%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU746^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:48 EDT 2024
% Result : Timeout 2.19s 300.08s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 653
% Syntax : Number of formulae : 743 ( 38 unt; 385 typ; 0 def)
% Number of atoms : 3498 ( 630 equ; 0 cnn)
% Maximal formula atoms : 1085 ( 9 avg)
% Number of connectives : 14111 ( 958 ~;1019 |; 585 &;9437 @)
% ( 356 <=>;1756 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1199 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 595 ( 595 >; 0 *; 0 +; 0 <<)
% Number of symbols : 389 ( 385 usr; 273 con; 0-4 aty)
% Number of variables : 2934 ( 182 ^2629 !; 123 ?;2934 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_90,type,
set2prop: $i > $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
setextT: $o ).
thf(decl_292,type,
subsetTI: $o ).
thf(decl_293,type,
powersetTI1: $o ).
thf(decl_294,type,
powersetTE1: $o ).
thf(decl_295,type,
complementTI1: $o ).
thf(decl_296,type,
complementTE1: $o ).
thf(decl_297,type,
binintersectTELcontra: $o ).
thf(decl_298,type,
binintersectTERcontra: $o ).
thf(decl_299,type,
contrasubsetT: $o ).
thf(decl_300,type,
contrasubsetT1: $o ).
thf(decl_301,type,
contrasubsetT2: $o ).
thf(decl_302,type,
contrasubsetT3: $o ).
thf(decl_303,type,
doubleComplementI1: $o ).
thf(decl_304,type,
doubleComplementE1: $o ).
thf(decl_305,type,
doubleComplementSub1: $o ).
thf(decl_306,type,
doubleComplementSub2: $o ).
thf(decl_307,type,
doubleComplementEq: $o ).
thf(decl_308,type,
complementTnotintersectT: $o ).
thf(decl_309,type,
complementImpComplementIntersect: $o ).
thf(decl_310,type,
complementSubsetComplementIntersect: $o ).
thf(decl_311,type,
complementInPowersetComplementIntersect: $o ).
thf(decl_312,type,
contraSubsetComplement: $o ).
thf(decl_313,type,
complementTcontraSubset: $o ).
thf(decl_314,type,
binunionTILcontra: $o ).
thf(decl_315,type,
binunionTIRcontra: $o ).
thf(decl_316,type,
inIntersectImpInUnion: $o ).
thf(decl_317,type,
inIntersectImpInUnion2: $o ).
thf(decl_318,type,
inIntersectImpInIntersectUnions: $o ).
thf(decl_319,type,
intersectInPowersetIntersectUnions: $o ).
thf(decl_320,type,
inComplementUnionImpNotIn1: $o ).
thf(decl_321,type,
inComplementUnionImpInComplement1: $o ).
thf(decl_322,type,
epred1_0: $o ).
thf(decl_323,type,
esk1_2: $i > $i > $i ).
thf(decl_324,type,
esk2_2: $i > $i > $i ).
thf(decl_325,type,
esk3_2: $i > $i > $i ).
thf(decl_326,type,
esk4_1: $i > $i ).
thf(decl_327,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_328,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_329,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_330,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_331,type,
esk9_1: $i > $i ).
thf(decl_332,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_333,type,
esk11_2: ( $i > $o ) > $i > $i ).
thf(decl_334,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_335,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_336,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_337,type,
esk15_2: $i > $i > $i ).
thf(decl_338,type,
esk16_2: $i > $i > $i ).
thf(decl_339,type,
esk17_1: $i > $i ).
thf(decl_340,type,
esk18_1: $i > $i ).
thf(decl_341,type,
esk19_1: $i > $i ).
thf(decl_342,type,
esk20_2: $i > $i > $i ).
thf(decl_343,type,
esk21_3: $i > $i > $o > $i ).
thf(decl_344,type,
esk22_2: ( $i > $o ) > $i > $i ).
thf(decl_345,type,
esk23_1: ( $i > $o ) > $i ).
thf(decl_346,type,
esk24_1: $i > $i ).
thf(decl_347,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_348,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_349,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_350,type,
esk28_2: $i > ( $i > $o ) > $i ).
thf(decl_351,type,
esk29_2: $i > ( $i > $o ) > $i ).
thf(decl_352,type,
esk30_2: $i > ( $i > $o ) > $i ).
thf(decl_353,type,
esk31_2: ( $i > $o ) > $i > $i ).
thf(decl_354,type,
esk32_1: ( $i > $o ) > $i ).
thf(decl_355,type,
esk33_1: ( $i > $o ) > $i ).
thf(decl_356,type,
esk34_1: ( $i > $o ) > $i ).
thf(decl_357,type,
esk35_1: ( $i > $o ) > $i ).
thf(decl_358,type,
esk36_2: ( $i > $o ) > $i > $i ).
thf(decl_359,type,
esk37_1: ( $i > $o ) > $i ).
thf(decl_360,type,
esk38_2: ( $i > $o ) > $i > $i ).
thf(decl_361,type,
esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_362,type,
esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_363,type,
esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_364,type,
esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_365,type,
esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_366,type,
esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_367,type,
esk45_2: ( $i > $o ) > $i > $i ).
thf(decl_368,type,
esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_369,type,
esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_370,type,
esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_371,type,
esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(decl_372,type,
esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_373,type,
esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_374,type,
esk52_2: $i > $i > $i ).
thf(decl_375,type,
esk53_2: $i > $i > $i ).
thf(decl_376,type,
esk54_2: $i > $i > $i ).
thf(decl_377,type,
esk55_3: $i > $i > $i > $i ).
thf(decl_378,type,
esk56_3: $i > $i > $i > $i ).
thf(decl_379,type,
esk57_2: $i > $i > $i ).
thf(decl_380,type,
esk58_2: $i > ( $i > $o ) > $i ).
thf(decl_381,type,
esk59_2: $i > ( $i > $o ) > $i ).
thf(decl_382,type,
esk60_2: $i > ( $i > $o ) > $i ).
thf(decl_383,type,
esk61_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_384,type,
esk62_2: $i > ( $i > $o ) > $i ).
thf(decl_385,type,
esk63_2: $i > ( $i > $o ) > $i ).
thf(decl_386,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_387,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_388,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_389,type,
esk67_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_390,type,
esk68_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_391,type,
esk69_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_392,type,
esk70_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_393,type,
esk71_4: $i > $i > $i > $i > $i ).
thf(decl_394,type,
esk72_4: $i > $i > $i > $i > $i ).
thf(decl_395,type,
esk73_4: $i > $i > $i > $i > $i ).
thf(decl_396,type,
esk74_4: $i > $i > $i > $i > $i ).
thf(decl_397,type,
esk75_4: $i > $i > $i > $i > $i ).
thf(decl_398,type,
esk76_4: $i > $i > $i > $i > $i ).
thf(decl_399,type,
esk77_4: $i > $i > $i > $i > $i ).
thf(decl_400,type,
esk78_4: $i > $i > $i > $i > $i ).
thf(decl_401,type,
esk79_4: $i > $i > $i > $i > $i ).
thf(decl_402,type,
esk80_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_403,type,
esk81_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_404,type,
esk82_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_405,type,
esk83_3: $i > $i > $i > $i ).
thf(decl_406,type,
esk84_3: $i > $i > $i > $i ).
thf(decl_407,type,
esk85_3: $i > $i > $i > $i ).
thf(decl_408,type,
esk86_3: $i > $i > $i > $i ).
thf(decl_409,type,
esk87_0: $i ).
thf(decl_410,type,
esk88_0: $i ).
thf(decl_411,type,
esk89_0: $i ).
thf(decl_412,type,
epred2_0: $o ).
thf(decl_413,type,
esk90_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1,axiom,
( ex1
= ( ^ [X4: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(binunionTE,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
=> ! [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(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(prop2set2propI,axiom,
( prop2set2propI
<=> ! [X16: $o] :
( X16
=> ( set2prop @ ( prop2set @ X16 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X4: $i,X45: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X45
=> ( ( if @ X4 @ X45 @ X2 @ X3 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iftrueorfalse,axiom,
( iftrueorfalse
<=> ! [X4: $i,X47: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(setextT,axiom,
( setextT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(powersetTI1,axiom,
( powersetTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetTE1,axiom,
( powersetTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X21 @ ( powerset @ X48 ) )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(complementTI1,axiom,
( complementTI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementTE1,axiom,
( complementTE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(binintersectTELcontra,axiom,
( binintersectTELcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X21 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,axiom,
( binintersectTERcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(contrasubsetT,axiom,
( contrasubsetT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(contrasubsetT1,axiom,
( contrasubsetT1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( subset @ X21 @ X48 )
=> ( ~ ( in @ X2 @ X48 )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,axiom,
( contrasubsetT2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ X48 )
=> ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(contrasubsetT3,axiom,
( contrasubsetT3
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
=> ( subset @ X21 @ X48 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(doubleComplementI1,axiom,
( doubleComplementI1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(doubleComplementE1,axiom,
( doubleComplementE1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
=> ( in @ X2 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementSub1,axiom,
( doubleComplementSub1
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,axiom,
( doubleComplementSub2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(doubleComplementEq,axiom,
( doubleComplementEq
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( X21
= ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(complementTnotintersectT,axiom,
( complementTnotintersectT
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(complementImpComplementIntersect,axiom,
( complementImpComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
=> ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementSubsetComplementIntersect,axiom,
( complementSubsetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementInPowersetComplementIntersect,axiom,
( complementInPowersetComplementIntersect
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(complementTcontraSubset,axiom,
( complementTcontraSubset
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
=> ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(binunionTILcontra,axiom,
( binunionTILcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X21 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,axiom,
( binunionTIRcontra
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
=> ~ ( in @ X2 @ X48 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inIntersectImpInIntersectUnions,axiom,
( inIntersectImpInIntersectUnions
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ! [X49: $i] :
( ( in @ X49 @ ( powerset @ X4 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
=> ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(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(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(c_0_267,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_268,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_269,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_270,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_271,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_272,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
( singleton
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_284,plain,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I]) ).
thf(c_0_285,plain,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1I2]) ).
thf(c_0_286,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_287,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_288,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_289,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X878: $i] :
( ( X6 @ X2 @ X878 )
& ! [X879: $i] :
( ( X6 @ X2 @ X879 )
=> ( X878 = X879 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_267,c_0_268]) ).
thf(c_0_290,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X880: $i] :
( ( X1 @ X880 )
& ! [X881: $i] :
( ( X1 @ X881 )
=> ( X880 = X881 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_269,c_0_268]) ).
thf(c_0_291,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_292,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_293,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_294,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X882: $i] :
( ( X1 @ X882 )
& ! [X883: $i] :
( ( X1 @ X883 )
=> ( X882 = X883 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_270,c_0_268]) ).
thf(c_0_295,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X884: $i] :
( ( X1 @ X884 )
& ! [X885: $i] :
( ( X1 @ X885 )
=> ( X884 = X885 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_271,c_0_268]) ).
thf(c_0_296,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_297,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_272]) ).
thf(c_0_298,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_273,c_0_272]) ).
thf(c_0_299,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_272]) ).
thf(c_0_300,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_301,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X886: $i] :
( ( X1 @ X886 )
& ! [X887: $i] :
( ( X1 @ X887 )
=> ( X886 = X887 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_274,c_0_268]) ).
thf(c_0_302,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_272]) ).
thf(c_0_303,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_304,plain,
( exuI1
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X888: $i] :
( ( X1 @ X888 )
& ! [X889: $i] :
( ( X1 @ X889 )
=> ( X888 = X889 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_275,c_0_268]) ).
thf(c_0_305,plain,
( exuI3
= ( ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ? [X890: $i] :
( ( X1 @ X890 )
& ! [X891: $i] :
( ( X1 @ X891 )
=> ( X890 = X891 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_276,c_0_268]) ).
thf(c_0_306,plain,
( exuI2
= ( ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ? [X892: $i] :
( ( X1 @ X892 )
& ! [X893: $i] :
( ( X1 @ X893 )
=> ( X892 = X893 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_277,c_0_268]) ).
thf(c_0_307,plain,
( exuE3u
= ( ! [X1: $i > $o] :
( ? [X894: $i] :
( ( X1 @ X894 )
& ! [X895: $i] :
( ( X1 @ X895 )
=> ( X894 = X895 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_278,c_0_268]) ).
thf(c_0_308,plain,
( exu__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X896: $i] :
( ( X1 @ X896 )
& ! [X897: $i] :
( ( X1 @ X897 )
=> ( X896 = X897 ) ) )
<=> ? [X898: $i] :
( ( X17 @ X898 )
& ! [X899: $i] :
( ( X17 @ X899 )
=> ( X898 = X899 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_279,c_0_268]) ).
thf(c_0_309,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X900: $i] :
( ( X1 @ X900 )
& ! [X901: $i] :
( ( X1 @ X901 )
=> ( X900 = X901 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_280,c_0_268]) ).
thf(c_0_310,plain,
( descr__Cong
= ( ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ? [X902: $i] :
( ( X1 @ X902 )
& ! [X903: $i] :
( ( X1 @ X903 )
=> ( X902 = X903 ) ) )
=> ( ? [X904: $i] :
( ( X17 @ X904 )
& ! [X905: $i] :
( ( X17 @ X905 )
=> ( X904 = X905 ) ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_281,c_0_268]) ).
thf(c_0_311,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_312,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_313,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_314,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_315,plain,
( ex1E1
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_282,c_0_283]) ).
thf(c_0_316,plain,
( ex1I
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_284,c_0_283]) ).
thf(c_0_317,plain,
( ex1I2
= ( ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_285,c_0_283]) ).
thf(c_0_318,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_319,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_320,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_321,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_322,plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
@ ( cartprod @ X4 @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_286,c_0_287]) ).
thf(c_0_323,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_324,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_325,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_326,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_327,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_328,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_329,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_330,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_331,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_332,axiom,
( brelnall1
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_287]) ).
thf(c_0_333,axiom,
( brelnall2
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall2,c_0_287]) ).
thf(c_0_334,plain,
( ex1E2
= ( ! [X4: $i,X1: $i > $o] :
( ( singleton
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_288,c_0_283]) ).
thf(c_0_335,axiom,
( subbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_287]) ).
thf(c_0_336,axiom,
( eqbreln
= ( ! [X4: $i,X5: $i,X33: $i] :
( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
=> ! [X35: $i] :
( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_287]) ).
thf(c_0_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,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_345,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_346,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_347,plain,
( epred1_0
<=> ! [X935: $i] :
? [X936: $i] :
( ! [X937: $i] :
( ( in @ X937 @ X936 )
=> ! [X938: $i] :
( ( in @ X938 @ X937 )
=> ( in @ X938 @ X935 ) ) )
& ! [X939: $i,X940: $i] :
( ( ( in @ X939 @ X935 )
& ( in @ X940 @ X935 ) )
=> ( ! [X941: $i] :
( ( in @ X941 @ X936 )
=> ( ( in @ X939 @ X941 )
<=> ( in @ X940 @ X941 ) ) )
=> ( X939 = X940 ) ) )
& ! [X942: $i,X943: $i] :
( ( ( in @ X942 @ X936 )
& ( in @ X943 @ X936 ) )
=> ( ! [X944: $i] :
( ( in @ X944 @ X942 )
=> ( in @ X944 @ X943 ) )
| ! [X945: $i] :
( ( in @ X945 @ X943 )
=> ( in @ X945 @ X942 ) ) ) )
& ! [X946: $i] :
( ( ! [X947: $i] :
( ( in @ X947 @ X946 )
=> ( in @ X947 @ X935 ) )
& ? [X948: $i] : ( in @ X948 @ X946 ) )
=> ? [X949: $i,X950: $i] :
( ( in @ X949 @ X936 )
& ( in @ X950 @ X946 )
& ~ ? [X951: $i] :
( ( in @ X951 @ X949 )
& ( in @ X951 @ X946 ) )
& ! [X952: $i] :
( ( in @ X952 @ X936 )
=> ( ! [X953: $i] :
( ( in @ X953 @ X952 )
=> ( in @ X953 @ X949 ) )
| ( in @ X950 @ X952 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_348,negated_conjecture,
~ ( ! [X906: $i,X907: $i] :
( ! [X908: $i] :
( ( in @ X908 @ X906 )
<=> ( in @ X908 @ X907 ) )
=> ( X906 = X907 ) )
=> ( ! [X909: $i] :
~ ( in @ X909 @ emptyset )
=> ( ! [X910: $i,X911: $i,X912: $i] :
( ( in @ X912 @ ( setadjoin @ X910 @ X911 ) )
<=> ( ( X912 = X910 )
| ( in @ X912 @ X911 ) ) )
=> ( ! [X913: $i,X914: $i] :
( ( in @ X914 @ ( powerset @ X913 ) )
<=> ! [X915: $i] :
( ( in @ X915 @ X914 )
=> ( in @ X915 @ X913 ) ) )
=> ( ! [X916: $i,X917: $i] :
( ( in @ X917 @ ( setunion @ X916 ) )
<=> ? [X918: $i] :
( ( in @ X917 @ X918 )
& ( in @ X918 @ X916 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X919: $i] :
( ( in @ X919 @ omega )
=> ( in @ ( setadjoin @ X919 @ X919 ) @ omega ) )
=> ( ! [X920: $i] :
( ( ( in @ emptyset @ X920 )
& ! [X921: $i] :
( ( ( in @ X921 @ omega )
& ( in @ X921 @ X920 ) )
=> ( in @ ( setadjoin @ X921 @ X921 ) @ X920 ) ) )
=> ! [X922: $i] :
( ( in @ X922 @ omega )
=> ( in @ X922 @ X920 ) ) )
=> ( ! [X923: $i > $i > $o,X924: $i] :
( ! [X925: $i] :
( ( in @ X925 @ X924 )
=> ? [X926: $i] :
( ( X923 @ X925 @ X926 )
& ! [X927: $i] :
( ( X923 @ X925 @ X927 )
=> ( X926 = X927 ) ) ) )
=> ? [X928: $i] :
! [X929: $i] :
( ( in @ X929 @ X928 )
<=> ? [X930: $i] :
( ( in @ X930 @ X924 )
& ( X923 @ X930 @ X929 ) ) ) )
=> ( ! [X931: $i] :
( ? [X932: $i] : ( in @ X932 @ X931 )
=> ? [X933: $i] :
( ( in @ X933 @ X931 )
& ~ ? [X934: $i] :
( ( in @ X934 @ X933 )
& ( in @ X934 @ X931 ) ) ) )
=> ( epred1_0
=> ( ! [X954: $i > $o] :
( ? [X955: $i] :
( ( X954 @ X955 )
& ! [X956: $i] :
( ( X954 @ X956 )
=> ( X955 = X956 ) ) )
=> ( X954
@ ( descr
@ ^ [Z0: $i] : ( X954 @ Z0 ) ) ) )
=> ( ! [X957: $i,X958: $i > $o,X959: $i] :
( ( in @ X959 @ X957 )
=> ( ( X958 @ X959 )
=> ( in @ X959 @ ( dsetconstr @ X957 @ X958 ) ) ) )
=> ( ! [X960: $i,X961: $i > $o,X962: $i] :
( ( in @ X962 @ ( dsetconstr @ X960 @ X961 ) )
=> ( in @ X962 @ X960 ) )
=> ( ! [X963: $i,X964: $i > $o,X965: $i] :
( ( in @ X965 @ ( dsetconstr @ X963 @ X964 ) )
=> ( X964 @ X965 ) )
=> ( ! [X966: $i > $o] :
( ? [X967: $i] :
( ( X966 @ X967 )
& ! [X968: $i] :
( ( X966 @ X968 )
=> ( X967 = X968 ) ) )
=> ? [X969: $i] :
( ( X966 @ X969 )
& ! [X970: $i] :
( ( X966 @ X970 )
=> ( X969 = X970 ) ) ) )
=> ( ! [X971: $o,X972: $i] :
( ( in @ X972 @ ( prop2set @ X971 ) )
=> X971 )
=> ( ! [X973: $i] :
( ( in @ X973 @ emptyset )
=> ! [X974: $o] : X974 )
=> ( ! [X975: $i] :
( ( in @ X975 @ emptyset )
=> ~ $true )
=> ( ! [X976: $i] :
~ ( in @ X976 @ emptyset )
=> ( ! [X977: $i > $o] :
( ? [X978: $i] :
( ( X977 @ X978 )
& ! [X979: $i] :
( ( X977 @ X979 )
=> ( X978 = X979 ) ) )
=> ? [X980: $i] : ( X977 @ X980 ) )
=> ( ! [X981: $i,X982: $i] :
( ! [X983: $i] :
( ( in @ X983 @ X981 )
=> ( in @ X983 @ X982 ) )
=> ( ! [X984: $i] :
( ( in @ X984 @ X982 )
=> ( in @ X984 @ X981 ) )
=> ( X981 = X982 ) ) )
=> ( ! [X985: $i] :
( ! [X986: $i] :
~ ( in @ X986 @ X985 )
=> ( X985 = emptyset ) )
=> ( ! [X987: $i] :
( ! [X988: $i] :
~ ( in @ X988 @ X987 )
=> ( X987 = emptyset ) )
=> ( ! [X989: $i,X990: $i > $o,X991: $i] :
( ( in @ X991 @ X989 )
=> ( ( in @ X991 @ ( dsetconstr @ X989 @ X990 ) )
<=> ( X990 @ X991 ) ) )
=> ( ! [X992: $i] :
( ( X992 != emptyset )
=> ? [X993: $i] : ( in @ X993 @ X992 ) )
=> ( ! [X994: $i,X995: $i > $o,X996: $i] :
( ( in @ X996 @ X994 )
=> ( ( X995 @ X996 )
=> ( ( dsetconstr @ X994 @ X995 )
!= emptyset ) ) )
=> ( ! [X997: $i] :
( ? [X998: $i] : ( in @ X998 @ X997 )
=> ( X997 != emptyset ) )
=> ( ! [X999: $i,X1000: $i] : ( in @ X999 @ ( setadjoin @ X999 @ X1000 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X1001: $i,X1002: $i,X1003: $i] :
( ( in @ X1003 @ X1002 )
=> ( in @ X1003 @ ( setadjoin @ X1001 @ X1002 ) ) )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( in @ X1006 @ ( setadjoin @ X1004 @ X1005 ) )
=> ! [X1007: $o] :
( ( ( X1006 = X1004 )
=> X1007 )
=> ( ( ( in @ X1006 @ X1005 )
=> X1007 )
=> X1007 ) ) )
=> ( ! [X1008: $i,X1009: $i,X1010: $i] :
( ( in @ X1010 @ ( setadjoin @ X1008 @ X1009 ) )
=> ( ( X1010 = X1008 )
| ( in @ X1010 @ X1009 ) ) )
=> ( ! [X1011: $i] :
( ( dsetconstr @ X1011
@ ^ [Z0: $i] : $true )
= X1011 )
=> ( ! [X1012: $i,X1013: $i] :
( ! [X1014: $i] :
( ( in @ X1014 @ X1013 )
=> ( in @ X1014 @ X1012 ) )
=> ( in @ X1013 @ ( powerset @ X1012 ) ) )
=> ( ! [X1015: $i] : ( in @ emptyset @ ( powerset @ X1015 ) )
=> ( ! [X1016: $i] : ( in @ emptyset @ ( powerset @ X1016 ) )
=> ( ! [X1017: $i,X1018: $i,X1019: $i] :
( ( in @ X1018 @ ( powerset @ X1017 ) )
=> ( ( in @ X1019 @ X1018 )
=> ( in @ X1019 @ X1017 ) ) )
=> ( ! [X1020: $i,X1021: $i,X1022: $i] :
( ( in @ X1021 @ X1022 )
=> ( ( in @ X1022 @ X1020 )
=> ( in @ X1021 @ ( setunion @ X1020 ) ) ) )
=> ( ! [X1023: $i,X1024: $i] :
( ( in @ X1024 @ ( setunion @ X1023 ) )
=> ! [X1025: $o] :
( ! [X1026: $i] :
( ( in @ X1024 @ X1026 )
=> ( ( in @ X1026 @ X1023 )
=> X1025 ) )
=> X1025 ) )
=> ( ! [X1027: $i,X1028: $i] :
( ( in @ X1028 @ X1027 )
=> ( in @ X1028 @ ( powerset @ ( setunion @ X1027 ) ) ) )
=> ( ! [X1029: $i > $o] :
( ? [X1030: $i] :
( ( X1029 @ X1030 )
& ! [X1031: $i] :
( ( X1029 @ X1031 )
=> ( X1030 = X1031 ) ) )
=> ? [X1032: $i] :
! [X1033: $i] :
( ( X1029 @ X1033 )
<=> ( X1033 = X1032 ) ) )
=> ( ! [X1034: $i] :
( ( X1034 != emptyset )
=> ? [X1035: $i] :
( ( in @ X1035 @ X1034 )
& $true ) )
=> ( ! [X1036: $i,X1037: $i] :
( ( in @ X1036 @ ( setadjoin @ X1037 @ emptyset ) )
=> ( X1036 = X1037 ) )
=> ( ! [X1038: $i,X1039: $i] :
( ( X1038 != X1039 )
=> ~ ( in @ X1039 @ ( setadjoin @ X1038 @ emptyset ) ) )
=> ( ! [X1040: $i,X1041: $i] :
( ( X1040 = X1041 )
=> ( in @ X1040 @ ( setadjoin @ X1041 @ emptyset ) ) )
=> ( ! [X1042: $i,X1043: $i] :
( ( in @ X1042 @ ( setadjoin @ X1043 @ emptyset ) )
=> ( in @ X1043 @ ( setadjoin @ X1042 @ emptyset ) ) )
=> ( ! [X1044: $i,X1045: $i,X1046: $i] :
( ( in @ X1046 @ ( setadjoin @ X1044 @ ( setadjoin @ X1045 @ emptyset ) ) )
=> ( ( X1046 = X1044 )
| ( X1046 = X1045 ) ) )
=> ( ! [X1047: $i,X1048: $i] : ( in @ X1047 @ ( setadjoin @ X1047 @ ( setadjoin @ X1048 @ emptyset ) ) )
=> ( ! [X1049: $i,X1050: $i] : ( in @ X1050 @ ( setadjoin @ X1049 @ ( setadjoin @ X1050 @ emptyset ) ) )
=> ( ! [X1051: $i,X1052: $i > $o] :
( ? [X1053: $i] :
( ( in @ X1053 @ X1051 )
& ( X1052 @ X1053 ) )
=> ( ( ( dsetconstr @ X1051 @ X1052 )
= emptyset )
=> ~ $true ) )
=> ( ! [X1054: $i > $o,X1055: $i] :
( ( in @ X1055 @ emptyset )
=> ( X1054 @ X1055 ) )
=> ( ! [X1056: $i,X1057: $i > $o] :
( ~ ! [X1058: $i] :
( ( in @ X1058 @ X1056 )
=> ( X1057 @ X1058 ) )
=> ? [X1059: $i] :
( ( in @ X1059 @ X1056 )
& ~ ( X1057 @ X1059 ) ) )
=> ( ! [X1060: $i,X1061: $i > $o] :
( ! [X1062: $i] :
( ( in @ X1062 @ X1060 )
=> ~ ( X1061 @ X1062 ) )
=> ~ ? [X1063: $i] :
( ( in @ X1063 @ X1060 )
& ( X1061 @ X1063 ) ) )
=> ( ! [X1064: $i,X1065: $i > $o] :
( ~ ? [X1066: $i] :
( ( in @ X1066 @ X1064 )
& ( X1065 @ X1066 ) )
=> ! [X1067: $i] :
( ( in @ X1067 @ X1064 )
=> ~ ( X1065 @ X1067 ) ) )
=> ( ! [X1068: $i,X1069: $i > $o] :
( ? [X1070: $i] :
( ( in @ X1070 @ X1068 )
& ~ ( X1069 @ X1070 ) )
=> ~ ! [X1071: $i] :
( ( in @ X1071 @ X1068 )
=> ( X1069 @ X1071 ) ) )
=> ( ! [X1072: $o] :
( X1072
=> ( in @ emptyset @ ( prop2set @ X1072 ) ) )
=> ( ! [X1073: $o] :
( X1073
=> ( set2prop @ ( prop2set @ X1073 ) ) )
=> ( ! [X1074: $i,X1075: $i > $o] :
( ~ ? [X1076: $i] :
( ( in @ X1076 @ X1074 )
& ( X1075 @ X1076 ) )
=> ! [X1077: $i] :
( ( in @ X1077 @ X1074 )
=> ~ ( X1075 @ X1077 ) ) )
=> ( ! [X1078: $i,X1079: $i > $o] :
( ~ ! [X1080: $i] :
( ( in @ X1080 @ X1078 )
=> ( X1079 @ X1080 ) )
=> ? [X1081: $i] :
( ( in @ X1081 @ X1078 )
& ~ ( X1079 @ X1081 ) ) )
=> ( ! [X1082: $i > $o] :
( ? [X1083: $i] :
( ( X1082 @ X1083 )
& ! [X1084: $i] :
( ( X1082 @ X1084 )
=> ( X1083 = X1084 ) ) )
=> ? [X1085: $i] :
( ( X1082 @ X1085 )
& ! [X1086: $i] :
( ( X1082 @ X1086 )
=> ( X1085 = X1086 ) ) ) )
=> ( ! [X1087: $i > $o] :
( ? [X1088: $i] : ( X1087 @ X1088 )
=> ( ! [X1089: $i,X1090: $i] :
( ( X1087 @ X1089 )
=> ( ( X1087 @ X1090 )
=> ( X1089 = X1090 ) ) )
=> ? [X1091: $i] :
( ( X1087 @ X1091 )
& ! [X1092: $i] :
( ( X1087 @ X1092 )
=> ( X1091 = X1092 ) ) ) ) )
=> ( ! [X1093: $i > $o] :
( ? [X1094: $i] :
! [X1095: $i] :
( ( X1093 @ X1095 )
<=> ( X1095 = X1094 ) )
=> ? [X1096: $i] :
( ( X1093 @ X1096 )
& ! [X1097: $i] :
( ( X1093 @ X1097 )
=> ( X1096 = X1097 ) ) ) )
=> ( ! [X1098: $i,X1099: $i] :
( ( X1098 = X1099 )
=> ! [X1100: $i,X1101: $i] :
( ( X1100 = X1101 )
=> ( ( in @ X1100 @ X1098 )
=> ( in @ X1101 @ X1099 ) ) ) )
=> ( ! [X1102: $i,X1103: $i] :
( ( X1102 = X1103 )
=> ! [X1104: $i,X1105: $i] :
( ( X1104 = X1105 )
=> ( ( in @ X1104 @ X1102 )
<=> ( in @ X1105 @ X1103 ) ) ) )
=> ( ! [X1106: $i > $o] :
( ? [X1107: $i] :
( ( X1106 @ X1107 )
& ! [X1108: $i] :
( ( X1106 @ X1108 )
=> ( X1107 = X1108 ) ) )
=> ! [X1109: $i,X1110: $i] :
( ( X1106 @ X1109 )
=> ( ( X1106 @ X1110 )
=> ( X1109 = X1110 ) ) ) )
=> ( ! [X1111: $i > $o,X1112: $i > $o] :
( ! [X1113: $i,X1114: $i] :
( ( X1113 = X1114 )
=> ( ( X1111 @ X1113 )
<=> ( X1112 @ X1114 ) ) )
=> ( ? [X1115: $i] :
( ( X1111 @ X1115 )
& ! [X1116: $i] :
( ( X1111 @ X1116 )
=> ( X1115 = X1116 ) ) )
<=> ? [X1117: $i] :
( ( X1112 @ X1117 )
& ! [X1118: $i] :
( ( X1112 @ X1118 )
=> ( X1117 = X1118 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X1119: $i,X1120: $i] :
( ( X1119 = X1120 )
=> ! [X1121: $i,X1122: $i] :
( ( X1121 = X1122 )
=> ( ( setadjoin @ X1119 @ X1121 )
= ( setadjoin @ X1120 @ X1122 ) ) ) )
=> ( ! [X1123: $i,X1124: $i] :
( ( X1123 = X1124 )
=> ( ( powerset @ X1123 )
= ( powerset @ X1124 ) ) )
=> ( ! [X1125: $i,X1126: $i] :
( ( X1125 = X1126 )
=> ( ( setunion @ X1125 )
= ( setunion @ X1126 ) ) )
=> ( ( omega = omega )
=> ( ! [X1127: $i > $o] :
( ? [X1128: $i] :
( ( X1127 @ X1128 )
& ! [X1129: $i] :
( ( X1127 @ X1129 )
=> ( X1128 = X1129 ) ) )
=> ! [X1130: $i,X1131: $i] :
( ( X1127 @ X1130 )
=> ( ( X1127 @ X1131 )
=> ( X1130 = X1131 ) ) ) )
=> ( ! [X1132: $i > $o,X1133: $i > $o] :
( ! [X1134: $i,X1135: $i] :
( ( X1134 = X1135 )
=> ( ( X1132 @ X1134 )
<=> ( X1133 @ X1135 ) ) )
=> ( ? [X1136: $i] :
( ( X1132 @ X1136 )
& ! [X1137: $i] :
( ( X1132 @ X1137 )
=> ( X1136 = X1137 ) ) )
=> ( ? [X1138: $i] :
( ( X1133 @ X1138 )
& ! [X1139: $i] :
( ( X1133 @ X1139 )
=> ( X1138 = X1139 ) ) )
=> ( ( descr @ X1132 )
= ( descr @ X1133 ) ) ) ) )
=> ( ! [X1140: $i,X1141: $i] :
( ( X1140 = X1141 )
=> ! [X1142: $i > $o,X1143: $i > $o] :
( ! [X1144: $i] :
( ( in @ X1144 @ X1140 )
=> ! [X1145: $i] :
( ( in @ X1145 @ X1141 )
=> ( ( X1144 = X1145 )
=> ( ( X1142 @ X1144 )
<=> ( X1143 @ X1145 ) ) ) ) )
=> ( ( dsetconstr @ X1140 @ X1142 )
= ( dsetconstr @ X1141 @ X1143 ) ) ) )
=> ( ! [X1146: $i,X1147: $i] :
( ! [X1148: $i] :
( ( in @ X1148 @ X1146 )
=> ( in @ X1148 @ X1147 ) )
=> ( subset @ X1146 @ X1147 ) )
=> ( ! [X1149: $i,X1150: $i] :
( ( X1149 = X1150 )
=> ( subset @ X1150 @ X1149 ) )
=> ( ! [X1151: $i,X1152: $i] :
( ( X1151 = X1152 )
=> ( subset @ X1151 @ X1152 ) )
=> ( ! [X1153: $i,X1154: $i] :
( ! [X1155: $i] :
( ( in @ X1155 @ X1153 )
=> ( in @ X1155 @ X1154 ) )
=> ( subset @ X1153 @ X1154 ) )
=> ( ! [X1156: $i] : ( subset @ emptyset @ X1156 )
=> ( ! [X1157: $i,X1158: $i,X1159: $i] :
( ( subset @ X1157 @ X1158 )
=> ( ( in @ X1159 @ X1157 )
=> ( in @ X1159 @ X1158 ) ) )
=> ( ! [X1160: $i,X1161: $i,X1162: $i] :
( ( subset @ X1160 @ X1161 )
=> ( ~ ( in @ X1162 @ X1161 )
=> ~ ( in @ X1162 @ X1160 ) ) )
=> ( ! [X1163: $i,X1164: $i,X1165: $i] :
( ( in @ X1165 @ X1163 )
=> ( ~ ( in @ X1165 @ X1164 )
=> ~ ( subset @ X1163 @ X1164 ) ) )
=> ( ! [X1166: $i,X1167: $i] :
( ~ ( subset @ X1166 @ X1167 )
=> ( X1166 != X1167 ) )
=> ( ! [X1168: $i,X1169: $i,X1170: $i] :
( ( in @ X1170 @ X1168 )
=> ( ~ ( in @ X1170 @ X1169 )
=> ( X1168 != X1169 ) ) )
=> ( ! [X1171: $i] : ( subset @ X1171 @ X1171 )
=> ( ! [X1172: $i,X1173: $i,X1174: $i] :
( ( subset @ X1172 @ X1173 )
=> ( ( subset @ X1173 @ X1174 )
=> ( subset @ X1172 @ X1174 ) ) )
=> ( ! [X1175: $i,X1176: $i] : ( subset @ X1176 @ ( setadjoin @ X1175 @ X1176 ) )
=> ( ! [X1177: $i,X1178: $i,X1179: $i] :
( ( subset @ X1177 @ X1179 )
=> ( subset @ X1177 @ ( setadjoin @ X1178 @ X1179 ) ) )
=> ( ! [X1180: $i,X1181: $i] :
( ( subset @ X1180 @ X1181 )
=> ( in @ X1180 @ ( powerset @ X1181 ) ) )
=> ( ! [X1182: $i,X1183: $i] :
( ( subset @ X1182 @ X1183 )
=> ( ( subset @ X1183 @ X1182 )
=> ( X1182 = X1183 ) ) )
=> ( ! [X1184: $i] :
( ( subset @ X1184 @ emptyset )
=> ( X1184 = emptyset ) )
=> ( ! [X1185: $i,X1186: $i] :
( ( subset @ X1186 @ X1185 )
=> ( in @ X1186 @ ( powerset @ X1185 ) ) )
=> ( ! [X1187: $i,X1188: $i] :
( ( in @ X1188 @ ( powerset @ X1187 ) )
=> ( subset @ X1188 @ X1187 ) )
=> ( ! [X1189: $i] : ( in @ X1189 @ ( powerset @ X1189 ) )
=> ( ! [X1190: $i,X1191: $i] :
( ( subset @ X1190 @ X1191 )
=> ( subset @ ( powerset @ X1190 ) @ ( powerset @ X1191 ) ) )
=> ( ! [X1192: $i,X1193: $i > $o] : ( in @ ( dsetconstr @ X1192 @ X1193 ) @ ( powerset @ X1192 ) )
=> ( ! [X1194: $i,X1195: $i > $o] : ( subset @ ( dsetconstr @ X1194 @ X1195 ) @ X1194 )
=> ( ! [X1196: $i,X1197: $i,X1198: $i] :
( ( in @ X1198 @ X1196 )
=> ( in @ X1198 @ ( binunion @ X1196 @ X1197 ) ) )
=> ( ! [X1199: $i,X1200: $i] : ( in @ X1200 @ ( setadjoin @ X1199 @ ( setadjoin @ X1200 @ emptyset ) ) )
=> ( ! [X1201: $i,X1202: $i,X1203: $i] :
( ( in @ X1203 @ X1202 )
=> ( in @ X1203 @ ( binunion @ X1201 @ X1202 ) ) )
=> ( ! [X1204: $i,X1205: $i,X1206: $i,X1207: $o] :
( ( in @ X1206 @ ( binunion @ X1204 @ X1205 ) )
=> ( ( ( in @ X1206 @ X1204 )
=> X1207 )
=> ( ( ( in @ X1206 @ X1205 )
=> X1207 )
=> X1207 ) ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ( in @ X1210 @ ( binunion @ X1208 @ X1209 ) )
=> ( ( in @ X1210 @ X1208 )
| ( in @ X1210 @ X1209 ) ) )
=> ( ! [X1211: $i,X1212: $i] : ( subset @ X1211 @ ( binunion @ X1211 @ X1212 ) )
=> ( ! [X1213: $i,X1214: $i] : ( subset @ X1214 @ ( binunion @ X1213 @ X1214 ) )
=> ( ! [X1215: $i,X1216: $i,X1217: $i] :
( ( in @ X1217 @ X1215 )
=> ( ( in @ X1217 @ X1216 )
=> ( in @ X1217 @ ( binintersect @ X1215 @ X1216 ) ) ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( subset @ X1220 @ X1218 )
=> ( ( subset @ X1220 @ X1219 )
=> ( subset @ X1220 @ ( binintersect @ X1218 @ X1219 ) ) ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i] :
( ( in @ X1223 @ ( binintersect @ X1221 @ X1222 ) )
=> ( in @ X1223 @ X1221 ) )
=> ( ! [X1224: $i,X1225: $i] : ( subset @ ( binintersect @ X1224 @ X1225 ) @ X1224 )
=> ( ! [X1226: $i,X1227: $i] :
( ( subset @ X1226 @ X1227 )
=> ( ( binintersect @ X1226 @ X1227 )
= X1226 ) )
=> ( ! [X1228: $i,X1229: $i] :
( ( ( binintersect @ X1228 @ X1229 )
= X1229 )
=> ( subset @ X1229 @ X1228 ) )
=> ( ! [X1230: $i,X1231: $i,X1232: $i] :
( ( in @ X1232 @ ( binintersect @ X1230 @ X1231 ) )
=> ( in @ X1232 @ X1231 ) )
=> ( ! [X1233: $i,X1234: $i] :
( ~ ? [X1235: $i] :
( ( in @ X1235 @ X1233 )
& ( in @ X1235 @ X1234 ) )
=> ( ( binintersect @ X1233 @ X1234 )
= emptyset ) )
=> ( ! [X1236: $i,X1237: $i] : ( subset @ ( binintersect @ X1236 @ X1237 ) @ X1237 )
=> ( ! [X1238: $i,X1239: $i] :
( ( subset @ X1239 @ X1238 )
=> ( ( binintersect @ X1238 @ X1239 )
= X1239 ) )
=> ( ! [X1240: $i,X1241: $i] :
( ( ( binintersect @ X1240 @ X1241 )
= X1240 )
=> ( subset @ X1240 @ X1241 ) )
=> ( ! [X1242: $i,X1243: $i,X1244: $i] :
( ( binintersect @ X1242 @ ( binunion @ X1243 @ X1244 ) )
= ( binunion @ ( binintersect @ X1242 @ X1243 ) @ ( binintersect @ X1242 @ X1244 ) ) )
=> ( ! [X1245: $i,X1246: $i,X1247: $i] :
( ( in @ X1247 @ X1245 )
=> ( ~ ( in @ X1247 @ X1246 )
=> ( in @ X1247 @ ( setminus @ X1245 @ X1246 ) ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ ( setminus @ X1248 @ X1249 ) )
=> ( in @ X1250 @ X1248 ) )
=> ( ! [X1251: $i,X1252: $i,X1253: $i] :
( ( in @ X1253 @ ( setminus @ X1251 @ X1252 ) )
=> ~ ( in @ X1253 @ X1252 ) )
=> ( ! [X1254: $i,X1255: $i] :
( ( subset @ X1254 @ X1255 )
=> ( ( setminus @ X1254 @ X1255 )
= emptyset ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i] :
( ~ ( in @ X1258 @ ( setminus @ X1256 @ X1257 ) )
=> ( ( in @ X1258 @ X1256 )
=> ( in @ X1258 @ X1257 ) ) )
=> ( ! [X1259: $i,X1260: $i,X1261: $i] :
( ~ ( in @ X1261 @ ( setminus @ X1259 @ X1260 ) )
=> ( ~ ( in @ X1261 @ X1260 )
=> ~ ( in @ X1261 @ X1259 ) ) )
=> ( ! [X1262: $i,X1263: $i,X1264: $i] :
( ~ ( in @ X1264 @ X1262 )
=> ~ ( in @ X1264 @ ( setminus @ X1262 @ X1263 ) ) )
=> ( ! [X1265: $i,X1266: $i,X1267: $i] :
( ( in @ X1267 @ X1266 )
=> ~ ( in @ X1267 @ ( setminus @ X1265 @ X1266 ) ) )
=> ( ! [X1268: $i,X1269: $i] : ( subset @ ( setminus @ X1268 @ X1269 ) @ X1268 )
=> ( ! [X1270: $i,X1271: $i] :
( ( ( setminus @ X1270 @ X1271 )
= emptyset )
=> ( subset @ X1270 @ X1271 ) )
=> ( ! [X1272: $i,X1273: $i,X1274: $i] :
( ( in @ X1274 @ ( symdiff @ X1272 @ X1273 ) )
=> ! [X1275: $o] :
( ( ( in @ X1274 @ X1272 )
=> ( ~ ( in @ X1274 @ X1273 )
=> X1275 ) )
=> ( ( ~ ( in @ X1274 @ X1272 )
=> ( ( in @ X1274 @ X1273 )
=> X1275 ) )
=> X1275 ) ) )
=> ( ! [X1276: $i,X1277: $i,X1278: $i] :
( ( in @ X1278 @ X1276 )
=> ( ~ ( in @ X1278 @ X1277 )
=> ( in @ X1278 @ ( symdiff @ X1276 @ X1277 ) ) ) )
=> ( ! [X1279: $i,X1280: $i,X1281: $i] :
( ~ ( in @ X1281 @ X1279 )
=> ( ( in @ X1281 @ X1280 )
=> ( in @ X1281 @ ( symdiff @ X1279 @ X1280 ) ) ) )
=> ( ! [X1282: $i,X1283: $i,X1284: $i] :
( ( in @ X1284 @ X1282 )
=> ( ( in @ X1284 @ X1283 )
=> ~ ( in @ X1284 @ ( symdiff @ X1282 @ X1283 ) ) ) )
=> ( ! [X1285: $i,X1286: $i,X1287: $i] :
( ~ ( in @ X1287 @ X1285 )
=> ( ~ ( in @ X1287 @ X1286 )
=> ~ ( in @ X1287 @ ( symdiff @ X1285 @ X1286 ) ) ) )
=> ( ! [X1288: $i,X1289: $i] : ( in @ X1289 @ ( setadjoin @ X1288 @ ( setadjoin @ X1289 @ emptyset ) ) )
=> ( ! [X1290: $i,X1291: $i] : ( in @ X1290 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1290 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1290 @ ( setadjoin @ X1291 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1292: $i,X1293: $i] : ( in @ X1293 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1292 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1292 @ ( setadjoin @ X1293 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1294: $i,X1295: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1294 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1294 @ ( setadjoin @ X1295 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1296: $i,X1297: $i] : ( iskpair @ ( kpair @ X1296 @ X1297 ) )
=> ( ! [X1298: $i,X1299: $i] :
( ( in @ X1299 @ X1298 )
=> ( subset @ ( setadjoin @ X1299 @ emptyset ) @ X1298 ) )
=> ( ! [X1300: $i,X1301: $i] :
( ( in @ X1301 @ X1300 )
=> ( in @ ( setadjoin @ X1301 @ emptyset ) @ ( powerset @ X1300 ) ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i] :
( ( in @ X1304 @ X1302 )
=> ( in @ ( setadjoin @ X1304 @ emptyset ) @ ( powerset @ ( binunion @ X1302 @ X1303 ) ) ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( in @ X1307 @ ( setadjoin @ X1305 @ ( setadjoin @ X1306 @ emptyset ) ) )
=> ( ( X1307 = X1305 )
| ( X1307 = X1306 ) ) )
=> ( ! [X1308: $i,X1309: $i,X1310: $i] :
( ( in @ X1310 @ X1308 )
=> ! [X1311: $i] :
( ( in @ X1311 @ X1309 )
=> ( subset @ ( setadjoin @ X1310 @ ( setadjoin @ X1311 @ emptyset ) ) @ ( binunion @ X1308 @ X1309 ) ) ) )
=> ( ! [X1312: $i,X1313: $i,X1314: $i] :
( ( in @ X1314 @ X1312 )
=> ! [X1315: $i] :
( ( in @ X1315 @ X1313 )
=> ( in @ ( setadjoin @ X1314 @ ( setadjoin @ X1315 @ emptyset ) ) @ ( powerset @ ( binunion @ X1312 @ X1313 ) ) ) ) )
=> ( ! [X1316: $i,X1317: $i,X1318: $i] :
( ( in @ X1318 @ X1316 )
=> ! [X1319: $i] :
( ( in @ X1319 @ X1317 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1318 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1318 @ ( setadjoin @ X1319 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1316 @ X1317 ) ) ) ) )
=> ( ! [X1320: $i,X1321: $i,X1322: $i] :
( ( in @ X1322 @ X1320 )
=> ! [X1323: $i] :
( ( in @ X1323 @ X1321 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1322 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1322 @ ( setadjoin @ X1323 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1320 @ X1321 ) ) ) ) ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i] :
( ( in @ X1326 @ X1324 )
=> ! [X1327: $i] :
( ( in @ X1327 @ X1325 )
=> ( in @ ( kpair @ X1326 @ X1327 ) @ ( powerset @ ( powerset @ ( binunion @ X1324 @ X1325 ) ) ) ) ) )
=> ( ! [X1328: $i,X1329: $i,X1330: $i] :
( ( in @ X1330 @ X1328 )
=> ! [X1331: $i] :
( ( in @ X1331 @ X1329 )
=> ( in @ ( kpair @ X1330 @ X1331 ) @ ( cartprod @ X1328 @ X1329 ) ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( in @ X1334 @ ( cartprod @ X1332 @ X1333 ) )
=> ? [X1335: $i] :
( ( in @ X1335 @ X1332 )
& ? [X1336: $i] :
( ( in @ X1336 @ X1333 )
& ( X1334
= ( kpair @ X1335 @ X1336 ) ) ) ) )
=> ( ! [X1337: $i,X1338: $i,X1339: $i] :
( ( in @ X1339 @ ( cartprod @ X1337 @ X1338 ) )
=> ( iskpair @ X1339 ) )
=> ( ! [X1340: $i,X1341: $i] :
( ( in @ X1341 @ ( setunion @ X1340 ) )
=> ? [X1342: $i] :
( ( in @ X1342 @ X1340 )
& ( in @ X1341 @ X1342 ) ) )
=> ( ! [X1343: $i] : ( subset @ ( setunion @ ( setadjoin @ X1343 @ emptyset ) ) @ X1343 )
=> ( ! [X1344: $i] : ( subset @ X1344 @ ( setunion @ ( setadjoin @ X1344 @ emptyset ) ) )
=> ( ! [X1345: $i] :
( ( setunion @ ( setadjoin @ X1345 @ emptyset ) )
= X1345 )
=> ( ! [X1346: $i,X1347: $i > $o] :
( ! [X1348: $i] :
( ( in @ X1348 @ X1346 )
=> ! [X1349: $i] :
( ( in @ X1349 @ X1346 )
=> ( ( X1347 @ X1348 )
=> ( ( X1347 @ X1349 )
=> ( X1348 = X1349 ) ) ) ) )
=> ( ? [X1350: $i] :
( ( in @ X1350 @ X1346 )
& ( X1347 @ X1350 ) )
=> ( singleton @ ( dsetconstr @ X1346 @ X1347 ) ) ) )
=> ( ! [X1351: $i,X1352: $i > $o] :
( ( singleton @ ( dsetconstr @ X1351 @ X1352 ) )
=> ? [X1353: $i] :
( ( in @ X1353 @ X1351 )
& ( X1352 @ X1353 ) ) )
=> ( ! [X1354: $i,X1355: $i > $o,X1356: $i] :
( ( in @ X1356 @ X1354 )
=> ( ( X1355 @ X1356 )
=> ( ! [X1357: $i] :
( ( in @ X1357 @ X1354 )
=> ( ( X1355 @ X1357 )
=> ( X1357 = X1356 ) ) )
=> ( singleton @ ( dsetconstr @ X1354 @ X1355 ) ) ) ) )
=> ( ! [X1358: $i,X1359: $i > $o] :
( ! [X1360: $i] :
( ( in @ X1360 @ X1358 )
=> ! [X1361: $i] :
( ( in @ X1361 @ X1358 )
=> ( ( X1359 @ X1360 )
=> ( ( X1359 @ X1361 )
=> ( X1360 = X1361 ) ) ) ) )
=> ( ? [X1362: $i] :
( ( in @ X1362 @ X1358 )
& ( X1359 @ X1362 ) )
=> ( singleton @ ( dsetconstr @ X1358 @ X1359 ) ) ) )
=> ( ! [X1363: $i,X1364: $i] :
( ( ( setadjoin @ X1363 @ emptyset )
= ( setadjoin @ X1364 @ emptyset ) )
=> ( X1363 = X1364 ) )
=> ( ! [X1365: $i,X1366: $i,X1367: $i] :
( ( in @ ( setadjoin @ X1367 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1365 @ ( setadjoin @ X1366 @ emptyset ) ) @ emptyset ) ) )
=> ( X1365 = X1367 ) )
=> ( ! [X1368: $i] :
( ( iskpair @ X1368 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1368 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1368 ) ) ) )
=> ( ! [X1369: $i] :
( ( singleton @ X1369 )
=> ( in @ ( setunion @ X1369 ) @ X1369 ) )
=> ( ! [X1370: $i,X1371: $i] :
( ( kfst @ ( kpair @ X1370 @ X1371 ) )
= X1370 )
=> ( ! [X1372: $i,X1373: $i,X1374: $i] :
( ( in @ X1374 @ ( cartprod @ X1372 @ X1373 ) )
=> ( in @ ( kfst @ X1374 ) @ X1372 ) )
=> ( ! [X1375: $i,X1376: $i,X1377: $i,X1378: $i] :
( ( ( setadjoin @ ( setadjoin @ X1375 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1375 @ ( setadjoin @ X1376 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1377 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1377 @ ( setadjoin @ X1378 @ emptyset ) ) @ emptyset ) ) )
=> ( X1375 = X1377 ) )
=> ( ! [X1379: $i,X1380: $i,X1381: $i,X1382: $i] :
( ( ( kpair @ X1379 @ X1380 )
= ( kpair @ X1381 @ X1382 ) )
=> ( X1379 = X1381 ) )
=> ( ! [X1383: $i,X1384: $i] :
( ( X1383 = X1384 )
=> ( ( setadjoin @ X1383 @ ( setadjoin @ X1384 @ emptyset ) )
= ( setadjoin @ X1383 @ emptyset ) ) )
=> ( ! [X1385: $i,X1386: $i] :
( ( X1385 = X1386 )
=> ( ( setadjoin @ ( setadjoin @ X1385 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1385 @ ( setadjoin @ X1386 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1385 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1387: $i,X1388: $i,X1389: $i,X1390: $i] :
( ( ( setadjoin @ ( setadjoin @ X1387 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1387 @ ( setadjoin @ X1388 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1389 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1389 @ ( setadjoin @ X1390 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1389 = X1390 )
=> ( X1388 = X1390 ) ) )
=> ( ! [X1391: $i,X1392: $i,X1393: $i] :
( ( ( setadjoin @ X1391 @ ( setadjoin @ X1392 @ emptyset ) )
= ( setadjoin @ X1393 @ emptyset ) )
=> ( X1391 = X1392 ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i,X1397: $i] :
( ( ( setadjoin @ ( setadjoin @ X1394 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1394 @ ( setadjoin @ X1395 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1396 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1396 @ ( setadjoin @ X1397 @ emptyset ) ) @ emptyset ) ) )
=> ( X1395 = X1397 ) )
=> ( ! [X1398: $i,X1399: $i,X1400: $i,X1401: $i] :
( ( ( kpair @ X1398 @ X1399 )
= ( kpair @ X1400 @ X1401 ) )
=> ( X1399 = X1401 ) )
=> ( ! [X1402: $i] :
( ( iskpair @ X1402 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1402 )
@ ^ [Z0: $i] :
( X1402
= ( kpair @ ( kfst @ X1402 ) @ Z0 ) ) ) ) )
=> ( ! [X1403: $i,X1404: $i] :
( ( ksnd @ ( kpair @ X1403 @ X1404 ) )
= X1404 )
=> ( ! [X1405: $i] :
( ( iskpair @ X1405 )
=> ( ( kpair @ ( kfst @ X1405 ) @ ( ksnd @ X1405 ) )
= X1405 ) )
=> ( ! [X1406: $i,X1407: $i,X1408: $i] :
( ( in @ X1408 @ ( cartprod @ X1406 @ X1407 ) )
=> ( in @ ( ksnd @ X1408 ) @ X1407 ) )
=> ( ! [X1409: $i,X1410: $i,X1411: $i,X1412: $i] :
( ( in @ ( kpair @ X1411 @ X1412 ) @ ( cartprod @ X1409 @ X1410 ) )
=> ( in @ X1411 @ X1409 ) )
=> ( ! [X1413: $i,X1414: $i,X1415: $i,X1416: $i] :
( ( in @ ( kpair @ X1415 @ X1416 ) @ ( cartprod @ X1413 @ X1414 ) )
=> ( in @ X1416 @ X1414 ) )
=> ( ! [X1417: $i,X1418: $i,X1419: $i] :
( ( in @ X1419 @ X1417 )
=> ! [X1420: $i] :
( ( in @ X1420 @ X1418 )
=> ( ( kpair @ X1419 @ X1420 )
= ( kpair @ X1419 @ X1420 ) ) ) )
=> ( ! [X1421: $i,X1422: $i,X1423: $i] :
( ( in @ X1423 @ X1421 )
=> ! [X1424: $i] :
( ( in @ X1424 @ X1422 )
=> ( ( kfst @ ( kpair @ X1423 @ X1424 ) )
= X1423 ) ) )
=> ( ! [X1425: $i,X1426: $i,X1427: $i] :
( ( in @ X1427 @ X1425 )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1426 )
=> ( ( ksnd @ ( kpair @ X1427 @ X1428 ) )
= X1428 ) ) )
=> ( ! [X1429: $i,X1430: $i,X1431: $i] :
( ( in @ X1431 @ ( cartprod @ X1429 @ X1430 ) )
=> ( ( kpair @ ( kfst @ X1431 ) @ ( ksnd @ X1431 ) )
= X1431 ) )
=> ( ! [X1432: $i,X1433: $i,X1434: $i > $i > $o,X1435: $i] :
( ( in @ X1435 @ X1432 )
=> ! [X1436: $i] :
( ( in @ X1436 @ X1433 )
=> ( ( X1434 @ X1435 @ X1436 )
=> ( in @ ( kpair @ X1435 @ X1436 ) @ ( dpsetconstr @ X1432 @ X1433 @ X1434 ) ) ) ) )
=> ( ! [X1437: $i,X1438: $i,X1439: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1437 @ X1438 @ X1439 ) @ ( cartprod @ X1437 @ X1438 ) )
=> ( ! [X1440: $i,X1441: $i,X1442: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1440 @ X1441 @ X1442 ) @ ( cartprod @ X1440 @ X1441 ) )
=> ( ! [X1443: $i,X1444: $i,X1445: $i > $i > $o,X1446: $i] :
( ( in @ X1446 @ X1443 )
=> ! [X1447: $i] :
( ( in @ X1447 @ X1444 )
=> ( ( in @ ( kpair @ X1446 @ X1447 ) @ ( dpsetconstr @ X1443 @ X1444 @ X1445 ) )
=> ( X1445 @ X1446 @ X1447 ) ) ) )
=> ( ! [X1448: $i,X1449: $i,X1450: $i > $i > $o,X1451: $i,X1452: $i] :
( ( in @ ( kpair @ X1451 @ X1452 ) @ ( dpsetconstr @ X1448 @ X1449 @ X1450 ) )
=> ( in @ X1451 @ X1448 ) )
=> ( ! [X1453: $i,X1454: $i,X1455: $i > $i > $o,X1456: $i,X1457: $i] :
( ( in @ ( kpair @ X1456 @ X1457 ) @ ( dpsetconstr @ X1453 @ X1454 @ X1455 ) )
=> ( in @ X1457 @ X1454 ) )
=> ( ! [X1458: $i,X1459: $i,X1460: $i > $i > $o,X1461: $i,X1462: $i] :
( ( in @ ( kpair @ X1461 @ X1462 ) @ ( dpsetconstr @ X1458 @ X1459 @ X1460 ) )
=> ( X1460 @ X1461 @ X1462 ) )
=> ( ! [X1463: $i,X1464: $i,X1465: $i] :
( ( func @ X1463 @ X1464 @ X1465 )
=> ! [X1466: $i] :
( ( in @ X1466 @ X1463 )
=> ( singleton
@ ( dsetconstr @ X1464
@ ^ [Z0: $i] : ( in @ ( kpair @ X1466 @ Z0 ) @ X1465 ) ) ) ) )
=> ( ! [X1467: $i,X1468: $i,X1469: $i] :
( ( func @ X1467 @ X1468 @ X1469 )
=> ! [X1470: $i] :
( ( in @ X1470 @ X1467 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1468
@ ^ [Z0: $i] : ( in @ ( kpair @ X1470 @ Z0 ) @ X1469 ) ) )
@ X1468 ) ) )
=> ( ! [X1471: $i,X1472: $i,X1473: $i] :
( ( func @ X1471 @ X1472 @ X1473 )
=> ! [X1474: $i] :
( ( in @ X1474 @ X1471 )
=> ( in @ ( ap @ X1471 @ X1472 @ X1473 @ X1474 ) @ X1472 ) ) )
=> ( ! [X1475: $i,X1476: $i,X1477: $i] :
( ( in @ X1477 @ ( funcSet @ X1475 @ X1476 ) )
=> ( func @ X1475 @ X1476 @ X1477 ) )
=> ( ! [X1478: $i,X1479: $i,X1480: $i] :
( ( in @ X1480 @ ( funcSet @ X1478 @ X1479 ) )
=> ! [X1481: $i] :
( ( in @ X1481 @ X1478 )
=> ( in @ ( ap @ X1478 @ X1479 @ X1480 @ X1481 ) @ X1479 ) ) )
=> ( ! [X1482: $i,X1483: $i,X1484: $i] :
( ( func @ X1482 @ X1483 @ X1484 )
=> ( in @ X1484 @ ( funcSet @ X1482 @ X1483 ) ) )
=> ( ! [X1485: $i,X1486: $i,X1487: $i > $i] :
( ! [X1488: $i] :
( ( in @ X1488 @ X1485 )
=> ( in @ ( X1487 @ X1488 ) @ X1486 ) )
=> ( func @ X1485 @ X1486
@ ( dpsetconstr @ X1485 @ X1486
@ ^ [Z0: $i] : ( $eq @ ( X1487 @ Z0 ) ) ) ) )
=> ( ! [X1489: $i,X1490: $i,X1491: $i > $i] :
( ! [X1492: $i] :
( ( in @ X1492 @ X1489 )
=> ( in @ ( X1491 @ X1492 ) @ X1490 ) )
=> ( func @ X1489 @ X1490 @ ( lam @ X1489 @ X1490 @ X1491 ) ) )
=> ( ! [X1493: $i,X1494: $i,X1495: $i > $i] :
( ! [X1496: $i] :
( ( in @ X1496 @ X1493 )
=> ( in @ ( X1495 @ X1496 ) @ X1494 ) )
=> ( in @ ( lam @ X1493 @ X1494 @ X1495 ) @ ( funcSet @ X1493 @ X1494 ) ) )
=> ( ! [X1497: $i,X1498: $i,X1499: $i] :
( ( subset @ X1499 @ ( cartprod @ X1497 @ X1498 ) )
=> ! [X1500: $i > $o] :
( ! [X1501: $i] :
( ( in @ X1501 @ X1497 )
=> ! [X1502: $i] :
( ( in @ X1502 @ X1498 )
=> ( ( in @ ( kpair @ X1501 @ X1502 ) @ X1499 )
=> ( X1500 @ ( kpair @ X1501 @ X1502 ) ) ) ) )
=> ! [X1503: $i] :
( ( in @ X1503 @ X1499 )
=> ( X1500 @ X1503 ) ) ) )
=> ( ! [X1504: $i,X1505: $i,X1506: $i] :
( ( subset @ X1506 @ ( cartprod @ X1504 @ X1505 ) )
=> ! [X1507: $i > $o] :
( ! [X1508: $i] :
( ( in @ X1508 @ X1504 )
=> ! [X1509: $i] :
( ( in @ X1509 @ X1505 )
=> ( ( in @ ( kpair @ X1508 @ X1509 ) @ X1506 )
=> ( X1507 @ ( kpair @ X1508 @ X1509 ) ) ) ) )
=> ! [X1510: $i] :
( ( in @ X1510 @ X1506 )
=> ( X1507 @ X1510 ) ) ) )
=> ( ! [X1511: $i,X1512: $i > $o] :
( ( singleton @ ( dsetconstr @ X1511 @ X1512 ) )
=> ! [X1513: $i] :
( ( in @ X1513 @ X1511 )
=> ! [X1514: $i] :
( ( in @ X1514 @ X1511 )
=> ( ( X1512 @ X1513 )
=> ( ( X1512 @ X1514 )
=> ( X1513 = X1514 ) ) ) ) ) )
=> ( ! [X1515: $i,X1516: $i,X1517: $i] :
( ( func @ X1515 @ X1516 @ X1517 )
=> ! [X1518: $i] :
( ( in @ X1518 @ X1515 )
=> ( in @ ( kpair @ X1518 @ ( ap @ X1515 @ X1516 @ X1517 @ X1518 ) ) @ X1517 ) ) )
=> ( ! [X1519: $i,X1520: $i,X1521: $i] :
( ( in @ X1521 @ ( funcSet @ X1519 @ X1520 ) )
=> ! [X1522: $i] :
( ( in @ X1522 @ X1519 )
=> ( in @ ( kpair @ X1522 @ ( ap @ X1519 @ X1520 @ X1521 @ X1522 ) ) @ X1521 ) ) )
=> ( ! [X1523: $i,X1524: $i,X1525: $i] :
( ( func @ X1523 @ X1524 @ X1525 )
=> ! [X1526: $i] :
( ( in @ X1526 @ X1523 )
=> ! [X1527: $i] :
( ( in @ X1527 @ X1524 )
=> ( ( in @ ( kpair @ X1526 @ X1527 ) @ X1525 )
=> ( ( ap @ X1523 @ X1524 @ X1525 @ X1526 )
= X1527 ) ) ) ) )
=> ( ! [X1528: $i,X1529: $i,X1530: $i] :
( ( func @ X1528 @ X1529 @ X1530 )
=> ! [X1531: $i] :
( ( func @ X1528 @ X1529 @ X1531 )
=> ( ! [X1532: $i] :
( ( in @ X1532 @ X1528 )
=> ( ( ap @ X1528 @ X1529 @ X1530 @ X1532 )
= ( ap @ X1528 @ X1529 @ X1531 @ X1532 ) ) )
=> ! [X1533: $i] :
( ( in @ X1533 @ X1528 )
=> ! [X1534: $i] :
( ( in @ X1534 @ X1529 )
=> ( ( in @ ( kpair @ X1533 @ X1534 ) @ X1531 )
=> ( in @ ( kpair @ X1533 @ X1534 ) @ X1530 ) ) ) ) ) ) )
=> ( ! [X1535: $i,X1536: $i,X1537: $i] :
( ( in @ X1537 @ ( funcSet @ X1535 @ X1536 ) )
=> ! [X1538: $i] :
( ( in @ X1538 @ X1535 )
=> ! [X1539: $i] :
( ( in @ X1539 @ X1536 )
=> ( ( in @ ( kpair @ X1538 @ X1539 ) @ X1537 )
=> ( ( ap @ X1535 @ X1536 @ X1537 @ X1538 )
= X1539 ) ) ) ) )
=> ( ! [X1540: $i,X1541: $i,X1542: $i] :
( ( subset @ X1542 @ ( cartprod @ X1540 @ X1541 ) )
=> ! [X1543: $i] :
( ( subset @ X1543 @ ( cartprod @ X1540 @ X1541 ) )
=> ( ! [X1544: $i] :
( ( in @ X1544 @ X1540 )
=> ! [X1545: $i] :
( ( in @ X1545 @ X1541 )
=> ( ( in @ ( kpair @ X1544 @ X1545 ) @ X1542 )
=> ( in @ ( kpair @ X1544 @ X1545 ) @ X1543 ) ) ) )
=> ( subset @ X1542 @ X1543 ) ) ) )
=> ( ! [X1546: $i,X1547: $i,X1548: $i] :
( ( subset @ X1548 @ ( cartprod @ X1546 @ X1547 ) )
=> ! [X1549: $i] :
( ( subset @ X1549 @ ( cartprod @ X1546 @ X1547 ) )
=> ( ! [X1550: $i] :
( ( in @ X1550 @ X1546 )
=> ! [X1551: $i] :
( ( in @ X1551 @ X1547 )
=> ( ( in @ ( kpair @ X1550 @ X1551 ) @ X1548 )
=> ( in @ ( kpair @ X1550 @ X1551 ) @ X1549 ) ) ) )
=> ( ! [X1552: $i] :
( ( in @ X1552 @ X1546 )
=> ! [X1553: $i] :
( ( in @ X1553 @ X1547 )
=> ( ( in @ ( kpair @ X1552 @ X1553 ) @ X1549 )
=> ( in @ ( kpair @ X1552 @ X1553 ) @ X1548 ) ) ) )
=> ( X1548 = X1549 ) ) ) ) )
=> ( ! [X1554: $i,X1555: $i,X1556: $i] :
( ( func @ X1554 @ X1555 @ X1556 )
=> ! [X1557: $i] :
( ( func @ X1554 @ X1555 @ X1557 )
=> ( ! [X1558: $i] :
( ( in @ X1558 @ X1554 )
=> ( ( ap @ X1554 @ X1555 @ X1556 @ X1558 )
= ( ap @ X1554 @ X1555 @ X1557 @ X1558 ) ) )
=> ( X1556 = X1557 ) ) ) )
=> ( ! [X1559: $i,X1560: $i,X1561: $i] :
( ( in @ X1561 @ ( funcSet @ X1559 @ X1560 ) )
=> ! [X1562: $i] :
( ( in @ X1562 @ ( funcSet @ X1559 @ X1560 ) )
=> ( ! [X1563: $i] :
( ( in @ X1563 @ X1559 )
=> ( ( ap @ X1559 @ X1560 @ X1561 @ X1563 )
= ( ap @ X1559 @ X1560 @ X1562 @ X1563 ) ) )
=> ( X1561 = X1562 ) ) ) )
=> ( ! [X1564: $i,X1565: $i,X1566: $i] :
( ( in @ X1566 @ ( funcSet @ X1564 @ X1565 ) )
=> ! [X1567: $i] :
( ( in @ X1567 @ X1564 )
=> ( ( ap @ X1564 @ X1565 @ X1566 @ X1567 )
= ( ap @ X1564 @ X1565 @ X1566 @ X1567 ) ) ) )
=> ( ! [X1568: $i,X1569: $i,X1570: $i] :
( ( func @ X1568 @ X1569 @ X1570 )
=> ! [X1571: $i] :
( ( in @ X1571 @ X1568 )
=> ( ( ap @ X1568 @ X1569 @ X1570 @ X1571 )
= ( ap @ X1568 @ X1569 @ X1570 @ X1571 ) ) ) )
=> ( ! [X1572: $i,X1573: $i,X1574: $i > $i] :
( ! [X1575: $i] :
( ( in @ X1575 @ X1572 )
=> ( in @ ( X1574 @ X1575 ) @ X1573 ) )
=> ! [X1576: $i] :
( ( in @ X1576 @ X1572 )
=> ( ( ap @ X1572 @ X1573 @ ( lam @ X1572 @ X1573 @ X1574 ) @ X1576 )
= ( X1574 @ X1576 ) ) ) )
=> ( ! [X1577: $i,X1578: $i,X1579: $i] :
( ( func @ X1577 @ X1578 @ X1579 )
=> ( ( lam @ X1577 @ X1578 @ ( ap @ X1577 @ X1578 @ X1579 ) )
= X1579 ) )
=> ( ! [X1580: $i,X1581: $i,X1582: $i > $i] :
( ! [X1583: $i] :
( ( in @ X1583 @ X1580 )
=> ( in @ ( X1582 @ X1583 ) @ X1581 ) )
=> ( ( lam @ X1580 @ X1581 @ X1582 )
= ( lam @ X1580 @ X1581 @ X1582 ) ) )
=> ( ! [X1584: $i,X1585: $i,X1586: $i > $i] :
( ! [X1587: $i] :
( ( in @ X1587 @ X1584 )
=> ( in @ ( X1586 @ X1587 ) @ X1585 ) )
=> ! [X1588: $i] :
( ( in @ X1588 @ X1584 )
=> ( ( ap @ X1584 @ X1585 @ ( lam @ X1584 @ X1585 @ X1586 ) @ X1588 )
= ( X1586 @ X1588 ) ) ) )
=> ( ! [X1589: $i,X1590: $i,X1591: $i] :
( ( in @ X1591 @ ( funcSet @ X1589 @ X1590 ) )
=> ( ( lam @ X1589 @ X1590 @ ( ap @ X1589 @ X1590 @ X1591 ) )
= X1591 ) )
=> ( ! [X1592: $i,X1593: $o,X1594: $i] :
( ( in @ X1594 @ X1592 )
=> ! [X1595: $i] :
( ( in @ X1595 @ X1592 )
=> ( ~ X1593
=> ( in @ X1595
@ ( dsetconstr @ X1592
@ ^ [Z0: $i] :
( ( X1593
& ( Z0 = X1594 ) )
| ( ~ X1593
& ( Z0 = X1595 ) ) ) ) ) ) ) )
=> ( ! [X1596: $i,X1597: $o,X1598: $i] :
( ( in @ X1598 @ X1596 )
=> ! [X1599: $i] :
( ( in @ X1599 @ X1596 )
=> ( ~ X1597
=> ( ( dsetconstr @ X1596
@ ^ [Z0: $i] :
( ( X1597
& ( Z0 = X1598 ) )
| ( ~ X1597
& ( Z0 = X1599 ) ) ) )
= ( setadjoin @ X1599 @ emptyset ) ) ) ) )
=> ( ! [X1600: $i,X1601: $o,X1602: $i] :
( ( in @ X1602 @ X1600 )
=> ! [X1603: $i] :
( ( in @ X1603 @ X1600 )
=> ( X1601
=> ( in @ X1602
@ ( 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 @ X1606 @ emptyset ) ) ) ) )
=> ( ! [X1608: $i,X1609: $o,X1610: $i] :
( ( in @ X1610 @ X1608 )
=> ! [X1611: $i] :
( ( in @ X1611 @ X1608 )
=> ( singleton
@ ( dsetconstr @ X1608
@ ^ [Z0: $i] :
( ( X1609
& ( Z0 = X1610 ) )
| ( ~ X1609
& ( Z0 = X1611 ) ) ) ) ) ) )
=> ( ! [X1612: $i,X1613: $o,X1614: $i] :
( ( in @ X1614 @ X1612 )
=> ! [X1615: $i] :
( ( in @ X1615 @ X1612 )
=> ( in @ ( if @ X1612 @ X1613 @ X1614 @ X1615 ) @ X1612 ) ) )
=> ( ! [X1616: $i] :
( ( singleton @ X1616 )
=> ! [X1617: $i] :
( ( in @ X1617 @ X1616 )
=> ( ( setunion @ X1616 )
= X1617 ) ) )
=> ( ! [X1618: $i,X1619: $o,X1620: $i] :
( ( in @ X1620 @ X1618 )
=> ! [X1621: $i] :
( ( in @ X1621 @ X1618 )
=> ( X1619
=> ( ( if @ X1618 @ X1619 @ X1620 @ X1621 )
= X1620 ) ) ) )
=> ( ! [X1622: $i,X1623: $o,X1624: $i] :
( ( in @ X1624 @ X1622 )
=> ! [X1625: $i] :
( ( in @ X1625 @ X1622 )
=> ( ~ X1623
=> ( ( if @ X1622 @ X1623 @ X1624 @ X1625 )
= X1625 ) ) ) )
=> ( ! [X1626: $i,X1627: $o,X1628: $i] :
( ( in @ X1628 @ X1626 )
=> ! [X1629: $i] :
( ( in @ X1629 @ X1626 )
=> ( in @ ( if @ X1626 @ X1627 @ X1628 @ X1629 ) @ ( setadjoin @ X1628 @ ( setadjoin @ X1629 @ emptyset ) ) ) ) )
=> ( ! [X1630: $i,X1631: $i] :
( ( in @ X1631 @ ( powerset @ X1630 ) )
=> ! [X1632: $i] :
( ( in @ X1632 @ ( powerset @ X1630 ) )
=> ( in @ ( binintersect @ X1631 @ X1632 ) @ ( powerset @ X1630 ) ) ) )
=> ( ! [X1633: $i,X1634: $i] :
( ( in @ X1634 @ ( powerset @ X1633 ) )
=> ! [X1635: $i] :
( ( in @ X1635 @ ( powerset @ X1633 ) )
=> ( in @ ( binunion @ X1634 @ X1635 ) @ ( powerset @ X1633 ) ) ) )
=> ( ! [X1636: $i,X1637: $i] :
( ( in @ X1637 @ ( powerset @ X1636 ) )
=> ( in @ ( powerset @ X1637 ) @ ( powerset @ ( powerset @ X1636 ) ) ) )
=> ( ! [X1638: $i,X1639: $i] :
( ( in @ X1639 @ ( powerset @ X1638 ) )
=> ! [X1640: $i] :
( ( in @ X1640 @ ( powerset @ X1638 ) )
=> ( in @ ( setminus @ X1639 @ X1640 ) @ ( powerset @ X1638 ) ) ) )
=> ( ! [X1641: $i,X1642: $i] :
( ( in @ X1642 @ ( powerset @ X1641 ) )
=> ( in @ ( setminus @ X1641 @ X1642 ) @ ( powerset @ X1641 ) ) )
=> ( ! [X1643: $i,X1644: $i] :
( ( in @ X1644 @ ( powerset @ X1643 ) )
=> ! [X1645: $i] :
( ( in @ X1645 @ ( powerset @ X1643 ) )
=> ( ! [X1646: $i] :
( ( in @ X1646 @ X1643 )
=> ( ( in @ X1646 @ X1644 )
=> ( in @ X1646 @ X1645 ) ) )
=> ( ! [X1647: $i] :
( ( in @ X1647 @ X1643 )
=> ( ( in @ X1647 @ X1645 )
=> ( in @ X1647 @ X1644 ) ) )
=> ( X1644 = X1645 ) ) ) ) )
=> ( ! [X1648: $i,X1649: $i] :
( ( in @ X1649 @ ( powerset @ X1648 ) )
=> ! [X1650: $i] :
( ( in @ X1650 @ ( powerset @ X1648 ) )
=> ( ! [X1651: $i] :
( ( in @ X1651 @ X1648 )
=> ( ( in @ X1651 @ X1649 )
=> ( in @ X1651 @ X1650 ) ) )
=> ( subset @ X1649 @ X1650 ) ) ) )
=> ( ! [X1652: $i,X1653: $i] :
( ( in @ X1653 @ ( powerset @ X1652 ) )
=> ! [X1654: $i] :
( ( in @ X1654 @ ( powerset @ X1652 ) )
=> ( ! [X1655: $i] :
( ( in @ X1655 @ X1652 )
=> ( ( in @ X1655 @ X1653 )
=> ( in @ X1655 @ X1654 ) ) )
=> ( in @ X1653 @ ( powerset @ X1654 ) ) ) ) )
=> ( ! [X1656: $i,X1657: $i] :
( ( in @ X1657 @ ( powerset @ X1656 ) )
=> ! [X1658: $i] :
( ( in @ X1658 @ ( powerset @ X1656 ) )
=> ! [X1659: $i] :
( ( in @ X1659 @ X1656 )
=> ( ( in @ X1657 @ ( powerset @ X1658 ) )
=> ( ( in @ X1659 @ X1657 )
=> ( in @ X1659 @ X1658 ) ) ) ) ) )
=> ( ! [X1660: $i,X1661: $i] :
( ( in @ X1661 @ ( powerset @ X1660 ) )
=> ! [X1662: $i] :
( ( in @ X1662 @ X1660 )
=> ( ( in @ X1662 @ X1661 )
=> ~ ( in @ X1662 @ ( setminus @ X1660 @ X1661 ) ) ) ) )
=> ( ! [X1663: $i,X1664: $i] :
( ( in @ X1664 @ ( powerset @ X1663 ) )
=> ! [X1665: $i] :
( ( in @ X1665 @ X1663 )
=> ( ~ ( in @ X1665 @ ( setminus @ X1663 @ X1664 ) )
=> ( in @ X1665 @ X1664 ) ) ) )
=> ( ! [X1666: $i,X1667: $i] :
( ( in @ X1667 @ ( powerset @ X1666 ) )
=> ! [X1668: $i] :
( ( in @ X1668 @ ( powerset @ X1666 ) )
=> ! [X1669: $i] :
( ( in @ X1669 @ X1666 )
=> ( ~ ( in @ X1669 @ X1667 )
=> ~ ( in @ X1669 @ ( binintersect @ X1667 @ X1668 ) ) ) ) ) )
=> ( ! [X1670: $i,X1671: $i] :
( ( in @ X1671 @ ( powerset @ X1670 ) )
=> ! [X1672: $i] :
( ( in @ X1672 @ ( powerset @ X1670 ) )
=> ! [X1673: $i] :
( ( in @ X1673 @ X1670 )
=> ( ~ ( in @ X1673 @ X1672 )
=> ~ ( in @ X1673 @ ( binintersect @ X1671 @ X1672 ) ) ) ) ) )
=> ( ! [X1674: $i,X1675: $i] :
( ( in @ X1675 @ ( powerset @ X1674 ) )
=> ! [X1676: $i] :
( ( in @ X1676 @ ( powerset @ X1674 ) )
=> ! [X1677: $i] :
( ( in @ X1677 @ X1674 )
=> ( ( subset @ X1675 @ ( setminus @ X1674 @ X1676 ) )
=> ( ( in @ X1677 @ X1676 )
=> ~ ( in @ X1677 @ X1675 ) ) ) ) ) )
=> ( ! [X1678: $i,X1679: $i] :
( ( in @ X1679 @ ( powerset @ X1678 ) )
=> ! [X1680: $i] :
( ( in @ X1680 @ ( powerset @ X1678 ) )
=> ! [X1681: $i] :
( ( in @ X1681 @ X1678 )
=> ( ( subset @ X1679 @ X1680 )
=> ( ~ ( in @ X1681 @ X1680 )
=> ~ ( in @ X1681 @ X1679 ) ) ) ) ) )
=> ( ! [X1682: $i,X1683: $i] :
( ( in @ X1683 @ ( powerset @ X1682 ) )
=> ! [X1684: $i] :
( ( in @ X1684 @ ( powerset @ X1682 ) )
=> ( ( subset @ X1683 @ X1684 )
=> ( subset @ ( setminus @ X1682 @ X1684 ) @ ( setminus @ X1682 @ X1683 ) ) ) ) )
=> ( ! [X1685: $i,X1686: $i] :
( ( in @ X1686 @ ( powerset @ X1685 ) )
=> ! [X1687: $i] :
( ( in @ X1687 @ ( powerset @ X1685 ) )
=> ( ( subset @ ( setminus @ X1685 @ X1687 ) @ ( setminus @ X1685 @ X1686 ) )
=> ( subset @ X1686 @ X1687 ) ) ) )
=> ( ! [X1688: $i,X1689: $i] :
( ( in @ X1689 @ ( powerset @ X1688 ) )
=> ! [X1690: $i] :
( ( in @ X1690 @ X1688 )
=> ( ( in @ X1690 @ X1689 )
=> ( in @ X1690 @ ( setminus @ X1688 @ ( setminus @ X1688 @ X1689 ) ) ) ) ) )
=> ( ! [X1691: $i,X1692: $i] :
( ( in @ X1692 @ ( powerset @ X1691 ) )
=> ! [X1693: $i] :
( ( in @ X1693 @ X1691 )
=> ( ( in @ X1693 @ ( setminus @ X1691 @ ( setminus @ X1691 @ X1692 ) ) )
=> ( in @ X1693 @ X1692 ) ) ) )
=> ( ! [X1694: $i,X1695: $i] :
( ( in @ X1695 @ ( powerset @ X1694 ) )
=> ( subset @ X1695 @ ( setminus @ X1694 @ ( setminus @ X1694 @ X1695 ) ) ) )
=> ( ! [X1696: $i,X1697: $i] :
( ( in @ X1697 @ ( powerset @ X1696 ) )
=> ( subset @ ( setminus @ X1696 @ ( setminus @ X1696 @ X1697 ) ) @ X1697 ) )
=> ( ! [X1698: $i,X1699: $i] :
( ( in @ X1699 @ ( powerset @ X1698 ) )
=> ( X1699
= ( setminus @ X1698 @ ( setminus @ X1698 @ X1699 ) ) ) )
=> ( ! [X1700: $i,X1701: $i] :
( ( in @ X1701 @ ( powerset @ X1700 ) )
=> ! [X1702: $i] :
( ( in @ X1702 @ ( powerset @ X1700 ) )
=> ! [X1703: $i] :
( ( in @ X1703 @ X1700 )
=> ( ( in @ X1703 @ ( setminus @ X1700 @ X1701 ) )
=> ~ ( in @ X1703 @ ( binintersect @ X1701 @ X1702 ) ) ) ) ) )
=> ( ! [X1704: $i,X1705: $i] :
( ( in @ X1705 @ ( powerset @ X1704 ) )
=> ! [X1706: $i] :
( ( in @ X1706 @ ( powerset @ X1704 ) )
=> ! [X1707: $i] :
( ( in @ X1707 @ X1704 )
=> ( ( in @ X1707 @ ( setminus @ X1704 @ X1705 ) )
=> ( in @ X1707 @ ( setminus @ X1704 @ ( binintersect @ X1705 @ X1706 ) ) ) ) ) ) )
=> ( ! [X1708: $i,X1709: $i] :
( ( in @ X1709 @ ( powerset @ X1708 ) )
=> ! [X1710: $i] :
( ( in @ X1710 @ ( powerset @ X1708 ) )
=> ( subset @ ( setminus @ X1708 @ X1709 ) @ ( setminus @ X1708 @ ( binintersect @ X1709 @ X1710 ) ) ) ) )
=> ( ! [X1711: $i,X1712: $i] :
( ( in @ X1712 @ ( powerset @ X1711 ) )
=> ! [X1713: $i] :
( ( in @ X1713 @ ( powerset @ X1711 ) )
=> ( in @ ( setminus @ X1711 @ X1712 ) @ ( powerset @ ( setminus @ X1711 @ ( binintersect @ X1712 @ X1713 ) ) ) ) ) )
=> ( ! [X1714: $i,X1715: $i] :
( ( in @ X1715 @ ( powerset @ X1714 ) )
=> ! [X1716: $i] :
( ( in @ X1716 @ ( powerset @ X1714 ) )
=> ( ( subset @ X1715 @ ( setminus @ X1714 @ X1716 ) )
=> ! [X1717: $i] :
( ( in @ X1717 @ X1714 )
=> ( ( in @ X1717 @ X1716 )
=> ( in @ X1717 @ ( setminus @ X1714 @ X1715 ) ) ) ) ) ) )
=> ( ! [X1718: $i,X1719: $i] :
( ( in @ X1719 @ ( powerset @ X1718 ) )
=> ! [X1720: $i] :
( ( in @ X1720 @ ( powerset @ X1718 ) )
=> ( ( subset @ X1719 @ ( setminus @ X1718 @ X1720 ) )
=> ( subset @ X1720 @ ( setminus @ X1718 @ X1719 ) ) ) ) )
=> ( ! [X1721: $i,X1722: $i] :
( ( in @ X1722 @ ( powerset @ X1721 ) )
=> ! [X1723: $i] :
( ( in @ X1723 @ ( powerset @ X1721 ) )
=> ! [X1724: $i] :
( ( in @ X1724 @ X1721 )
=> ( ~ ( in @ X1724 @ ( binunion @ X1722 @ X1723 ) )
=> ~ ( in @ X1724 @ X1722 ) ) ) ) )
=> ( ! [X1725: $i,X1726: $i] :
( ( in @ X1726 @ ( powerset @ X1725 ) )
=> ! [X1727: $i] :
( ( in @ X1727 @ ( powerset @ X1725 ) )
=> ! [X1728: $i] :
( ( in @ X1728 @ X1725 )
=> ( ~ ( in @ X1728 @ ( binunion @ X1726 @ X1727 ) )
=> ~ ( in @ X1728 @ X1727 ) ) ) ) )
=> ( ! [X1729: $i,X1730: $i] :
( ( in @ X1730 @ ( powerset @ X1729 ) )
=> ! [X1731: $i] :
( ( in @ X1731 @ ( powerset @ X1729 ) )
=> ! [X1732: $i] :
( ( in @ X1732 @ ( powerset @ X1729 ) )
=> ! [X1733: $i] :
( ( in @ X1733 @ X1729 )
=> ( ( in @ X1733 @ ( binintersect @ X1730 @ X1731 ) )
=> ( in @ X1733 @ ( binunion @ X1730 @ X1732 ) ) ) ) ) ) )
=> ( ! [X1734: $i,X1735: $i] :
( ( in @ X1735 @ ( powerset @ X1734 ) )
=> ! [X1736: $i] :
( ( in @ X1736 @ ( powerset @ X1734 ) )
=> ! [X1737: $i] :
( ( in @ X1737 @ ( powerset @ X1734 ) )
=> ! [X1738: $i] :
( ( in @ X1738 @ X1734 )
=> ( ( in @ X1738 @ ( binintersect @ X1735 @ X1736 ) )
=> ( in @ X1738 @ ( binunion @ X1736 @ X1737 ) ) ) ) ) ) )
=> ( ! [X1739: $i,X1740: $i] :
( ( in @ X1740 @ ( powerset @ X1739 ) )
=> ! [X1741: $i] :
( ( in @ X1741 @ ( powerset @ X1739 ) )
=> ! [X1742: $i] :
( ( in @ X1742 @ ( powerset @ X1739 ) )
=> ! [X1743: $i] :
( ( in @ X1743 @ X1739 )
=> ( ( in @ X1743 @ ( binintersect @ X1740 @ X1741 ) )
=> ( in @ X1743 @ ( binintersect @ ( binunion @ X1740 @ X1742 ) @ ( binunion @ X1741 @ X1742 ) ) ) ) ) ) ) )
=> ( ! [X1744: $i,X1745: $i] :
( ( in @ X1745 @ ( powerset @ X1744 ) )
=> ! [X1746: $i] :
( ( in @ X1746 @ ( powerset @ X1744 ) )
=> ! [X1747: $i] :
( ( in @ X1747 @ ( powerset @ X1744 ) )
=> ( in @ ( binintersect @ X1745 @ X1746 ) @ ( powerset @ ( binintersect @ ( binunion @ X1745 @ X1747 ) @ ( binunion @ X1746 @ X1747 ) ) ) ) ) ) )
=> ( ! [X1748: $i,X1749: $i] :
( ( in @ X1749 @ ( powerset @ X1748 ) )
=> ! [X1750: $i] :
( ( in @ X1750 @ ( powerset @ X1748 ) )
=> ! [X1751: $i] :
( ( in @ X1751 @ X1748 )
=> ( ( in @ X1751 @ ( setminus @ X1748 @ ( binunion @ X1749 @ X1750 ) ) )
=> ~ ( in @ X1751 @ X1749 ) ) ) ) )
=> ( ! [X1752: $i,X1753: $i] :
( ( in @ X1753 @ ( powerset @ X1752 ) )
=> ! [X1754: $i] :
( ( in @ X1754 @ ( powerset @ X1752 ) )
=> ! [X1755: $i] :
( ( in @ X1755 @ X1752 )
=> ( ( in @ X1755 @ ( setminus @ X1752 @ ( binunion @ X1753 @ X1754 ) ) )
=> ( in @ X1755 @ ( setminus @ X1752 @ X1753 ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binunionTE]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_289]),foundationAx]),wellorderingAx]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),c_0_294]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_295]),setext]),emptyI]),noeltsimpempty]),c_0_296]),c_0_297]),c_0_298]),c_0_299]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_300]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_301]),c_0_302]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_303]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_304]),c_0_305]),c_0_306]),inCongP]),in__Cong]),c_0_307]),c_0_308]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_309]),c_0_310]),c_0_311]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_312]),c_0_313]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_314]),c_0_315]),c_0_316]),c_0_317]),singletonsuniq]),setukpairinjL1]),c_0_318]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_319]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),c_0_324]),c_0_325]),c_0_326]),c_0_327]),c_0_328]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_329]),c_0_330]),c_0_331]),c_0_332]),c_0_333]),c_0_334]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_335]),c_0_336]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_337]),c_0_338]),c_0_339]),c_0_340]),c_0_341]),c_0_342]),c_0_343]),c_0_344]),c_0_345]),c_0_346]),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])])]),c_0_347]) ).
thf(c_0_349,negated_conjecture,
! 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$i,X1991: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2037: $i > $o,X2038: $i,X2039: $i > $o,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $o,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2080: $i,X2081: $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $o,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $i,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i,X2191: $i > $o,X2194: $i,X2195: $i,X2196: $i > $o,X2198: $i,X2199: $i > $o,X2200: $i,X2202: $i,X2203: $i > $o,X2206: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i,X2236: $i,X2237: $i,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i,X2243: $i,X2244: $i,X2245: $i,X2246: $i,X2247: $i,X2248: $i,X2249: $i,X2250: $i,X2251: $i,X2252: $i,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2267: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i,X2272: $i,X2273: $i,X2274: $i,X2275: $i,X2276: $i,X2277: $i,X2278: $i > $i > $o,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i > $i > $o,X2284: $i,X2285: $i,X2286: $i > $i > $o,X2287: $i,X2288: $i,X2289: $i > $i > $o,X2290: $i,X2291: $i,X2292: $i,X2293: $i,X2294: $i > $i > $o,X2295: $i,X2296: $i,X2297: $i,X2298: $i,X2299: $i > $i > $o,X2300: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i > $i > $o,X2305: $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i,X2311: $i,X2312: $i,X2313: $i,X2314: $i,X2315: $i,X2316: $i,X2317: $i,X2318: $i,X2319: $i,X2320: $i,X2321: $i,X2322: $i,X2323: $i,X2324: $i,X2325: $i,X2326: $i,X2327: $i,X2328: $i,X2329: $i,X2330: $i,X2331: $i > $i,X2333: $i,X2334: $i,X2335: $i > $i,X2337: $i,X2338: $i,X2339: $i > $i,X2341: $i,X2342: $i,X2343: $i,X2344: $i > $o,X2347: $i,X2348: $i,X2349: $i,X2350: $i,X2351: $i > $o,X2354: $i,X2355: $i,X2356: $i > $o,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,X2363: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2368: $i,X2369: $i,X2370: $i,X2371: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2381: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2390: $i,X2391: $i,X2392: $i,X2393: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $i,X2412: $i,X2413: $i,X2414: $i,X2415: $i,X2416: $i,X2417: $i,X2418: $i > $i,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i,X2425: $i,X2426: $i > $i,X2428: $i,X2429: $i,X2430: $i > $i,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2436: $i,X2437: $o,X2438: $i,X2439: $i,X2440: $i,X2441: $o,X2442: $i,X2443: $i,X2444: $i,X2445: $o,X2446: $i,X2447: $i,X2448: $i,X2449: $o,X2450: $i,X2451: $i,X2452: $i,X2453: $o,X2454: $i,X2455: $i,X2456: $i,X2457: $o,X2458: $i,X2459: $i,X2460: $i,X2461: $i,X2462: $i,X2463: $o,X2464: $i,X2465: $i,X2466: $i,X2467: $o,X2468: $i,X2469: $i,X2470: $i,X2471: $o,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2492: $i,X2493: $i,X2494: $i,X2496: $i,X2497: $i,X2498: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i,X2517: $i,X2518: $i,X2519: $i,X2520: $i,X2521: $i,X2522: $i,X2523: $i,X2524: $i,X2525: $i,X2526: $i,X2527: $i,X2528: $i,X2529: $i,X2530: $i,X2531: $i,X2532: $i,X2533: $i,X2534: $i,X2535: $i,X2536: $i,X2537: $i,X2538: $i,X2539: $i,X2540: $i,X2541: $i,X2542: $i,X2543: $i,X2544: $i,X2545: $i,X2546: $i,X2547: $i,X2548: $i,X2549: $i,X2550: $i,X2551: $i,X2552: $i,X2553: $i,X2554: $i,X2555: $i,X2556: $i,X2557: $i,X2558: $i,X2559: $i,X2560: $i,X2561: $i,X2562: $i,X2563: $i,X2564: $i,X2565: $i,X2566: $i,X2567: $i,X2568: $i,X2569: $i,X2570: $i,X2571: $i,X2572: $i,X2573: $i,X2574: $i,X2575: $i,X2576: $i,X2577: $i,X2578: $i,X2579: $i,X2580: $i,X2581: $i,X2582: $i,X2583: $i,X2584: $i,X2585: $i,X2586: $i,X2587: $i,X2588: $i,X2589: $i,X2590: $i,X2591: $i,X2592: $i,X2593: $i,X2594: $i,X2595: $i,X2596: $i,X2597: $i,X2598: $i,X2599: $i] :
( ( ~ ( in @ ( esk1_2 @ X1756 @ X1757 ) @ X1756 )
| ~ ( in @ ( esk1_2 @ X1756 @ X1757 ) @ X1757 )
| ( X1756 = X1757 ) )
& ( ( in @ ( esk1_2 @ X1756 @ X1757 ) @ X1756 )
| ( in @ ( esk1_2 @ X1756 @ X1757 ) @ X1757 )
| ( X1756 = X1757 ) )
& ~ ( in @ X1759 @ emptyset )
& ( ~ ( in @ X1762 @ ( setadjoin @ X1760 @ X1761 ) )
| ( X1762 = X1760 )
| ( in @ X1762 @ X1761 ) )
& ( ( X1762 != X1760 )
| ( in @ X1762 @ ( setadjoin @ X1760 @ X1761 ) ) )
& ( ~ ( in @ X1762 @ X1761 )
| ( in @ X1762 @ ( setadjoin @ X1760 @ X1761 ) ) )
& ( ~ ( in @ X1764 @ ( powerset @ X1763 ) )
| ~ ( in @ X1765 @ X1764 )
| ( in @ X1765 @ X1763 ) )
& ( ( in @ ( esk2_2 @ X1766 @ X1767 ) @ X1767 )
| ( in @ X1767 @ ( powerset @ X1766 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1766 @ X1767 ) @ X1766 )
| ( in @ X1767 @ ( powerset @ X1766 ) ) )
& ( ( in @ X1770 @ ( esk3_2 @ X1769 @ X1770 ) )
| ~ ( in @ X1770 @ ( setunion @ X1769 ) ) )
& ( ( in @ ( esk3_2 @ X1769 @ X1770 ) @ X1769 )
| ~ ( in @ X1770 @ ( setunion @ X1769 ) ) )
& ( ~ ( in @ X1773 @ X1774 )
| ~ ( in @ X1774 @ X1772 )
| ( in @ X1773 @ ( setunion @ X1772 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1775 @ omega )
| ( in @ ( setadjoin @ X1775 @ X1775 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1776 ) @ omega )
| ~ ( in @ emptyset @ X1776 )
| ~ ( in @ X1778 @ omega )
| ( in @ X1778 @ X1776 ) )
& ( ( in @ ( esk4_1 @ X1776 ) @ X1776 )
| ~ ( in @ emptyset @ X1776 )
| ~ ( in @ X1778 @ omega )
| ( in @ X1778 @ X1776 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1776 ) @ ( esk4_1 @ X1776 ) ) @ X1776 )
| ~ ( in @ emptyset @ X1776 )
| ~ ( in @ X1778 @ omega )
| ( in @ X1778 @ X1776 ) )
& ( ( in @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1780 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( in @ ( esk5_2 @ X1779 @ X1780 ) @ X1780 ) )
& ( ( X1779 @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1785 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( in @ ( esk5_2 @ X1779 @ X1780 ) @ X1780 ) )
& ( ~ ( in @ X1788 @ X1780 )
| ~ ( X1779 @ X1788 @ X1787 )
| ( in @ X1787 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( in @ ( esk5_2 @ X1779 @ X1780 ) @ X1780 ) )
& ( ( in @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1780 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ( X1779 @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1785 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ~ ( in @ X1788 @ X1780 )
| ~ ( X1779 @ X1788 @ X1787 )
| ( in @ X1787 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ( in @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1780 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1782
!= ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ( X1779 @ ( esk8_3 @ X1779 @ X1780 @ X1785 ) @ X1785 )
| ~ ( in @ X1785 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1782
!= ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ~ ( in @ X1788 @ X1780 )
| ~ ( X1779 @ X1788 @ X1787 )
| ( in @ X1787 @ ( esk7_2 @ X1779 @ X1780 ) )
| ( X1782
!= ( esk6_3 @ X1779 @ X1780 @ X1782 ) )
| ~ ( X1779 @ ( esk5_2 @ X1779 @ X1780 ) @ X1782 ) )
& ( ( in @ ( esk9_1 @ X1789 ) @ X1789 )
| ~ ( in @ X1790 @ X1789 ) )
& ( ~ ( in @ X1792 @ ( esk9_1 @ X1789 ) )
| ~ ( in @ X1792 @ X1789 )
| ~ ( in @ X1790 @ X1789 ) )
& epred1_0
& ( ( X1793 @ ( esk10_2 @ X1793 @ X1794 ) )
| ~ ( X1793 @ X1794 )
| ( X1793 @ ( descr @ X1793 ) ) )
& ( ( X1794
!= ( esk10_2 @ X1793 @ X1794 ) )
| ~ ( X1793 @ X1794 )
| ( X1793 @ ( descr @ X1793 ) ) )
& ( ~ ( in @ X1798 @ X1796 )
| ~ ( X1797 @ X1798 )
| ( in @ X1798 @ ( dsetconstr @ X1796 @ X1797 ) ) )
& ( ~ ( in @ X1801 @ ( dsetconstr @ X1799 @ X1800 ) )
| ( in @ X1801 @ X1799 ) )
& ( ~ ( in @ X1804 @ ( dsetconstr @ X1802 @ X1803 ) )
| ( X1803 @ X1804 ) )
& ( ( X1805 @ ( esk12_1 @ X1805 ) )
| ( X1805 @ ( esk11_2 @ X1805 @ X1806 ) )
| ~ ( X1805 @ X1806 ) )
& ( ~ ( X1805 @ X1809 )
| ( ( esk12_1 @ X1805 )
= X1809 )
| ( X1805 @ ( esk11_2 @ X1805 @ X1806 ) )
| ~ ( X1805 @ X1806 ) )
& ( ( X1805 @ ( esk12_1 @ X1805 ) )
| ( X1806
!= ( esk11_2 @ X1805 @ X1806 ) )
| ~ ( X1805 @ X1806 ) )
& ( ~ ( X1805 @ X1809 )
| ( ( esk12_1 @ X1805 )
= X1809 )
| ( X1806
!= ( esk11_2 @ X1805 @ X1806 ) )
| ~ ( X1805 @ X1806 ) )
& ( ~ ( in @ X1811 @ ( prop2set @ X1810 ) )
| X1810 )
& ( ~ ( in @ X1812 @ emptyset )
| X1813 )
& ( ~ ( in @ X1814 @ emptyset )
| ~ $true )
& ~ ( in @ X1815 @ emptyset )
& ( ( X1816 @ ( esk13_2 @ X1816 @ X1817 ) )
| ~ ( X1816 @ X1817 )
| ( X1816 @ ( esk14_1 @ X1816 ) ) )
& ( ( X1817
!= ( esk13_2 @ X1816 @ X1817 ) )
| ~ ( X1816 @ X1817 )
| ( X1816 @ ( esk14_1 @ X1816 ) ) )
& ( ( in @ ( esk16_2 @ X1820 @ X1821 ) @ X1821 )
| ( X1820 = X1821 )
| ( in @ ( esk15_2 @ X1820 @ X1821 ) @ X1820 ) )
& ( ~ ( in @ ( esk16_2 @ X1820 @ X1821 ) @ X1820 )
| ( X1820 = X1821 )
| ( in @ ( esk15_2 @ X1820 @ X1821 ) @ X1820 ) )
& ( ( in @ ( esk16_2 @ X1820 @ X1821 ) @ X1821 )
| ( X1820 = X1821 )
| ~ ( in @ ( esk15_2 @ X1820 @ X1821 ) @ X1821 ) )
& ( ~ ( in @ ( esk16_2 @ X1820 @ X1821 ) @ X1820 )
| ( X1820 = X1821 )
| ~ ( in @ ( esk15_2 @ X1820 @ X1821 ) @ X1821 ) )
& ( ( in @ ( esk17_1 @ X1824 ) @ X1824 )
| ( X1824 = emptyset ) )
& ( ( in @ ( esk18_1 @ X1826 ) @ X1826 )
| ( X1826 = emptyset ) )
& ( ~ ( in @ X1830 @ ( dsetconstr @ X1828 @ X1829 ) )
| ( X1829 @ X1830 )
| ~ ( in @ X1830 @ X1828 ) )
& ( ~ ( X1829 @ X1830 )
| ( in @ X1830 @ ( dsetconstr @ X1828 @ X1829 ) )
| ~ ( in @ X1830 @ X1828 ) )
& ( ( X1831 = emptyset )
| ( in @ ( esk19_1 @ X1831 ) @ X1831 ) )
& ( ~ ( in @ X1835 @ X1833 )
| ~ ( X1834 @ X1835 )
| ( ( dsetconstr @ X1833 @ X1834 )
!= emptyset ) )
& ( ~ ( in @ X1837 @ X1836 )
| ( X1836 != emptyset ) )
& ( in @ X1838 @ ( setadjoin @ X1838 @ X1839 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1842 @ X1841 )
| ( in @ X1842 @ ( setadjoin @ X1840 @ X1841 ) ) )
& ( ( in @ X1845 @ X1844 )
| X1846
| ( X1845 = X1843 )
| ~ ( in @ X1845 @ ( setadjoin @ X1843 @ X1844 ) ) )
& ( ~ X1846
| X1846
| ( X1845 = X1843 )
| ~ ( in @ X1845 @ ( setadjoin @ X1843 @ X1844 ) ) )
& ( ( in @ X1845 @ X1844 )
| X1846
| ~ X1846
| ~ ( in @ X1845 @ ( setadjoin @ X1843 @ X1844 ) ) )
& ( ~ X1846
| X1846
| ~ X1846
| ~ ( in @ X1845 @ ( setadjoin @ X1843 @ X1844 ) ) )
& ( ~ ( in @ X1849 @ ( setadjoin @ X1847 @ X1848 ) )
| ( X1849 = X1847 )
| ( in @ X1849 @ X1848 ) )
& ( ( dsetconstr @ X1850
@ ^ [Z0: $i] : $true )
= X1850 )
& ( ( in @ ( esk20_2 @ X1851 @ X1852 ) @ X1852 )
| ( in @ X1852 @ ( powerset @ X1851 ) ) )
& ( ~ ( in @ ( esk20_2 @ X1851 @ X1852 ) @ X1851 )
| ( in @ X1852 @ ( powerset @ X1851 ) ) )
& ( in @ emptyset @ ( powerset @ X1854 ) )
& ( in @ emptyset @ ( powerset @ X1855 ) )
& ( ~ ( in @ X1857 @ ( powerset @ X1856 ) )
| ~ ( in @ X1858 @ X1857 )
| ( in @ X1858 @ X1856 ) )
& ( ~ ( in @ X1860 @ X1861 )
| ~ ( in @ X1861 @ X1859 )
| ( in @ X1860 @ ( setunion @ X1859 ) ) )
& ( ( in @ X1863 @ ( esk21_3 @ X1862 @ X1863 @ X1864 ) )
| X1864
| ~ ( in @ X1863 @ ( setunion @ X1862 ) ) )
& ( ( in @ ( esk21_3 @ X1862 @ X1863 @ X1864 ) @ X1862 )
| X1864
| ~ ( in @ X1863 @ ( setunion @ X1862 ) ) )
& ( ~ X1864
| X1864
| ~ ( in @ X1863 @ ( setunion @ X1862 ) ) )
& ( ~ ( in @ X1867 @ X1866 )
| ( in @ X1867 @ ( powerset @ ( setunion @ X1866 ) ) ) )
& ( ~ ( X1868 @ X1872 )
| ( X1872
= ( esk23_1 @ X1868 ) )
| ( X1868 @ ( esk22_2 @ X1868 @ X1869 ) )
| ~ ( X1868 @ X1869 ) )
& ( ( X1873
!= ( esk23_1 @ X1868 ) )
| ( X1868 @ X1873 )
| ( X1868 @ ( esk22_2 @ X1868 @ X1869 ) )
| ~ ( X1868 @ X1869 ) )
& ( ~ ( X1868 @ X1872 )
| ( X1872
= ( esk23_1 @ X1868 ) )
| ( X1869
!= ( esk22_2 @ X1868 @ X1869 ) )
| ~ ( X1868 @ X1869 ) )
& ( ( X1873
!= ( esk23_1 @ X1868 ) )
| ( X1868 @ X1873 )
| ( X1869
!= ( esk22_2 @ X1868 @ X1869 ) )
| ~ ( X1868 @ X1869 ) )
& ( ( in @ ( esk24_1 @ X1874 ) @ X1874 )
| ( X1874 = emptyset ) )
& ( $true
| ( X1874 = emptyset ) )
& ( ~ ( in @ X1876 @ ( setadjoin @ X1877 @ emptyset ) )
| ( X1876 = X1877 ) )
& ( ( X1878 = X1879 )
| ~ ( in @ X1879 @ ( setadjoin @ X1878 @ emptyset ) ) )
& ( ( X1880 != X1881 )
| ( in @ X1880 @ ( setadjoin @ X1881 @ emptyset ) ) )
& ( ~ ( in @ X1882 @ ( setadjoin @ X1883 @ emptyset ) )
| ( in @ X1883 @ ( setadjoin @ X1882 @ emptyset ) ) )
& ( ~ ( in @ X1886 @ ( setadjoin @ X1884 @ ( setadjoin @ X1885 @ emptyset ) ) )
| ( X1886 = X1884 )
| ( X1886 = X1885 ) )
& ( in @ X1887 @ ( setadjoin @ X1887 @ ( setadjoin @ X1888 @ emptyset ) ) )
& ( in @ X1890 @ ( setadjoin @ X1889 @ ( setadjoin @ X1890 @ emptyset ) ) )
& ( ~ ( in @ X1893 @ X1891 )
| ~ ( X1892 @ X1893 )
| ( ( dsetconstr @ X1891 @ X1892 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1895 @ emptyset )
| ( X1894 @ X1895 ) )
& ( ( in @ ( esk25_2 @ X1896 @ X1897 ) @ X1896 )
| ~ ( in @ X1898 @ X1896 )
| ( X1897 @ X1898 ) )
& ( ~ ( X1897 @ ( esk25_2 @ X1896 @ X1897 ) )
| ~ ( in @ X1898 @ X1896 )
| ( X1897 @ X1898 ) )
& ( ( in @ ( esk26_2 @ X1900 @ X1901 ) @ X1900 )
| ~ ( in @ X1903 @ X1900 )
| ~ ( X1901 @ X1903 ) )
& ( ( X1901 @ ( esk26_2 @ X1900 @ X1901 ) )
| ~ ( in @ X1903 @ X1900 )
| ~ ( X1901 @ X1903 ) )
& ( ( in @ ( esk27_2 @ X1904 @ X1905 ) @ X1904 )
| ~ ( in @ X1907 @ X1904 )
| ~ ( X1905 @ X1907 ) )
& ( ( X1905 @ ( esk27_2 @ X1904 @ X1905 ) )
| ~ ( in @ X1907 @ X1904 )
| ~ ( X1905 @ X1907 ) )
& ( ( in @ ( esk28_2 @ X1908 @ X1909 ) @ X1908 )
| ~ ( in @ X1910 @ X1908 )
| ( X1909 @ X1910 ) )
& ( ~ ( X1909 @ ( esk28_2 @ X1908 @ X1909 ) )
| ~ ( in @ X1910 @ X1908 )
| ( X1909 @ X1910 ) )
& ( ~ X1912
| ( in @ emptyset @ ( prop2set @ X1912 ) ) )
& ( ~ X1913
| ( set2prop @ ( prop2set @ X1913 ) ) )
& ( ( in @ ( esk29_2 @ X1914 @ X1915 ) @ X1914 )
| ~ ( in @ X1917 @ X1914 )
| ~ ( X1915 @ X1917 ) )
& ( ( X1915 @ ( esk29_2 @ X1914 @ X1915 ) )
| ~ ( in @ X1917 @ X1914 )
| ~ ( X1915 @ X1917 ) )
& ( ( in @ ( esk30_2 @ X1918 @ X1919 ) @ X1918 )
| ~ ( in @ X1920 @ X1918 )
| ( X1919 @ X1920 ) )
& ( ~ ( X1919 @ ( esk30_2 @ X1918 @ X1919 ) )
| ~ ( in @ X1920 @ X1918 )
| ( X1919 @ X1920 ) )
& ( ( X1922 @ ( esk32_1 @ X1922 ) )
| ( X1922 @ ( esk31_2 @ X1922 @ X1923 ) )
| ~ ( X1922 @ X1923 ) )
& ( ~ ( X1922 @ X1926 )
| ( ( esk32_1 @ X1922 )
= X1926 )
| ( X1922 @ ( esk31_2 @ X1922 @ X1923 ) )
| ~ ( X1922 @ X1923 ) )
& ( ( X1922 @ ( esk32_1 @ X1922 ) )
| ( X1923
!= ( esk31_2 @ X1922 @ X1923 ) )
| ~ ( X1922 @ X1923 ) )
& ( ~ ( X1922 @ X1926 )
| ( ( esk32_1 @ X1922 )
= X1926 )
| ( X1923
!= ( esk31_2 @ X1922 @ X1923 ) )
| ~ ( X1922 @ X1923 ) )
& ( ( X1927 @ ( esk35_1 @ X1927 ) )
| ( X1927 @ ( esk33_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ~ ( X1927 @ X1932 )
| ( ( esk35_1 @ X1927 )
= X1932 )
| ( X1927 @ ( esk33_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ( X1927 @ ( esk35_1 @ X1927 ) )
| ( X1927 @ ( esk34_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ~ ( X1927 @ X1932 )
| ( ( esk35_1 @ X1927 )
= X1932 )
| ( X1927 @ ( esk34_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ( X1927 @ ( esk35_1 @ X1927 ) )
| ( ( esk33_1 @ X1927 )
!= ( esk34_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ~ ( X1927 @ X1932 )
| ( ( esk35_1 @ X1927 )
= X1932 )
| ( ( esk33_1 @ X1927 )
!= ( esk34_1 @ X1927 ) )
| ~ ( X1927 @ X1928 ) )
& ( ( X1933 @ ( esk37_1 @ X1933 ) )
| ~ ( X1933 @ ( esk36_2 @ X1933 @ X1934 ) )
| ( ( esk36_2 @ X1933 @ X1934 )
!= X1934 ) )
& ( ~ ( X1933 @ X1937 )
| ( ( esk37_1 @ X1933 )
= X1937 )
| ~ ( X1933 @ ( esk36_2 @ X1933 @ X1934 ) )
| ( ( esk36_2 @ X1933 @ X1934 )
!= X1934 ) )
& ( ( X1933 @ ( esk37_1 @ X1933 ) )
| ( X1933 @ ( esk36_2 @ X1933 @ X1934 ) )
| ( ( esk36_2 @ X1933 @ X1934 )
= X1934 ) )
& ( ~ ( X1933 @ X1937 )
| ( ( esk37_1 @ X1933 )
= X1937 )
| ( X1933 @ ( esk36_2 @ X1933 @ X1934 ) )
| ( ( esk36_2 @ X1933 @ X1934 )
= X1934 ) )
& ( ( X1938 != X1939 )
| ( X1940 != X1941 )
| ~ ( in @ X1940 @ X1938 )
| ( in @ X1941 @ X1939 ) )
& ( ~ ( in @ X1944 @ X1942 )
| ( in @ X1945 @ X1943 )
| ( X1944 != X1945 )
| ( X1942 != X1943 ) )
& ( ~ ( in @ X1945 @ X1943 )
| ( in @ X1944 @ X1942 )
| ( X1944 != X1945 )
| ( X1942 != X1943 ) )
& ( ( X1946 @ ( esk38_2 @ X1946 @ X1947 ) )
| ~ ( X1946 @ X1947 )
| ~ ( X1946 @ X1949 )
| ~ ( X1946 @ X1950 )
| ( X1949 = X1950 ) )
& ( ( X1947
!= ( esk38_2 @ X1946 @ X1947 ) )
| ~ ( X1946 @ X1947 )
| ~ ( X1946 @ X1949 )
| ~ ( X1946 @ X1950 )
| ( X1949 = X1950 ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( ( esk39_2 @ X1951 @ X1952 )
= ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ~ ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ~ ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1951 @ ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1952 @ ( esk42_2 @ X1951 @ X1952 ) )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1952 @ X1958 )
| ( ( esk42_2 @ X1951 @ X1952 )
= X1958 )
| ( X1955
!= ( esk41_3 @ X1951 @ X1952 @ X1955 ) )
| ~ ( X1951 @ X1955 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1952 @ ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ( X1951 @ ( esk44_2 @ X1951 @ X1952 ) )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( ~ ( X1951 @ X1962 )
| ( ( esk44_2 @ X1951 @ X1952 )
= X1962 )
| ( X1959
!= ( esk43_3 @ X1951 @ X1952 @ X1959 ) )
| ~ ( X1952 @ X1959 )
| ( X1951 @ ( esk39_2 @ X1951 @ X1952 ) )
| ( X1952 @ ( esk40_2 @ X1951 @ X1952 ) ) )
& ( emptyset = emptyset )
& ( ( X1963 != X1964 )
| ( X1965 != X1966 )
| ( ( setadjoin @ X1963 @ X1965 )
= ( setadjoin @ X1964 @ X1966 ) ) )
& ( ( X1967 != X1968 )
| ( ( powerset @ X1967 )
= ( powerset @ X1968 ) ) )
& ( ( X1969 != X1970 )
| ( ( setunion @ X1969 )
= ( setunion @ X1970 ) ) )
& ( omega = omega )
& ( ( X1971 @ ( esk45_2 @ X1971 @ X1972 ) )
| ~ ( X1971 @ X1972 )
| ~ ( X1971 @ X1974 )
| ~ ( X1971 @ X1975 )
| ( X1974 = X1975 ) )
& ( ( X1972
!= ( esk45_2 @ X1971 @ X1972 ) )
| ~ ( X1971 @ X1972 )
| ~ ( X1971 @ X1974 )
| ~ ( X1971 @ X1975 )
| ( X1974 = X1975 ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( ( esk46_2 @ X1976 @ X1977 )
= ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( ( esk46_2 @ X1976 @ X1977 )
= ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( ( esk46_2 @ X1976 @ X1977 )
= ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( ( esk46_2 @ X1976 @ X1977 )
= ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ~ ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ~ ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ~ ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ~ ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ~ ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ~ ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ~ ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ~ ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1976 @ ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1977 @ ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( X1982
!= ( esk49_3 @ X1976 @ X1977 @ X1982 ) )
| ~ ( X1977 @ X1982 )
| ( ( descr @ X1976 )
= ( descr @ X1977 ) )
| ( X1980
!= ( esk48_3 @ X1976 @ X1977 @ X1980 ) )
| ~ ( X1976 @ X1980 )
| ( X1976 @ ( esk46_2 @ X1976 @ X1977 ) )
| ( X1977 @ ( esk47_2 @ X1976 @ X1977 ) ) )
& ( ( in @ ( esk50_4 @ X1984 @ X1985 @ X1986 @ X1987 ) @ X1984 )
| ( ( dsetconstr @ X1984 @ X1986 )
= ( dsetconstr @ X1985 @ X1987 ) )
| ( X1984 != X1985 ) )
& ( ( in @ ( esk51_4 @ X1984 @ X1985 @ X1986 @ X1987 ) @ X1985 )
| ( ( dsetconstr @ X1984 @ X1986 )
= ( dsetconstr @ X1985 @ X1987 ) )
| ( X1984 != X1985 ) )
& ( ( ( esk50_4 @ X1984 @ X1985 @ X1986 @ X1987 )
= ( esk51_4 @ X1984 @ X1985 @ X1986 @ X1987 ) )
| ( ( dsetconstr @ X1984 @ X1986 )
= ( dsetconstr @ X1985 @ X1987 ) )
| ( X1984 != X1985 ) )
& ( ~ ( X1986 @ ( esk50_4 @ X1984 @ X1985 @ X1986 @ X1987 ) )
| ~ ( X1987 @ ( esk51_4 @ X1984 @ X1985 @ X1986 @ X1987 ) )
| ( ( dsetconstr @ X1984 @ X1986 )
= ( dsetconstr @ X1985 @ X1987 ) )
| ( X1984 != X1985 ) )
& ( ( X1986 @ ( esk50_4 @ X1984 @ X1985 @ X1986 @ X1987 ) )
| ( X1987 @ ( esk51_4 @ X1984 @ X1985 @ X1986 @ X1987 ) )
| ( ( dsetconstr @ X1984 @ X1986 )
= ( dsetconstr @ X1985 @ X1987 ) )
| ( X1984 != X1985 ) )
& ( ( in @ ( esk52_2 @ X1990 @ X1991 ) @ X1990 )
| ( subset @ X1990 @ X1991 ) )
& ( ~ ( in @ ( esk52_2 @ X1990 @ X1991 ) @ X1991 )
| ( subset @ X1990 @ X1991 ) )
& ( ( X1993 != X1994 )
| ( subset @ X1994 @ X1993 ) )
& ( ( X1995 != X1996 )
| ( subset @ X1995 @ X1996 ) )
& ( ( in @ ( esk53_2 @ X1997 @ X1998 ) @ X1997 )
| ( subset @ X1997 @ X1998 ) )
& ( ~ ( in @ ( esk53_2 @ X1997 @ X1998 ) @ X1998 )
| ( subset @ X1997 @ X1998 ) )
& ( subset @ emptyset @ X2000 )
& ( ~ ( subset @ X2001 @ X2002 )
| ~ ( in @ X2003 @ X2001 )
| ( in @ X2003 @ X2002 ) )
& ( ~ ( subset @ X2004 @ X2005 )
| ( in @ X2006 @ X2005 )
| ~ ( in @ X2006 @ X2004 ) )
& ( ~ ( in @ X2009 @ X2007 )
| ( in @ X2009 @ X2008 )
| ~ ( subset @ X2007 @ X2008 ) )
& ( ( subset @ X2010 @ X2011 )
| ( X2010 != X2011 ) )
& ( ~ ( in @ X2014 @ X2012 )
| ( in @ X2014 @ X2013 )
| ( X2012 != X2013 ) )
& ( subset @ X2015 @ X2015 )
& ( ~ ( subset @ X2016 @ X2017 )
| ~ ( subset @ X2017 @ X2018 )
| ( subset @ X2016 @ X2018 ) )
& ( subset @ X2020 @ ( setadjoin @ X2019 @ X2020 ) )
& ( ~ ( subset @ X2021 @ X2023 )
| ( subset @ X2021 @ ( setadjoin @ X2022 @ X2023 ) ) )
& ( ~ ( subset @ X2024 @ X2025 )
| ( in @ X2024 @ ( powerset @ X2025 ) ) )
& ( ~ ( subset @ X2026 @ X2027 )
| ~ ( subset @ X2027 @ X2026 )
| ( X2026 = X2027 ) )
& ( ~ ( subset @ X2028 @ emptyset )
| ( X2028 = emptyset ) )
& ( ~ ( subset @ X2030 @ X2029 )
| ( in @ X2030 @ ( powerset @ X2029 ) ) )
& ( ~ ( in @ X2032 @ ( powerset @ X2031 ) )
| ( subset @ X2032 @ X2031 ) )
& ( in @ X2033 @ ( powerset @ X2033 ) )
& ( ~ ( subset @ X2034 @ X2035 )
| ( subset @ ( powerset @ X2034 ) @ ( powerset @ X2035 ) ) )
& ( in @ ( dsetconstr @ X2036 @ X2037 ) @ ( powerset @ X2036 ) )
& ( subset @ ( dsetconstr @ X2038 @ X2039 ) @ X2038 )
& ( ~ ( in @ X2042 @ X2040 )
| ( in @ X2042 @ ( binunion @ X2040 @ X2041 ) ) )
& ( in @ X2044 @ ( setadjoin @ X2043 @ ( setadjoin @ X2044 @ emptyset ) ) )
& ( ~ ( in @ X2047 @ X2046 )
| ( in @ X2047 @ ( binunion @ X2045 @ X2046 ) ) )
& ( ( in @ X2050 @ X2049 )
| X2051
| ( in @ X2050 @ X2048 )
| ~ ( in @ X2050 @ ( binunion @ X2048 @ X2049 ) ) )
& ( ~ X2051
| X2051
| ( in @ X2050 @ X2048 )
| ~ ( in @ X2050 @ ( binunion @ X2048 @ X2049 ) ) )
& ( ( in @ X2050 @ X2049 )
| X2051
| ~ X2051
| ~ ( in @ X2050 @ ( binunion @ X2048 @ X2049 ) ) )
& ( ~ X2051
| X2051
| ~ X2051
| ~ ( in @ X2050 @ ( binunion @ X2048 @ X2049 ) ) )
& ( ~ ( in @ X2054 @ ( binunion @ X2052 @ X2053 ) )
| ( in @ X2054 @ X2052 )
| ( in @ X2054 @ X2053 ) )
& ( subset @ X2055 @ ( binunion @ X2055 @ X2056 ) )
& ( subset @ X2058 @ ( binunion @ X2057 @ X2058 ) )
& ( ~ ( in @ X2061 @ X2059 )
| ~ ( in @ X2061 @ X2060 )
| ( in @ X2061 @ ( binintersect @ X2059 @ X2060 ) ) )
& ( ~ ( subset @ X2064 @ X2062 )
| ~ ( subset @ X2064 @ X2063 )
| ( subset @ X2064 @ ( binintersect @ X2062 @ X2063 ) ) )
& ( ~ ( in @ X2067 @ ( binintersect @ X2065 @ X2066 ) )
| ( in @ X2067 @ X2065 ) )
& ( subset @ ( binintersect @ X2068 @ X2069 ) @ X2068 )
& ( ~ ( subset @ X2070 @ X2071 )
| ( ( binintersect @ X2070 @ X2071 )
= X2070 ) )
& ( ( ( binintersect @ X2072 @ X2073 )
!= X2073 )
| ( subset @ X2073 @ X2072 ) )
& ( ~ ( in @ X2076 @ ( binintersect @ X2074 @ X2075 ) )
| ( in @ X2076 @ X2075 ) )
& ( ( in @ ( esk54_2 @ X2077 @ X2078 ) @ X2077 )
| ( ( binintersect @ X2077 @ X2078 )
= emptyset ) )
& ( ( in @ ( esk54_2 @ X2077 @ X2078 ) @ X2078 )
| ( ( binintersect @ X2077 @ X2078 )
= emptyset ) )
& ( subset @ ( binintersect @ X2080 @ X2081 ) @ X2081 )
& ( ~ ( subset @ X2083 @ X2082 )
| ( ( binintersect @ X2082 @ X2083 )
= X2083 ) )
& ( ( ( binintersect @ X2084 @ X2085 )
!= X2084 )
| ( subset @ X2084 @ X2085 ) )
& ( ( binintersect @ X2086 @ ( binunion @ X2087 @ X2088 ) )
= ( binunion @ ( binintersect @ X2086 @ X2087 ) @ ( binintersect @ X2086 @ X2088 ) ) )
& ( ~ ( in @ X2091 @ X2089 )
| ( in @ X2091 @ X2090 )
| ( in @ X2091 @ ( setminus @ X2089 @ X2090 ) ) )
& ( ~ ( in @ X2094 @ ( setminus @ X2092 @ X2093 ) )
| ( in @ X2094 @ X2092 ) )
& ( ~ ( in @ X2097 @ ( setminus @ X2095 @ X2096 ) )
| ~ ( in @ X2097 @ X2096 ) )
& ( ~ ( subset @ X2098 @ X2099 )
| ( ( setminus @ X2098 @ X2099 )
= emptyset ) )
& ( ( in @ X2102 @ ( setminus @ X2100 @ X2101 ) )
| ~ ( in @ X2102 @ X2100 )
| ( in @ X2102 @ X2101 ) )
& ( ( in @ X2105 @ ( setminus @ X2103 @ X2104 ) )
| ( in @ X2105 @ X2104 )
| ~ ( in @ X2105 @ X2103 ) )
& ( ( in @ X2108 @ X2106 )
| ~ ( in @ X2108 @ ( setminus @ X2106 @ X2107 ) ) )
& ( ~ ( in @ X2111 @ X2110 )
| ~ ( in @ X2111 @ ( setminus @ X2109 @ X2110 ) ) )
& ( subset @ ( setminus @ X2112 @ X2113 ) @ X2112 )
& ( ( ( setminus @ X2114 @ X2115 )
!= emptyset )
| ( subset @ X2114 @ X2115 ) )
& ( ~ ( in @ X2118 @ X2116 )
| X2119
| ( in @ X2118 @ X2116 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ( in @ X2118 @ X2117 )
| X2119
| ( in @ X2118 @ X2116 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ X2119
| X2119
| ( in @ X2118 @ X2116 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ ( in @ X2118 @ X2116 )
| X2119
| ~ ( in @ X2118 @ X2117 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ( in @ X2118 @ X2117 )
| X2119
| ~ ( in @ X2118 @ X2117 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ X2119
| X2119
| ~ ( in @ X2118 @ X2117 )
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ ( in @ X2118 @ X2116 )
| X2119
| ~ X2119
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ( in @ X2118 @ X2117 )
| X2119
| ~ X2119
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ X2119
| X2119
| ~ X2119
| ~ ( in @ X2118 @ ( symdiff @ X2116 @ X2117 ) ) )
& ( ~ ( in @ X2122 @ X2120 )
| ( in @ X2122 @ X2121 )
| ( in @ X2122 @ ( symdiff @ X2120 @ X2121 ) ) )
& ( ( in @ X2125 @ X2123 )
| ~ ( in @ X2125 @ X2124 )
| ( in @ X2125 @ ( symdiff @ X2123 @ X2124 ) ) )
& ( ~ ( in @ X2128 @ X2126 )
| ~ ( in @ X2128 @ X2127 )
| ~ ( in @ X2128 @ ( symdiff @ X2126 @ X2127 ) ) )
& ( ( in @ X2131 @ X2129 )
| ( in @ X2131 @ X2130 )
| ~ ( in @ X2131 @ ( symdiff @ X2129 @ X2130 ) ) )
& ( in @ X2133 @ ( setadjoin @ X2132 @ ( setadjoin @ X2133 @ emptyset ) ) )
& ( in @ X2134 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2134 @ ( setadjoin @ X2135 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X2137 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2136 @ ( setadjoin @ X2137 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X2138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2138 @ ( setadjoin @ X2139 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X2140 @ X2141 ) )
& ( ~ ( in @ X2143 @ X2142 )
| ( subset @ ( setadjoin @ X2143 @ emptyset ) @ X2142 ) )
& ( ~ ( in @ X2145 @ X2144 )
| ( in @ ( setadjoin @ X2145 @ emptyset ) @ ( powerset @ X2144 ) ) )
& ( ~ ( in @ X2148 @ X2146 )
| ( in @ ( setadjoin @ X2148 @ emptyset ) @ ( powerset @ ( binunion @ X2146 @ X2147 ) ) ) )
& ( ~ ( in @ X2151 @ ( setadjoin @ X2149 @ ( setadjoin @ X2150 @ emptyset ) ) )
| ( X2151 = X2149 )
| ( X2151 = X2150 ) )
& ( ~ ( in @ X2154 @ X2152 )
| ~ ( in @ X2155 @ X2153 )
| ( subset @ ( setadjoin @ X2154 @ ( setadjoin @ X2155 @ emptyset ) ) @ ( binunion @ X2152 @ X2153 ) ) )
& ( ~ ( in @ X2158 @ X2156 )
| ~ ( in @ X2159 @ X2157 )
| ( in @ ( setadjoin @ X2158 @ ( setadjoin @ X2159 @ emptyset ) ) @ ( powerset @ ( binunion @ X2156 @ X2157 ) ) ) )
& ( ~ ( in @ X2162 @ X2160 )
| ~ ( in @ X2163 @ X2161 )
| ( subset @ ( setadjoin @ ( setadjoin @ X2162 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2162 @ ( setadjoin @ X2163 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2160 @ X2161 ) ) ) )
& ( ~ ( in @ X2166 @ X2164 )
| ~ ( in @ X2167 @ X2165 )
| ( in @ ( setadjoin @ ( setadjoin @ X2166 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2166 @ ( setadjoin @ X2167 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2164 @ X2165 ) ) ) ) )
& ( ~ ( in @ X2170 @ X2168 )
| ~ ( in @ X2171 @ X2169 )
| ( in @ ( kpair @ X2170 @ X2171 ) @ ( powerset @ ( powerset @ ( binunion @ X2168 @ X2169 ) ) ) ) )
& ( ~ ( in @ X2174 @ X2172 )
| ~ ( in @ X2175 @ X2173 )
| ( in @ ( kpair @ X2174 @ X2175 ) @ ( cartprod @ X2172 @ X2173 ) ) )
& ( ( in @ ( esk55_3 @ X2176 @ X2177 @ X2178 ) @ X2176 )
| ~ ( in @ X2178 @ ( cartprod @ X2176 @ X2177 ) ) )
& ( ( in @ ( esk56_3 @ X2176 @ X2177 @ X2178 ) @ X2177 )
| ~ ( in @ X2178 @ ( cartprod @ X2176 @ X2177 ) ) )
& ( ( X2178
= ( kpair @ ( esk55_3 @ X2176 @ X2177 @ X2178 ) @ ( esk56_3 @ X2176 @ X2177 @ X2178 ) ) )
| ~ ( in @ X2178 @ ( cartprod @ X2176 @ X2177 ) ) )
& ( ~ ( in @ X2183 @ ( cartprod @ X2181 @ X2182 ) )
| ( iskpair @ X2183 ) )
& ( ( in @ ( esk57_2 @ X2184 @ X2185 ) @ X2184 )
| ~ ( in @ X2185 @ ( setunion @ X2184 ) ) )
& ( ( in @ X2185 @ ( esk57_2 @ X2184 @ X2185 ) )
| ~ ( in @ X2185 @ ( setunion @ X2184 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X2187 @ emptyset ) ) @ X2187 )
& ( subset @ X2188 @ ( setunion @ ( setadjoin @ X2188 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X2189 @ emptyset ) )
= X2189 )
& ( ( in @ ( esk58_2 @ X2190 @ X2191 ) @ X2190 )
| ~ ( in @ X2194 @ X2190 )
| ~ ( X2191 @ X2194 )
| ( singleton @ ( dsetconstr @ X2190 @ X2191 ) ) )
& ( ( in @ ( esk59_2 @ X2190 @ X2191 ) @ X2190 )
| ~ ( in @ X2194 @ X2190 )
| ~ ( X2191 @ X2194 )
| ( singleton @ ( dsetconstr @ X2190 @ X2191 ) ) )
& ( ( X2191 @ ( esk58_2 @ X2190 @ X2191 ) )
| ~ ( in @ X2194 @ X2190 )
| ~ ( X2191 @ X2194 )
| ( singleton @ ( dsetconstr @ X2190 @ X2191 ) ) )
& ( ( X2191 @ ( esk59_2 @ X2190 @ X2191 ) )
| ~ ( in @ X2194 @ X2190 )
| ~ ( X2191 @ X2194 )
| ( singleton @ ( dsetconstr @ X2190 @ X2191 ) ) )
& ( ( ( esk58_2 @ X2190 @ X2191 )
!= ( esk59_2 @ X2190 @ X2191 ) )
| ~ ( in @ X2194 @ X2190 )
| ~ ( X2191 @ X2194 )
| ( singleton @ ( dsetconstr @ X2190 @ X2191 ) ) )
& ( ( in @ ( esk60_2 @ X2195 @ X2196 ) @ X2195 )
| ~ ( singleton @ ( dsetconstr @ X2195 @ X2196 ) ) )
& ( ( X2196 @ ( esk60_2 @ X2195 @ X2196 ) )
| ~ ( singleton @ ( dsetconstr @ X2195 @ X2196 ) ) )
& ( ( in @ ( esk61_3 @ X2198 @ X2199 @ X2200 ) @ X2198 )
| ( singleton @ ( dsetconstr @ X2198 @ X2199 ) )
| ~ ( X2199 @ X2200 )
| ~ ( in @ X2200 @ X2198 ) )
& ( ( X2199 @ ( esk61_3 @ X2198 @ X2199 @ X2200 ) )
| ( singleton @ ( dsetconstr @ X2198 @ X2199 ) )
| ~ ( X2199 @ X2200 )
| ~ ( in @ X2200 @ X2198 ) )
& ( ( ( esk61_3 @ X2198 @ X2199 @ X2200 )
!= X2200 )
| ( singleton @ ( dsetconstr @ X2198 @ X2199 ) )
| ~ ( X2199 @ X2200 )
| ~ ( in @ X2200 @ X2198 ) )
& ( ( in @ ( esk62_2 @ X2202 @ X2203 ) @ X2202 )
| ~ ( in @ X2206 @ X2202 )
| ~ ( X2203 @ X2206 )
| ( singleton @ ( dsetconstr @ X2202 @ X2203 ) ) )
& ( ( in @ ( esk63_2 @ X2202 @ X2203 ) @ X2202 )
| ~ ( in @ X2206 @ X2202 )
| ~ ( X2203 @ X2206 )
| ( singleton @ ( dsetconstr @ X2202 @ X2203 ) ) )
& ( ( X2203 @ ( esk62_2 @ X2202 @ X2203 ) )
| ~ ( in @ X2206 @ X2202 )
| ~ ( X2203 @ X2206 )
| ( singleton @ ( dsetconstr @ X2202 @ X2203 ) ) )
& ( ( X2203 @ ( esk63_2 @ X2202 @ X2203 ) )
| ~ ( in @ X2206 @ X2202 )
| ~ ( X2203 @ X2206 )
| ( singleton @ ( dsetconstr @ X2202 @ X2203 ) ) )
& ( ( ( esk62_2 @ X2202 @ X2203 )
!= ( esk63_2 @ X2202 @ X2203 ) )
| ~ ( in @ X2206 @ X2202 )
| ~ ( X2203 @ X2206 )
| ( singleton @ ( dsetconstr @ X2202 @ X2203 ) ) )
& ( ( ( setadjoin @ X2207 @ emptyset )
!= ( setadjoin @ X2208 @ emptyset ) )
| ( X2207 = X2208 ) )
& ( ~ ( in @ ( setadjoin @ X2211 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2209 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2209 @ ( setadjoin @ X2210 @ emptyset ) ) @ emptyset ) ) )
| ( X2209 = X2211 ) )
& ( ~ ( iskpair @ X2212 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2212 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2212 ) ) ) )
& ( ~ ( singleton @ X2213 )
| ( in @ ( setunion @ X2213 ) @ X2213 ) )
& ( ( kfst @ ( kpair @ X2214 @ X2215 ) )
= X2214 )
& ( ~ ( in @ X2218 @ ( cartprod @ X2216 @ X2217 ) )
| ( in @ ( kfst @ X2218 ) @ X2216 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2219 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2219 @ ( setadjoin @ X2220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2221 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2221 @ ( setadjoin @ X2222 @ emptyset ) ) @ emptyset ) ) )
| ( X2219 = X2221 ) )
& ( ( ( kpair @ X2223 @ X2224 )
!= ( kpair @ X2225 @ X2226 ) )
| ( X2223 = X2225 ) )
& ( ( X2227 != X2228 )
| ( ( setadjoin @ X2227 @ ( setadjoin @ X2228 @ emptyset ) )
= ( setadjoin @ X2227 @ emptyset ) ) )
& ( ( X2229 != X2230 )
| ( ( setadjoin @ ( setadjoin @ X2229 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2229 @ ( setadjoin @ X2230 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2229 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X2231 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2231 @ ( setadjoin @ X2232 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2233 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2233 @ ( setadjoin @ X2234 @ emptyset ) ) @ emptyset ) ) )
| ( X2233 != X2234 )
| ( X2232 = X2234 ) )
& ( ( ( setadjoin @ X2235 @ ( setadjoin @ X2236 @ emptyset ) )
!= ( setadjoin @ X2237 @ emptyset ) )
| ( X2235 = X2236 ) )
& ( ( ( setadjoin @ ( setadjoin @ X2238 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2238 @ ( setadjoin @ X2239 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2240 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2240 @ ( setadjoin @ X2241 @ emptyset ) ) @ emptyset ) ) )
| ( X2239 = X2241 ) )
& ( ( ( kpair @ X2242 @ X2243 )
!= ( kpair @ X2244 @ X2245 ) )
| ( X2243 = X2245 ) )
& ( ~ ( iskpair @ X2246 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X2246 )
@ ^ [Z0: $i] :
( X2246
= ( kpair @ ( kfst @ X2246 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X2247 @ X2248 ) )
= X2248 )
& ( ~ ( iskpair @ X2249 )
| ( ( kpair @ ( kfst @ X2249 ) @ ( ksnd @ X2249 ) )
= X2249 ) )
& ( ~ ( in @ X2252 @ ( cartprod @ X2250 @ X2251 ) )
| ( in @ ( ksnd @ X2252 ) @ X2251 ) )
& ( ~ ( in @ ( kpair @ X2255 @ X2256 ) @ ( cartprod @ X2253 @ X2254 ) )
| ( in @ X2255 @ X2253 ) )
& ( ~ ( in @ ( kpair @ X2259 @ X2260 ) @ ( cartprod @ X2257 @ X2258 ) )
| ( in @ X2260 @ X2258 ) )
& ( ~ ( in @ X2263 @ X2261 )
| ~ ( in @ X2264 @ X2262 )
| ( ( kpair @ X2263 @ X2264 )
= ( kpair @ X2263 @ X2264 ) ) )
& ( ~ ( in @ X2267 @ X2265 )
| ~ ( in @ X2268 @ X2266 )
| ( ( kfst @ ( kpair @ X2267 @ X2268 ) )
= X2267 ) )
& ( ~ ( in @ X2271 @ X2269 )
| ~ ( in @ X2272 @ X2270 )
| ( ( ksnd @ ( kpair @ X2271 @ X2272 ) )
= X2272 ) )
& ( ~ ( in @ X2275 @ ( cartprod @ X2273 @ X2274 ) )
| ( ( kpair @ ( kfst @ X2275 ) @ ( ksnd @ X2275 ) )
= X2275 ) )
& ( ~ ( in @ X2279 @ X2276 )
| ~ ( in @ X2280 @ X2277 )
| ~ ( X2278 @ X2279 @ X2280 )
| ( in @ ( kpair @ X2279 @ X2280 ) @ ( dpsetconstr @ X2276 @ X2277 @ X2278 ) ) )
& ( subset @ ( dpsetconstr @ X2281 @ X2282 @ X2283 ) @ ( cartprod @ X2281 @ X2282 ) )
& ( subset @ ( dpsetconstr @ X2284 @ X2285 @ X2286 ) @ ( cartprod @ X2284 @ X2285 ) )
& ( ~ ( in @ X2290 @ X2287 )
| ~ ( in @ X2291 @ X2288 )
| ~ ( in @ ( kpair @ X2290 @ X2291 ) @ ( dpsetconstr @ X2287 @ X2288 @ X2289 ) )
| ( X2289 @ X2290 @ X2291 ) )
& ( ~ ( in @ ( kpair @ X2295 @ X2296 ) @ ( dpsetconstr @ X2292 @ X2293 @ X2294 ) )
| ( in @ X2295 @ X2292 ) )
& ( ~ ( in @ ( kpair @ X2300 @ X2301 ) @ ( dpsetconstr @ X2297 @ X2298 @ X2299 ) )
| ( in @ X2301 @ X2298 ) )
& ( ~ ( in @ ( kpair @ X2305 @ X2306 ) @ ( dpsetconstr @ X2302 @ X2303 @ X2304 ) )
| ( X2304 @ X2305 @ X2306 ) )
& ( ~ ( func @ X2307 @ X2308 @ X2309 )
| ~ ( in @ X2310 @ X2307 )
| ( singleton
@ ( dsetconstr @ X2308
@ ^ [Z0: $i] : ( in @ ( kpair @ X2310 @ Z0 ) @ X2309 ) ) ) )
& ( ~ ( func @ X2311 @ X2312 @ X2313 )
| ~ ( in @ X2314 @ X2311 )
| ( in
@ ( setunion
@ ( dsetconstr @ X2312
@ ^ [Z0: $i] : ( in @ ( kpair @ X2314 @ Z0 ) @ X2313 ) ) )
@ X2312 ) )
& ( ~ ( func @ X2315 @ X2316 @ X2317 )
| ~ ( in @ X2318 @ X2315 )
| ( in @ ( ap @ X2315 @ X2316 @ X2317 @ X2318 ) @ X2316 ) )
& ( ~ ( in @ X2321 @ ( funcSet @ X2319 @ X2320 ) )
| ( func @ X2319 @ X2320 @ X2321 ) )
& ( ~ ( in @ X2324 @ ( funcSet @ X2322 @ X2323 ) )
| ~ ( in @ X2325 @ X2322 )
| ( in @ ( ap @ X2322 @ X2323 @ X2324 @ X2325 ) @ X2323 ) )
& ( ~ ( func @ X2326 @ X2327 @ X2328 )
| ( in @ X2328 @ ( funcSet @ X2326 @ X2327 ) ) )
& ( ( in @ ( esk64_3 @ X2329 @ X2330 @ X2331 ) @ X2329 )
| ( func @ X2329 @ X2330
@ ( dpsetconstr @ X2329 @ X2330
@ ^ [Z0: $i] : ( $eq @ ( X2331 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2331 @ ( esk64_3 @ X2329 @ X2330 @ X2331 ) ) @ X2330 )
| ( func @ X2329 @ X2330
@ ( dpsetconstr @ X2329 @ X2330
@ ^ [Z0: $i] : ( $eq @ ( X2331 @ Z0 ) ) ) ) )
& ( ( in @ ( esk65_3 @ X2333 @ X2334 @ X2335 ) @ X2333 )
| ( func @ X2333 @ X2334 @ ( lam @ X2333 @ X2334 @ X2335 ) ) )
& ( ~ ( in @ ( X2335 @ ( esk65_3 @ X2333 @ X2334 @ X2335 ) ) @ X2334 )
| ( func @ X2333 @ X2334 @ ( lam @ X2333 @ X2334 @ X2335 ) ) )
& ( ( in @ ( esk66_3 @ X2337 @ X2338 @ X2339 ) @ X2337 )
| ( in @ ( lam @ X2337 @ X2338 @ X2339 ) @ ( funcSet @ X2337 @ X2338 ) ) )
& ( ~ ( in @ ( X2339 @ ( esk66_3 @ X2337 @ X2338 @ X2339 ) ) @ X2338 )
| ( in @ ( lam @ X2337 @ X2338 @ X2339 ) @ ( funcSet @ X2337 @ X2338 ) ) )
& ( ( in @ ( esk67_4 @ X2341 @ X2342 @ X2343 @ X2344 ) @ X2341 )
| ~ ( in @ X2347 @ X2343 )
| ( X2344 @ X2347 )
| ~ ( subset @ X2343 @ ( cartprod @ X2341 @ X2342 ) ) )
& ( ( in @ ( esk68_4 @ X2341 @ X2342 @ X2343 @ X2344 ) @ X2342 )
| ~ ( in @ X2347 @ X2343 )
| ( X2344 @ X2347 )
| ~ ( subset @ X2343 @ ( cartprod @ X2341 @ X2342 ) ) )
& ( ( in @ ( kpair @ ( esk67_4 @ X2341 @ X2342 @ X2343 @ X2344 ) @ ( esk68_4 @ X2341 @ X2342 @ X2343 @ X2344 ) ) @ X2343 )
| ~ ( in @ X2347 @ X2343 )
| ( X2344 @ X2347 )
| ~ ( subset @ X2343 @ ( cartprod @ X2341 @ X2342 ) ) )
& ( ~ ( X2344 @ ( kpair @ ( esk67_4 @ X2341 @ X2342 @ X2343 @ X2344 ) @ ( esk68_4 @ X2341 @ X2342 @ X2343 @ X2344 ) ) )
| ~ ( in @ X2347 @ X2343 )
| ( X2344 @ X2347 )
| ~ ( subset @ X2343 @ ( cartprod @ X2341 @ X2342 ) ) )
& ( ( in @ ( esk69_4 @ X2348 @ X2349 @ X2350 @ X2351 ) @ X2348 )
| ~ ( in @ X2354 @ X2350 )
| ( X2351 @ X2354 )
| ~ ( subset @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ( in @ ( esk70_4 @ X2348 @ X2349 @ X2350 @ X2351 ) @ X2349 )
| ~ ( in @ X2354 @ X2350 )
| ( X2351 @ X2354 )
| ~ ( subset @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ( in @ ( kpair @ ( esk69_4 @ X2348 @ X2349 @ X2350 @ X2351 ) @ ( esk70_4 @ X2348 @ X2349 @ X2350 @ X2351 ) ) @ X2350 )
| ~ ( in @ X2354 @ X2350 )
| ( X2351 @ X2354 )
| ~ ( subset @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ~ ( X2351 @ ( kpair @ ( esk69_4 @ X2348 @ X2349 @ X2350 @ X2351 ) @ ( esk70_4 @ X2348 @ X2349 @ X2350 @ X2351 ) ) )
| ~ ( in @ X2354 @ X2350 )
| ( X2351 @ X2354 )
| ~ ( subset @ X2350 @ ( cartprod @ X2348 @ X2349 ) ) )
& ( ~ ( singleton @ ( dsetconstr @ X2355 @ X2356 ) )
| ~ ( in @ X2357 @ X2355 )
| ~ ( in @ X2358 @ X2355 )
| ~ ( X2356 @ X2357 )
| ~ ( X2356 @ X2358 )
| ( X2357 = X2358 ) )
& ( ~ ( func @ X2359 @ X2360 @ X2361 )
| ~ ( in @ X2362 @ X2359 )
| ( in @ ( kpair @ X2362 @ ( ap @ X2359 @ X2360 @ X2361 @ X2362 ) ) @ X2361 ) )
& ( ~ ( in @ X2365 @ ( funcSet @ X2363 @ X2364 ) )
| ~ ( in @ X2366 @ X2363 )
| ( in @ ( kpair @ X2366 @ ( ap @ X2363 @ X2364 @ X2365 @ X2366 ) ) @ X2365 ) )
& ( ~ ( func @ X2367 @ X2368 @ X2369 )
| ~ ( in @ X2370 @ X2367 )
| ~ ( in @ X2371 @ X2368 )
| ~ ( in @ ( kpair @ X2370 @ X2371 ) @ X2369 )
| ( ( ap @ X2367 @ X2368 @ X2369 @ X2370 )
= X2371 ) )
& ( ( in @ ( esk71_4 @ X2372 @ X2373 @ X2374 @ X2375 ) @ X2372 )
| ~ ( in @ X2377 @ X2372 )
| ~ ( in @ X2378 @ X2373 )
| ~ ( in @ ( kpair @ X2377 @ X2378 ) @ X2375 )
| ( in @ ( kpair @ X2377 @ X2378 ) @ X2374 )
| ~ ( func @ X2372 @ X2373 @ X2375 )
| ~ ( func @ X2372 @ X2373 @ X2374 ) )
& ( ( ( ap @ X2372 @ X2373 @ X2374 @ ( esk71_4 @ X2372 @ X2373 @ X2374 @ X2375 ) )
!= ( ap @ X2372 @ X2373 @ X2375 @ ( esk71_4 @ X2372 @ X2373 @ X2374 @ X2375 ) ) )
| ~ ( in @ X2377 @ X2372 )
| ~ ( in @ X2378 @ X2373 )
| ~ ( in @ ( kpair @ X2377 @ X2378 ) @ X2375 )
| ( in @ ( kpair @ X2377 @ X2378 ) @ X2374 )
| ~ ( func @ X2372 @ X2373 @ X2375 )
| ~ ( func @ X2372 @ X2373 @ X2374 ) )
& ( ~ ( in @ X2381 @ ( funcSet @ X2379 @ X2380 ) )
| ~ ( in @ X2382 @ X2379 )
| ~ ( in @ X2383 @ X2380 )
| ~ ( in @ ( kpair @ X2382 @ X2383 ) @ X2381 )
| ( ( ap @ X2379 @ X2380 @ X2381 @ X2382 )
= X2383 ) )
& ( ( in @ ( esk72_4 @ X2384 @ X2385 @ X2386 @ X2387 ) @ X2384 )
| ( subset @ X2386 @ X2387 )
| ~ ( subset @ X2387 @ ( cartprod @ X2384 @ X2385 ) )
| ~ ( subset @ X2386 @ ( cartprod @ X2384 @ X2385 ) ) )
& ( ( in @ ( esk73_4 @ X2384 @ X2385 @ X2386 @ X2387 ) @ X2385 )
| ( subset @ X2386 @ X2387 )
| ~ ( subset @ X2387 @ ( cartprod @ X2384 @ X2385 ) )
| ~ ( subset @ X2386 @ ( cartprod @ X2384 @ X2385 ) ) )
& ( ( in @ ( kpair @ ( esk72_4 @ X2384 @ X2385 @ X2386 @ X2387 ) @ ( esk73_4 @ X2384 @ X2385 @ X2386 @ X2387 ) ) @ X2386 )
| ( subset @ X2386 @ X2387 )
| ~ ( subset @ X2387 @ ( cartprod @ X2384 @ X2385 ) )
| ~ ( subset @ X2386 @ ( cartprod @ X2384 @ X2385 ) ) )
& ( ~ ( in @ ( kpair @ ( esk72_4 @ X2384 @ X2385 @ X2386 @ X2387 ) @ ( esk73_4 @ X2384 @ X2385 @ X2386 @ X2387 ) ) @ X2387 )
| ( subset @ X2386 @ X2387 )
| ~ ( subset @ X2387 @ ( cartprod @ X2384 @ X2385 ) )
| ~ ( subset @ X2386 @ ( cartprod @ X2384 @ X2385 ) ) )
& ( ( in @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ( X2392 = X2393 )
| ( in @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ( X2392 = X2393 )
| ( in @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ( X2392 = X2393 )
| ( in @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ( X2392 = X2393 )
| ( in @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ( X2392 = X2393 )
| ( in @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ( X2392 = X2393 )
| ( in @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ( X2392 = X2393 )
| ( in @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ( X2392 = X2393 )
| ( in @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ( X2392 = X2393 )
| ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ( X2392 = X2393 )
| ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ( X2392 = X2393 )
| ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ( X2392 = X2393 )
| ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2390 )
| ( X2392 = X2393 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ X2391 )
| ( X2392 = X2393 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ( X2392 = X2393 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ~ ( in @ ( kpair @ ( esk76_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk77_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2392 )
| ( X2392 = X2393 )
| ~ ( in @ ( kpair @ ( esk74_4 @ X2390 @ X2391 @ X2392 @ X2393 ) @ ( esk75_4 @ X2390 @ X2391 @ X2392 @ X2393 ) ) @ X2393 )
| ~ ( subset @ X2393 @ ( cartprod @ X2390 @ X2391 ) )
| ~ ( subset @ X2392 @ ( cartprod @ X2390 @ X2391 ) ) )
& ( ( in @ ( esk78_4 @ X2398 @ X2399 @ X2400 @ X2401 ) @ X2398 )
| ( X2400 = X2401 )
| ~ ( func @ X2398 @ X2399 @ X2401 )
| ~ ( func @ X2398 @ X2399 @ X2400 ) )
& ( ( ( ap @ X2398 @ X2399 @ X2400 @ ( esk78_4 @ X2398 @ X2399 @ X2400 @ X2401 ) )
!= ( ap @ X2398 @ X2399 @ X2401 @ ( esk78_4 @ X2398 @ X2399 @ X2400 @ X2401 ) ) )
| ( X2400 = X2401 )
| ~ ( func @ X2398 @ X2399 @ X2401 )
| ~ ( func @ X2398 @ X2399 @ X2400 ) )
& ( ( in @ ( esk79_4 @ X2403 @ X2404 @ X2405 @ X2406 ) @ X2403 )
| ( X2405 = X2406 )
| ~ ( in @ X2406 @ ( funcSet @ X2403 @ X2404 ) )
| ~ ( in @ X2405 @ ( funcSet @ X2403 @ X2404 ) ) )
& ( ( ( ap @ X2403 @ X2404 @ X2405 @ ( esk79_4 @ X2403 @ X2404 @ X2405 @ X2406 ) )
!= ( ap @ X2403 @ X2404 @ X2406 @ ( esk79_4 @ X2403 @ X2404 @ X2405 @ X2406 ) ) )
| ( X2405 = X2406 )
| ~ ( in @ X2406 @ ( funcSet @ X2403 @ X2404 ) )
| ~ ( in @ X2405 @ ( funcSet @ X2403 @ X2404 ) ) )
& ( ~ ( in @ X2410 @ ( funcSet @ X2408 @ X2409 ) )
| ~ ( in @ X2411 @ X2408 )
| ( ( ap @ X2408 @ X2409 @ X2410 @ X2411 )
= ( ap @ X2408 @ X2409 @ X2410 @ X2411 ) ) )
& ( ~ ( func @ X2412 @ X2413 @ X2414 )
| ~ ( in @ X2415 @ X2412 )
| ( ( ap @ X2412 @ X2413 @ X2414 @ X2415 )
= ( ap @ X2412 @ X2413 @ X2414 @ X2415 ) ) )
& ( ( in @ ( esk80_3 @ X2416 @ X2417 @ X2418 ) @ X2416 )
| ~ ( in @ X2420 @ X2416 )
| ( ( ap @ X2416 @ X2417 @ ( lam @ X2416 @ X2417 @ X2418 ) @ X2420 )
= ( X2418 @ X2420 ) ) )
& ( ~ ( in @ ( X2418 @ ( esk80_3 @ X2416 @ X2417 @ X2418 ) ) @ X2417 )
| ~ ( in @ X2420 @ X2416 )
| ( ( ap @ X2416 @ X2417 @ ( lam @ X2416 @ X2417 @ X2418 ) @ X2420 )
= ( X2418 @ X2420 ) ) )
& ( ~ ( func @ X2421 @ X2422 @ X2423 )
| ( ( lam @ X2421 @ X2422 @ ( ap @ X2421 @ X2422 @ X2423 ) )
= X2423 ) )
& ( ( in @ ( esk81_3 @ X2424 @ X2425 @ X2426 ) @ X2424 )
| ( ( lam @ X2424 @ X2425 @ X2426 )
= ( lam @ X2424 @ X2425 @ X2426 ) ) )
& ( ~ ( in @ ( X2426 @ ( esk81_3 @ X2424 @ X2425 @ X2426 ) ) @ X2425 )
| ( ( lam @ X2424 @ X2425 @ X2426 )
= ( lam @ X2424 @ X2425 @ X2426 ) ) )
& ( ( in @ ( esk82_3 @ X2428 @ X2429 @ X2430 ) @ X2428 )
| ~ ( in @ X2432 @ X2428 )
| ( ( ap @ X2428 @ X2429 @ ( lam @ X2428 @ X2429 @ X2430 ) @ X2432 )
= ( X2430 @ X2432 ) ) )
& ( ~ ( in @ ( X2430 @ ( esk82_3 @ X2428 @ X2429 @ X2430 ) ) @ X2429 )
| ~ ( in @ X2432 @ X2428 )
| ( ( ap @ X2428 @ X2429 @ ( lam @ X2428 @ X2429 @ X2430 ) @ X2432 )
= ( X2430 @ X2432 ) ) )
& ( ~ ( in @ X2435 @ ( funcSet @ X2433 @ X2434 ) )
| ( ( lam @ X2433 @ X2434 @ ( ap @ X2433 @ X2434 @ X2435 ) )
= X2435 ) )
& ( ~ ( in @ X2438 @ X2436 )
| ~ ( in @ X2439 @ X2436 )
| X2437
| ( in @ X2439
@ ( dsetconstr @ X2436
@ ^ [Z0: $i] :
( ( X2437
& ( Z0 = X2438 ) )
| ( ~ X2437
& ( Z0 = X2439 ) ) ) ) ) )
& ( ~ ( in @ X2442 @ X2440 )
| ~ ( in @ X2443 @ X2440 )
| X2441
| ( ( dsetconstr @ X2440
@ ^ [Z0: $i] :
( ( X2441
& ( Z0 = X2442 ) )
| ( ~ X2441
& ( Z0 = X2443 ) ) ) )
= ( setadjoin @ X2443 @ emptyset ) ) )
& ( ~ ( in @ X2446 @ X2444 )
| ~ ( in @ X2447 @ X2444 )
| ~ X2445
| ( in @ X2446
@ ( dsetconstr @ X2444
@ ^ [Z0: $i] :
( ( X2445
& ( Z0 = X2446 ) )
| ( ~ X2445
& ( Z0 = X2447 ) ) ) ) ) )
& ( ~ ( in @ X2450 @ X2448 )
| ~ ( in @ X2451 @ X2448 )
| ~ X2449
| ( ( dsetconstr @ X2448
@ ^ [Z0: $i] :
( ( X2449
& ( Z0 = X2450 ) )
| ( ~ X2449
& ( Z0 = X2451 ) ) ) )
= ( setadjoin @ X2450 @ emptyset ) ) )
& ( ~ ( in @ X2454 @ X2452 )
| ~ ( in @ X2455 @ X2452 )
| ( singleton
@ ( dsetconstr @ X2452
@ ^ [Z0: $i] :
( ( X2453
& ( Z0 = X2454 ) )
| ( ~ X2453
& ( Z0 = X2455 ) ) ) ) ) )
& ( ~ ( in @ X2458 @ X2456 )
| ~ ( in @ X2459 @ X2456 )
| ( in @ ( if @ X2456 @ X2457 @ X2458 @ X2459 ) @ X2456 ) )
& ( ~ ( singleton @ X2460 )
| ~ ( in @ X2461 @ X2460 )
| ( ( setunion @ X2460 )
= X2461 ) )
& ( ~ ( in @ X2464 @ X2462 )
| ~ ( in @ X2465 @ X2462 )
| ~ X2463
| ( ( if @ X2462 @ X2463 @ X2464 @ X2465 )
= X2464 ) )
& ( ~ ( in @ X2468 @ X2466 )
| ~ ( in @ X2469 @ X2466 )
| X2467
| ( ( if @ X2466 @ X2467 @ X2468 @ X2469 )
= X2469 ) )
& ( ~ ( in @ X2472 @ X2470 )
| ~ ( in @ X2473 @ X2470 )
| ( in @ ( if @ X2470 @ X2471 @ X2472 @ X2473 ) @ ( setadjoin @ X2472 @ ( setadjoin @ X2473 @ emptyset ) ) ) )
& ( ~ ( in @ X2475 @ ( powerset @ X2474 ) )
| ~ ( in @ X2476 @ ( powerset @ X2474 ) )
| ( in @ ( binintersect @ X2475 @ X2476 ) @ ( powerset @ X2474 ) ) )
& ( ~ ( in @ X2478 @ ( powerset @ X2477 ) )
| ~ ( in @ X2479 @ ( powerset @ X2477 ) )
| ( in @ ( binunion @ X2478 @ X2479 ) @ ( powerset @ X2477 ) ) )
& ( ~ ( in @ X2481 @ ( powerset @ X2480 ) )
| ( in @ ( powerset @ X2481 ) @ ( powerset @ ( powerset @ X2480 ) ) ) )
& ( ~ ( in @ X2483 @ ( powerset @ X2482 ) )
| ~ ( in @ X2484 @ ( powerset @ X2482 ) )
| ( in @ ( setminus @ X2483 @ X2484 ) @ ( powerset @ X2482 ) ) )
& ( ~ ( in @ X2486 @ ( powerset @ X2485 ) )
| ( in @ ( setminus @ X2485 @ X2486 ) @ ( powerset @ X2485 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ( X2488 = X2489 )
| ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2487 )
| ( X2488 = X2489 )
| ~ ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ( X2488 = X2489 )
| ~ ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ~ ( in @ ( esk84_3 @ X2487 @ X2488 @ X2489 ) @ X2488 )
| ( X2488 = X2489 )
| ~ ( in @ ( esk83_3 @ X2487 @ X2488 @ X2489 ) @ X2489 )
| ~ ( in @ X2489 @ ( powerset @ X2487 ) )
| ~ ( in @ X2488 @ ( powerset @ X2487 ) ) )
& ( ( in @ ( esk85_3 @ X2492 @ X2493 @ X2494 ) @ X2492 )
| ( subset @ X2493 @ X2494 )
| ~ ( in @ X2494 @ ( powerset @ X2492 ) )
| ~ ( in @ X2493 @ ( powerset @ X2492 ) ) )
& ( ( in @ ( esk85_3 @ X2492 @ X2493 @ X2494 ) @ X2493 )
| ( subset @ X2493 @ X2494 )
| ~ ( in @ X2494 @ ( powerset @ X2492 ) )
| ~ ( in @ X2493 @ ( powerset @ X2492 ) ) )
& ( ~ ( in @ ( esk85_3 @ X2492 @ X2493 @ X2494 ) @ X2494 )
| ( subset @ X2493 @ X2494 )
| ~ ( in @ X2494 @ ( powerset @ X2492 ) )
| ~ ( in @ X2493 @ ( powerset @ X2492 ) ) )
& ( ( in @ ( esk86_3 @ X2496 @ X2497 @ X2498 ) @ X2496 )
| ( in @ X2497 @ ( powerset @ X2498 ) )
| ~ ( in @ X2498 @ ( powerset @ X2496 ) )
| ~ ( in @ X2497 @ ( powerset @ X2496 ) ) )
& ( ( in @ ( esk86_3 @ X2496 @ X2497 @ X2498 ) @ X2497 )
| ( in @ X2497 @ ( powerset @ X2498 ) )
| ~ ( in @ X2498 @ ( powerset @ X2496 ) )
| ~ ( in @ X2497 @ ( powerset @ X2496 ) ) )
& ( ~ ( in @ ( esk86_3 @ X2496 @ X2497 @ X2498 ) @ X2498 )
| ( in @ X2497 @ ( powerset @ X2498 ) )
| ~ ( in @ X2498 @ ( powerset @ X2496 ) )
| ~ ( in @ X2497 @ ( powerset @ X2496 ) ) )
& ( ~ ( in @ X2501 @ ( powerset @ X2500 ) )
| ~ ( in @ X2502 @ ( powerset @ X2500 ) )
| ~ ( in @ X2503 @ X2500 )
| ~ ( in @ X2501 @ ( powerset @ X2502 ) )
| ~ ( in @ X2503 @ X2501 )
| ( in @ X2503 @ X2502 ) )
& ( ~ ( in @ X2505 @ ( powerset @ X2504 ) )
| ~ ( in @ X2506 @ X2504 )
| ~ ( in @ X2506 @ X2505 )
| ~ ( in @ X2506 @ ( setminus @ X2504 @ X2505 ) ) )
& ( ~ ( in @ X2508 @ ( powerset @ X2507 ) )
| ~ ( in @ X2509 @ X2507 )
| ( in @ X2509 @ ( setminus @ X2507 @ X2508 ) )
| ( in @ X2509 @ X2508 ) )
& ( ~ ( in @ X2511 @ ( powerset @ X2510 ) )
| ~ ( in @ X2512 @ ( powerset @ X2510 ) )
| ~ ( in @ X2513 @ X2510 )
| ( in @ X2513 @ X2511 )
| ~ ( in @ X2513 @ ( binintersect @ X2511 @ X2512 ) ) )
& ( ~ ( in @ X2515 @ ( powerset @ X2514 ) )
| ~ ( in @ X2516 @ ( powerset @ X2514 ) )
| ~ ( in @ X2517 @ X2514 )
| ( in @ X2517 @ X2516 )
| ~ ( in @ X2517 @ ( binintersect @ X2515 @ X2516 ) ) )
& ( ~ ( in @ X2519 @ ( powerset @ X2518 ) )
| ~ ( in @ X2520 @ ( powerset @ X2518 ) )
| ~ ( in @ X2521 @ X2518 )
| ~ ( subset @ X2519 @ ( setminus @ X2518 @ X2520 ) )
| ~ ( in @ X2521 @ X2520 )
| ~ ( in @ X2521 @ X2519 ) )
& ( ~ ( in @ X2523 @ ( powerset @ X2522 ) )
| ~ ( in @ X2524 @ ( powerset @ X2522 ) )
| ~ ( in @ X2525 @ X2522 )
| ~ ( subset @ X2523 @ X2524 )
| ( in @ X2525 @ X2524 )
| ~ ( in @ X2525 @ X2523 ) )
& ( ~ ( in @ X2527 @ ( powerset @ X2526 ) )
| ~ ( in @ X2528 @ ( powerset @ X2526 ) )
| ~ ( subset @ X2527 @ X2528 )
| ( subset @ ( setminus @ X2526 @ X2528 ) @ ( setminus @ X2526 @ X2527 ) ) )
& ( ~ ( in @ X2530 @ ( powerset @ X2529 ) )
| ~ ( in @ X2531 @ ( powerset @ X2529 ) )
| ~ ( subset @ ( setminus @ X2529 @ X2531 ) @ ( setminus @ X2529 @ X2530 ) )
| ( subset @ X2530 @ X2531 ) )
& ( ~ ( in @ X2533 @ ( powerset @ X2532 ) )
| ~ ( in @ X2534 @ X2532 )
| ~ ( in @ X2534 @ X2533 )
| ( in @ X2534 @ ( setminus @ X2532 @ ( setminus @ X2532 @ X2533 ) ) ) )
& ( ~ ( in @ X2536 @ ( powerset @ X2535 ) )
| ~ ( in @ X2537 @ X2535 )
| ~ ( in @ X2537 @ ( setminus @ X2535 @ ( setminus @ X2535 @ X2536 ) ) )
| ( in @ X2537 @ X2536 ) )
& ( ~ ( in @ X2539 @ ( powerset @ X2538 ) )
| ( subset @ X2539 @ ( setminus @ X2538 @ ( setminus @ X2538 @ X2539 ) ) ) )
& ( ~ ( in @ X2541 @ ( powerset @ X2540 ) )
| ( subset @ ( setminus @ X2540 @ ( setminus @ X2540 @ X2541 ) ) @ X2541 ) )
& ( ~ ( in @ X2543 @ ( powerset @ X2542 ) )
| ( X2543
= ( setminus @ X2542 @ ( setminus @ X2542 @ X2543 ) ) ) )
& ( ~ ( in @ X2545 @ ( powerset @ X2544 ) )
| ~ ( in @ X2546 @ ( powerset @ X2544 ) )
| ~ ( in @ X2547 @ X2544 )
| ~ ( in @ X2547 @ ( setminus @ X2544 @ X2545 ) )
| ~ ( in @ X2547 @ ( binintersect @ X2545 @ X2546 ) ) )
& ( ~ ( in @ X2549 @ ( powerset @ X2548 ) )
| ~ ( in @ X2550 @ ( powerset @ X2548 ) )
| ~ ( in @ X2551 @ X2548 )
| ~ ( in @ X2551 @ ( setminus @ X2548 @ X2549 ) )
| ( in @ X2551 @ ( setminus @ X2548 @ ( binintersect @ X2549 @ X2550 ) ) ) )
& ( ~ ( in @ X2553 @ ( powerset @ X2552 ) )
| ~ ( in @ X2554 @ ( powerset @ X2552 ) )
| ( subset @ ( setminus @ X2552 @ X2553 ) @ ( setminus @ X2552 @ ( binintersect @ X2553 @ X2554 ) ) ) )
& ( ~ ( in @ X2556 @ ( powerset @ X2555 ) )
| ~ ( in @ X2557 @ ( powerset @ X2555 ) )
| ( in @ ( setminus @ X2555 @ X2556 ) @ ( powerset @ ( setminus @ X2555 @ ( binintersect @ X2556 @ X2557 ) ) ) ) )
& ( ~ ( in @ X2559 @ ( powerset @ X2558 ) )
| ~ ( in @ X2560 @ ( powerset @ X2558 ) )
| ~ ( subset @ X2559 @ ( setminus @ X2558 @ X2560 ) )
| ~ ( in @ X2561 @ X2558 )
| ~ ( in @ X2561 @ X2560 )
| ( in @ X2561 @ ( setminus @ X2558 @ X2559 ) ) )
& ( ~ ( in @ X2563 @ ( powerset @ X2562 ) )
| ~ ( in @ X2564 @ ( powerset @ X2562 ) )
| ~ ( subset @ X2563 @ ( setminus @ X2562 @ X2564 ) )
| ( subset @ X2564 @ ( setminus @ X2562 @ X2563 ) ) )
& ( ~ ( in @ X2566 @ ( powerset @ X2565 ) )
| ~ ( in @ X2567 @ ( powerset @ X2565 ) )
| ~ ( in @ X2568 @ X2565 )
| ( in @ X2568 @ ( binunion @ X2566 @ X2567 ) )
| ~ ( in @ X2568 @ X2566 ) )
& ( ~ ( in @ X2570 @ ( powerset @ X2569 ) )
| ~ ( in @ X2571 @ ( powerset @ X2569 ) )
| ~ ( in @ X2572 @ X2569 )
| ( in @ X2572 @ ( binunion @ X2570 @ X2571 ) )
| ~ ( in @ X2572 @ X2571 ) )
& ( ~ ( in @ X2574 @ ( powerset @ X2573 ) )
| ~ ( in @ X2575 @ ( powerset @ X2573 ) )
| ~ ( in @ X2576 @ ( powerset @ X2573 ) )
| ~ ( in @ X2577 @ X2573 )
| ~ ( in @ X2577 @ ( binintersect @ X2574 @ X2575 ) )
| ( in @ X2577 @ ( binunion @ X2574 @ X2576 ) ) )
& ( ~ ( in @ X2579 @ ( powerset @ X2578 ) )
| ~ ( in @ X2580 @ ( powerset @ X2578 ) )
| ~ ( in @ X2581 @ ( powerset @ X2578 ) )
| ~ ( in @ X2582 @ X2578 )
| ~ ( in @ X2582 @ ( binintersect @ X2579 @ X2580 ) )
| ( in @ X2582 @ ( binunion @ X2580 @ X2581 ) ) )
& ( ~ ( in @ X2584 @ ( powerset @ X2583 ) )
| ~ ( in @ X2585 @ ( powerset @ X2583 ) )
| ~ ( in @ X2586 @ ( powerset @ X2583 ) )
| ~ ( in @ X2587 @ X2583 )
| ~ ( in @ X2587 @ ( binintersect @ X2584 @ X2585 ) )
| ( in @ X2587 @ ( binintersect @ ( binunion @ X2584 @ X2586 ) @ ( binunion @ X2585 @ X2586 ) ) ) )
& ( ~ ( in @ X2589 @ ( powerset @ X2588 ) )
| ~ ( in @ X2590 @ ( powerset @ X2588 ) )
| ~ ( in @ X2591 @ ( powerset @ X2588 ) )
| ( in @ ( binintersect @ X2589 @ X2590 ) @ ( powerset @ ( binintersect @ ( binunion @ X2589 @ X2591 ) @ ( binunion @ X2590 @ X2591 ) ) ) ) )
& ( ~ ( in @ X2593 @ ( powerset @ X2592 ) )
| ~ ( in @ X2594 @ ( powerset @ X2592 ) )
| ~ ( in @ X2595 @ X2592 )
| ~ ( in @ X2595 @ ( setminus @ X2592 @ ( binunion @ X2593 @ X2594 ) ) )
| ~ ( in @ X2595 @ X2593 ) )
& ( ~ ( in @ X2597 @ ( powerset @ X2596 ) )
| ~ ( in @ X2598 @ ( powerset @ X2596 ) )
| ~ ( in @ X2599 @ X2596 )
| ~ ( in @ X2599 @ ( setminus @ X2596 @ ( binunion @ X2597 @ X2598 ) ) )
| ( in @ X2599 @ ( setminus @ X2596 @ X2597 ) ) )
& ( in @ esk88_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk89_0 @ ( powerset @ esk87_0 ) )
& ( in @ esk90_0 @ esk87_0 )
& ( in @ esk90_0 @ ( binunion @ esk88_0 @ esk89_0 ) )
& ( ~ ( in @ esk90_0 @ esk88_0 )
| epred2_0 )
& ( ~ ( in @ esk90_0 @ esk89_0 )
| epred2_0 )
& ~ epred2_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_348])])])])])])]) ).
thf(c_0_350,negated_conjecture,
( epred2_0
| ~ ( in @ esk90_0 @ esk88_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
thf(c_0_351,negated_conjecture,
~ epred2_0,
inference(split_conjunct,[status(thm)],[c_0_349]) ).
thf(c_0_352,negated_conjecture,
( epred2_0
| ~ ( in @ esk90_0 @ esk89_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
thf(c_0_353,negated_conjecture,
! [X2: $i,X4: $i,X3: $i] :
( ( in @ X2 @ X3 )
| ( in @ X2 @ X4 )
| ~ ( in @ X2 @ ( binunion @ X4 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_349])])]) ).
thf(c_0_354,negated_conjecture,
in @ esk90_0 @ ( binunion @ esk88_0 @ esk89_0 ),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
thf(c_0_355,negated_conjecture,
~ ( in @ esk90_0 @ esk88_0 ),
inference(sr,[status(thm)],[c_0_350,c_0_351]) ).
thf(c_0_356,negated_conjecture,
~ ( in @ esk90_0 @ esk89_0 ),
inference(sr,[status(thm)],[c_0_352,c_0_351]) ).
thf(c_0_357,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_354]),c_0_355]),c_0_356]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU746^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 17:29:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.49 Running higher-order theorem proving
% 0.22/0.49 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
% 2.19/300.08 # Version: 3.1.0-ho
% 2.19/300.08 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.19/300.08 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/300.08 # Starting ehoh_best5 with 300s (1) cores
% 2.19/300.08 # Starting almost_fo_3_lam with 300s (1) cores
% 2.19/300.08 # Starting new_bool_5 with 300s (1) cores
% 2.19/300.08 # Starting pre_casc_3 with 300s (1) cores
% 2.19/300.08 # Starting ho_unfolding_8 with 300s (1) cores
% 2.19/300.08 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.19/300.08 # Starting new_bool_3 with 300s (1) cores
% 2.19/300.08 # Starting new_ho_5 with 300s (1) cores
% 2.19/300.08 # pre_casc_3 with pid 28807 completed with status 8
% 2.19/300.08 # new_ho_5 with pid 28811 completed with status 8
% 2.19/300.08 # ehoh_best5 with pid 28804 completed with status 0
% 2.19/300.08 # Result found by ehoh_best5
% 2.19/300.08 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.19/300.08 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/300.08 # Starting ehoh_best5 with 300s (1) cores
% 2.19/300.08 # No SInE strategy applied
% 2.19/300.08 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.19/300.08 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.19/300.08 # Starting ho_unfolding_8 with 55s (1) cores
% 2.19/300.08 # ho_unfolding_8 with pid 28835 completed with status 0
% 2.19/300.08 # Result found by ho_unfolding_8
% 2.19/300.08 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.19/300.08 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/300.08 # Starting ehoh_best5 with 300s (1) cores
% 2.19/300.08 # No SInE strategy applied
% 2.19/300.08 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.19/300.08 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.19/300.08 # Starting ho_unfolding_8 with 55s (1) cores
% 2.19/300.08 # Preprocessing time : 0.049 s
% 2.19/300.08 # Presaturation interreduction done
% 2.19/300.08
% 2.19/300.08 # Proof found!
% 2.19/300.08 # SZS status Theorem
% 2.19/300.08 # SZS output start CNFRefutation
% See solution above
% 2.19/300.08 # Parsed axioms : 567
% 2.19/300.08 # Removed by relevancy pruning/SinE : 0
% 2.19/300.08 # Initial clauses : 771
% 2.19/300.08 # Removed in clause preprocessing : 334
% 2.19/300.08 # Initial clauses in saturation : 437
% 2.19/300.08 # Processed clauses : 618
% 2.19/300.08 # ...of these trivial : 10
% 2.19/300.08 # ...subsumed : 36
% 2.19/300.08 # ...remaining for further processing : 572
% 2.19/300.08 # Other redundant clauses eliminated : 31
% 2.19/300.08 # Clauses deleted for lack of memory : 0
% 2.19/300.08 # Backward-subsumed : 0
% 2.19/300.08 # Backward-rewritten : 1
% 2.19/300.08 # Generated clauses : 1243
% 2.19/300.08 # ...of the previous two non-redundant : 1125
% 2.19/300.08 # ...aggressively subsumed : 0
% 2.19/300.08 # Contextual simplify-reflections : 7
% 2.19/300.08 # Paramodulations : 1203
% 2.19/300.08 # Factorizations : 0
% 2.19/300.08 # NegExts : 0
% 2.19/300.08 # Equation resolutions : 36
% 2.19/300.08 # Disequality decompositions : 0
% 2.19/300.08 # Total rewrite steps : 118
% 2.19/300.08 # ...of those cached : 84
% 2.19/300.08 # Propositional unsat checks : 0
% 2.19/300.08 # Propositional check models : 0
% 2.19/300.08 # Propositional check unsatisfiable : 0
% 2.19/300.08 # Propositional clauses : 0
% 2.19/300.08 # Propositional clauses after purity: 0
% 2.19/300.08 # Propositional unsat core size : 0
% 2.19/300.08 # Propositional preprocessing time : 0.000
% 2.19/300.08 # Propositional encoding time : 0.000
% 2.19/300.08 # Propositional solver time : 0.000
% 2.19/300.08 # Success case prop preproc time : 0.000
% 2.19/300.08 # Success case prop encoding time : 0.000
% 2.19/300.08 # Success case prop solver time : 0.000
% 2.19/300.08 # Current number of processed clauses : 168
% 2.19/300.08 # Positive orientable unit clauses : 38
% 2.19/300.08 # Positive unorientable unit clauses: 0
% 2.19/300.08 # Negative unit clauses : 5
% 2.19/300.08 # Non-unit-clauses : 125
% 2.19/300.08 # Current number of unprocessed clauses: 1328
% 2.19/300.08 # ...number of literals in the above : 3992
% 2.19/300.08 # Current number of archived formulas : 0
% 2.19/300.08 # Current number of archived clauses : 386
% 2.19/300.08 # Clause-clause subsumption calls (NU) : 28834
% 2.19/300.08 # Rec. Clause-clause subsumption calls : 9438
% 2.19/300.08 # Non-unit clause-clause subsumptions : 38
% 2.19/300.08 # Unit Clause-clause subsumption calls : 452
% 2.19/300.08 # Rewrite failures with RHS unbound : 0
% 2.19/300.08 # BW rewrite match attempts : 32
% 2.19/300.08 # BW rewrite match successes : 1
% 2.19/300.08 # Condensation attempts : 0
% 2.19/300.08 # Condensation successes : 0
% 2.19/300.08 # Termbank termtop insertions : 98223
% 2.19/300.08 # Search garbage collected termcells : 27822
% 2.19/300.08
% 2.19/300.08 # -------------------------------------------------
% 2.19/300.08 # User time : 0.226 s
% 2.19/300.08 # System time : 0.021 s
% 2.19/300.08 # Total time : 0.247 s
% 2.19/300.08 # Maximum resident set size: 8376 pages
% 2.19/300.08
% 2.19/300.08 # -------------------------------------------------
% 2.19/300.08 # User time : 0.482 s
% 2.19/300.08 # System time : 0.115 s
% 2.19/300.08 # Total time : 0.598 s
% 2.19/300.08 # Maximum resident set size: 3140 pages
% 2.19/300.08 % E---3.1 exiting
% 2.19/300.08 % E exiting
%------------------------------------------------------------------------------