=> ( ( in @ ( kpair @ X1534 @ X1535 ) @ X1533 )
=> ( ( ap @ X1531 @ X1532 @ X1533 @ X1534 )
= X1535 ) ) ) ) )
=> ( ! [X1536: $i,X1537: $i,X1538: $i] :
( ( func @ X1536 @ X1537 @ X1538 )
=> ! [X1539: $i] :
( ( func @ X1536 @ X1537 @ X1539 )
=> ( ! [X1540: $i] :
( ( in @ X1540 @ X1536 )
=> ( ( ap @ X1536 @ X1537 @ X1538 @ X1540 )
= ( ap @ X1536 @ X1537 @ X1539 @ X1540 ) ) )
=> ! [X1541: $i] :
( ( in @ X1541 @ X1536 )
=> ! [X1542: $i] :
( ( in @ X1542 @ X1537 )
=> ( ( in @ ( kpair @ X1541 @ X1542 ) @ X1539 )
=> ( in @ ( kpair @ X1541 @ X1542 ) @ X1538 ) ) ) ) ) ) )
=> ( ! [X1543: $i,X1544: $i,X1545: $i] :
( ( in @ X1545 @ ( funcSet @ X1543 @ X1544 ) )
=> ! [X1546: $i] :
( ( in @ X1546 @ X1543 )
=> ! [X1547: $i] :
( ( in @ X1547 @ X1544 )
=> ( ( in @ ( kpair @ X1546 @ X1547 ) @ X1545 )
=> ( ( ap @ X1543 @ X1544 @ X1545 @ X1546 )
= X1547 ) ) ) ) )
=> ( ! [X1548: $i,X1549: $i,X1550: $i] :
( ( breln @ X1548 @ X1549 @ X1550 )
=> ! [X1551: $i] :
( ( breln @ X1548 @ X1549 @ X1551 )
=> ( ! [X1552: $i] :
( ( in @ X1552 @ X1548 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1549 )
=> ( ( in @ ( kpair @ X1552 @ X1553 ) @ X1550 )
=> ( in @ ( kpair @ X1552 @ X1553 ) @ X1551 ) ) ) )
=> ( subset @ X1550 @ X1551 ) ) ) )
=> ( ! [X1554: $i,X1555: $i,X1556: $i] :
( ( breln @ X1554 @ X1555 @ X1556 )
=> ! [X1557: $i] :
( ( breln @ X1554 @ X1555 @ X1557 )
=> ( ! [X1558: $i] :
( ( in @ X1558 @ X1554 )
=> ! [X1559: $i] :
( ( in @ X1559 @ X1555 )
=> ( ( in @ ( kpair @ X1558 @ X1559 ) @ X1556 )
=> ( in @ ( kpair @ X1558 @ X1559 ) @ X1557 ) ) ) )
=> ( ! [X1560: $i] :
( ( in @ X1560 @ X1554 )
=> ! [X1561: $i] :
( ( in @ X1561 @ X1555 )
=> ( ( in @ ( kpair @ X1560 @ X1561 ) @ X1557 )
=> ( in @ ( kpair @ X1560 @ X1561 ) @ X1556 ) ) ) )
=> ( X1556 = X1557 ) ) ) ) )
=> ( ! [X1562: $i,X1563: $i,X1564: $i] :
( ( func @ X1562 @ X1563 @ X1564 )
=> ! [X1565: $i] :
( ( func @ X1562 @ X1563 @ X1565 )
=> ( ! [X1566: $i] :
( ( in @ X1566 @ X1562 )
=> ( ( ap @ X1562 @ X1563 @ X1564 @ X1566 )
= ( ap @ X1562 @ X1563 @ X1565 @ X1566 ) ) )
=> ( X1564 = X1565 ) ) ) )
=> ( ! [X1567: $i,X1568: $i,X1569: $i] :
( ( in @ X1569 @ ( funcSet @ X1567 @ X1568 ) )
=> ! [X1570: $i] :
( ( in @ X1570 @ ( funcSet @ X1567 @ X1568 ) )
=> ( ! [X1571: $i] :
( ( in @ X1571 @ X1567 )
=> ( ( ap @ X1567 @ X1568 @ X1569 @ X1571 )
= ( ap @ X1567 @ X1568 @ X1570 @ X1571 ) ) )
=> ( X1569 = X1570 ) ) ) )
=> ( ! [X1572: $i,X1573: $i,X1574: $i] :
( ( in @ X1574 @ ( funcSet @ X1572 @ X1573 ) )
=> ! [X1575: $i] :
( ( in @ X1575 @ X1572 )
=> ( ( ap @ X1572 @ X1573 @ X1574 @ X1575 )
= ( ap @ X1572 @ X1573 @ X1574 @ X1575 ) ) ) )
=> ( ! [X1576: $i,X1577: $i,X1578: $i] :
( ( func @ X1576 @ X1577 @ X1578 )
=> ! [X1579: $i] :
( ( in @ X1579 @ X1576 )
=> ( ( ap @ X1576 @ X1577 @ X1578 @ X1579 )
= ( ap @ X1576 @ X1577 @ X1578 @ X1579 ) ) ) )
=> ( ! [X1580: $i,X1581: $i,X1582: $i > $i] :
( ! [X1583: $i] :
( ( in @ X1583 @ X1580 )
=> ( in @ ( X1582 @ X1583 ) @ X1581 ) )
=> ! [X1584: $i] :
( ( in @ X1584 @ X1580 )
=> ( ( ap @ X1580 @ X1581 @ ( lam @ X1580 @ X1581 @ X1582 ) @ X1584 )
= ( X1582 @ X1584 ) ) ) )
=> ( ! [X1585: $i,X1586: $i,X1587: $i] :
( ( func @ X1585 @ X1586 @ X1587 )
=> ( ( lam @ X1585 @ X1586 @ ( ap @ X1585 @ X1586 @ X1587 ) )
= X1587 ) )
=> ( ! [X1588: $i,X1589: $i,X1590: $i > $i] :
( ! [X1591: $i] :
( ( in @ X1591 @ X1588 )
=> ( in @ ( X1590 @ X1591 ) @ X1589 ) )
=> ( ( lam @ X1588 @ X1589 @ X1590 )
= ( lam @ X1588 @ X1589 @ X1590 ) ) )
=> ( ! [X1592: $i,X1593: $i,X1594: $i > $i] :
( ! [X1595: $i] :
( ( in @ X1595 @ X1592 )
=> ( in @ ( X1594 @ X1595 ) @ X1593 ) )
=> ! [X1596: $i] :
( ( in @ X1596 @ X1592 )
=> ( ( ap @ X1592 @ X1593 @ ( lam @ X1592 @ X1593 @ X1594 ) @ X1596 )
= ( X1594 @ X1596 ) ) ) )
=> ( ! [X1597: $i,X1598: $i,X1599: $i] :
( ( in @ X1599 @ ( funcSet @ X1597 @ X1598 ) )
=> ( ( lam @ X1597 @ X1598 @ ( ap @ X1597 @ X1598 @ X1599 ) )
= X1599 ) )
=> ( ! [X1600: $i,X1601: $o,X1602: $i] :
( ( in @ X1602 @ X1600 )
=> ! [X1603: $i] :
( ( in @ X1603 @ X1600 )
=> ( ~ X1601
=> ( in @ X1603
@ ( dsetconstr @ X1600
@ ^ [Z0: $i] :
( ( X1601
& ( Z0 = X1602 ) )
| ( ~ X1601
& ( Z0 = X1603 ) ) ) ) ) ) ) )
=> ( ! [X1604: $i,X1605: $o,X1606: $i] :
( ( in @ X1606 @ X1604 )
=> ! [X1607: $i] :
( ( in @ X1607 @ X1604 )
=> ( ~ X1605
=> ( ( dsetconstr @ X1604
@ ^ [Z0: $i] :
( ( X1605
& ( Z0 = X1606 ) )
| ( ~ X1605
& ( Z0 = X1607 ) ) ) )
= ( setadjoin @ X1607 @ emptyset ) ) ) ) )
=> ( ! [X1608: $i,X1609: $o,X1610: $i] :
( ( in @ X1610 @ X1608 )
=> ! [X1611: $i] :
( ( in @ X1611 @ X1608 )
=> ( X1609
=> ( in @ X1610
@ ( dsetconstr @ X1608
@ ^ [Z0: $i] :
( ( X1609
& ( Z0 = X1610 ) )
| ( ~ X1609
& ( Z0 = X1611 ) ) ) ) ) ) ) )
=> ( ! [X1612: $i,X1613: $o,X1614: $i] :
( ( in @ X1614 @ X1612 )
=> ! [X1615: $i] :
( ( in @ X1615 @ X1612 )
=> ( X1613
=> ( ( dsetconstr @ X1612
@ ^ [Z0: $i] :
( ( X1613
& ( Z0 = X1614 ) )
| ( ~ X1613
& ( Z0 = X1615 ) ) ) )
= ( setadjoin @ X1614 @ emptyset ) ) ) ) )
=> ( ! [X1616: $i,X1617: $o,X1618: $i] :
( ( in @ X1618 @ X1616 )
=> ! [X1619: $i] :
( ( in @ X1619 @ X1616 )
=> ( singleton
@ ( dsetconstr @ X1616
@ ^ [Z0: $i] :
( ( X1617
& ( Z0 = X1618 ) )
| ( ~ X1617
& ( Z0 = X1619 ) ) ) ) ) ) )
=> ( ! [X1620: $i,X1621: $o,X1622: $i] :
( ( in @ X1622 @ X1620 )
=> ! [X1623: $i] :
( ( in @ X1623 @ X1620 )
=> ( in @ ( if @ X1620 @ X1621 @ X1622 @ X1623 ) @ X1620 ) ) )
=> ( ! [X1624: $i] :
( ( singleton @ X1624 )
=> ! [X1625: $i] :
( ( in @ X1625 @ X1624 )
=> ( ( setunion @ X1624 )
= X1625 ) ) )
=> ( ! [X1626: $i,X1627: $o,X1628: $i] :
( ( in @ X1628 @ X1626 )
=> ! [X1629: $i] :
( ( in @ X1629 @ X1626 )
=> ( X1627
=> ( ( if @ X1626 @ X1627 @ X1628 @ X1629 )
= X1628 ) ) ) )
=> ( ! [X1630: $i,X1631: $o,X1632: $i] :
( ( in @ X1632 @ X1630 )
=> ! [X1633: $i] :
( ( in @ X1633 @ X1630 )
=> ( ~ X1631
=> ( ( if @ X1630 @ X1631 @ X1632 @ X1633 )
= X1633 ) ) ) )
=> ( ! [X1634: $i,X1635: $o,X1636: $i] :
( ( in @ X1636 @ X1634 )
=> ! [X1637: $i] :
( ( in @ X1637 @ X1634 )
=> ( in @ ( if @ X1634 @ X1635 @ X1636 @ X1637 ) @ ( setadjoin @ X1636 @ ( setadjoin @ X1637 @ emptyset ) ) ) ) )
=> ( ! [X1638: $i,X1639: $i] :
( ( in @ X1639 @ ( powerset @ X1638 ) )
=> ! [X1640: $i] :
( ( in @ X1640 @ ( powerset @ X1638 ) )
=> ( in @ ( binintersect @ X1639 @ X1640 ) @ ( powerset @ X1638 ) ) ) )
=> ( ! [X1641: $i,X1642: $i] :
( ( in @ X1642 @ ( powerset @ X1641 ) )
=> ! [X1643: $i] :
( ( in @ X1643 @ ( powerset @ X1641 ) )
=> ( in @ ( binunion @ X1642 @ X1643 ) @ ( powerset @ X1641 ) ) ) )
=> ( ! [X1644: $i,X1645: $i] :
( ( in @ X1645 @ ( powerset @ X1644 ) )
=> ( in @ ( powerset @ X1645 ) @ ( powerset @ ( powerset @ X1644 ) ) ) )
=> ( ! [X1646: $i,X1647: $i] :
( ( in @ X1647 @ ( powerset @ X1646 ) )
=> ! [X1648: $i] :
( ( in @ X1648 @ ( powerset @ X1646 ) )
=> ( in @ ( setminus @ X1647 @ X1648 ) @ ( powerset @ X1646 ) ) ) )
=> ( ! [X1649: $i,X1650: $i] :
( ( in @ X1650 @ ( powerset @ X1649 ) )
=> ( in @ ( setminus @ X1649 @ X1650 ) @ ( powerset @ X1649 ) ) )
=> ( ! [X1651: $i,X1652: $i] :
( ( in @ X1652 @ ( powerset @ X1651 ) )
=> ! [X1653: $i] :
( ( in @ X1653 @ ( powerset @ X1651 ) )
=> ( ! [X1654: $i] :
( ( in @ X1654 @ X1651 )
=> ( ( in @ X1654 @ X1652 )
=> ( in @ X1654 @ X1653 ) ) )
=> ( ! [X1655: $i] :
( ( in @ X1655 @ X1651 )
=> ( ( in @ X1655 @ X1653 )
=> ( in @ X1655 @ X1652 ) ) )
=> ( X1652 = X1653 ) ) ) ) )
=> ( ! [X1656: $i,X1657: $i] :
( ( in @ X1657 @ ( powerset @ X1656 ) )
=> ! [X1658: $i] :
( ( in @ X1658 @ ( powerset @ X1656 ) )
=> ( ! [X1659: $i] :
( ( in @ X1659 @ X1656 )
=> ( ( in @ X1659 @ X1657 )
=> ( in @ X1659 @ X1658 ) ) )
=> ( subset @ X1657 @ X1658 ) ) ) )
=> ( ! [X1660: $i,X1661: $i] :
( ( in @ X1661 @ ( powerset @ X1660 ) )
=> ! [X1662: $i] :
( ( in @ X1662 @ ( powerset @ X1660 ) )
=> ( ! [X1663: $i] :
( ( in @ X1663 @ X1660 )
=> ( ( in @ X1663 @ X1661 )
=> ( in @ X1663 @ X1662 ) ) )
=> ( in @ X1661 @ ( powerset @ X1662 ) ) ) ) )
=> ( ! [X1664: $i,X1665: $i] :
( ( in @ X1665 @ ( powerset @ X1664 ) )
=> ! [X1666: $i] :
( ( in @ X1666 @ ( powerset @ X1664 ) )
=> ! [X1667: $i] :
( ( in @ X1667 @ X1664 )
=> ( ( in @ X1665 @ ( powerset @ X1666 ) )
=> ( ( in @ X1667 @ X1665 )
=> ( in @ X1667 @ X1666 ) ) ) ) ) )
=> ( ! [X1668: $i,X1669: $i] :
( ( in @ X1669 @ ( powerset @ X1668 ) )
=> ! [X1670: $i] :
( ( in @ X1670 @ X1668 )
=> ( ( in @ X1670 @ X1669 )
=> ~ ( in @ X1670 @ ( setminus @ X1668 @ X1669 ) ) ) ) )
=> ( ! [X1671: $i,X1672: $i] :
( ( in @ X1672 @ ( powerset @ X1671 ) )
=> ! [X1673: $i] :
( ( in @ X1673 @ X1671 )
=> ( ~ ( in @ X1673 @ ( setminus @ X1671 @ X1672 ) )
=> ( in @ X1673 @ X1672 ) ) ) )
=> ( ! [X1674: $i,X1675: $i] :
( ( in @ X1675 @ ( powerset @ X1674 ) )
=> ! [X1676: $i] :
( ( in @ X1676 @ ( powerset @ X1674 ) )
=> ! [X1677: $i] :
( ( in @ X1677 @ X1674 )
=> ( ~ ( in @ X1677 @ X1675 )
=> ~ ( in @ X1677 @ ( binintersect @ X1675 @ X1676 ) ) ) ) ) )
=> ( ! [X1678: $i,X1679: $i] :
( ( in @ X1679 @ ( powerset @ X1678 ) )
=> ! [X1680: $i] :
( ( in @ X1680 @ ( powerset @ X1678 ) )
=> ! [X1681: $i] :
( ( in @ X1681 @ X1678 )
=> ( ~ ( in @ X1681 @ X1680 )
=> ~ ( in @ X1681 @ ( binintersect @ X1679 @ X1680 ) ) ) ) ) )
=> ( ! [X1682: $i,X1683: $i] :
( ( in @ X1683 @ ( powerset @ X1682 ) )
=> ! [X1684: $i] :
( ( in @ X1684 @ ( powerset @ X1682 ) )
=> ! [X1685: $i] :
( ( in @ X1685 @ X1682 )
=> ( ( subset @ X1683 @ ( setminus @ X1682 @ X1684 ) )
=> ( ( in @ X1685 @ X1684 )
=> ~ ( in @ X1685 @ X1683 ) ) ) ) ) )
=> ( ! [X1686: $i,X1687: $i] :
( ( in @ X1687 @ ( powerset @ X1686 ) )
=> ! [X1688: $i] :
( ( in @ X1688 @ ( powerset @ X1686 ) )
=> ! [X1689: $i] :
( ( in @ X1689 @ X1686 )
=> ( ( subset @ X1687 @ X1688 )
=> ( ~ ( in @ X1689 @ X1688 )
=> ~ ( in @ X1689 @ X1687 ) ) ) ) ) )
=> ( ! [X1690: $i,X1691: $i] :
( ( in @ X1691 @ ( powerset @ X1690 ) )
=> ! [X1692: $i] :
( ( in @ X1692 @ ( powerset @ X1690 ) )
=> ( ( subset @ X1691 @ X1692 )
=> ( subset @ ( setminus @ X1690 @ X1692 ) @ ( setminus @ X1690 @ X1691 ) ) ) ) )
=> ( ! [X1693: $i,X1694: $i] :
( ( in @ X1694 @ ( powerset @ X1693 ) )
=> ! [X1695: $i] :
( ( in @ X1695 @ ( powerset @ X1693 ) )
=> ( ( subset @ ( setminus @ X1693 @ X1695 ) @ ( setminus @ X1693 @ X1694 ) )
=> ( subset @ X1694 @ X1695 ) ) ) )
=> ( ! [X1696: $i,X1697: $i] :
( ( in @ X1697 @ ( powerset @ X1696 ) )
=> ! [X1698: $i] :
( ( in @ X1698 @ X1696 )
=> ( ( in @ X1698 @ X1697 )
=> ( in @ X1698 @ ( setminus @ X1696 @ ( setminus @ X1696 @ X1697 ) ) ) ) ) )
=> ( ! [X1699: $i,X1700: $i] :
( ( in @ X1700 @ ( powerset @ X1699 ) )
=> ! [X1701: $i] :
( ( in @ X1701 @ X1699 )
=> ( ( in @ X1701 @ ( setminus @ X1699 @ ( setminus @ X1699 @ X1700 ) ) )
=> ( in @ X1701 @ X1700 ) ) ) )
=> ( ! [X1702: $i,X1703: $i] :
( ( in @ X1703 @ ( powerset @ X1702 ) )
=> ( subset @ X1703 @ ( setminus @ X1702 @ ( setminus @ X1702 @ X1703 ) ) ) )
=> ( ! [X1704: $i,X1705: $i] :
( ( in @ X1705 @ ( powerset @ X1704 ) )
=> ( subset @ ( setminus @ X1704 @ ( setminus @ X1704 @ X1705 ) ) @ X1705 ) )
=> ( ! [X1706: $i,X1707: $i] :
( ( in @ X1707 @ ( powerset @ X1706 ) )
=> ( X1707
= ( setminus @ X1706 @ ( setminus @ X1706 @ X1707 ) ) ) )
=> ( ! [X1708: $i,X1709: $i] :
( ( in @ X1709 @ ( powerset @ X1708 ) )
=> ! [X1710: $i] :
( ( in @ X1710 @ ( powerset @ X1708 ) )
=> ! [X1711: $i] :
( ( in @ X1711 @ X1708 )
=> ( ( in @ X1711 @ ( setminus @ X1708 @ X1709 ) )
=> ~ ( in @ X1711 @ ( binintersect @ X1709 @ X1710 ) ) ) ) ) )
=> ( ! [X1712: $i,X1713: $i] :
( ( in @ X1713 @ ( powerset @ X1712 ) )
=> ! [X1714: $i] :
( ( in @ X1714 @ ( powerset @ X1712 ) )
=> ! [X1715: $i] :
( ( in @ X1715 @ X1712 )
=> ( ( in @ X1715 @ ( setminus @ X1712 @ X1713 ) )
=> ( in @ X1715 @ ( setminus @ X1712 @ ( binintersect @ X1713 @ X1714 ) ) ) ) ) ) )
=> ( ! [X1716: $i,X1717: $i] :
( ( in @ X1717 @ ( powerset @ X1716 ) )
=> ! [X1718: $i] :
( ( in @ X1718 @ ( powerset @ X1716 ) )
=> ( subset @ ( setminus @ X1716 @ X1717 ) @ ( setminus @ X1716 @ ( binintersect @ X1717 @ X1718 ) ) ) ) )
=> ( ! [X1719: $i,X1720: $i] :
( ( in @ X1720 @ ( powerset @ X1719 ) )
=> ! [X1721: $i] :
( ( in @ X1721 @ ( powerset @ X1719 ) )
=> ( in @ ( setminus @ X1719 @ X1720 ) @ ( powerset @ ( setminus @ X1719 @ ( binintersect @ X1720 @ X1721 ) ) ) ) ) )
=> ( ! [X1722: $i,X1723: $i] :
( ( in @ X1723 @ ( powerset @ X1722 ) )
=> ! [X1724: $i] :
( ( in @ X1724 @ ( powerset @ X1722 ) )
=> ( ( subset @ X1723 @ ( setminus @ X1722 @ X1724 ) )
=> ! [X1725: $i] :
( ( in @ X1725 @ X1722 )
=> ( ( in @ X1725 @ X1724 )
=> ( in @ X1725 @ ( setminus @ X1722 @ X1723 ) ) ) ) ) ) )
=> ( ! [X1726: $i,X1727: $i] :
( ( in @ X1727 @ ( powerset @ X1726 ) )
=> ! [X1728: $i] :
( ( in @ X1728 @ ( powerset @ X1726 ) )
=> ( ( subset @ X1727 @ ( setminus @ X1726 @ X1728 ) )
=> ( subset @ X1728 @ ( setminus @ X1726 @ X1727 ) ) ) ) )
=> ( ! [X1729: $i,X1730: $i] :
( ( in @ X1730 @ ( powerset @ X1729 ) )
=> ! [X1731: $i] :
( ( in @ X1731 @ ( powerset @ X1729 ) )
=> ! [X1732: $i] :
( ( in @ X1732 @ X1729 )
=> ( ~ ( in @ X1732 @ ( binunion @ X1730 @ X1731 ) )
=> ~ ( in @ X1732 @ X1730 ) ) ) ) )
=> ( ! [X1733: $i,X1734: $i] :
( ( in @ X1734 @ ( powerset @ X1733 ) )
=> ! [X1735: $i] :
( ( in @ X1735 @ ( powerset @ X1733 ) )
=> ! [X1736: $i] :
( ( in @ X1736 @ X1733 )
=> ( ~ ( in @ X1736 @ ( binunion @ X1734 @ X1735 ) )
=> ~ ( in @ X1736 @ X1735 ) ) ) ) )
=> ( ! [X1737: $i,X1738: $i] :
( ( in @ X1738 @ ( powerset @ X1737 ) )
=> ! [X1739: $i] :
( ( in @ X1739 @ ( powerset @ X1737 ) )
=> ! [X1740: $i] :
( ( in @ X1740 @ ( powerset @ X1737 ) )
=> ! [X1741: $i] :
( ( in @ X1741 @ X1737 )
=> ( ( in @ X1741 @ ( binintersect @ X1738 @ X1739 ) )
=> ( in @ X1741 @ ( binunion @ X1738 @ X1740 ) ) ) ) ) ) )
=> ( ! [X1742: $i,X1743: $i] :
( ( in @ X1743 @ ( powerset @ X1742 ) )
=> ! [X1744: $i] :
( ( in @ X1744 @ ( powerset @ X1742 ) )
=> ! [X1745: $i] :
( ( in @ X1745 @ ( powerset @ X1742 ) )
=> ! [X1746: $i] :
( ( in @ X1746 @ X1742 )
=> ( ( in @ X1746 @ ( binintersect @ X1743 @ X1744 ) )
=> ( in @ X1746 @ ( binunion @ X1744 @ X1745 ) ) ) ) ) ) )
=> ( ! [X1747: $i,X1748: $i] :
( ( in @ X1748 @ ( powerset @ X1747 ) )
=> ! [X1749: $i] :
( ( in @ X1749 @ ( powerset @ X1747 ) )
=> ! [X1750: $i] :
( ( in @ X1750 @ ( powerset @ X1747 ) )
=> ! [X1751: $i] :
( ( in @ X1751 @ X1747 )
=> ( ( in @ X1751 @ ( binintersect @ X1748 @ X1749 ) )
=> ( in @ X1751 @ ( binintersect @ ( binunion @ X1748 @ X1750 ) @ ( binunion @ X1749 @ X1750 ) ) ) ) ) ) ) )
=> ( ! [X1752: $i,X1753: $i] :
( ( in @ X1753 @ ( powerset @ X1752 ) )
=> ! [X1754: $i] :
( ( in @ X1754 @ ( powerset @ X1752 ) )
=> ! [X1755: $i] :
( ( in @ X1755 @ ( powerset @ X1752 ) )
=> ( in @ ( binintersect @ X1753 @ X1754 ) @ ( powerset @ ( binintersect @ ( binunion @ X1753 @ X1755 ) @ ( binunion @ X1754 @ X1755 ) ) ) ) ) ) )
=> ( ! [X1756: $i,X1757: $i] :
( ( in @ X1757 @ ( powerset @ X1756 ) )
=> ! [X1758: $i] :
( ( in @ X1758 @ ( powerset @ X1756 ) )
=> ! [X1759: $i] :
( ( in @ X1759 @ X1756 )
=> ( ( in @ X1759 @ ( setminus @ X1756 @ ( binunion @ X1757 @ X1758 ) ) )
=> ~ ( in @ X1759 @ X1757 ) ) ) ) )
=> ( ! [X1760: $i,X1761: $i] :
( ( in @ X1761 @ ( powerset @ X1760 ) )
=> ! [X1762: $i] :
( ( in @ X1762 @ ( powerset @ X1760 ) )
=> ! [X1763: $i] :
( ( in @ X1763 @ X1760 )
=> ( ( in @ X1763 @ ( setminus @ X1760 @ ( binunion @ X1761 @ X1762 ) ) )
=> ( in @ X1763 @ ( setminus @ X1760 @ X1761 ) ) ) ) ) )
=> ( ! [X1764: $i,X1765: $i] :
( ( in @ X1765 @ ( powerset @ X1764 ) )
=> ! [X1766: $i] :
( ( in @ X1766 @ ( powerset @ X1764 ) )
=> ! [X1767: $o,X1768: $i] :
( ( in @ X1768 @ X1764 )
=> ( ( in @ X1768 @ ( binunion @ X1765 @ X1766 ) )
=> ( ( ( in @ X1768 @ X1765 )
=> X1767 )
=> ( ( ( in @ X1768 @ X1766 )
=> X1767 )
=> X1767 ) ) ) ) ) )
=> ( ! [X1769: $i,X1770: $i] :
( ( in @ X1770 @ ( powerset @ X1769 ) )
=> ! [X1771: $i] :
( ( in @ X1771 @ ( powerset @ X1769 ) )
=> ! [X1772: $i] :
( ( in @ X1772 @ X1769 )
=> ( ~ ( in @ X1772 @ X1770 )
=> ( ~ ( in @ X1772 @ X1771 )
=> ~ ( in @ X1772 @ ( binunion @ X1770 @ X1771 ) ) ) ) ) ) )
=> ( ! [X1773: $i,X1774: $i] :
( ( in @ X1774 @ ( powerset @ X1773 ) )
=> ! [X1775: $i] :
( ( in @ X1775 @ ( powerset @ X1773 ) )
=> ! [X1776: $i] :
( ( in @ X1776 @ X1773 )
=> ( ( in @ X1776 @ ( setminus @ X1773 @ ( binunion @ X1774 @ X1775 ) ) )
=> ( in @ X1776 @ ( setminus @ X1773 @ X1774 ) ) ) ) ) )
=> ( ! [X1777: $i,X1778: $i] :
( ( in @ X1778 @ ( powerset @ X1777 ) )
=> ! [X1779: $i] :
( ( in @ X1779 @ ( powerset @ X1777 ) )
=> ( in @ ( setminus @ X1777 @ ( binunion @ X1778 @ X1779 ) ) @ ( powerset @ ( setminus @ X1777 @ X1778 ) ) ) ) )
=> ( ! [X1780: $i,X1781: $i] :
( ( in @ X1781 @ ( powerset @ X1780 ) )
=> ! [X1782: $i] :
( ( in @ X1782 @ ( powerset @ X1780 ) )
=> ! [X1783: $i] :
( ( in @ X1783 @ X1780 )
=> ( ( in @ X1783 @ ( setminus @ X1780 @ ( binunion @ X1781 @ X1782 ) ) )
=> ( in @ X1783 @ ( setminus @ X1780 @ X1782 ) ) ) ) ) )
=> ( ! [X1784: $i,X1785: $i] :
( ( in @ X1785 @ ( powerset @ X1784 ) )
=> ! [X1786: $i] :
( ( in @ X1786 @ ( powerset @ X1784 ) )
=> ! [X1787: $i] :
( ( in @ X1787 @ X1784 )
=> ( ( in @ X1787 @ ( setminus @ X1784 @ ( binintersect @ X1785 @ X1786 ) ) )
=> ( in @ X1787 @ ( binunion @ ( setminus @ X1784 @ X1785 ) @ ( setminus @ X1784 @ X1786 ) ) ) ) ) ) )
=> ( ! [X1788: $i,X1789: $i] :
( ( in @ X1789 @ ( powerset @ X1788 ) )
=> ! [X1790: $i] :
( ( in @ X1790 @ ( powerset @ X1788 ) )
=> ! [X1791: $i] :
( ( in @ X1791 @ X1788 )
=> ( ( in @ X1791 @ ( binunion @ ( setminus @ X1788 @ X1789 ) @ ( setminus @ X1788 @ X1790 ) ) )
=> ( in @ X1791 @ ( setminus @ X1788 @ ( binintersect @ X1789 @ X1790 ) ) ) ) ) ) )
=> ( ! [X1792: $i,X1793: $i] :
( ( in @ X1793 @ ( powerset @ X1792 ) )
=> ! [X1794: $i] :
( ( in @ X1794 @ ( powerset @ X1792 ) )
=> ( ( setminus @ X1792 @ ( binintersect @ X1793 @ X1794 ) )
= ( binunion @ ( setminus @ X1792 @ X1793 ) @ ( setminus @ X1792 @ X1794 ) ) ) ) )
=> ( ! [X1795: $i,X1796: $i] :
( ( in @ X1796 @ ( powerset @ X1795 ) )
=> ! [X1797: $i] :
( ( in @ X1797 @ ( powerset @ X1795 ) )
=> ! [X1798: $i] :
( ( in @ X1798 @ X1795 )
=> ( ( in @ X1798 @ ( setminus @ X1795 @ ( binunion @ X1796 @ X1797 ) ) )
=> ( in @ X1798 @ ( binintersect @ ( setminus @ X1795 @ X1796 ) @ ( setminus @ X1795 @ X1797 ) ) ) ) ) ) )
=> ( ! [X1799: $i,X1800: $i] :
( ( in @ X1800 @ ( powerset @ X1799 ) )
=> ! [X1801: $i] :
( ( in @ X1801 @ ( powerset @ X1799 ) )
=> ! [X1802: $i] :
( ( in @ X1802 @ X1799 )
=> ( ( in @ X1802 @ ( setminus @ X1799 @ X1800 ) )
=> ( ( in @ X1802 @ ( setminus @ X1799 @ X1801 ) )
=> ( in @ X1802 @ ( setminus @ X1799 @ ( binunion @ X1800 @ X1801 ) ) ) ) ) ) ) )
=> ( ! [X1803: $i,X1804: $i] :
( ( in @ X1804 @ ( powerset @ X1803 ) )
=> ! [X1805: $i] :
( ( in @ X1805 @ ( powerset @ X1803 ) )
=> ! [X1806: $i] :
( ( in @ X1806 @ X1803 )
=> ( ( in @ X1806 @ ( binintersect @ ( setminus @ X1803 @ X1804 ) @ ( setminus @ X1803 @ X1805 ) ) )
=> ( in @ X1806 @ ( setminus @ X1803 @ ( binunion @ X1804 @ X1805 ) ) ) ) ) ) )
=> ( ! [X1807: $i,X1808: $i] :
( ( in @ X1808 @ ( powerset @ X1807 ) )
=> ! [X1809: $i] :
( ( in @ X1809 @ ( powerset @ X1807 ) )
=> ( ( setminus @ X1807 @ ( binunion @ X1808 @ X1809 ) )
= ( binintersect @ ( setminus @ X1807 @ X1808 ) @ ( setminus @ X1807 @ X1809 ) ) ) ) )
=> ( ! [X1810: $i,X1811: $i] :
( ( in @ X1811 @ ( powerset @ X1810 ) )
=> ! [X1812: $i] :
( ( in @ X1812 @ ( powerset @ X1810 ) )
=> ! [X1813: $i] :
( ( in @ X1813 @ ( binintersect @ X1811 @ X1812 ) )
=> ( in @ X1813 @ X1810 ) ) ) )
=> ( ! [X1814: $i,X1815: $i] :
( ( in @ X1815 @ ( powerset @ X1814 ) )
=> ! [X1816: $i] :
( ( in @ X1816 @ ( powerset @ X1814 ) )
=> ! [X1817: $i] :
( ( in @ X1817 @ ( powerset @ X1814 ) )
=> ( ( subset @ X1815 @ X1817 )
=> ( subset @ ( binintersect @ X1815 @ X1816 ) @ X1817 ) ) ) ) )
=> ( ! [X1818: $i,X1819: $i] :
( ( in @ X1819 @ ( powerset @ X1818 ) )
=> ! [X1820: $i] :
( ( in @ X1820 @ ( powerset @ X1818 ) )
=> ! [X1821: $i] :
( ( in @ X1821 @ ( powerset @ X1818 ) )
=> ( ( subset @ X1820 @ X1821 )
=> ( subset @ ( binintersect @ X1819 @ X1820 ) @ X1821 ) ) ) ) )
=> ( ! [X1822: $i,X1823: $i] :
( ( in @ X1823 @ ( powerset @ X1822 ) )
=> ! [X1824: $i] :
( ( in @ X1824 @ ( powerset @ X1822 ) )
=> ! [X1825: $i] :
( ( in @ X1825 @ ( powerset @ X1822 ) )
=> ( ( subset @ X1823 @ X1824 )
=> ( ( subset @ X1823 @ X1825 )
=> ( subset @ X1823 @ ( binintersect @ X1824 @ X1825 ) ) ) ) ) ) )
=> ( ! [X1826: $i,X1827: $i] :
( ( in @ X1827 @ ( powerset @ X1826 ) )
=> ! [X1828: $i] :
( ( in @ X1828 @ ( powerset @ X1826 ) )
=> ! [X1829: $i] :
( ( in @ X1829 @ ( powerset @ X1826 ) )
=> ! [X1830: $i] :
( ( in @ X1830 @ ( powerset @ X1826 ) )
=> ( ( subset @ X1827 @ X1829 )
=> ( ( subset @ X1828 @ X1830 )
=> ( subset @ ( binintersect @ X1827 @ X1828 ) @ ( binintersect @ X1829 @ X1830 ) ) ) ) ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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intersectTELcontra]),binintersectEL]),binintersectTERcontra]),contrasubsetT]),binintersectLsub]),contrasubsetT1]),contrasubsetT2]),binintersectSubset2]),contrasubsetT3]),doubleComplementI1]),binintersectSubset3]),doubleComplementE1]),doubleComplementSub1]),binintersectER]),doubleComplementSub2]),doubleComplementEq]),disjointsetsI1]),complementTnotintersectT]),binintersectRsub]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),complementInPowersetComplementIntersect]),binintersectSubset4]),contraSubsetComplement]),complementTcontraSubset]),binunionTILcontra]),binintersectSubset1]),setukpairIR]),inIntersectImpInUnion]),inIntersectImpInUnion2]),bs114d]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),setminusI]),inComplementUnionImpNotIn1]),inComplementUnionImpInComplement1]),setminusEL]),binunionTE]),binunionTEcontra]),demorgan2a1]),complementUnionInPowersetComplement]),setminusER]),demorgan2a2]),demorgan1a]),setminusSubset2]),demorgan1b]),demorgan1]),setminusERneg]),demorgan2a]),demorgan2b2]),setminusELneg]),demorgan2b]),demorgan2]),setminusILneg]),woz13rule0]),woz13rule1]),setminusIRneg]),woz13rule2]),woz13rule3]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairinjR]),c_0_279]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_280]),c_0_281]),c_0_282]),c_0_283]),singletonsuniq]),setukpairinjL1]),c_0_284]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),powersetsubset]),setukpairinjL]),c_0_285]),setukpairinjR11]),setukpairinjR12]),c_0_286]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),complementT_lem]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),binunionIL]),cartprodpairsurjEq]),c_0_287]),c_0_288]),c_0_289]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),c_0_294]),c_0_295]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_296]),c_0_297]),c_0_298]),brelnall1]),brelnall2]),c_0_299]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_300]),c_0_301]),c_0_302]),c_0_303]),c_0_304]),c_0_305]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),ifp]),theeq]),iftrue]),iffalse]),upairset2IR]),binunionIR]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),binunionEcases]),powersetT_lem]),binunionE]),binunionLsub]),setminusT_lem]),binunionRsub]),binintersectI]),setextT]),subsetTI]),powersetTI1]),inPowerset]),powersetE1]),powersetI1]),subsetemptysetimpeq]),setextsub]),subset2powerset]),setadjoinSub2]),setadjoinSub]),subsetTrans]),subsetRefl]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_310]),c_0_311]),c_0_312]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_313]),c_0_314]),in__Cong]),inCongP]),c_0_315]),c_0_316]),c_0_317]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_318]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_319]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_320]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_321]),nonemptyE1]),c_0_322]),noeltsimpempty]),emptyI]),setext]),c_0_323]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_324]),c_0_325]),c_0_326]),c_0_327]),c_0_328]),wellorderingAx]),foundationAx]),c_0_329]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_330]) ).
thf(c_0_332,negated_conjecture,
! 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$i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,X2363: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2368: $i,X2369: $i,X2370: $i,X2371: $i,X2372: $i,X2373: $i > $i,X2375: $i,X2376: $i,X2377: $i > $i,X2379: $i,X2380: $i,X2381: $i > $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i > $o,X2389: $i,X2390: $i,X2391: $i,X2392: $i,X2393: $i > $o,X2396: $i,X2397: $i,X2398: $i > $o,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $i,X2412: $i,X2413: $i,X2414: $i,X2415: $i,X2416: $i,X2417: $i,X2419: $i,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i,X2425: $i,X2426: $i,X2427: $i,X2428: $i,X2429: $i,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2440: $i,X2441: $i,X2442: $i,X2443: $i,X2445: $i,X2446: $i,X2447: $i,X2448: $i,X2450: $i,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i,X2456: $i,X2457: $i,X2458: $i,X2459: $i,X2460: $i > $i,X2462: $i,X2463: $i,X2464: 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$i,X2670: $i,X2671: $i,X2672: $i,X2673: $i,X2674: $i,X2675: $i,X2676: $i,X2677: $i,X2678: $i,X2679: $i,X2680: $i,X2681: $i,X2682: $i,X2683: $i,X2684: $i,X2685: $i,X2686: $i,X2687: $i,X2688: $i,X2689: $i,X2690: $i,X2691: $i,X2692: $i,X2693: $i,X2694: $i,X2695: $i,X2696: $i,X2697: $i,X2698: $i,X2699: $i,X2700: $i,X2701: $i,X2702: $i,X2703: $i,X2704: $i,X2705: $i,X2706: $i,X2707: $i,X2708: $i] :
( ( ~ ( in @ ( esk1_2 @ X1831 @ X1832 ) @ X1831 )
| ~ ( in @ ( esk1_2 @ X1831 @ X1832 ) @ X1832 )
| ( X1831 = X1832 ) )
& ( ( in @ ( esk1_2 @ X1831 @ X1832 ) @ X1831 )
| ( in @ ( esk1_2 @ X1831 @ X1832 ) @ X1832 )
| ( X1831 = X1832 ) )
& ~ ( in @ X1834 @ emptyset )
& ( ~ ( in @ X1837 @ ( setadjoin @ X1835 @ X1836 ) )
| ( X1837 = X1835 )
| ( in @ X1837 @ X1836 ) )
& ( ( X1837 != X1835 )
| ( in @ X1837 @ ( setadjoin @ X1835 @ X1836 ) ) )
& ( ~ ( in @ X1837 @ X1836 )
| ( in @ X1837 @ ( setadjoin @ X1835 @ X1836 ) ) )
& ( ~ ( in @ X1839 @ ( powerset @ X1838 ) )
| ~ ( in @ X1840 @ X1839 )
| ( in @ X1840 @ X1838 ) )
& ( ( in @ ( esk2_2 @ X1841 @ X1842 ) @ X1842 )
| ( in @ X1842 @ ( powerset @ X1841 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1841 @ X1842 ) @ X1841 )
| ( in @ X1842 @ ( powerset @ X1841 ) ) )
& ( ( in @ X1845 @ ( esk3_2 @ X1844 @ X1845 ) )
| ~ ( in @ X1845 @ ( setunion @ X1844 ) ) )
& ( ( in @ ( esk3_2 @ X1844 @ X1845 ) @ X1844 )
| ~ ( in @ X1845 @ ( setunion @ X1844 ) ) )
& ( ~ ( in @ X1848 @ X1849 )
| ~ ( in @ X1849 @ X1847 )
| ( in @ X1848 @ ( setunion @ X1847 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1850 @ omega )
| ( in @ ( setadjoin @ X1850 @ X1850 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1851 ) @ omega )
| ~ ( in @ emptyset @ X1851 )
| ~ ( in @ X1853 @ omega )
| ( in @ X1853 @ X1851 ) )
& ( ( in @ ( esk4_1 @ X1851 ) @ X1851 )
| ~ ( in @ emptyset @ X1851 )
| ~ ( in @ X1853 @ omega )
| ( in @ X1853 @ X1851 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1851 ) @ ( esk4_1 @ X1851 ) ) @ X1851 )
| ~ ( in @ emptyset @ X1851 )
| ~ ( in @ X1853 @ omega )
| ( in @ X1853 @ X1851 ) )
& ( ( in @ ( esk7_3 @ X1854 @ X1855 @ X1858 ) @ X1855 )
| ~ ( in @ X1858 @ ( esk6_2 @ X1854 @ X1855 ) )
| ( in @ ( esk5_2 @ X1854 @ X1855 ) @ X1855 ) )
& ( ( X1854 @ ( esk7_3 @ X1854 @ X1855 @ X1858 ) @ X1858 )
| ~ ( in @ X1858 @ ( esk6_2 @ X1854 @ X1855 ) )
| ( in @ ( esk5_2 @ X1854 @ X1855 ) @ X1855 ) )
& ( ~ ( in @ X1861 @ X1855 )
| ~ ( X1854 @ X1861 @ X1860 )
| ( in @ X1860 @ ( esk6_2 @ X1854 @ X1855 ) )
| ( in @ ( esk5_2 @ X1854 @ X1855 ) @ X1855 ) )
& ( ( in @ ( esk7_3 @ X1854 @ X1855 @ X1858 ) @ X1855 )
| ~ ( in @ X1858 @ ( esk6_2 @ X1854 @ X1855 ) )
| ~ ( exu @ ( X1854 @ ( esk5_2 @ X1854 @ X1855 ) ) ) )
& ( ( X1854 @ ( esk7_3 @ X1854 @ X1855 @ X1858 ) @ X1858 )
| ~ ( in @ X1858 @ ( esk6_2 @ X1854 @ X1855 ) )
| ~ ( exu @ ( X1854 @ ( esk5_2 @ X1854 @ X1855 ) ) ) )
& ( ~ ( in @ X1861 @ X1855 )
| ~ ( X1854 @ X1861 @ X1860 )
| ( in @ X1860 @ ( esk6_2 @ X1854 @ X1855 ) )
| ~ ( exu @ ( X1854 @ ( esk5_2 @ X1854 @ X1855 ) ) ) )
& ( ( in @ ( esk8_1 @ X1862 ) @ X1862 )
| ~ ( in @ X1863 @ X1862 ) )
& ( ~ ( in @ X1865 @ ( esk8_1 @ X1862 ) )
| ~ ( in @ X1865 @ X1862 )
| ~ ( in @ X1863 @ X1862 ) )
& epred1_0
& ( ~ ( exu @ X1866 )
| ( X1866 @ ( descr @ X1866 ) ) )
& ( ~ ( in @ X1869 @ X1867 )
| ~ ( X1868 @ X1869 )
| ( in @ X1869 @ ( dsetconstr @ X1867 @ X1868 ) ) )
& ( ~ ( in @ X1872 @ ( dsetconstr @ X1870 @ X1871 ) )
| ( in @ X1872 @ X1870 ) )
& ( ~ ( in @ X1875 @ ( dsetconstr @ X1873 @ X1874 ) )
| ( X1874 @ X1875 ) )
& ( ( X1876 @ ( esk9_1 @ X1876 ) )
| ~ ( exu @ X1876 ) )
& ( ~ ( X1876 @ X1878 )
| ( ( esk9_1 @ X1876 )
= X1878 )
| ~ ( exu @ X1876 ) )
& ( ~ ( in @ X1880 @ ( prop2set @ X1879 ) )
| X1879 )
& ( ~ ( in @ X1881 @ emptyset )
| X1882 )
& ( ~ ( in @ X1883 @ emptyset )
| ~ $true )
& ~ ( in @ X1884 @ emptyset )
& ( ~ ( exu @ X1885 )
| ( X1885 @ ( esk10_1 @ X1885 ) ) )
& ( ( in @ ( esk12_2 @ X1887 @ X1888 ) @ X1888 )
| ( X1887 = X1888 )
| ( in @ ( esk11_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ~ ( in @ ( esk12_2 @ X1887 @ X1888 ) @ X1887 )
| ( X1887 = X1888 )
| ( in @ ( esk11_2 @ X1887 @ X1888 ) @ X1887 ) )
& ( ( in @ ( esk12_2 @ X1887 @ X1888 ) @ X1888 )
| ( X1887 = X1888 )
| ~ ( in @ ( esk11_2 @ X1887 @ X1888 ) @ X1888 ) )
& ( ~ ( in @ ( esk12_2 @ X1887 @ X1888 ) @ X1887 )
| ( X1887 = X1888 )
| ~ ( in @ ( esk11_2 @ X1887 @ X1888 ) @ X1888 ) )
& ( ( in @ ( esk13_1 @ X1891 ) @ X1891 )
| ( X1891 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1893 ) @ X1893 )
| ( X1893 = emptyset ) )
& ( ~ ( in @ X1897 @ ( dsetconstr @ X1895 @ X1896 ) )
| ( X1896 @ X1897 )
| ~ ( in @ X1897 @ X1895 ) )
& ( ~ ( X1896 @ X1897 )
| ( in @ X1897 @ ( dsetconstr @ X1895 @ X1896 ) )
| ~ ( in @ X1897 @ X1895 ) )
& ( ~ ( nonempty @ X1898 )
| ( in @ ( esk15_1 @ X1898 ) @ X1898 ) )
& ( ~ ( in @ X1902 @ X1900 )
| ~ ( X1901 @ X1902 )
| ( nonempty @ ( dsetconstr @ X1900 @ X1901 ) ) )
& ( ~ ( in @ X1904 @ X1903 )
| ( nonempty @ X1903 ) )
& ( in @ X1905 @ ( setadjoin @ X1905 @ X1906 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1909 @ X1908 )
| ( in @ X1909 @ ( setadjoin @ X1907 @ X1908 ) ) )
& ( ( in @ X1912 @ X1911 )
| X1913
| ( X1912 = X1910 )
| ~ ( in @ X1912 @ ( setadjoin @ X1910 @ X1911 ) ) )
& ( ~ X1913
| X1913
| ( X1912 = X1910 )
| ~ ( in @ X1912 @ ( setadjoin @ X1910 @ X1911 ) ) )
& ( ( in @ X1912 @ X1911 )
| X1913
| ~ X1913
| ~ ( in @ X1912 @ ( setadjoin @ X1910 @ X1911 ) ) )
& ( ~ X1913
| X1913
| ~ X1913
| ~ ( in @ X1912 @ ( setadjoin @ X1910 @ X1911 ) ) )
& ( ~ ( in @ X1916 @ ( setadjoin @ X1914 @ X1915 ) )
| ( X1916 = X1914 )
| ( in @ X1916 @ X1915 ) )
& ( ( dsetconstr @ X1917
@ ^ [Z0: $i] : $true )
= X1917 )
& ( ( in @ ( esk16_2 @ X1918 @ X1919 ) @ X1919 )
| ( in @ X1919 @ ( powerset @ X1918 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1918 @ X1919 ) @ X1918 )
| ( in @ X1919 @ ( powerset @ X1918 ) ) )
& ( in @ emptyset @ ( powerset @ X1921 ) )
& ( in @ emptyset @ ( powerset @ X1922 ) )
& ( ~ ( in @ X1924 @ ( powerset @ X1923 ) )
| ~ ( in @ X1925 @ X1924 )
| ( in @ X1925 @ X1923 ) )
& ( ~ ( in @ X1927 @ X1928 )
| ~ ( in @ X1928 @ X1926 )
| ( in @ X1927 @ ( setunion @ X1926 ) ) )
& ( ( in @ X1930 @ ( esk17_3 @ X1929 @ X1930 @ X1931 ) )
| X1931
| ~ ( in @ X1930 @ ( setunion @ X1929 ) ) )
& ( ( in @ ( esk17_3 @ X1929 @ X1930 @ X1931 ) @ X1929 )
| X1931
| ~ ( in @ X1930 @ ( setunion @ X1929 ) ) )
& ( ~ X1931
| X1931
| ~ ( in @ X1930 @ ( setunion @ X1929 ) ) )
& ( ~ ( in @ X1934 @ X1933 )
| ( in @ X1934 @ ( powerset @ ( setunion @ X1933 ) ) ) )
& ( ~ ( X1935 @ X1937 )
| ( X1937
= ( esk18_1 @ X1935 ) )
| ~ ( exu @ X1935 ) )
& ( ( X1938
!= ( esk18_1 @ X1935 ) )
| ( X1935 @ X1938 )
| ~ ( exu @ X1935 ) )
& ( ( in @ ( esk19_1 @ X1939 ) @ X1939 )
| ~ ( nonempty @ X1939 ) )
& ( $true
| ~ ( nonempty @ X1939 ) )
& ( ~ ( in @ X1941 @ ( setadjoin @ X1942 @ emptyset ) )
| ( X1941 = X1942 ) )
& ( ( X1943 = X1944 )
| ~ ( in @ X1944 @ ( setadjoin @ X1943 @ emptyset ) ) )
& ( ( X1945 != X1946 )
| ( in @ X1945 @ ( setadjoin @ X1946 @ emptyset ) ) )
& ( ~ ( in @ X1947 @ ( setadjoin @ X1948 @ emptyset ) )
| ( in @ X1948 @ ( setadjoin @ X1947 @ emptyset ) ) )
& ( ~ ( in @ X1951 @ ( setadjoin @ X1949 @ ( setadjoin @ X1950 @ emptyset ) ) )
| ( X1951 = X1949 )
| ( X1951 = X1950 ) )
& ( in @ X1952 @ ( setadjoin @ X1952 @ ( setadjoin @ X1953 @ emptyset ) ) )
& ( in @ X1955 @ ( setadjoin @ X1954 @ ( setadjoin @ X1955 @ emptyset ) ) )
& ( ~ ( in @ X1958 @ X1956 )
| ~ ( X1957 @ X1958 )
| ( ( dsetconstr @ X1956 @ X1957 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1960 @ emptyset )
| ( X1959 @ X1960 ) )
& ( ( in @ ( esk20_2 @ X1961 @ X1962 ) @ X1961 )
| ~ ( in @ X1963 @ X1961 )
| ( X1962 @ X1963 ) )
& ( ~ ( X1962 @ ( esk20_2 @ X1961 @ X1962 ) )
| ~ ( in @ X1963 @ X1961 )
| ( X1962 @ X1963 ) )
& ( ( in @ ( esk21_2 @ X1965 @ X1966 ) @ X1965 )
| ~ ( in @ X1968 @ X1965 )
| ~ ( X1966 @ X1968 ) )
& ( ( X1966 @ ( esk21_2 @ X1965 @ X1966 ) )
| ~ ( in @ X1968 @ X1965 )
| ~ ( X1966 @ X1968 ) )
& ( ( in @ ( esk22_2 @ X1969 @ X1970 ) @ X1969 )
| ~ ( in @ X1972 @ X1969 )
| ~ ( X1970 @ X1972 ) )
& ( ( X1970 @ ( esk22_2 @ X1969 @ X1970 ) )
| ~ ( in @ X1972 @ X1969 )
| ~ ( X1970 @ X1972 ) )
& ( ( in @ ( esk23_2 @ X1973 @ X1974 ) @ X1973 )
| ~ ( in @ X1975 @ X1973 )
| ( X1974 @ X1975 ) )
& ( ~ ( X1974 @ ( esk23_2 @ X1973 @ X1974 ) )
| ~ ( in @ X1975 @ X1973 )
| ( X1974 @ X1975 ) )
& ( ~ X1977
| ( in @ emptyset @ ( prop2set @ X1977 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1978 @ X1979 ) @ X1978 )
| ~ ( in @ X1981 @ X1978 )
| ~ ( X1979 @ X1981 ) )
& ( ( X1979 @ ( esk24_2 @ X1978 @ X1979 ) )
| ~ ( in @ X1981 @ X1978 )
| ~ ( X1979 @ X1981 ) )
& ( ( in @ ( esk25_2 @ X1982 @ X1983 ) @ X1982 )
| ~ ( in @ X1984 @ X1982 )
| ( X1983 @ X1984 ) )
& ( ~ ( X1983 @ ( esk25_2 @ X1982 @ X1983 ) )
| ~ ( in @ X1984 @ X1982 )
| ( X1983 @ X1984 ) )
& ( ( X1986 @ ( esk26_2 @ X1986 @ X1987 ) )
| ~ ( X1986 @ X1987 )
| ( exu @ X1986 ) )
& ( ( X1987
!= ( esk26_2 @ X1986 @ X1987 ) )
| ~ ( X1986 @ X1987 )
| ( exu @ X1986 ) )
& ( ( X1989 @ ( esk27_1 @ X1989 ) )
| ( exu @ X1989 )
| ~ ( X1989 @ X1990 ) )
& ( ( X1989 @ ( esk28_1 @ X1989 ) )
| ( exu @ X1989 )
| ~ ( X1989 @ X1990 ) )
& ( ( ( esk27_1 @ X1989 )
!= ( esk28_1 @ X1989 ) )
| ( exu @ X1989 )
| ~ ( X1989 @ X1990 ) )
& ( ~ ( X1993 @ ( esk29_2 @ X1993 @ X1994 ) )
| ( ( esk29_2 @ X1993 @ X1994 )
!= X1994 )
| ( exu @ X1993 ) )
& ( ( X1993 @ ( esk29_2 @ X1993 @ X1994 ) )
| ( ( esk29_2 @ X1993 @ X1994 )
= X1994 )
| ( exu @ X1993 ) )
& ( ( X1996 != X1997 )
| ( X1998 != X1999 )
| ~ ( in @ X1998 @ X1996 )
| ( in @ X1999 @ X1997 ) )
& ( ~ ( in @ X2002 @ X2000 )
| ( in @ X2003 @ X2001 )
| ( X2002 != X2003 )
| ( X2000 != X2001 ) )
& ( ~ ( in @ X2003 @ X2001 )
| ( in @ X2002 @ X2000 )
| ( X2002 != X2003 )
| ( X2000 != X2001 ) )
& ( ~ ( exu @ X2004 )
| ~ ( X2004 @ X2005 )
| ~ ( X2004 @ X2006 )
| ( X2005 = X2006 ) )
& ( ~ ( exu @ X2007 )
| ( exu @ X2008 )
| ( ( esk30_2 @ X2007 @ X2008 )
= ( esk31_2 @ X2007 @ X2008 ) ) )
& ( ~ ( exu @ X2008 )
| ( exu @ X2007 )
| ( ( esk30_2 @ X2007 @ X2008 )
= ( esk31_2 @ X2007 @ X2008 ) ) )
& ( ~ ( exu @ X2007 )
| ( exu @ X2008 )
| ~ ( X2007 @ ( esk30_2 @ X2007 @ X2008 ) )
| ~ ( X2008 @ ( esk31_2 @ X2007 @ X2008 ) ) )
& ( ~ ( exu @ X2008 )
| ( exu @ X2007 )
| ~ ( X2007 @ ( esk30_2 @ X2007 @ X2008 ) )
| ~ ( X2008 @ ( esk31_2 @ X2007 @ X2008 ) ) )
& ( ~ ( exu @ X2007 )
| ( exu @ X2008 )
| ( X2007 @ ( esk30_2 @ X2007 @ X2008 ) )
| ( X2008 @ ( esk31_2 @ X2007 @ X2008 ) ) )
& ( ~ ( exu @ X2008 )
| ( exu @ X2007 )
| ( X2007 @ ( esk30_2 @ X2007 @ X2008 ) )
| ( X2008 @ ( esk31_2 @ X2007 @ X2008 ) ) )
& ( emptyset = emptyset )
& ( ( X2011 != X2012 )
| ( X2013 != X2014 )
| ( ( setadjoin @ X2011 @ X2013 )
= ( setadjoin @ X2012 @ X2014 ) ) )
& ( ( X2015 != X2016 )
| ( ( powerset @ X2015 )
= ( powerset @ X2016 ) ) )
& ( ( X2017 != X2018 )
| ( ( setunion @ X2017 )
= ( setunion @ X2018 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X2019 )
| ~ ( X2019 @ X2020 )
| ~ ( X2019 @ X2021 )
| ( X2020 = X2021 ) )
& ( ( ( esk32_2 @ X2022 @ X2023 )
= ( esk33_2 @ X2022 @ X2023 ) )
| ~ ( exu @ X2022 )
| ~ ( exu @ X2023 )
| ( ( descr @ X2022 )
= ( descr @ X2023 ) ) )
& ( ~ ( X2022 @ ( esk32_2 @ X2022 @ X2023 ) )
| ~ ( X2023 @ ( esk33_2 @ X2022 @ X2023 ) )
| ~ ( exu @ X2022 )
| ~ ( exu @ X2023 )
| ( ( descr @ X2022 )
= ( descr @ X2023 ) ) )
& ( ( X2022 @ ( esk32_2 @ X2022 @ X2023 ) )
| ( X2023 @ ( esk33_2 @ X2022 @ X2023 ) )
| ~ ( exu @ X2022 )
| ~ ( exu @ X2023 )
| ( ( descr @ X2022 )
= ( descr @ X2023 ) ) )
& ( ( in @ ( esk34_4 @ X2026 @ X2027 @ X2028 @ X2029 ) @ X2026 )
| ( ( dsetconstr @ X2026 @ X2028 )
= ( dsetconstr @ X2027 @ X2029 ) )
| ( X2026 != X2027 ) )
& ( ( in @ ( esk35_4 @ X2026 @ X2027 @ X2028 @ X2029 ) @ X2027 )
| ( ( dsetconstr @ X2026 @ X2028 )
= ( dsetconstr @ X2027 @ X2029 ) )
| ( X2026 != X2027 ) )
& ( ( ( esk34_4 @ X2026 @ X2027 @ X2028 @ X2029 )
= ( esk35_4 @ X2026 @ X2027 @ X2028 @ X2029 ) )
| ( ( dsetconstr @ X2026 @ X2028 )
= ( dsetconstr @ X2027 @ X2029 ) )
| ( X2026 != X2027 ) )
& ( ~ ( X2028 @ ( esk34_4 @ X2026 @ X2027 @ X2028 @ X2029 ) )
| ~ ( X2029 @ ( esk35_4 @ X2026 @ X2027 @ X2028 @ X2029 ) )
| ( ( dsetconstr @ X2026 @ X2028 )
= ( dsetconstr @ X2027 @ X2029 ) )
| ( X2026 != X2027 ) )
& ( ( X2028 @ ( esk34_4 @ X2026 @ X2027 @ X2028 @ X2029 ) )
| ( X2029 @ ( esk35_4 @ X2026 @ X2027 @ X2028 @ X2029 ) )
| ( ( dsetconstr @ X2026 @ X2028 )
= ( dsetconstr @ X2027 @ X2029 ) )
| ( X2026 != X2027 ) )
& ( ( in @ ( esk36_2 @ X2032 @ X2033 ) @ X2032 )
| ( subset @ X2032 @ X2033 ) )
& ( ~ ( in @ ( esk36_2 @ X2032 @ X2033 ) @ X2033 )
| ( subset @ X2032 @ X2033 ) )
& ( ( X2035 != X2036 )
| ( subset @ X2036 @ X2035 ) )
& ( ( X2037 != X2038 )
| ( subset @ X2037 @ X2038 ) )
& ( ( in @ ( esk37_2 @ X2039 @ X2040 ) @ X2039 )
| ( subset @ X2039 @ X2040 ) )
& ( ~ ( in @ ( esk37_2 @ X2039 @ X2040 ) @ X2040 )
| ( subset @ X2039 @ X2040 ) )
& ( subset @ emptyset @ X2042 )
& ( ~ ( subset @ X2043 @ X2044 )
| ~ ( in @ X2045 @ X2043 )
| ( in @ X2045 @ X2044 ) )
& ( ~ ( subset @ X2046 @ X2047 )
| ( in @ X2048 @ X2047 )
| ~ ( in @ X2048 @ X2046 ) )
& ( ~ ( in @ X2051 @ X2049 )
| ( in @ X2051 @ X2050 )
| ~ ( subset @ X2049 @ X2050 ) )
& ( ( subset @ X2052 @ X2053 )
| ( X2052 != X2053 ) )
& ( ~ ( in @ X2056 @ X2054 )
| ( in @ X2056 @ X2055 )
| ( X2054 != X2055 ) )
& ( subset @ X2057 @ X2057 )
& ( ~ ( subset @ X2058 @ X2059 )
| ~ ( subset @ X2059 @ X2060 )
| ( subset @ X2058 @ X2060 ) )
& ( subset @ X2062 @ ( setadjoin @ X2061 @ X2062 ) )
& ( ~ ( subset @ X2063 @ X2065 )
| ( subset @ X2063 @ ( setadjoin @ X2064 @ X2065 ) ) )
& ( ~ ( subset @ X2066 @ X2067 )
| ( in @ X2066 @ ( powerset @ X2067 ) ) )
& ( ~ ( subset @ X2068 @ X2069 )
| ~ ( subset @ X2069 @ X2068 )
| ( X2068 = X2069 ) )
& ( ~ ( subset @ X2070 @ emptyset )
| ( X2070 = emptyset ) )
& ( ~ ( subset @ X2072 @ X2071 )
| ( in @ X2072 @ ( powerset @ X2071 ) ) )
& ( ~ ( in @ X2074 @ ( powerset @ X2073 ) )
| ( subset @ X2074 @ X2073 ) )
& ( in @ X2075 @ ( powerset @ X2075 ) )
& ( ~ ( subset @ X2076 @ X2077 )
| ( subset @ ( powerset @ X2076 ) @ ( powerset @ X2077 ) ) )
& ( in @ ( dsetconstr @ X2078 @ X2079 ) @ ( powerset @ X2078 ) )
& ( subset @ ( dsetconstr @ X2080 @ X2081 ) @ X2080 )
& ( ~ ( in @ X2084 @ X2082 )
| ( in @ X2084 @ ( binunion @ X2082 @ X2083 ) ) )
& ( in @ X2086 @ ( setadjoin @ X2085 @ ( setadjoin @ X2086 @ emptyset ) ) )
& ( ~ ( in @ X2089 @ X2088 )
| ( in @ X2089 @ ( binunion @ X2087 @ X2088 ) ) )
& ( ( in @ X2092 @ X2091 )
| X2093
| ( in @ X2092 @ X2090 )
| ~ ( in @ X2092 @ ( binunion @ X2090 @ X2091 ) ) )
& ( ~ X2093
| X2093
| ( in @ X2092 @ X2090 )
| ~ ( in @ X2092 @ ( binunion @ X2090 @ X2091 ) ) )
& ( ( in @ X2092 @ X2091 )
| X2093
| ~ X2093
| ~ ( in @ X2092 @ ( binunion @ X2090 @ X2091 ) ) )
& ( ~ X2093
| X2093
| ~ X2093
| ~ ( in @ X2092 @ ( binunion @ X2090 @ X2091 ) ) )
& ( ~ ( in @ X2096 @ ( binunion @ X2094 @ X2095 ) )
| ( in @ X2096 @ X2094 )
| ( in @ X2096 @ X2095 ) )
& ( subset @ X2097 @ ( binunion @ X2097 @ X2098 ) )
& ( subset @ X2100 @ ( binunion @ X2099 @ X2100 ) )
& ( ~ ( in @ X2103 @ X2101 )
| ~ ( in @ X2103 @ X2102 )
| ( in @ X2103 @ ( binintersect @ X2101 @ X2102 ) ) )
& ( ~ ( subset @ X2106 @ X2104 )
| ~ ( subset @ X2106 @ X2105 )
| ( subset @ X2106 @ ( binintersect @ X2104 @ X2105 ) ) )
& ( ~ ( in @ X2109 @ ( binintersect @ X2107 @ X2108 ) )
| ( in @ X2109 @ X2107 ) )
& ( subset @ ( binintersect @ X2110 @ X2111 ) @ X2110 )
& ( ~ ( subset @ X2112 @ X2113 )
| ( ( binintersect @ X2112 @ X2113 )
= X2112 ) )
& ( ( ( binintersect @ X2114 @ X2115 )
!= X2115 )
| ( subset @ X2115 @ X2114 ) )
& ( ~ ( in @ X2118 @ ( binintersect @ X2116 @ X2117 ) )
| ( in @ X2118 @ X2117 ) )
& ( ( in @ ( esk38_2 @ X2119 @ X2120 ) @ X2119 )
| ( ( binintersect @ X2119 @ X2120 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X2119 @ X2120 ) @ X2120 )
| ( ( binintersect @ X2119 @ X2120 )
= emptyset ) )
& ( subset @ ( binintersect @ X2122 @ X2123 ) @ X2123 )
& ( ~ ( subset @ X2125 @ X2124 )
| ( ( binintersect @ X2124 @ X2125 )
= X2125 ) )
& ( ( ( binintersect @ X2126 @ X2127 )
!= X2126 )
| ( subset @ X2126 @ X2127 ) )
& ( ( binintersect @ X2128 @ ( binunion @ X2129 @ X2130 ) )
= ( binunion @ ( binintersect @ X2128 @ X2129 ) @ ( binintersect @ X2128 @ X2130 ) ) )
& ( ~ ( in @ X2133 @ X2131 )
| ( in @ X2133 @ X2132 )
| ( in @ X2133 @ ( setminus @ X2131 @ X2132 ) ) )
& ( ~ ( in @ X2136 @ ( setminus @ X2134 @ X2135 ) )
| ( in @ X2136 @ X2134 ) )
& ( ~ ( in @ X2139 @ ( setminus @ X2137 @ X2138 ) )
| ~ ( in @ X2139 @ X2138 ) )
& ( ~ ( subset @ X2140 @ X2141 )
| ( ( setminus @ X2140 @ X2141 )
= emptyset ) )
& ( ( in @ X2144 @ ( setminus @ X2142 @ X2143 ) )
| ~ ( in @ X2144 @ X2142 )
| ( in @ X2144 @ X2143 ) )
& ( ( in @ X2147 @ ( setminus @ X2145 @ X2146 ) )
| ( in @ X2147 @ X2146 )
| ~ ( in @ X2147 @ X2145 ) )
& ( ( in @ X2150 @ X2148 )
| ~ ( in @ X2150 @ ( setminus @ X2148 @ X2149 ) ) )
& ( ~ ( in @ X2153 @ X2152 )
| ~ ( in @ X2153 @ ( setminus @ X2151 @ X2152 ) ) )
& ( subset @ ( setminus @ X2154 @ X2155 ) @ X2154 )
& ( ( ( setminus @ X2156 @ X2157 )
!= emptyset )
| ( subset @ X2156 @ X2157 ) )
& ( ~ ( in @ X2160 @ X2158 )
| X2161
| ( in @ X2160 @ X2158 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ( in @ X2160 @ X2159 )
| X2161
| ( in @ X2160 @ X2158 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ X2161
| X2161
| ( in @ X2160 @ X2158 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ ( in @ X2160 @ X2158 )
| X2161
| ~ ( in @ X2160 @ X2159 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ( in @ X2160 @ X2159 )
| X2161
| ~ ( in @ X2160 @ X2159 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ X2161
| X2161
| ~ ( in @ X2160 @ X2159 )
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ ( in @ X2160 @ X2158 )
| X2161
| ~ X2161
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ( in @ X2160 @ X2159 )
| X2161
| ~ X2161
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ X2161
| X2161
| ~ X2161
| ~ ( in @ X2160 @ ( symdiff @ X2158 @ X2159 ) ) )
& ( ~ ( in @ X2164 @ X2162 )
| ( in @ X2164 @ X2163 )
| ( in @ X2164 @ ( symdiff @ X2162 @ X2163 ) ) )
& ( ( in @ X2167 @ X2165 )
| ~ ( in @ X2167 @ X2166 )
| ( in @ X2167 @ ( symdiff @ X2165 @ X2166 ) ) )
& ( ~ ( in @ X2170 @ X2168 )
| ~ ( in @ X2170 @ X2169 )
| ~ ( in @ X2170 @ ( symdiff @ X2168 @ X2169 ) ) )
& ( ( in @ X2173 @ X2171 )
| ( in @ X2173 @ X2172 )
| ~ ( in @ X2173 @ ( symdiff @ X2171 @ X2172 ) ) )
& ( in @ X2175 @ ( setadjoin @ X2174 @ ( setadjoin @ X2175 @ emptyset ) ) )
& ( in @ X2176 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2176 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2176 @ ( setadjoin @ X2177 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2179 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2178 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2178 @ ( setadjoin @ X2179 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2180 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2180 @ ( setadjoin @ X2181 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2182 @ X2183 ) )
& ( ~ ( in @ X2185 @ X2184 )
| ( subset @ ( setadjoin @ X2185 @ emptyset ) @ X2184 ) )
& ( ~ ( in @ X2187 @ X2186 )
| ( in @ ( setadjoin @ X2187 @ emptyset ) @ ( powerset @ X2186 ) ) )
& ( ~ ( in @ X2190 @ X2188 )
| ( in @ ( setadjoin @ X2190 @ emptyset ) @ ( powerset @ ( binunion @ X2188 @ X2189 ) ) ) )
& ( ~ ( in @ X2193 @ ( setadjoin @ X2191 @ ( setadjoin @ X2192 @ emptyset ) ) )
| ( X2193 = X2191 )
| ( X2193 = X2192 ) )
& ( ~ ( in @ X2196 @ X2194 )
| ~ ( in @ X2197 @ X2195 )
| ( subset @ ( setadjoin @ X2196 @ ( setadjoin @ X2197 @ emptyset ) ) @ ( binunion @ X2194 @ X2195 ) ) )
& ( ~ ( in @ X2200 @ X2198 )
| ~ ( in @ X2201 @ X2199 )
| ( in @ ( setadjoin @ X2200 @ ( setadjoin @ X2201 @ emptyset ) ) @ ( powerset @ ( binunion @ X2198 @ X2199 ) ) ) )
& ( ~ ( in @ X2204 @ X2202 )
| ~ ( in @ X2205 @ X2203 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2204 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2204 @ ( setadjoin @ X2205 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2202 @ X2203 ) ) ) )
& ( ~ ( in @ X2208 @ X2206 )
| ~ ( in @ X2209 @ X2207 )
| ( in @ ( setadjoin @ ( setadjoin @ X2208 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2208 @ ( setadjoin @ X2209 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2206 @ X2207 ) ) ) ) )
& ( ~ ( in @ X2212 @ X2210 )
| ~ ( in @ X2213 @ X2211 )
| ( in @ ( kpair @ X2212 @ X2213 ) @ ( powerset @ ( powerset @ ( binunion @ X2210 @ X2211 ) ) ) ) )
& ( ~ ( in @ X2216 @ X2214 )
| ~ ( in @ X2217 @ X2215 )
| ( in @ ( kpair @ X2216 @ X2217 ) @ ( cartprod @ X2214 @ X2215 ) ) )
& ( ( in @ ( esk39_3 @ X2218 @ X2219 @ X2220 ) @ X2218 )
| ~ ( in @ X2220 @ ( cartprod @ X2218 @ X2219 ) ) )
& ( ( in @ ( esk40_3 @ X2218 @ X2219 @ X2220 ) @ X2219 )
| ~ ( in @ X2220 @ ( cartprod @ X2218 @ X2219 ) ) )
& ( ( X2220
= ( kpair @ ( esk39_3 @ X2218 @ X2219 @ X2220 ) @ ( esk40_3 @ X2218 @ X2219 @ X2220 ) ) )
| ~ ( in @ X2220 @ ( cartprod @ X2218 @ X2219 ) ) )
& ( ~ ( in @ X2225 @ ( cartprod @ X2223 @ X2224 ) )
| ( iskpair @ X2225 ) )
& ( ( in @ ( esk41_2 @ X2226 @ X2227 ) @ X2226 )
| ~ ( in @ X2227 @ ( setunion @ X2226 ) ) )
& ( ( in @ X2227 @ ( esk41_2 @ X2226 @ X2227 ) )
| ~ ( in @ X2227 @ ( setunion @ X2226 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2229 @ emptyset ) ) @ X2229 )
& ( subset @ X2230 @ ( setunion @ ( setadjoin @ X2230 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2231 @ emptyset ) )
= X2231 )
& ( ( in @ ( esk42_2 @ X2232 @ X2233 ) @ X2232 )
| ~ ( in @ X2236 @ X2232 )
| ~ ( X2233 @ X2236 )
| ( singleton @ ( dsetconstr @ X2232 @ X2233 ) ) )
& ( ( in @ ( esk43_2 @ X2232 @ X2233 ) @ X2232 )
| ~ ( in @ X2236 @ X2232 )
| ~ ( X2233 @ X2236 )
| ( singleton @ ( dsetconstr @ X2232 @ X2233 ) ) )
& ( ( X2233 @ ( esk42_2 @ X2232 @ X2233 ) )
| ~ ( in @ X2236 @ X2232 )
| ~ ( X2233 @ X2236 )
| ( singleton @ ( dsetconstr @ X2232 @ X2233 ) ) )
& ( ( X2233 @ ( esk43_2 @ X2232 @ X2233 ) )
| ~ ( in @ X2236 @ X2232 )
| ~ ( X2233 @ X2236 )
| ( singleton @ ( dsetconstr @ X2232 @ X2233 ) ) )
& ( ( ( esk42_2 @ X2232 @ X2233 )
!= ( esk43_2 @ X2232 @ X2233 ) )
| ~ ( in @ X2236 @ X2232 )
| ~ ( X2233 @ X2236 )
| ( singleton @ ( dsetconstr @ X2232 @ X2233 ) ) )
& ( ( in @ ( esk44_2 @ X2237 @ X2238 ) @ X2237 )
| ~ ( ex1 @ X2237 @ X2238 ) )
& ( ( X2238 @ ( esk44_2 @ X2237 @ X2238 ) )
| ~ ( ex1 @ X2237 @ X2238 ) )
& ( ( in @ ( esk45_3 @ X2240 @ X2241 @ X2242 ) @ X2240 )
| ( ex1 @ X2240 @ X2241 )
| ~ ( X2241 @ X2242 )
| ~ ( in @ X2242 @ X2240 ) )
& ( ( X2241 @ ( esk45_3 @ X2240 @ X2241 @ X2242 ) )
| ( ex1 @ X2240 @ X2241 )
| ~ ( X2241 @ X2242 )
| ~ ( in @ X2242 @ X2240 ) )
& ( ( ( esk45_3 @ X2240 @ X2241 @ X2242 )
!= X2242 )
| ( ex1 @ X2240 @ X2241 )
| ~ ( X2241 @ X2242 )
| ~ ( in @ X2242 @ X2240 ) )
& ( ( in @ ( esk46_2 @ X2244 @ X2245 ) @ X2244 )
| ~ ( in @ X2248 @ X2244 )
| ~ ( X2245 @ X2248 )
| ( ex1 @ X2244 @ X2245 ) )
& ( ( in @ ( esk47_2 @ X2244 @ X2245 ) @ X2244 )
| ~ ( in @ X2248 @ X2244 )
| ~ ( X2245 @ X2248 )
| ( ex1 @ X2244 @ X2245 ) )
& ( ( X2245 @ ( esk46_2 @ X2244 @ X2245 ) )
| ~ ( in @ X2248 @ X2244 )
| ~ ( X2245 @ X2248 )
| ( ex1 @ X2244 @ X2245 ) )
& ( ( X2245 @ ( esk47_2 @ X2244 @ X2245 ) )
| ~ ( in @ X2248 @ X2244 )
| ~ ( X2245 @ X2248 )
| ( ex1 @ X2244 @ X2245 ) )
& ( ( ( esk46_2 @ X2244 @ X2245 )
!= ( esk47_2 @ X2244 @ X2245 ) )
| ~ ( in @ X2248 @ X2244 )
| ~ ( X2245 @ X2248 )
| ( ex1 @ X2244 @ X2245 ) )
& ( ( ( setadjoin @ X2249 @ emptyset )
!= ( setadjoin @ X2250 @ emptyset ) )
| ( X2249 = X2250 ) )
& ( ~ ( in @ ( setadjoin @ X2253 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2251 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2251 @ ( setadjoin @ X2252 @ emptyset ) ) @ emptyset ) ) )
| ( X2251 = X2253 ) )
& ( ~ ( iskpair @ X2254 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2254 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2254 ) ) ) )
& ( ~ ( singleton @ X2255 )
| ( in @ ( setunion @ X2255 ) @ X2255 ) )
& ( ( kfst @ ( kpair @ X2256 @ X2257 ) )
= X2256 )
& ( ~ ( in @ X2260 @ ( cartprod @ X2258 @ X2259 ) )
| ( in @ ( kfst @ X2260 ) @ X2258 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2261 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2261 @ ( setadjoin @ X2262 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2263 @ ( setadjoin @ X2264 @ emptyset ) ) @ emptyset ) ) )
| ( X2261 = X2263 ) )
& ( ( ( kpair @ X2265 @ X2266 )
!= ( kpair @ X2267 @ X2268 ) )
| ( X2265 = X2267 ) )
& ( ( X2269 != X2270 )
| ( ( setadjoin @ X2269 @ ( setadjoin @ X2270 @ emptyset ) )
= ( setadjoin @ X2269 @ emptyset ) ) )
& ( ( X2271 != X2272 )
| ( ( setadjoin @ ( setadjoin @ X2271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2271 @ ( setadjoin @ X2272 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2271 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2273 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2273 @ ( setadjoin @ X2274 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2275 @ ( setadjoin @ X2276 @ emptyset ) ) @ emptyset ) ) )
| ( X2275 != X2276 )
| ( X2274 = X2276 ) )
& ( ( ( setadjoin @ X2277 @ ( setadjoin @ X2278 @ emptyset ) )
!= ( setadjoin @ X2279 @ emptyset ) )
| ( X2277 = X2278 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2280 @ ( setadjoin @ X2281 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2282 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2282 @ ( setadjoin @ X2283 @ emptyset ) ) @ emptyset ) ) )
| ( X2281 = X2283 ) )
& ( ( ( kpair @ X2284 @ X2285 )
!= ( kpair @ X2286 @ X2287 ) )
| ( X2285 = X2287 ) )
& ( ~ ( iskpair @ X2288 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2288 )
@ ^ [Z0: $i] :
( X2288
= ( kpair @ ( kfst @ X2288 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2289 @ X2290 ) )
= X2290 )
& ( ~ ( iskpair @ X2291 )
| ( ( kpair @ ( kfst @ X2291 ) @ ( ksnd @ X2291 ) )
= X2291 ) )
& ( ~ ( in @ X2294 @ ( cartprod @ X2292 @ X2293 ) )
| ( in @ ( ksnd @ X2294 ) @ X2293 ) )
& ( ~ ( in @ ( kpair @ X2297 @ X2298 ) @ ( cartprod @ X2295 @ X2296 ) )
| ( in @ X2297 @ X2295 ) )
& ( ~ ( in @ ( kpair @ X2301 @ X2302 ) @ ( cartprod @ X2299 @ X2300 ) )
| ( in @ X2302 @ X2300 ) )
& ( ~ ( in @ X2305 @ X2303 )
| ~ ( in @ X2306 @ X2304 )
| ( ( kpair @ X2305 @ X2306 )
= ( kpair @ X2305 @ X2306 ) ) )
& ( ~ ( in @ X2309 @ X2307 )
| ~ ( in @ X2310 @ X2308 )
| ( ( kfst @ ( kpair @ X2309 @ X2310 ) )
= X2309 ) )
& ( ~ ( in @ X2313 @ X2311 )
| ~ ( in @ X2314 @ X2312 )
| ( ( ksnd @ ( kpair @ X2313 @ X2314 ) )
= X2314 ) )
& ( ~ ( in @ X2317 @ ( cartprod @ X2315 @ X2316 ) )
| ( ( kpair @ ( kfst @ X2317 ) @ ( ksnd @ X2317 ) )
= X2317 ) )
& ( ~ ( in @ X2321 @ X2318 )
| ~ ( in @ X2322 @ X2319 )
| ~ ( X2320 @ X2321 @ X2322 )
| ( in @ ( kpair @ X2321 @ X2322 ) @ ( dpsetconstr @ X2318 @ X2319 @ X2320 ) ) )
& ( subset @ ( dpsetconstr @ X2323 @ X2324 @ X2325 ) @ ( cartprod @ X2323 @ X2324 ) )
& ( breln @ X2326 @ X2327 @ ( dpsetconstr @ X2326 @ X2327 @ X2328 ) )
& ( ~ ( in @ X2332 @ X2329 )
| ~ ( in @ X2333 @ X2330 )
| ~ ( in @ ( kpair @ X2332 @ X2333 ) @ ( dpsetconstr @ X2329 @ X2330 @ X2331 ) )
| ( X2331 @ X2332 @ X2333 ) )
& ( ~ ( in @ ( kpair @ X2337 @ X2338 ) @ ( dpsetconstr @ X2334 @ X2335 @ X2336 ) )
| ( in @ X2337 @ X2334 ) )
& ( ~ ( in @ ( kpair @ X2342 @ X2343 ) @ ( dpsetconstr @ X2339 @ X2340 @ X2341 ) )
| ( in @ X2343 @ X2340 ) )
& ( ~ ( in @ ( kpair @ X2347 @ X2348 ) @ ( dpsetconstr @ X2344 @ X2345 @ X2346 ) )
| ( X2346 @ X2347 @ X2348 ) )
& ( ~ ( func @ X2349 @ X2350 @ X2351 )
| ~ ( in @ X2352 @ X2349 )
| ( singleton
@ ( dsetconstr @ X2350
@ ^ [Z0: $i] : ( in @ ( kpair @ X2352 @ Z0 ) @ X2351 ) ) ) )
& ( ~ ( func @ X2353 @ X2354 @ X2355 )
| ~ ( in @ X2356 @ X2353 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2354
@ ^ [Z0: $i] : ( in @ ( kpair @ X2356 @ Z0 ) @ X2355 ) ) )
@ X2354 ) )
& ( ~ ( func @ X2357 @ X2358 @ X2359 )
| ~ ( in @ X2360 @ X2357 )
| ( in @ ( ap @ X2357 @ X2358 @ X2359 @ X2360 ) @ X2358 ) )
& ( ~ ( in @ X2363 @ ( funcSet @ X2361 @ X2362 ) )
| ( func @ X2361 @ X2362 @ X2363 ) )
& ( ~ ( in @ X2366 @ ( funcSet @ X2364 @ X2365 ) )
| ~ ( in @ X2367 @ X2364 )
| ( in @ ( ap @ X2364 @ X2365 @ X2366 @ X2367 ) @ X2365 ) )
& ( ~ ( func @ X2368 @ X2369 @ X2370 )
| ( in @ X2370 @ ( funcSet @ X2368 @ X2369 ) ) )
& ( ( in @ ( esk48_3 @ X2371 @ X2372 @ X2373 ) @ X2371 )
| ( func @ X2371 @ X2372
@ ( dpsetconstr @ X2371 @ X2372
@ ^ [Z0: $i] : ( $eq @ ( X2373 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2373 @ ( esk48_3 @ X2371 @ X2372 @ X2373 ) ) @ X2372 )
| ( func @ X2371 @ X2372
@ ( dpsetconstr @ X2371 @ X2372
@ ^ [Z0: $i] : ( $eq @ ( X2373 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2375 @ X2376 @ X2377 ) @ X2375 )
| ( func @ X2375 @ X2376 @ ( lam @ X2375 @ X2376 @ X2377 ) ) )
& ( ~ ( in @ ( X2377 @ ( esk49_3 @ X2375 @ X2376 @ X2377 ) ) @ X2376 )
| ( func @ X2375 @ X2376 @ ( lam @ X2375 @ X2376 @ X2377 ) ) )
& ( ( in @ ( esk50_3 @ X2379 @ X2380 @ X2381 ) @ X2379 )
| ( in @ ( lam @ X2379 @ X2380 @ X2381 ) @ ( funcSet @ X2379 @ X2380 ) ) )
& ( ~ ( in @ ( X2381 @ ( esk50_3 @ X2379 @ X2380 @ X2381 ) ) @ X2380 )
| ( in @ ( lam @ X2379 @ X2380 @ X2381 ) @ ( funcSet @ X2379 @ X2380 ) ) )
& ( ( in @ ( esk51_4 @ X2383 @ X2384 @ X2385 @ X2386 ) @ X2383 )
| ~ ( in @ X2389 @ X2385 )
| ( X2386 @ X2389 )
| ~ ( breln @ X2383 @ X2384 @ X2385 ) )
& ( ( in @ ( esk52_4 @ X2383 @ X2384 @ X2385 @ X2386 ) @ X2384 )
| ~ ( in @ X2389 @ X2385 )
| ( X2386 @ X2389 )
| ~ ( breln @ X2383 @ X2384 @ X2385 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2383 @ X2384 @ X2385 @ X2386 ) @ ( esk52_4 @ X2383 @ X2384 @ X2385 @ X2386 ) ) @ X2385 )
| ~ ( in @ X2389 @ X2385 )
| ( X2386 @ X2389 )
| ~ ( breln @ X2383 @ X2384 @ X2385 ) )
& ( ~ ( X2386 @ ( kpair @ ( esk51_4 @ X2383 @ X2384 @ X2385 @ X2386 ) @ ( esk52_4 @ X2383 @ X2384 @ X2385 @ X2386 ) ) )
| ~ ( in @ X2389 @ X2385 )
| ( X2386 @ X2389 )
| ~ ( breln @ X2383 @ X2384 @ X2385 ) )
& ( ( in @ ( esk53_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ~ ( in @ X2396 @ X2392 )
| ( X2393 @ X2396 )
| ~ ( breln @ X2390 @ X2391 @ X2392 ) )
& ( ( in @ ( esk54_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ~ ( in @ X2396 @ X2392 )
| ( X2393 @ X2396 )
| ~ ( breln @ X2390 @ X2391 @ X2392 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk54_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ~ ( in @ X2396 @ X2392 )
| ( X2393 @ X2396 )
| ~ ( breln @ X2390 @ X2391 @ X2392 ) )
& ( ~ ( X2393 @ ( kpair @ ( esk53_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk54_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) )
| ~ ( in @ X2396 @ X2392 )
| ( X2393 @ X2396 )
| ~ ( breln @ X2390 @ X2391 @ X2392 ) )
& ( ~ ( ex1 @ X2397 @ X2398 )
| ~ ( in @ X2399 @ X2397 )
| ~ ( in @ X2400 @ X2397 )
| ~ ( X2398 @ X2399 )
| ~ ( X2398 @ X2400 )
| ( X2399 = X2400 ) )
& ( ~ ( func @ X2401 @ X2402 @ X2403 )
| ~ ( in @ X2404 @ X2401 )
| ( in @ ( kpair @ X2404 @ ( ap @ X2401 @ X2402 @ X2403 @ X2404 ) ) @ X2403 ) )
& ( ~ ( in @ X2407 @ ( funcSet @ X2405 @ X2406 ) )
| ~ ( in @ X2408 @ X2405 )
| ( in @ ( kpair @ X2408 @ ( ap @ X2405 @ X2406 @ X2407 @ X2408 ) ) @ X2407 ) )
& ( ~ ( func @ X2409 @ X2410 @ X2411 )
| ~ ( in @ X2412 @ X2409 )
| ~ ( in @ X2413 @ X2410 )
| ~ ( in @ ( kpair @ X2412 @ X2413 ) @ X2411 )
| ( ( ap @ X2409 @ X2410 @ X2411 @ X2412 )
= X2413 ) )
& ( ( in @ ( esk55_4 @ X2414 @ X2415 @ X2416 @ X2417 ) @ X2414 )
| ~ ( in @ X2419 @ X2414 )
| ~ ( in @ X2420 @ X2415 )
| ~ ( in @ ( kpair @ X2419 @ X2420 ) @ X2417 )
| ( in @ ( kpair @ X2419 @ X2420 ) @ X2416 )
| ~ ( func @ X2414 @ X2415 @ X2417 )
| ~ ( func @ X2414 @ X2415 @ X2416 ) )
& ( ( ( ap @ X2414 @ X2415 @ X2416 @ ( esk55_4 @ X2414 @ X2415 @ X2416 @ X2417 ) )
!= ( ap @ X2414 @ X2415 @ X2417 @ ( esk55_4 @ X2414 @ X2415 @ X2416 @ X2417 ) ) )
| ~ ( in @ X2419 @ X2414 )
| ~ ( in @ X2420 @ X2415 )
| ~ ( in @ ( kpair @ X2419 @ X2420 ) @ X2417 )
| ( in @ ( kpair @ X2419 @ X2420 ) @ X2416 )
| ~ ( func @ X2414 @ X2415 @ X2417 )
| ~ ( func @ X2414 @ X2415 @ X2416 ) )
& ( ~ ( in @ X2423 @ ( funcSet @ X2421 @ X2422 ) )
| ~ ( in @ X2424 @ X2421 )
| ~ ( in @ X2425 @ X2422 )
| ~ ( in @ ( kpair @ X2424 @ X2425 ) @ X2423 )
| ( ( ap @ X2421 @ X2422 @ X2423 @ X2424 )
= X2425 ) )
& ( ( in @ ( esk56_4 @ X2426 @ X2427 @ X2428 @ X2429 ) @ X2426 )
| ( subset @ X2428 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2428 ) )
& ( ( in @ ( esk57_4 @ X2426 @ X2427 @ X2428 @ X2429 ) @ X2427 )
| ( subset @ X2428 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2428 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2426 @ X2427 @ X2428 @ X2429 ) @ ( esk57_4 @ X2426 @ X2427 @ X2428 @ X2429 ) ) @ X2428 )
| ( subset @ X2428 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2428 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2426 @ X2427 @ X2428 @ X2429 ) @ ( esk57_4 @ X2426 @ X2427 @ X2428 @ X2429 ) ) @ X2429 )
| ( subset @ X2428 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2429 )
| ~ ( breln @ X2426 @ X2427 @ X2428 ) )
& ( ( in @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ( X2434 = X2435 )
| ( in @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ( X2434 = X2435 )
| ( in @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ( X2434 = X2435 )
| ( in @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ( X2434 = X2435 )
| ( in @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ( X2434 = X2435 )
| ( in @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ( X2434 = X2435 )
| ( in @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ( X2434 = X2435 )
| ( in @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ( X2434 = X2435 )
| ( in @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ( X2434 = X2435 )
| ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ( X2434 = X2435 )
| ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ( X2434 = X2435 )
| ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ( X2434 = X2435 )
| ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2432 )
| ( X2434 = X2435 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ X2433 )
| ( X2434 = X2435 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ( X2434 = X2435 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk61_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2434 )
| ( X2434 = X2435 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2432 @ X2433 @ X2434 @ X2435 ) @ ( esk59_4 @ X2432 @ X2433 @ X2434 @ X2435 ) ) @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2435 )
| ~ ( breln @ X2432 @ X2433 @ X2434 ) )
& ( ( in @ ( esk62_4 @ X2440 @ X2441 @ X2442 @ X2443 ) @ X2440 )
| ( X2442 = X2443 )
| ~ ( func @ X2440 @ X2441 @ X2443 )
| ~ ( func @ X2440 @ X2441 @ X2442 ) )
& ( ( ( ap @ X2440 @ X2441 @ X2442 @ ( esk62_4 @ X2440 @ X2441 @ X2442 @ X2443 ) )
!= ( ap @ X2440 @ X2441 @ X2443 @ ( esk62_4 @ X2440 @ X2441 @ X2442 @ X2443 ) ) )
| ( X2442 = X2443 )
| ~ ( func @ X2440 @ X2441 @ X2443 )
| ~ ( func @ X2440 @ X2441 @ X2442 ) )
& ( ( in @ ( esk63_4 @ X2445 @ X2446 @ X2447 @ X2448 ) @ X2445 )
| ( X2447 = X2448 )
| ~ ( in @ X2448 @ ( funcSet @ X2445 @ X2446 ) )
| ~ ( in @ X2447 @ ( funcSet @ X2445 @ X2446 ) ) )
& ( ( ( ap @ X2445 @ X2446 @ X2447 @ ( esk63_4 @ X2445 @ X2446 @ X2447 @ X2448 ) )
!= ( ap @ X2445 @ X2446 @ X2448 @ ( esk63_4 @ X2445 @ X2446 @ X2447 @ X2448 ) ) )
| ( X2447 = X2448 )
| ~ ( in @ X2448 @ ( funcSet @ X2445 @ X2446 ) )
| ~ ( in @ X2447 @ ( funcSet @ X2445 @ X2446 ) ) )
& ( ~ ( in @ X2452 @ ( funcSet @ X2450 @ X2451 ) )
| ~ ( in @ X2453 @ X2450 )
| ( ( ap @ X2450 @ X2451 @ X2452 @ X2453 )
= ( ap @ X2450 @ X2451 @ X2452 @ X2453 ) ) )
& ( ~ ( func @ X2454 @ X2455 @ X2456 )
| ~ ( in @ X2457 @ X2454 )
| ( ( ap @ X2454 @ X2455 @ X2456 @ X2457 )
= ( ap @ X2454 @ X2455 @ X2456 @ X2457 ) ) )
& ( ( in @ ( esk64_3 @ X2458 @ X2459 @ X2460 ) @ X2458 )
| ~ ( in @ X2462 @ X2458 )
| ( ( ap @ X2458 @ X2459 @ ( lam @ X2458 @ X2459 @ X2460 ) @ X2462 )
= ( X2460 @ X2462 ) ) )
& ( ~ ( in @ ( X2460 @ ( esk64_3 @ X2458 @ X2459 @ X2460 ) ) @ X2459 )
| ~ ( in @ X2462 @ X2458 )
| ( ( ap @ X2458 @ X2459 @ ( lam @ X2458 @ X2459 @ X2460 ) @ X2462 )
= ( X2460 @ X2462 ) ) )
& ( ~ ( func @ X2463 @ X2464 @ X2465 )
| ( ( lam @ X2463 @ X2464 @ ( ap @ X2463 @ X2464 @ X2465 ) )
= X2465 ) )
& ( ( in @ ( esk65_3 @ X2466 @ X2467 @ X2468 ) @ X2466 )
| ( ( lam @ X2466 @ X2467 @ X2468 )
= ( lam @ X2466 @ X2467 @ X2468 ) ) )
& ( ~ ( in @ ( X2468 @ ( esk65_3 @ X2466 @ X2467 @ X2468 ) ) @ X2467 )
| ( ( lam @ X2466 @ X2467 @ X2468 )
= ( lam @ X2466 @ X2467 @ X2468 ) ) )
& ( ( in @ ( esk66_3 @ X2470 @ X2471 @ X2472 ) @ X2470 )
| ~ ( in @ X2474 @ X2470 )
| ( ( ap @ X2470 @ X2471 @ ( lam @ X2470 @ X2471 @ X2472 ) @ X2474 )
= ( X2472 @ X2474 ) ) )
& ( ~ ( in @ ( X2472 @ ( esk66_3 @ X2470 @ X2471 @ X2472 ) ) @ X2471 )
| ~ ( in @ X2474 @ X2470 )
| ( ( ap @ X2470 @ X2471 @ ( lam @ X2470 @ X2471 @ X2472 ) @ X2474 )
= ( X2472 @ X2474 ) ) )
& ( ~ ( in @ X2477 @ ( funcSet @ X2475 @ X2476 ) )
| ( ( lam @ X2475 @ X2476 @ ( ap @ X2475 @ X2476 @ X2477 ) )
= X2477 ) )
& ( ~ ( in @ X2480 @ X2478 )
| ~ ( in @ X2481 @ X2478 )
| X2479
| ( in @ X2481
@ ( dsetconstr @ X2478
@ ^ [Z0: $i] :
( ( X2479
& ( Z0 = X2480 ) )
| ( ~ X2479
& ( Z0 = X2481 ) ) ) ) ) )
& ( ~ ( in @ X2484 @ X2482 )
| ~ ( in @ X2485 @ X2482 )
| X2483
| ( ( dsetconstr @ X2482
@ ^ [Z0: $i] :
( ( X2483
& ( Z0 = X2484 ) )
| ( ~ X2483
& ( Z0 = X2485 ) ) ) )
= ( setadjoin @ X2485 @ emptyset ) ) )
& ( ~ ( in @ X2488 @ X2486 )
| ~ ( in @ X2489 @ X2486 )
| ~ X2487
| ( in @ X2488
@ ( dsetconstr @ X2486
@ ^ [Z0: $i] :
( ( X2487
& ( Z0 = X2488 ) )
| ( ~ X2487
& ( Z0 = X2489 ) ) ) ) ) )
& ( ~ ( in @ X2492 @ X2490 )
| ~ ( in @ X2493 @ X2490 )
| ~ X2491
| ( ( dsetconstr @ X2490
@ ^ [Z0: $i] :
( ( X2491
& ( Z0 = X2492 ) )
| ( ~ X2491
& ( Z0 = X2493 ) ) ) )
= ( setadjoin @ X2492 @ emptyset ) ) )
& ( ~ ( in @ X2496 @ X2494 )
| ~ ( in @ X2497 @ X2494 )
| ( singleton
@ ( dsetconstr @ X2494
@ ^ [Z0: $i] :
( ( X2495
& ( Z0 = X2496 ) )
| ( ~ X2495
& ( Z0 = X2497 ) ) ) ) ) )
& ( ~ ( in @ X2500 @ X2498 )
| ~ ( in @ X2501 @ X2498 )
| ( in @ ( if @ X2498 @ X2499 @ X2500 @ X2501 ) @ X2498 ) )
& ( ~ ( singleton @ X2502 )
| ~ ( in @ X2503 @ X2502 )
| ( ( setunion @ X2502 )
= X2503 ) )
& ( ~ ( in @ X2506 @ X2504 )
| ~ ( in @ X2507 @ X2504 )
| ~ X2505
| ( ( if @ X2504 @ X2505 @ X2506 @ X2507 )
= X2506 ) )
& ( ~ ( in @ X2510 @ X2508 )
| ~ ( in @ X2511 @ X2508 )
| X2509
| ( ( if @ X2508 @ X2509 @ X2510 @ X2511 )
= X2511 ) )
& ( ~ ( in @ X2514 @ X2512 )
| ~ ( in @ X2515 @ X2512 )
| ( in @ ( if @ X2512 @ X2513 @ X2514 @ X2515 ) @ ( setadjoin @ X2514 @ ( setadjoin @ X2515 @ emptyset ) ) ) )
& ( ~ ( in @ X2517 @ ( powerset @ X2516 ) )
| ~ ( in @ X2518 @ ( powerset @ X2516 ) )
| ( in @ ( binintersect @ X2517 @ X2518 ) @ ( powerset @ X2516 ) ) )
& ( ~ ( in @ X2520 @ ( powerset @ X2519 ) )
| ~ ( in @ X2521 @ ( powerset @ X2519 ) )
| ( in @ ( binunion @ X2520 @ X2521 ) @ ( powerset @ X2519 ) ) )
& ( ~ ( in @ X2523 @ ( powerset @ X2522 ) )
| ( in @ ( powerset @ X2523 ) @ ( powerset @ ( powerset @ X2522 ) ) ) )
& ( ~ ( in @ X2525 @ ( powerset @ X2524 ) )
| ~ ( in @ X2526 @ ( powerset @ X2524 ) )
| ( in @ ( setminus @ X2525 @ X2526 ) @ ( powerset @ X2524 ) ) )
& ( ~ ( in @ X2528 @ ( powerset @ X2527 ) )
| ( in @ ( setminus @ X2527 @ X2528 ) @ ( powerset @ X2527 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ( X2530 = X2531 )
| ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2529 )
| ( X2530 = X2531 )
| ~ ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ( X2530 = X2531 )
| ~ ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ~ ( in @ ( esk68_3 @ X2529 @ X2530 @ X2531 ) @ X2530 )
| ( X2530 = X2531 )
| ~ ( in @ ( esk67_3 @ X2529 @ X2530 @ X2531 ) @ X2531 )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( in @ X2530 @ ( powerset @ X2529 ) ) )
& ( ( in @ ( esk69_3 @ X2534 @ X2535 @ X2536 ) @ X2534 )
| ( subset @ X2535 @ X2536 )
| ~ ( in @ X2536 @ ( powerset @ X2534 ) )
| ~ ( in @ X2535 @ ( powerset @ X2534 ) ) )
& ( ( in @ ( esk69_3 @ X2534 @ X2535 @ X2536 ) @ X2535 )
| ( subset @ X2535 @ X2536 )
| ~ ( in @ X2536 @ ( powerset @ X2534 ) )
| ~ ( in @ X2535 @ ( powerset @ X2534 ) ) )
& ( ~ ( in @ ( esk69_3 @ X2534 @ X2535 @ X2536 ) @ X2536 )
| ( subset @ X2535 @ X2536 )
| ~ ( in @ X2536 @ ( powerset @ X2534 ) )
| ~ ( in @ X2535 @ ( powerset @ X2534 ) ) )
& ( ( in @ ( esk70_3 @ X2538 @ X2539 @ X2540 ) @ X2538 )
| ( in @ X2539 @ ( powerset @ X2540 ) )
| ~ ( in @ X2540 @ ( powerset @ X2538 ) )
| ~ ( in @ X2539 @ ( powerset @ X2538 ) ) )
& ( ( in @ ( esk70_3 @ X2538 @ X2539 @ X2540 ) @ X2539 )
| ( in @ X2539 @ ( powerset @ X2540 ) )
| ~ ( in @ X2540 @ ( powerset @ X2538 ) )
| ~ ( in @ X2539 @ ( powerset @ X2538 ) ) )
& ( ~ ( in @ ( esk70_3 @ X2538 @ X2539 @ X2540 ) @ X2540 )
| ( in @ X2539 @ ( powerset @ X2540 ) )
| ~ ( in @ X2540 @ ( powerset @ X2538 ) )
| ~ ( in @ X2539 @ ( powerset @ X2538 ) ) )
& ( ~ ( in @ X2543 @ ( powerset @ X2542 ) )
| ~ ( in @ X2544 @ ( powerset @ X2542 ) )
| ~ ( in @ X2545 @ X2542 )
| ~ ( in @ X2543 @ ( powerset @ X2544 ) )
| ~ ( in @ X2545 @ X2543 )
| ( in @ X2545 @ X2544 ) )
& ( ~ ( in @ X2547 @ ( powerset @ X2546 ) )
| ~ ( in @ X2548 @ X2546 )
| ~ ( in @ X2548 @ X2547 )
| ~ ( in @ X2548 @ ( setminus @ X2546 @ X2547 ) ) )
& ( ~ ( in @ X2550 @ ( powerset @ X2549 ) )
| ~ ( in @ X2551 @ X2549 )
| ( in @ X2551 @ ( setminus @ X2549 @ X2550 ) )
| ( in @ X2551 @ X2550 ) )
& ( ~ ( in @ X2553 @ ( powerset @ X2552 ) )
| ~ ( in @ X2554 @ ( powerset @ X2552 ) )
| ~ ( in @ X2555 @ X2552 )
| ( in @ X2555 @ X2553 )
| ~ ( in @ X2555 @ ( binintersect @ X2553 @ X2554 ) ) )
& ( ~ ( in @ X2557 @ ( powerset @ X2556 ) )
| ~ ( in @ X2558 @ ( powerset @ X2556 ) )
| ~ ( in @ X2559 @ X2556 )
| ( in @ X2559 @ X2558 )
| ~ ( in @ X2559 @ ( binintersect @ X2557 @ X2558 ) ) )
& ( ~ ( in @ X2561 @ ( powerset @ X2560 ) )
| ~ ( in @ X2562 @ ( powerset @ X2560 ) )
| ~ ( in @ X2563 @ X2560 )
| ~ ( subset @ X2561 @ ( setminus @ X2560 @ X2562 ) )
| ~ ( in @ X2563 @ X2562 )
| ~ ( in @ X2563 @ X2561 ) )
& ( ~ ( in @ X2565 @ ( powerset @ X2564 ) )
| ~ ( in @ X2566 @ ( powerset @ X2564 ) )
| ~ ( in @ X2567 @ X2564 )
| ~ ( subset @ X2565 @ X2566 )
| ( in @ X2567 @ X2566 )
| ~ ( in @ X2567 @ X2565 ) )
& ( ~ ( in @ X2569 @ ( powerset @ X2568 ) )
| ~ ( in @ X2570 @ ( powerset @ X2568 ) )
| ~ ( subset @ X2569 @ X2570 )
| ( subset @ ( setminus @ X2568 @ X2570 ) @ ( setminus @ X2568 @ X2569 ) ) )
& ( ~ ( in @ X2572 @ ( powerset @ X2571 ) )
| ~ ( in @ X2573 @ ( powerset @ X2571 ) )
| ~ ( subset @ ( setminus @ X2571 @ X2573 ) @ ( setminus @ X2571 @ X2572 ) )
| ( subset @ X2572 @ X2573 ) )
& ( ~ ( in @ X2575 @ ( powerset @ X2574 ) )
| ~ ( in @ X2576 @ X2574 )
| ~ ( in @ X2576 @ X2575 )
| ( in @ X2576 @ ( setminus @ X2574 @ ( setminus @ X2574 @ X2575 ) ) ) )
& ( ~ ( in @ X2578 @ ( powerset @ X2577 ) )
| ~ ( in @ X2579 @ X2577 )
| ~ ( in @ X2579 @ ( setminus @ X2577 @ ( setminus @ X2577 @ X2578 ) ) )
| ( in @ X2579 @ X2578 ) )
& ( ~ ( in @ X2581 @ ( powerset @ X2580 ) )
| ( subset @ X2581 @ ( setminus @ X2580 @ ( setminus @ X2580 @ X2581 ) ) ) )
& ( ~ ( in @ X2583 @ ( powerset @ X2582 ) )
| ( subset @ ( setminus @ X2582 @ ( setminus @ X2582 @ X2583 ) ) @ X2583 ) )
& ( ~ ( in @ X2585 @ ( powerset @ X2584 ) )
| ( X2585
= ( setminus @ X2584 @ ( setminus @ X2584 @ X2585 ) ) ) )
& ( ~ ( in @ X2587 @ ( powerset @ X2586 ) )
| ~ ( in @ X2588 @ ( powerset @ X2586 ) )
| ~ ( in @ X2589 @ X2586 )
| ~ ( in @ X2589 @ ( setminus @ X2586 @ X2587 ) )
| ~ ( in @ X2589 @ ( binintersect @ X2587 @ X2588 ) ) )
& ( ~ ( in @ X2591 @ ( powerset @ X2590 ) )
| ~ ( in @ X2592 @ ( powerset @ X2590 ) )
| ~ ( in @ X2593 @ X2590 )
| ~ ( in @ X2593 @ ( setminus @ X2590 @ X2591 ) )
| ( in @ X2593 @ ( setminus @ X2590 @ ( binintersect @ X2591 @ X2592 ) ) ) )
& ( ~ ( in @ X2595 @ ( powerset @ X2594 ) )
| ~ ( in @ X2596 @ ( powerset @ X2594 ) )
| ( subset @ ( setminus @ X2594 @ X2595 ) @ ( setminus @ X2594 @ ( binintersect @ X2595 @ X2596 ) ) ) )
& ( ~ ( in @ X2598 @ ( powerset @ X2597 ) )
| ~ ( in @ X2599 @ ( powerset @ X2597 ) )
| ( in @ ( setminus @ X2597 @ X2598 ) @ ( powerset @ ( setminus @ X2597 @ ( binintersect @ X2598 @ X2599 ) ) ) ) )
& ( ~ ( in @ X2601 @ ( powerset @ X2600 ) )
| ~ ( in @ X2602 @ ( powerset @ X2600 ) )
| ~ ( subset @ X2601 @ ( setminus @ X2600 @ X2602 ) )
| ~ ( in @ X2603 @ X2600 )
| ~ ( in @ X2603 @ X2602 )
| ( in @ X2603 @ ( setminus @ X2600 @ X2601 ) ) )
& ( ~ ( in @ X2605 @ ( powerset @ X2604 ) )
| ~ ( in @ X2606 @ ( powerset @ X2604 ) )
| ~ ( subset @ X2605 @ ( setminus @ X2604 @ X2606 ) )
| ( subset @ X2606 @ ( setminus @ X2604 @ X2605 ) ) )
& ( ~ ( in @ X2608 @ ( powerset @ X2607 ) )
| ~ ( in @ X2609 @ ( powerset @ X2607 ) )
| ~ ( in @ X2610 @ X2607 )
| ( in @ X2610 @ ( binunion @ X2608 @ X2609 ) )
| ~ ( in @ X2610 @ X2608 ) )
& ( ~ ( in @ X2612 @ ( powerset @ X2611 ) )
| ~ ( in @ X2613 @ ( powerset @ X2611 ) )
| ~ ( in @ X2614 @ X2611 )
| ( in @ X2614 @ ( binunion @ X2612 @ X2613 ) )
| ~ ( in @ X2614 @ X2613 ) )
& ( ~ ( in @ X2616 @ ( powerset @ X2615 ) )
| ~ ( in @ X2617 @ ( powerset @ X2615 ) )
| ~ ( in @ X2618 @ ( powerset @ X2615 ) )
| ~ ( in @ X2619 @ X2615 )
| ~ ( in @ X2619 @ ( binintersect @ X2616 @ X2617 ) )
| ( in @ X2619 @ ( binunion @ X2616 @ X2618 ) ) )
& ( ~ ( in @ X2621 @ ( powerset @ X2620 ) )
| ~ ( in @ X2622 @ ( powerset @ X2620 ) )
| ~ ( in @ X2623 @ ( powerset @ X2620 ) )
| ~ ( in @ X2624 @ X2620 )
| ~ ( in @ X2624 @ ( binintersect @ X2621 @ X2622 ) )
| ( in @ X2624 @ ( binunion @ X2622 @ X2623 ) ) )
& ( ~ ( in @ X2626 @ ( powerset @ X2625 ) )
| ~ ( in @ X2627 @ ( powerset @ X2625 ) )
| ~ ( in @ X2628 @ ( powerset @ X2625 ) )
| ~ ( in @ X2629 @ X2625 )
| ~ ( in @ X2629 @ ( binintersect @ X2626 @ X2627 ) )
| ( in @ X2629 @ ( binintersect @ ( binunion @ X2626 @ X2628 ) @ ( binunion @ X2627 @ X2628 ) ) ) )
& ( ~ ( in @ X2631 @ ( powerset @ X2630 ) )
| ~ ( in @ X2632 @ ( powerset @ X2630 ) )
| ~ ( in @ X2633 @ ( powerset @ X2630 ) )
| ( in @ ( binintersect @ X2631 @ X2632 ) @ ( powerset @ ( binintersect @ ( binunion @ X2631 @ X2633 ) @ ( binunion @ X2632 @ X2633 ) ) ) ) )
& ( ~ ( in @ X2635 @ ( powerset @ X2634 ) )
| ~ ( in @ X2636 @ ( powerset @ X2634 ) )
| ~ ( in @ X2637 @ X2634 )
| ~ ( in @ X2637 @ ( setminus @ X2634 @ ( binunion @ X2635 @ X2636 ) ) )
| ~ ( in @ X2637 @ X2635 ) )
& ( ~ ( in @ X2639 @ ( powerset @ X2638 ) )
| ~ ( in @ X2640 @ ( powerset @ X2638 ) )
| ~ ( in @ X2641 @ X2638 )
| ~ ( in @ X2641 @ ( setminus @ X2638 @ ( binunion @ X2639 @ X2640 ) ) )
| ( in @ X2641 @ ( setminus @ X2638 @ X2639 ) ) )
& ( ( in @ X2646 @ X2644 )
| X2645
| ( in @ X2646 @ X2643 )
| ~ ( in @ X2646 @ ( binunion @ X2643 @ X2644 ) )
| ~ ( in @ X2646 @ X2642 )
| ~ ( in @ X2644 @ ( powerset @ X2642 ) )
| ~ ( in @ X2643 @ ( powerset @ X2642 ) ) )
& ( ~ X2645
| X2645
| ( in @ X2646 @ X2643 )
| ~ ( in @ X2646 @ ( binunion @ X2643 @ X2644 ) )
| ~ ( in @ X2646 @ X2642 )
| ~ ( in @ X2644 @ ( powerset @ X2642 ) )
| ~ ( in @ X2643 @ ( powerset @ X2642 ) ) )
& ( ( in @ X2646 @ X2644 )
| X2645
| ~ X2645
| ~ ( in @ X2646 @ ( binunion @ X2643 @ X2644 ) )
| ~ ( in @ X2646 @ X2642 )
| ~ ( in @ X2644 @ ( powerset @ X2642 ) )
| ~ ( in @ X2643 @ ( powerset @ X2642 ) ) )
& ( ~ X2645
| X2645
| ~ X2645
| ~ ( in @ X2646 @ ( binunion @ X2643 @ X2644 ) )
| ~ ( in @ X2646 @ X2642 )
| ~ ( in @ X2644 @ ( powerset @ X2642 ) )
| ~ ( in @ X2643 @ ( powerset @ X2642 ) ) )
& ( ~ ( in @ X2648 @ ( powerset @ X2647 ) )
| ~ ( in @ X2649 @ ( powerset @ X2647 ) )
| ~ ( in @ X2650 @ X2647 )
| ( in @ X2650 @ X2648 )
| ( in @ X2650 @ X2649 )
| ~ ( in @ X2650 @ ( binunion @ X2648 @ X2649 ) ) )
& ( ~ ( in @ X2652 @ ( powerset @ X2651 ) )
| ~ ( in @ X2653 @ ( powerset @ X2651 ) )
| ~ ( in @ X2654 @ X2651 )
| ~ ( in @ X2654 @ ( setminus @ X2651 @ ( binunion @ X2652 @ X2653 ) ) )
| ( in @ X2654 @ ( setminus @ X2651 @ X2652 ) ) )
& ( ~ ( in @ X2656 @ ( powerset @ X2655 ) )
| ~ ( in @ X2657 @ ( powerset @ X2655 ) )
| ( in @ ( setminus @ X2655 @ ( binunion @ X2656 @ X2657 ) ) @ ( powerset @ ( setminus @ X2655 @ X2656 ) ) ) )
& ( ~ ( in @ X2659 @ ( powerset @ X2658 ) )
| ~ ( in @ X2660 @ ( powerset @ X2658 ) )
| ~ ( in @ X2661 @ X2658 )
| ~ ( in @ X2661 @ ( setminus @ X2658 @ ( binunion @ X2659 @ X2660 ) ) )
| ( in @ X2661 @ ( setminus @ X2658 @ X2660 ) ) )
& ( ~ ( in @ X2663 @ ( powerset @ X2662 ) )
| ~ ( in @ X2664 @ ( powerset @ X2662 ) )
| ~ ( in @ X2665 @ X2662 )
| ~ ( in @ X2665 @ ( setminus @ X2662 @ ( binintersect @ X2663 @ X2664 ) ) )
| ( in @ X2665 @ ( binunion @ ( setminus @ X2662 @ X2663 ) @ ( setminus @ X2662 @ X2664 ) ) ) )
& ( ~ ( in @ X2667 @ ( powerset @ X2666 ) )
| ~ ( in @ X2668 @ ( powerset @ X2666 ) )
| ~ ( in @ X2669 @ X2666 )
| ~ ( in @ X2669 @ ( binunion @ ( setminus @ X2666 @ X2667 ) @ ( setminus @ X2666 @ X2668 ) ) )
| ( in @ X2669 @ ( setminus @ X2666 @ ( binintersect @ X2667 @ X2668 ) ) ) )
& ( ~ ( in @ X2671 @ ( powerset @ X2670 ) )
| ~ ( in @ X2672 @ ( powerset @ X2670 ) )
| ( ( setminus @ X2670 @ ( binintersect @ X2671 @ X2672 ) )
= ( binunion @ ( setminus @ X2670 @ X2671 ) @ ( setminus @ X2670 @ X2672 ) ) ) )
& ( ~ ( in @ X2674 @ ( powerset @ X2673 ) )
| ~ ( in @ X2675 @ ( powerset @ X2673 ) )
| ~ ( in @ X2676 @ X2673 )
| ~ ( in @ X2676 @ ( setminus @ X2673 @ ( binunion @ X2674 @ X2675 ) ) )
| ( in @ X2676 @ ( binintersect @ ( setminus @ X2673 @ X2674 ) @ ( setminus @ X2673 @ X2675 ) ) ) )
& ( ~ ( in @ X2678 @ ( powerset @ X2677 ) )
| ~ ( in @ X2679 @ ( powerset @ X2677 ) )
| ~ ( in @ X2680 @ X2677 )
| ~ ( in @ X2680 @ ( setminus @ X2677 @ X2678 ) )
| ~ ( in @ X2680 @ ( setminus @ X2677 @ X2679 ) )
| ( in @ X2680 @ ( setminus @ X2677 @ ( binunion @ X2678 @ X2679 ) ) ) )
& ( ~ ( in @ X2682 @ ( powerset @ X2681 ) )
| ~ ( in @ X2683 @ ( powerset @ X2681 ) )
| ~ ( in @ X2684 @ X2681 )
| ~ ( in @ X2684 @ ( binintersect @ ( setminus @ X2681 @ X2682 ) @ ( setminus @ X2681 @ X2683 ) ) )
| ( in @ X2684 @ ( setminus @ X2681 @ ( binunion @ X2682 @ X2683 ) ) ) )
& ( ~ ( in @ X2686 @ ( powerset @ X2685 ) )
| ~ ( in @ X2687 @ ( powerset @ X2685 ) )
| ( ( setminus @ X2685 @ ( binunion @ X2686 @ X2687 ) )
= ( binintersect @ ( setminus @ X2685 @ X2686 ) @ ( setminus @ X2685 @ X2687 ) ) ) )
& ( ~ ( in @ X2689 @ ( powerset @ X2688 ) )
| ~ ( in @ X2690 @ ( powerset @ X2688 ) )
| ~ ( in @ X2691 @ ( binintersect @ X2689 @ X2690 ) )
| ( in @ X2691 @ X2688 ) )
& ( ~ ( in @ X2693 @ ( powerset @ X2692 ) )
| ~ ( in @ X2694 @ ( powerset @ X2692 ) )
| ~ ( in @ X2695 @ ( powerset @ X2692 ) )
| ~ ( subset @ X2693 @ X2695 )
| ( subset @ ( binintersect @ X2693 @ X2694 ) @ X2695 ) )
& ( ~ ( in @ X2697 @ ( powerset @ X2696 ) )
| ~ ( in @ X2698 @ ( powerset @ X2696 ) )
| ~ ( in @ X2699 @ ( powerset @ X2696 ) )
| ~ ( subset @ X2698 @ X2699 )
| ( subset @ ( binintersect @ X2697 @ X2698 ) @ X2699 ) )
& ( ~ ( in @ X2701 @ ( powerset @ X2700 ) )
| ~ ( in @ X2702 @ ( powerset @ X2700 ) )
| ~ ( in @ X2703 @ ( powerset @ X2700 ) )
| ~ ( subset @ X2701 @ X2702 )
| ~ ( subset @ X2701 @ X2703 )
| ( subset @ X2701 @ ( binintersect @ X2702 @ X2703 ) ) )
& ( ~ ( in @ X2705 @ ( powerset @ X2704 ) )
| ~ ( in @ X2706 @ ( powerset @ X2704 ) )
| ~ ( in @ X2707 @ ( powerset @ X2704 ) )
| ~ ( in @ X2708 @ ( powerset @ X2704 ) )
| ~ ( subset @ X2705 @ X2707 )
| ~ ( subset @ X2706 @ X2708 )
| ( subset @ ( binintersect @ X2705 @ X2706 ) @ ( binintersect @ X2707 @ X2708 ) ) )
& ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
& ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
& ~ ( in @ ( setminus @ esk71_0 @ esk72_0 ) @ ( powerset @ ( setminus @ esk71_0 @ ( binintersect @ esk72_0 @ esk73_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_331])])])])])])]) ).
thf(c_0_333,negated_conjecture,
~ ( in @ ( setminus @ esk71_0 @ esk72_0 ) @ ( powerset @ ( setminus @ esk71_0 @ ( binintersect @ esk72_0 @ esk73_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
thf(c_0_334,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ ( setminus @ X3 @ X2 ) @ ( powerset @ ( setminus @ X3 @ ( binintersect @ X2 @ X4 ) ) ) )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
thf(c_0_335,negated_conjecture,
in @ esk73_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
thf(c_0_336,negated_conjecture,
in @ esk72_0 @ ( powerset @ esk71_0 ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
thf(c_0_337,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_334]),c_0_335]),c_0_336])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU763^1 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n025.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sun May 19 15:23:08 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.17/0.43 Running higher-order theorem proving
% 0.17/0.43 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
% 2.37/0.92 # Version: 3.1.0-ho
% 2.37/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.37/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.37/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.37/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.37/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.37/0.92 # Starting pre_casc_3 with 300s (1) cores
% 2.37/0.92 # Starting ho_unfolding_8 with 300s (1) cores
% 2.37/0.92 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.37/0.92 # Starting new_bool_3 with 300s (1) cores
% 2.37/0.92 # Starting new_ho_5 with 300s (1) cores
% 2.37/0.92 # new_ho_5 with pid 980 completed with status 8
% 2.37/0.92 # pre_casc_3 with pid 976 completed with status 8
% 2.37/0.92 # new_bool_5 with pid 975 completed with status 0
% 2.37/0.92 # Result found by new_bool_5
% 2.37/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.37/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.37/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.37/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.37/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.37/0.92 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.37/0.92 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.37/0.92 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.37/0.92 # Starting ho_unfolding_8 with 55s (1) cores
% 2.37/0.92 # ho_unfolding_8 with pid 1004 completed with status 0
% 2.37/0.92 # Result found by ho_unfolding_8
% 2.37/0.92 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.37/0.92 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.37/0.92 # Starting ehoh_best5 with 300s (1) cores
% 2.37/0.92 # Starting almost_fo_3_lam with 300s (1) cores
% 2.37/0.92 # Starting new_bool_5 with 300s (1) cores
% 2.37/0.92 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.37/0.92 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.37/0.92 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.37/0.92 # Starting ho_unfolding_8 with 55s (1) cores
% 2.37/0.92 # Preprocessing time : 0.075 s
% 2.37/0.92 # Presaturation interreduction done
% 2.37/0.92
% 2.37/0.92 # Proof found!
% 2.37/0.92 # SZS status Theorem
% 2.37/0.92 # SZS output start CNFRefutation
% See solution above
% 2.37/0.92 # Parsed axioms : 601
% 2.37/0.92 # Removed by relevancy pruning/SinE : 322
% 2.37/0.92 # Initial clauses : 442
% 2.37/0.92 # Removed in clause preprocessing : 37
% 2.37/0.92 # Initial clauses in saturation : 405
% 2.37/0.92 # Processed clauses : 711
% 2.37/0.92 # ...of these trivial : 9
% 2.37/0.92 # ...subsumed : 39
% 2.37/0.92 # ...remaining for further processing : 663
% 2.37/0.92 # Other redundant clauses eliminated : 49
% 2.37/0.92 # Clauses deleted for lack of memory : 0
% 2.37/0.92 # Backward-subsumed : 0
% 2.37/0.92 # Backward-rewritten : 1
% 2.37/0.92 # Generated clauses : 5345
% 2.37/0.92 # ...of the previous two non-redundant : 5127
% 2.37/0.92 # ...aggressively subsumed : 0
% 2.37/0.92 # Contextual simplify-reflections : 14
% 2.37/0.92 # Paramodulations : 5263
% 2.37/0.92 # Factorizations : 2
% 2.37/0.92 # NegExts : 0
% 2.37/0.92 # Equation resolutions : 56
% 2.37/0.92 # Disequality decompositions : 0
% 2.37/0.92 # Total rewrite steps : 151
% 2.37/0.92 # ...of those cached : 99
% 2.37/0.92 # Propositional unsat checks : 0
% 2.37/0.92 # Propositional check models : 0
% 2.37/0.92 # Propositional check unsatisfiable : 0
% 2.37/0.92 # Propositional clauses : 0
% 2.37/0.92 # Propositional clauses after purity: 0
% 2.37/0.92 # Propositional unsat core size : 0
% 2.37/0.92 # Propositional preprocessing time : 0.000
% 2.37/0.92 # Propositional encoding time : 0.000
% 2.37/0.93 # Propositional solver time : 0.000
% 2.37/0.93 # Success case prop preproc time : 0.000
% 2.37/0.93 # Success case prop encoding time : 0.000
% 2.37/0.93 # Success case prop solver time : 0.000
% 2.37/0.93 # Current number of processed clauses : 295
% 2.37/0.93 # Positive orientable unit clauses : 37
% 2.37/0.93 # Positive unorientable unit clauses: 0
% 2.37/0.93 # Negative unit clauses : 3
% 2.37/0.93 # Non-unit-clauses : 255
% 2.37/0.93 # Current number of unprocessed clauses: 5138
% 2.37/0.93 # ...number of literals in the above : 19039
% 2.37/0.93 # Current number of archived formulas : 0
% 2.37/0.93 # Current number of archived clauses : 352
% 2.37/0.93 # Clause-clause subsumption calls (NU) : 48309
% 2.37/0.93 # Rec. Clause-clause subsumption calls : 22545
% 2.37/0.93 # Non-unit clause-clause subsumptions : 49
% 2.37/0.93 # Unit Clause-clause subsumption calls : 456
% 2.37/0.93 # Rewrite failures with RHS unbound : 0
% 2.37/0.93 # BW rewrite match attempts : 34
% 2.37/0.93 # BW rewrite match successes : 1
% 2.37/0.93 # Condensation attempts : 0
% 2.37/0.93 # Condensation successes : 0
% 2.37/0.93 # Termbank termtop insertions : 161381
% 2.37/0.93 # Search garbage collected termcells : 28534
% 2.37/0.93
% 2.37/0.93 # -------------------------------------------------
% 2.37/0.93 # User time : 0.413 s
% 2.37/0.93 # System time : 0.030 s
% 2.37/0.93 # Total time : 0.443 s
% 2.37/0.93 # Maximum resident set size: 8924 pages
% 2.37/0.93
% 2.37/0.93 # -------------------------------------------------
% 2.37/0.93 # User time : 0.684 s
% 2.37/0.93 # System time : 0.116 s
% 2.37/0.93 # Total time : 0.800 s
% 2.37/0.93 # Maximum resident set size: 2748 pages
% 2.37/0.93 % E---3.1 exiting
% 2.37/0.93 % E exiting
%------------------------------------------------------------------------------