%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU712^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:29:23 EDT 2024
% Result : Theorem 2.11s 0.97s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 556
% Syntax : Number of formulae : 617 ( 5 unt; 327 typ; 0 def)
% Number of atoms : 2698 ( 443 equ; 0 cnn)
% Maximal formula atoms : 826 ( 9 avg)
% Number of connectives : 10239 ( 633 ~; 653 |; 453 &;6859 @)
% ( 315 <=>;1326 =>; 0 <=; 0 <~>)
% Maximal formula depth : 971 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 497 ( 497 >; 0 *; 0 +; 0 <<)
% Number of symbols : 331 ( 327 usr; 236 con; 0-4 aty)
% Number of variables : 2375 ( 156 ^2139 !; 80 ?;2375 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
epred1_0: $o ).
thf(decl_289,type,
esk1_2: $i > $i > $i ).
thf(decl_290,type,
esk2_2: $i > $i > $i ).
thf(decl_291,type,
esk3_2: $i > $i > $i ).
thf(decl_292,type,
esk4_1: $i > $i ).
thf(decl_293,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_294,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_295,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_296,type,
esk8_1: $i > $i ).
thf(decl_297,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_298,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_299,type,
esk11_2: $i > $i > $i ).
thf(decl_300,type,
esk12_2: $i > $i > $i ).
thf(decl_301,type,
esk13_1: $i > $i ).
thf(decl_302,type,
esk14_1: $i > $i ).
thf(decl_303,type,
esk15_1: $i > $i ).
thf(decl_304,type,
esk16_2: $i > $i > $i ).
thf(decl_305,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_306,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_307,type,
esk19_1: $i > $i ).
thf(decl_308,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_309,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_310,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_311,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_312,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_313,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_314,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_315,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_316,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_317,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_318,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_319,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_320,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_321,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_322,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_323,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_324,type,
esk36_2: $i > $i > $i ).
thf(decl_325,type,
esk37_2: $i > $i > $i ).
thf(decl_326,type,
esk38_2: $i > $i > $i ).
thf(decl_327,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_328,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_329,type,
esk41_2: $i > $i > $i ).
thf(decl_330,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_331,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_332,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_333,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_334,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_335,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_336,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_337,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_338,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_339,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_340,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_341,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_342,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_344,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_345,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_346,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_347,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_348,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_349,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_350,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_351,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_352,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_353,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_354,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_355,type,
esk67_0: $i ).
thf(decl_356,type,
esk68_0: $i ).
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/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
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/sandbox2/benchmark/theBenchmark.p',exuEu) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2) ).
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/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).
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/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
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/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(powersetT_lem,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).
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/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
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/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
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/sandbox2/benchmark/theBenchmark.p',app) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(funcinfuncset,axiom,
( funcinfuncset
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
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/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
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/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcextLem) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcext2) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
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/sandbox2/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
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/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_254,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_255,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_256,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_257,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_258,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_259,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_260,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_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_270,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_271,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_272,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_273,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_274,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_275,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_276,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_277,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_278,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_279,plain,
( epred1_0
<=> ! [X779: $i] :
? [X780: $i] :
( ! [X781: $i] :
( ( in @ X781 @ X780 )
=> ! [X782: $i] :
( ( in @ X782 @ X781 )
=> ( in @ X782 @ X779 ) ) )
& ! [X783: $i,X784: $i] :
( ( ( in @ X783 @ X779 )
& ( in @ X784 @ X779 ) )
=> ( ! [X785: $i] :
( ( in @ X785 @ X780 )
=> ( ( in @ X783 @ X785 )
<=> ( in @ X784 @ X785 ) ) )
=> ( X783 = X784 ) ) )
& ! [X786: $i,X787: $i] :
( ( ( in @ X786 @ X780 )
& ( in @ X787 @ X780 ) )
=> ( ! [X788: $i] :
( ( in @ X788 @ X786 )
=> ( in @ X788 @ X787 ) )
| ! [X789: $i] :
( ( in @ X789 @ X787 )
=> ( in @ X789 @ X786 ) ) ) )
& ! [X790: $i] :
( ( ! [X791: $i] :
( ( in @ X791 @ X790 )
=> ( in @ X791 @ X779 ) )
& ? [X792: $i] : ( in @ X792 @ X790 ) )
=> ? [X793: $i,X794: $i] :
( ( in @ X793 @ X780 )
& ( in @ X794 @ X790 )
& ~ ? [X795: $i] :
( ( in @ X795 @ X793 )
& ( in @ X795 @ X790 ) )
& ! [X796: $i] :
( ( in @ X796 @ X780 )
=> ( ! [X797: $i] :
( ( in @ X797 @ X796 )
=> ( in @ X797 @ X793 ) )
| ( in @ X794 @ X796 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_280,negated_conjecture,
~ ( ! [X752: $i,X753: $i] :
( ! [X754: $i] :
( ( in @ X754 @ X752 )
<=> ( in @ X754 @ X753 ) )
=> ( X752 = X753 ) )
=> ( ! [X755: $i] :
~ ( in @ X755 @ emptyset )
=> ( ! [X756: $i,X757: $i,X758: $i] :
( ( in @ X758 @ ( setadjoin @ X756 @ X757 ) )
<=> ( ( X758 = X756 )
| ( in @ X758 @ X757 ) ) )
=> ( ! [X759: $i,X760: $i] :
( ( in @ X760 @ ( powerset @ X759 ) )
<=> ! [X761: $i] :
( ( in @ X761 @ X760 )
=> ( in @ X761 @ X759 ) ) )
=> ( ! [X762: $i,X763: $i] :
( ( in @ X763 @ ( setunion @ X762 ) )
<=> ? [X764: $i] :
( ( in @ X763 @ X764 )
& ( in @ X764 @ X762 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X765: $i] :
( ( in @ X765 @ omega )
=> ( in @ ( setadjoin @ X765 @ X765 ) @ omega ) )
=> ( ! [X766: $i] :
( ( ( in @ emptyset @ X766 )
& ! [X767: $i] :
( ( ( in @ X767 @ omega )
& ( in @ X767 @ X766 ) )
=> ( in @ ( setadjoin @ X767 @ X767 ) @ X766 ) ) )
=> ! [X768: $i] :
( ( in @ X768 @ omega )
=> ( in @ X768 @ X766 ) ) )
=> ( ! [X769: $i > $i > $o,X770: $i] :
( ! [X771: $i] :
( ( in @ X771 @ X770 )
=> ( exu @ ( X769 @ X771 ) ) )
=> ? [X772: $i] :
! [X773: $i] :
( ( in @ X773 @ X772 )
<=> ? [X774: $i] :
( ( in @ X774 @ X770 )
& ( X769 @ X774 @ X773 ) ) ) )
=> ( ! [X775: $i] :
( ? [X776: $i] : ( in @ X776 @ X775 )
=> ? [X777: $i] :
( ( in @ X777 @ X775 )
& ~ ? [X778: $i] :
( ( in @ X778 @ X777 )
& ( in @ X778 @ X775 ) ) ) )
=> ( epred1_0
=> ( ! [X798: $i > $o] :
( ( exu @ X798 )
=> ( X798
@ ( descr
@ ^ [Z0: $i] : ( X798 @ Z0 ) ) ) )
=> ( ! [X799: $i,X800: $i > $o,X801: $i] :
( ( in @ X801 @ X799 )
=> ( ( X800 @ X801 )
=> ( in @ X801 @ ( dsetconstr @ X799 @ X800 ) ) ) )
=> ( ! [X802: $i,X803: $i > $o,X804: $i] :
( ( in @ X804 @ ( dsetconstr @ X802 @ X803 ) )
=> ( in @ X804 @ X802 ) )
=> ( ! [X805: $i,X806: $i > $o,X807: $i] :
( ( in @ X807 @ ( dsetconstr @ X805 @ X806 ) )
=> ( X806 @ X807 ) )
=> ( ! [X808: $i > $o] :
( ( exu @ X808 )
=> ? [X809: $i] :
( ( X808 @ X809 )
& ! [X810: $i] :
( ( X808 @ X810 )
=> ( X809 = X810 ) ) ) )
=> ( ! [X811: $o,X812: $i] :
( ( in @ X812 @ ( prop2set @ X811 ) )
=> X811 )
=> ( ! [X813: $i] :
( ( in @ X813 @ emptyset )
=> ! [X814: $o] : X814 )
=> ( ! [X815: $i] :
( ( in @ X815 @ emptyset )
=> ~ $true )
=> ( ! [X816: $i] :
~ ( in @ X816 @ emptyset )
=> ( ! [X817: $i > $o] :
( ( exu @ X817 )
=> ? [X818: $i] : ( X817 @ X818 ) )
=> ( ! [X819: $i,X820: $i] :
( ! [X821: $i] :
( ( in @ X821 @ X819 )
=> ( in @ X821 @ X820 ) )
=> ( ! [X822: $i] :
( ( in @ X822 @ X820 )
=> ( in @ X822 @ X819 ) )
=> ( X819 = X820 ) ) )
=> ( ! [X823: $i] :
( ! [X824: $i] :
~ ( in @ X824 @ X823 )
=> ( X823 = emptyset ) )
=> ( ! [X825: $i] :
( ! [X826: $i] :
~ ( in @ X826 @ X825 )
=> ( X825 = emptyset ) )
=> ( ! [X827: $i,X828: $i > $o,X829: $i] :
( ( in @ X829 @ X827 )
=> ( ( in @ X829 @ ( dsetconstr @ X827 @ X828 ) )
<=> ( X828 @ X829 ) ) )
=> ( ! [X830: $i] :
( ( nonempty @ X830 )
=> ? [X831: $i] : ( in @ X831 @ X830 ) )
=> ( ! [X832: $i,X833: $i > $o,X834: $i] :
( ( in @ X834 @ X832 )
=> ( ( X833 @ X834 )
=> ( nonempty @ ( dsetconstr @ X832 @ X833 ) ) ) )
=> ( ! [X835: $i] :
( ? [X836: $i] : ( in @ X836 @ X835 )
=> ( nonempty @ X835 ) )
=> ( ! [X837: $i,X838: $i] : ( in @ X837 @ ( setadjoin @ X837 @ X838 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X839: $i,X840: $i,X841: $i] :
( ( in @ X841 @ X840 )
=> ( in @ X841 @ ( setadjoin @ X839 @ X840 ) ) )
=> ( ! [X842: $i,X843: $i,X844: $i] :
( ( in @ X844 @ ( setadjoin @ X842 @ X843 ) )
=> ! [X845: $o] :
( ( ( X844 = X842 )
=> X845 )
=> ( ( ( in @ X844 @ X843 )
=> X845 )
=> X845 ) ) )
=> ( ! [X846: $i,X847: $i,X848: $i] :
( ( in @ X848 @ ( setadjoin @ X846 @ X847 ) )
=> ( ( X848 = X846 )
| ( in @ X848 @ X847 ) ) )
=> ( ! [X849: $i] :
( ( dsetconstr @ X849
@ ^ [Z0: $i] : $true )
= X849 )
=> ( ! [X850: $i,X851: $i] :
( ! [X852: $i] :
( ( in @ X852 @ X851 )
=> ( in @ X852 @ X850 ) )
=> ( in @ X851 @ ( powerset @ X850 ) ) )
=> ( ! [X853: $i] : ( in @ emptyset @ ( powerset @ X853 ) )
=> ( ! [X854: $i] : ( in @ emptyset @ ( powerset @ X854 ) )
=> ( ! [X855: $i,X856: $i,X857: $i] :
( ( in @ X856 @ ( powerset @ X855 ) )
=> ( ( in @ X857 @ X856 )
=> ( in @ X857 @ X855 ) ) )
=> ( ! [X858: $i,X859: $i,X860: $i] :
( ( in @ X859 @ X860 )
=> ( ( in @ X860 @ X858 )
=> ( in @ X859 @ ( setunion @ X858 ) ) ) )
=> ( ! [X861: $i,X862: $i] :
( ( in @ X862 @ ( setunion @ X861 ) )
=> ! [X863: $o] :
( ! [X864: $i] :
( ( in @ X862 @ X864 )
=> ( ( in @ X864 @ X861 )
=> X863 ) )
=> X863 ) )
=> ( ! [X865: $i,X866: $i] :
( ( in @ X866 @ X865 )
=> ( in @ X866 @ ( powerset @ ( setunion @ X865 ) ) ) )
=> ( ! [X867: $i > $o] :
( ( exu @ X867 )
=> ? [X868: $i] :
! [X869: $i] :
( ( X867 @ X869 )
<=> ( X869 = X868 ) ) )
=> ( ! [X870: $i] :
( ( nonempty @ X870 )
=> ? [X871: $i] :
( ( in @ X871 @ X870 )
& $true ) )
=> ( ! [X872: $i,X873: $i] :
( ( in @ X872 @ ( setadjoin @ X873 @ emptyset ) )
=> ( X872 = X873 ) )
=> ( ! [X874: $i,X875: $i] :
( ( X874 != X875 )
=> ~ ( in @ X875 @ ( setadjoin @ X874 @ emptyset ) ) )
=> ( ! [X876: $i,X877: $i] :
( ( X876 = X877 )
=> ( in @ X876 @ ( setadjoin @ X877 @ emptyset ) ) )
=> ( ! [X878: $i,X879: $i] :
( ( in @ X878 @ ( setadjoin @ X879 @ emptyset ) )
=> ( in @ X879 @ ( setadjoin @ X878 @ emptyset ) ) )
=> ( ! [X880: $i,X881: $i,X882: $i] :
( ( in @ X882 @ ( setadjoin @ X880 @ ( setadjoin @ X881 @ emptyset ) ) )
=> ( ( X882 = X880 )
| ( X882 = X881 ) ) )
=> ( ! [X883: $i,X884: $i] : ( in @ X883 @ ( setadjoin @ X883 @ ( setadjoin @ X884 @ emptyset ) ) )
=> ( ! [X885: $i,X886: $i] : ( in @ X886 @ ( setadjoin @ X885 @ ( setadjoin @ X886 @ emptyset ) ) )
=> ( ! [X887: $i,X888: $i > $o] :
( ? [X889: $i] :
( ( in @ X889 @ X887 )
& ( X888 @ X889 ) )
=> ( ( ( dsetconstr @ X887 @ X888 )
= emptyset )
=> ~ $true ) )
=> ( ! [X890: $i > $o,X891: $i] :
( ( in @ X891 @ emptyset )
=> ( X890 @ X891 ) )
=> ( ! [X892: $i,X893: $i > $o] :
( ~ ! [X894: $i] :
( ( in @ X894 @ X892 )
=> ( X893 @ X894 ) )
=> ? [X895: $i] :
( ( in @ X895 @ X892 )
& ~ ( X893 @ X895 ) ) )
=> ( ! [X896: $i,X897: $i > $o] :
( ! [X898: $i] :
( ( in @ X898 @ X896 )
=> ~ ( X897 @ X898 ) )
=> ~ ? [X899: $i] :
( ( in @ X899 @ X896 )
& ( X897 @ X899 ) ) )
=> ( ! [X900: $i,X901: $i > $o] :
( ~ ? [X902: $i] :
( ( in @ X902 @ X900 )
& ( X901 @ X902 ) )
=> ! [X903: $i] :
( ( in @ X903 @ X900 )
=> ~ ( X901 @ X903 ) ) )
=> ( ! [X904: $i,X905: $i > $o] :
( ? [X906: $i] :
( ( in @ X906 @ X904 )
& ~ ( X905 @ X906 ) )
=> ~ ! [X907: $i] :
( ( in @ X907 @ X904 )
=> ( X905 @ X907 ) ) )
=> ( ! [X908: $o] :
( X908
=> ( in @ emptyset @ ( prop2set @ X908 ) ) )
=> ( prop2set2propI
=> ( ! [X909: $i,X910: $i > $o] :
( ~ ? [X911: $i] :
( ( in @ X911 @ X909 )
& ( X910 @ X911 ) )
=> ! [X912: $i] :
( ( in @ X912 @ X909 )
=> ~ ( X910 @ X912 ) ) )
=> ( ! [X913: $i,X914: $i > $o] :
( ~ ! [X915: $i] :
( ( in @ X915 @ X913 )
=> ( X914 @ X915 ) )
=> ? [X916: $i] :
( ( in @ X916 @ X913 )
& ~ ( X914 @ X916 ) ) )
=> ( ! [X917: $i > $o] :
( ? [X918: $i] :
( ( X917 @ X918 )
& ! [X919: $i] :
( ( X917 @ X919 )
=> ( X918 = X919 ) ) )
=> ( exu @ X917 ) )
=> ( ! [X920: $i > $o] :
( ? [X921: $i] : ( X920 @ X921 )
=> ( ! [X922: $i,X923: $i] :
( ( X920 @ X922 )
=> ( ( X920 @ X923 )
=> ( X922 = X923 ) ) )
=> ( exu @ X920 ) ) )
=> ( ! [X924: $i > $o] :
( ? [X925: $i] :
! [X926: $i] :
( ( X924 @ X926 )
<=> ( X926 = X925 ) )
=> ( exu @ X924 ) )
=> ( ! [X927: $i,X928: $i] :
( ( X927 = X928 )
=> ! [X929: $i,X930: $i] :
( ( X929 = X930 )
=> ( ( in @ X929 @ X927 )
=> ( in @ X930 @ X928 ) ) ) )
=> ( ! [X931: $i,X932: $i] :
( ( X931 = X932 )
=> ! [X933: $i,X934: $i] :
( ( X933 = X934 )
=> ( ( in @ X933 @ X931 )
<=> ( in @ X934 @ X932 ) ) ) )
=> ( ! [X935: $i > $o] :
( ( exu @ X935 )
=> ! [X936: $i,X937: $i] :
( ( X935 @ X936 )
=> ( ( X935 @ X937 )
=> ( X936 = X937 ) ) ) )
=> ( ! [X938: $i > $o,X939: $i > $o] :
( ! [X940: $i,X941: $i] :
( ( X940 = X941 )
=> ( ( X938 @ X940 )
<=> ( X939 @ X941 ) ) )
=> ( ( exu @ X938 )
<=> ( exu @ X939 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X942: $i,X943: $i] :
( ( X942 = X943 )
=> ! [X944: $i,X945: $i] :
( ( X944 = X945 )
=> ( ( setadjoin @ X942 @ X944 )
= ( setadjoin @ X943 @ X945 ) ) ) )
=> ( ! [X946: $i,X947: $i] :
( ( X946 = X947 )
=> ( ( powerset @ X946 )
= ( powerset @ X947 ) ) )
=> ( ! [X948: $i,X949: $i] :
( ( X948 = X949 )
=> ( ( setunion @ X948 )
= ( setunion @ X949 ) ) )
=> ( ( omega = omega )
=> ( ! [X950: $i > $o] :
( ( exu @ X950 )
=> ! [X951: $i,X952: $i] :
( ( X950 @ X951 )
=> ( ( X950 @ X952 )
=> ( X951 = X952 ) ) ) )
=> ( ! [X953: $i > $o,X954: $i > $o] :
( ! [X955: $i,X956: $i] :
( ( X955 = X956 )
=> ( ( X953 @ X955 )
<=> ( X954 @ X956 ) ) )
=> ( ( exu @ X953 )
=> ( ( exu @ X954 )
=> ( ( descr @ X953 )
= ( descr @ X954 ) ) ) ) )
=> ( ! [X957: $i,X958: $i] :
( ( X957 = X958 )
=> ! [X959: $i > $o,X960: $i > $o] :
( ! [X961: $i] :
( ( in @ X961 @ X957 )
=> ! [X962: $i] :
( ( in @ X962 @ X958 )
=> ( ( X961 = X962 )
=> ( ( X959 @ X961 )
<=> ( X960 @ X962 ) ) ) ) )
=> ( ( dsetconstr @ X957 @ X959 )
= ( dsetconstr @ X958 @ X960 ) ) ) )
=> ( ! [X963: $i,X964: $i] :
( ! [X965: $i] :
( ( in @ X965 @ X963 )
=> ( in @ X965 @ X964 ) )
=> ( subset @ X963 @ X964 ) )
=> ( ! [X966: $i,X967: $i] :
( ( X966 = X967 )
=> ( subset @ X967 @ X966 ) )
=> ( ! [X968: $i,X969: $i] :
( ( X968 = X969 )
=> ( subset @ X968 @ X969 ) )
=> ( ! [X970: $i,X971: $i] :
( ! [X972: $i] :
( ( in @ X972 @ X970 )
=> ( in @ X972 @ X971 ) )
=> ( subset @ X970 @ X971 ) )
=> ( ! [X973: $i] : ( subset @ emptyset @ X973 )
=> ( ! [X974: $i,X975: $i,X976: $i] :
( ( subset @ X974 @ X975 )
=> ( ( in @ X976 @ X974 )
=> ( in @ X976 @ X975 ) ) )
=> ( ! [X977: $i,X978: $i,X979: $i] :
( ( subset @ X977 @ X978 )
=> ( ~ ( in @ X979 @ X978 )
=> ~ ( in @ X979 @ X977 ) ) )
=> ( ! [X980: $i,X981: $i,X982: $i] :
( ( in @ X982 @ X980 )
=> ( ~ ( in @ X982 @ X981 )
=> ~ ( subset @ X980 @ X981 ) ) )
=> ( ! [X983: $i,X984: $i] :
( ~ ( subset @ X983 @ X984 )
=> ( X983 != X984 ) )
=> ( ! [X985: $i,X986: $i,X987: $i] :
( ( in @ X987 @ X985 )
=> ( ~ ( in @ X987 @ X986 )
=> ( X985 != X986 ) ) )
=> ( ! [X988: $i] : ( subset @ X988 @ X988 )
=> ( ! [X989: $i,X990: $i,X991: $i] :
( ( subset @ X989 @ X990 )
=> ( ( subset @ X990 @ X991 )
=> ( subset @ X989 @ X991 ) ) )
=> ( ! [X992: $i,X993: $i] : ( subset @ X993 @ ( setadjoin @ X992 @ X993 ) )
=> ( ! [X994: $i,X995: $i,X996: $i] :
( ( subset @ X994 @ X996 )
=> ( subset @ X994 @ ( setadjoin @ X995 @ X996 ) ) )
=> ( ! [X997: $i,X998: $i] :
( ( subset @ X997 @ X998 )
=> ( in @ X997 @ ( powerset @ X998 ) ) )
=> ( ! [X999: $i,X1000: $i] :
( ( subset @ X999 @ X1000 )
=> ( ( subset @ X1000 @ X999 )
=> ( X999 = X1000 ) ) )
=> ( ! [X1001: $i] :
( ( subset @ X1001 @ emptyset )
=> ( X1001 = emptyset ) )
=> ( ! [X1002: $i,X1003: $i] :
( ( subset @ X1003 @ X1002 )
=> ( in @ X1003 @ ( powerset @ X1002 ) ) )
=> ( ! [X1004: $i,X1005: $i] :
( ( in @ X1005 @ ( powerset @ X1004 ) )
=> ( subset @ X1005 @ X1004 ) )
=> ( ! [X1006: $i] : ( in @ X1006 @ ( powerset @ X1006 ) )
=> ( ! [X1007: $i,X1008: $i] :
( ( subset @ X1007 @ X1008 )
=> ( subset @ ( powerset @ X1007 ) @ ( powerset @ X1008 ) ) )
=> ( ! [X1009: $i,X1010: $i > $o] : ( in @ ( dsetconstr @ X1009 @ X1010 ) @ ( powerset @ X1009 ) )
=> ( ! [X1011: $i,X1012: $i > $o] : ( subset @ ( dsetconstr @ X1011 @ X1012 ) @ X1011 )
=> ( ! [X1013: $i,X1014: $i,X1015: $i] :
( ( in @ X1015 @ X1013 )
=> ( in @ X1015 @ ( binunion @ X1013 @ X1014 ) ) )
=> ( ! [X1016: $i,X1017: $i] : ( in @ X1017 @ ( setadjoin @ X1016 @ ( setadjoin @ X1017 @ emptyset ) ) )
=> ( ! [X1018: $i,X1019: $i,X1020: $i] :
( ( in @ X1020 @ X1019 )
=> ( in @ X1020 @ ( binunion @ X1018 @ X1019 ) ) )
=> ( ! [X1021: $i,X1022: $i,X1023: $i,X1024: $o] :
( ( in @ X1023 @ ( binunion @ X1021 @ X1022 ) )
=> ( ( ( in @ X1023 @ X1021 )
=> X1024 )
=> ( ( ( in @ X1023 @ X1022 )
=> X1024 )
=> X1024 ) ) )
=> ( ! [X1025: $i,X1026: $i,X1027: $i] :
( ( in @ X1027 @ ( binunion @ X1025 @ X1026 ) )
=> ( ( in @ X1027 @ X1025 )
| ( in @ X1027 @ X1026 ) ) )
=> ( ! [X1028: $i,X1029: $i] : ( subset @ X1028 @ ( binunion @ X1028 @ X1029 ) )
=> ( ! [X1030: $i,X1031: $i] : ( subset @ X1031 @ ( binunion @ X1030 @ X1031 ) )
=> ( ! [X1032: $i,X1033: $i,X1034: $i] :
( ( in @ X1034 @ X1032 )
=> ( ( in @ X1034 @ X1033 )
=> ( in @ X1034 @ ( binintersect @ X1032 @ X1033 ) ) ) )
=> ( ! [X1035: $i,X1036: $i,X1037: $i] :
( ( subset @ X1037 @ X1035 )
=> ( ( subset @ X1037 @ X1036 )
=> ( subset @ X1037 @ ( binintersect @ X1035 @ X1036 ) ) ) )
=> ( ! [X1038: $i,X1039: $i,X1040: $i] :
( ( in @ X1040 @ ( binintersect @ X1038 @ X1039 ) )
=> ( in @ X1040 @ X1038 ) )
=> ( ! [X1041: $i,X1042: $i] : ( subset @ ( binintersect @ X1041 @ X1042 ) @ X1041 )
=> ( ! [X1043: $i,X1044: $i] :
( ( subset @ X1043 @ X1044 )
=> ( ( binintersect @ X1043 @ X1044 )
= X1043 ) )
=> ( ! [X1045: $i,X1046: $i] :
( ( ( binintersect @ X1045 @ X1046 )
= X1046 )
=> ( subset @ X1046 @ X1045 ) )
=> ( ! [X1047: $i,X1048: $i,X1049: $i] :
( ( in @ X1049 @ ( binintersect @ X1047 @ X1048 ) )
=> ( in @ X1049 @ X1048 ) )
=> ( ! [X1050: $i,X1051: $i] :
( ~ ? [X1052: $i] :
( ( in @ X1052 @ X1050 )
& ( in @ X1052 @ X1051 ) )
=> ( ( binintersect @ X1050 @ X1051 )
= emptyset ) )
=> ( ! [X1053: $i,X1054: $i] : ( subset @ ( binintersect @ X1053 @ X1054 ) @ X1054 )
=> ( ! [X1055: $i,X1056: $i] :
( ( subset @ X1056 @ X1055 )
=> ( ( binintersect @ X1055 @ X1056 )
= X1056 ) )
=> ( ! [X1057: $i,X1058: $i] :
( ( ( binintersect @ X1057 @ X1058 )
= X1057 )
=> ( subset @ X1057 @ X1058 ) )
=> ( ! [X1059: $i,X1060: $i,X1061: $i] :
( ( binintersect @ X1059 @ ( binunion @ X1060 @ X1061 ) )
= ( binunion @ ( binintersect @ X1059 @ X1060 ) @ ( binintersect @ X1059 @ X1061 ) ) )
=> ( ! [X1062: $i,X1063: $i,X1064: $i] :
( ( in @ X1064 @ X1062 )
=> ( ~ ( in @ X1064 @ X1063 )
=> ( in @ X1064 @ ( setminus @ X1062 @ X1063 ) ) ) )
=> ( ! [X1065: $i,X1066: $i,X1067: $i] :
( ( in @ X1067 @ ( setminus @ X1065 @ X1066 ) )
=> ( in @ X1067 @ X1065 ) )
=> ( ! [X1068: $i,X1069: $i,X1070: $i] :
( ( in @ X1070 @ ( setminus @ X1068 @ X1069 ) )
=> ~ ( in @ X1070 @ X1069 ) )
=> ( ! [X1071: $i,X1072: $i] :
( ( subset @ X1071 @ X1072 )
=> ( ( setminus @ X1071 @ X1072 )
= emptyset ) )
=> ( ! [X1073: $i,X1074: $i,X1075: $i] :
( ~ ( in @ X1075 @ ( setminus @ X1073 @ X1074 ) )
=> ( ( in @ X1075 @ X1073 )
=> ( in @ X1075 @ X1074 ) ) )
=> ( ! [X1076: $i,X1077: $i,X1078: $i] :
( ~ ( in @ X1078 @ ( setminus @ X1076 @ X1077 ) )
=> ( ~ ( in @ X1078 @ X1077 )
=> ~ ( in @ X1078 @ X1076 ) ) )
=> ( ! [X1079: $i,X1080: $i,X1081: $i] :
( ~ ( in @ X1081 @ X1079 )
=> ~ ( in @ X1081 @ ( setminus @ X1079 @ X1080 ) ) )
=> ( ! [X1082: $i,X1083: $i,X1084: $i] :
( ( in @ X1084 @ X1083 )
=> ~ ( in @ X1084 @ ( setminus @ X1082 @ X1083 ) ) )
=> ( ! [X1085: $i,X1086: $i] : ( subset @ ( setminus @ X1085 @ X1086 ) @ X1085 )
=> ( ! [X1087: $i,X1088: $i] :
( ( ( setminus @ X1087 @ X1088 )
= emptyset )
=> ( subset @ X1087 @ X1088 ) )
=> ( ! [X1089: $i,X1090: $i,X1091: $i] :
( ( in @ X1091 @ ( symdiff @ X1089 @ X1090 ) )
=> ! [X1092: $o] :
( ( ( in @ X1091 @ X1089 )
=> ( ~ ( in @ X1091 @ X1090 )
=> X1092 ) )
=> ( ( ~ ( in @ X1091 @ X1089 )
=> ( ( in @ X1091 @ X1090 )
=> X1092 ) )
=> X1092 ) ) )
=> ( ! [X1093: $i,X1094: $i,X1095: $i] :
( ( in @ X1095 @ X1093 )
=> ( ~ ( in @ X1095 @ X1094 )
=> ( in @ X1095 @ ( symdiff @ X1093 @ X1094 ) ) ) )
=> ( ! [X1096: $i,X1097: $i,X1098: $i] :
( ~ ( in @ X1098 @ X1096 )
=> ( ( in @ X1098 @ X1097 )
=> ( in @ X1098 @ ( symdiff @ X1096 @ X1097 ) ) ) )
=> ( ! [X1099: $i,X1100: $i,X1101: $i] :
( ( in @ X1101 @ X1099 )
=> ( ( in @ X1101 @ X1100 )
=> ~ ( in @ X1101 @ ( symdiff @ X1099 @ X1100 ) ) ) )
=> ( ! [X1102: $i,X1103: $i,X1104: $i] :
( ~ ( in @ X1104 @ X1102 )
=> ( ~ ( in @ X1104 @ X1103 )
=> ~ ( in @ X1104 @ ( symdiff @ X1102 @ X1103 ) ) ) )
=> ( ! [X1105: $i,X1106: $i] : ( in @ X1106 @ ( setadjoin @ X1105 @ ( setadjoin @ X1106 @ emptyset ) ) )
=> ( ! [X1107: $i,X1108: $i] : ( in @ X1107 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1107 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1107 @ ( setadjoin @ X1108 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1109: $i,X1110: $i] : ( in @ X1110 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1109 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1109 @ ( setadjoin @ X1110 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1111: $i,X1112: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1111 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1111 @ ( setadjoin @ X1112 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1113: $i,X1114: $i] : ( iskpair @ ( kpair @ X1113 @ X1114 ) )
=> ( ! [X1115: $i,X1116: $i] :
( ( in @ X1116 @ X1115 )
=> ( subset @ ( setadjoin @ X1116 @ emptyset ) @ X1115 ) )
=> ( ! [X1117: $i,X1118: $i] :
( ( in @ X1118 @ X1117 )
=> ( in @ ( setadjoin @ X1118 @ emptyset ) @ ( powerset @ X1117 ) ) )
=> ( ! [X1119: $i,X1120: $i,X1121: $i] :
( ( in @ X1121 @ X1119 )
=> ( in @ ( setadjoin @ X1121 @ emptyset ) @ ( powerset @ ( binunion @ X1119 @ X1120 ) ) ) )
=> ( ! [X1122: $i,X1123: $i,X1124: $i] :
( ( in @ X1124 @ ( setadjoin @ X1122 @ ( setadjoin @ X1123 @ emptyset ) ) )
=> ( ( X1124 = X1122 )
| ( X1124 = X1123 ) ) )
=> ( ! [X1125: $i,X1126: $i,X1127: $i] :
( ( in @ X1127 @ X1125 )
=> ! [X1128: $i] :
( ( in @ X1128 @ X1126 )
=> ( subset @ ( setadjoin @ X1127 @ ( setadjoin @ X1128 @ emptyset ) ) @ ( binunion @ X1125 @ X1126 ) ) ) )
=> ( ! [X1129: $i,X1130: $i,X1131: $i] :
( ( in @ X1131 @ X1129 )
=> ! [X1132: $i] :
( ( in @ X1132 @ X1130 )
=> ( in @ ( setadjoin @ X1131 @ ( setadjoin @ X1132 @ emptyset ) ) @ ( powerset @ ( binunion @ X1129 @ X1130 ) ) ) ) )
=> ( ! [X1133: $i,X1134: $i,X1135: $i] :
( ( in @ X1135 @ X1133 )
=> ! [X1136: $i] :
( ( in @ X1136 @ X1134 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1135 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1135 @ ( setadjoin @ X1136 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1133 @ X1134 ) ) ) ) )
=> ( ! [X1137: $i,X1138: $i,X1139: $i] :
( ( in @ X1139 @ X1137 )
=> ! [X1140: $i] :
( ( in @ X1140 @ X1138 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1139 @ ( setadjoin @ X1140 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1137 @ X1138 ) ) ) ) ) )
=> ( ! [X1141: $i,X1142: $i,X1143: $i] :
( ( in @ X1143 @ X1141 )
=> ! [X1144: $i] :
( ( in @ X1144 @ X1142 )
=> ( in @ ( kpair @ X1143 @ X1144 ) @ ( powerset @ ( powerset @ ( binunion @ X1141 @ X1142 ) ) ) ) ) )
=> ( ! [X1145: $i,X1146: $i,X1147: $i] :
( ( in @ X1147 @ X1145 )
=> ! [X1148: $i] :
( ( in @ X1148 @ X1146 )
=> ( in @ ( kpair @ X1147 @ X1148 ) @ ( cartprod @ X1145 @ X1146 ) ) ) )
=> ( ! [X1149: $i,X1150: $i,X1151: $i] :
( ( in @ X1151 @ ( cartprod @ X1149 @ X1150 ) )
=> ? [X1152: $i] :
( ( in @ X1152 @ X1149 )
& ? [X1153: $i] :
( ( in @ X1153 @ X1150 )
& ( X1151
= ( kpair @ X1152 @ X1153 ) ) ) ) )
=> ( ! [X1154: $i,X1155: $i,X1156: $i] :
( ( in @ X1156 @ ( cartprod @ X1154 @ X1155 ) )
=> ( iskpair @ X1156 ) )
=> ( ! [X1157: $i,X1158: $i] :
( ( in @ X1158 @ ( setunion @ X1157 ) )
=> ? [X1159: $i] :
( ( in @ X1159 @ X1157 )
& ( in @ X1158 @ X1159 ) ) )
=> ( ! [X1160: $i] : ( subset @ ( setunion @ ( setadjoin @ X1160 @ emptyset ) ) @ X1160 )
=> ( ! [X1161: $i] : ( subset @ X1161 @ ( setunion @ ( setadjoin @ X1161 @ emptyset ) ) )
=> ( ! [X1162: $i] :
( ( setunion @ ( setadjoin @ X1162 @ emptyset ) )
= X1162 )
=> ( ! [X1163: $i,X1164: $i > $o] :
( ! [X1165: $i] :
( ( in @ X1165 @ X1163 )
=> ! [X1166: $i] :
( ( in @ X1166 @ X1163 )
=> ( ( X1164 @ X1165 )
=> ( ( X1164 @ X1166 )
=> ( X1165 = X1166 ) ) ) ) )
=> ( ? [X1167: $i] :
( ( in @ X1167 @ X1163 )
& ( X1164 @ X1167 ) )
=> ( singleton @ ( dsetconstr @ X1163 @ X1164 ) ) ) )
=> ( ! [X1168: $i,X1169: $i > $o] :
( ( ex1 @ X1168 @ X1169 )
=> ? [X1170: $i] :
( ( in @ X1170 @ X1168 )
& ( X1169 @ X1170 ) ) )
=> ( ! [X1171: $i,X1172: $i > $o,X1173: $i] :
( ( in @ X1173 @ X1171 )
=> ( ( X1172 @ X1173 )
=> ( ! [X1174: $i] :
( ( in @ X1174 @ X1171 )
=> ( ( X1172 @ X1174 )
=> ( X1174 = X1173 ) ) )
=> ( ex1 @ X1171 @ X1172 ) ) ) )
=> ( ! [X1175: $i,X1176: $i > $o] :
( ! [X1177: $i] :
( ( in @ X1177 @ X1175 )
=> ! [X1178: $i] :
( ( in @ X1178 @ X1175 )
=> ( ( X1176 @ X1177 )
=> ( ( X1176 @ X1178 )
=> ( X1177 = X1178 ) ) ) ) )
=> ( ? [X1179: $i] :
( ( in @ X1179 @ X1175 )
& ( X1176 @ X1179 ) )
=> ( ex1 @ X1175 @ X1176 ) ) )
=> ( ! [X1180: $i,X1181: $i] :
( ( ( setadjoin @ X1180 @ emptyset )
= ( setadjoin @ X1181 @ emptyset ) )
=> ( X1180 = X1181 ) )
=> ( ! [X1182: $i,X1183: $i,X1184: $i] :
( ( in @ ( setadjoin @ X1184 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1182 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1182 @ ( setadjoin @ X1183 @ emptyset ) ) @ emptyset ) ) )
=> ( X1182 = X1184 ) )
=> ( ! [X1185: $i] :
( ( iskpair @ X1185 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1185 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1185 ) ) ) )
=> ( ! [X1186: $i] :
( ( singleton @ X1186 )
=> ( in @ ( setunion @ X1186 ) @ X1186 ) )
=> ( ! [X1187: $i,X1188: $i] :
( ( kfst @ ( kpair @ X1187 @ X1188 ) )
= X1187 )
=> ( ! [X1189: $i,X1190: $i,X1191: $i] :
( ( in @ X1191 @ ( cartprod @ X1189 @ X1190 ) )
=> ( in @ ( kfst @ X1191 ) @ X1189 ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i,X1195: $i] :
( ( ( setadjoin @ ( setadjoin @ X1192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1192 @ ( setadjoin @ X1193 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1194 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1194 @ ( setadjoin @ X1195 @ emptyset ) ) @ emptyset ) ) )
=> ( X1192 = X1194 ) )
=> ( ! [X1196: $i,X1197: $i,X1198: $i,X1199: $i] :
( ( ( kpair @ X1196 @ X1197 )
= ( kpair @ X1198 @ X1199 ) )
=> ( X1196 = X1198 ) )
=> ( ! [X1200: $i,X1201: $i] :
( ( X1200 = X1201 )
=> ( ( setadjoin @ X1200 @ ( setadjoin @ X1201 @ emptyset ) )
= ( setadjoin @ X1200 @ emptyset ) ) )
=> ( ! [X1202: $i,X1203: $i] :
( ( X1202 = X1203 )
=> ( ( setadjoin @ ( setadjoin @ X1202 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1202 @ ( setadjoin @ X1203 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1202 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1204: $i,X1205: $i,X1206: $i,X1207: $i] :
( ( ( setadjoin @ ( setadjoin @ X1204 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1204 @ ( setadjoin @ X1205 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1206 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1206 @ ( setadjoin @ X1207 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1206 = X1207 )
=> ( X1205 = X1207 ) ) )
=> ( ! [X1208: $i,X1209: $i,X1210: $i] :
( ( ( setadjoin @ X1208 @ ( setadjoin @ X1209 @ emptyset ) )
= ( setadjoin @ X1210 @ emptyset ) )
=> ( X1208 = X1209 ) )
=> ( ! [X1211: $i,X1212: $i,X1213: $i,X1214: $i] :
( ( ( setadjoin @ ( setadjoin @ X1211 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1211 @ ( setadjoin @ X1212 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1213 @ ( setadjoin @ X1214 @ emptyset ) ) @ emptyset ) ) )
=> ( X1212 = X1214 ) )
=> ( ! [X1215: $i,X1216: $i,X1217: $i,X1218: $i] :
( ( ( kpair @ X1215 @ X1216 )
= ( kpair @ X1217 @ X1218 ) )
=> ( X1216 = X1218 ) )
=> ( ! [X1219: $i] :
( ( iskpair @ X1219 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1219 )
@ ^ [Z0: $i] :
( X1219
= ( kpair @ ( kfst @ X1219 ) @ Z0 ) ) ) ) )
=> ( ! [X1220: $i,X1221: $i] :
( ( ksnd @ ( kpair @ X1220 @ X1221 ) )
= X1221 )
=> ( ! [X1222: $i] :
( ( iskpair @ X1222 )
=> ( ( kpair @ ( kfst @ X1222 ) @ ( ksnd @ X1222 ) )
= X1222 ) )
=> ( ! [X1223: $i,X1224: $i,X1225: $i] :
( ( in @ X1225 @ ( cartprod @ X1223 @ X1224 ) )
=> ( in @ ( ksnd @ X1225 ) @ X1224 ) )
=> ( ! [X1226: $i,X1227: $i,X1228: $i,X1229: $i] :
( ( in @ ( kpair @ X1228 @ X1229 ) @ ( cartprod @ X1226 @ X1227 ) )
=> ( in @ X1228 @ X1226 ) )
=> ( ! [X1230: $i,X1231: $i,X1232: $i,X1233: $i] :
( ( in @ ( kpair @ X1232 @ X1233 ) @ ( cartprod @ X1230 @ X1231 ) )
=> ( in @ X1233 @ X1231 ) )
=> ( ! [X1234: $i,X1235: $i,X1236: $i] :
( ( in @ X1236 @ X1234 )
=> ! [X1237: $i] :
( ( in @ X1237 @ X1235 )
=> ( ( kpair @ X1236 @ X1237 )
= ( kpair @ X1236 @ X1237 ) ) ) )
=> ( ! [X1238: $i,X1239: $i,X1240: $i] :
( ( in @ X1240 @ X1238 )
=> ! [X1241: $i] :
( ( in @ X1241 @ X1239 )
=> ( ( kfst @ ( kpair @ X1240 @ X1241 ) )
= X1240 ) ) )
=> ( ! [X1242: $i,X1243: $i,X1244: $i] :
( ( in @ X1244 @ X1242 )
=> ! [X1245: $i] :
( ( in @ X1245 @ X1243 )
=> ( ( ksnd @ ( kpair @ X1244 @ X1245 ) )
= X1245 ) ) )
=> ( ! [X1246: $i,X1247: $i,X1248: $i] :
( ( in @ X1248 @ ( cartprod @ X1246 @ X1247 ) )
=> ( ( kpair @ ( kfst @ X1248 ) @ ( ksnd @ X1248 ) )
= X1248 ) )
=> ( ! [X1249: $i,X1250: $i,X1251: $i > $i > $o,X1252: $i] :
( ( in @ X1252 @ X1249 )
=> ! [X1253: $i] :
( ( in @ X1253 @ X1250 )
=> ( ( X1251 @ X1252 @ X1253 )
=> ( in @ ( kpair @ X1252 @ X1253 ) @ ( dpsetconstr @ X1249 @ X1250 @ X1251 ) ) ) ) )
=> ( ! [X1254: $i,X1255: $i,X1256: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1254 @ X1255 @ X1256 ) @ ( cartprod @ X1254 @ X1255 ) )
=> ( ! [X1257: $i,X1258: $i,X1259: $i > $i > $o] : ( breln @ X1257 @ X1258 @ ( dpsetconstr @ X1257 @ X1258 @ X1259 ) )
=> ( ! [X1260: $i,X1261: $i,X1262: $i > $i > $o,X1263: $i] :
( ( in @ X1263 @ X1260 )
=> ! [X1264: $i] :
( ( in @ X1264 @ X1261 )
=> ( ( in @ ( kpair @ X1263 @ X1264 ) @ ( dpsetconstr @ X1260 @ X1261 @ X1262 ) )
=> ( X1262 @ X1263 @ X1264 ) ) ) )
=> ( ! [X1265: $i,X1266: $i,X1267: $i > $i > $o,X1268: $i,X1269: $i] :
( ( in @ ( kpair @ X1268 @ X1269 ) @ ( dpsetconstr @ X1265 @ X1266 @ X1267 ) )
=> ( in @ X1268 @ X1265 ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i > $i > $o,X1273: $i,X1274: $i] :
( ( in @ ( kpair @ X1273 @ X1274 ) @ ( dpsetconstr @ X1270 @ X1271 @ X1272 ) )
=> ( in @ X1274 @ X1271 ) )
=> ( ! [X1275: $i,X1276: $i,X1277: $i > $i > $o,X1278: $i,X1279: $i] :
( ( in @ ( kpair @ X1278 @ X1279 ) @ ( dpsetconstr @ X1275 @ X1276 @ X1277 ) )
=> ( X1277 @ X1278 @ X1279 ) )
=> ( ! [X1280: $i,X1281: $i,X1282: $i] :
( ( func @ X1280 @ X1281 @ X1282 )
=> ! [X1283: $i] :
( ( in @ X1283 @ X1280 )
=> ( singleton
@ ( dsetconstr @ X1281
@ ^ [Z0: $i] : ( in @ ( kpair @ X1283 @ Z0 ) @ X1282 ) ) ) ) )
=> ( ! [X1284: $i,X1285: $i,X1286: $i] :
( ( func @ X1284 @ X1285 @ X1286 )
=> ! [X1287: $i] :
( ( in @ X1287 @ X1284 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1285
@ ^ [Z0: $i] : ( in @ ( kpair @ X1287 @ Z0 ) @ X1286 ) ) )
@ X1285 ) ) )
=> ( ! [X1288: $i,X1289: $i,X1290: $i] :
( ( func @ X1288 @ X1289 @ X1290 )
=> ! [X1291: $i] :
( ( in @ X1291 @ X1288 )
=> ( in @ ( ap @ X1288 @ X1289 @ X1290 @ X1291 ) @ X1289 ) ) )
=> ( ! [X1292: $i,X1293: $i,X1294: $i] :
( ( in @ X1294 @ ( funcSet @ X1292 @ X1293 ) )
=> ( func @ X1292 @ X1293 @ X1294 ) )
=> ( ! [X1295: $i,X1296: $i,X1297: $i] :
( ( in @ X1297 @ ( funcSet @ X1295 @ X1296 ) )
=> ! [X1298: $i] :
( ( in @ X1298 @ X1295 )
=> ( in @ ( ap @ X1295 @ X1296 @ X1297 @ X1298 ) @ X1296 ) ) )
=> ( ! [X1299: $i,X1300: $i,X1301: $i] :
( ( func @ X1299 @ X1300 @ X1301 )
=> ( in @ X1301 @ ( funcSet @ X1299 @ X1300 ) ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i > $i] :
( ! [X1305: $i] :
( ( in @ X1305 @ X1302 )
=> ( in @ ( X1304 @ X1305 ) @ X1303 ) )
=> ( func @ X1302 @ X1303
@ ( dpsetconstr @ X1302 @ X1303
@ ^ [Z0: $i] : ( $eq @ ( X1304 @ Z0 ) ) ) ) )
=> ( ! [X1306: $i,X1307: $i,X1308: $i > $i] :
( ! [X1309: $i] :
( ( in @ X1309 @ X1306 )
=> ( in @ ( X1308 @ X1309 ) @ X1307 ) )
=> ( func @ X1306 @ X1307 @ ( lam @ X1306 @ X1307 @ X1308 ) ) )
=> ( ! [X1310: $i,X1311: $i,X1312: $i > $i] :
( ! [X1313: $i] :
( ( in @ X1313 @ X1310 )
=> ( in @ ( X1312 @ X1313 ) @ X1311 ) )
=> ( in @ ( lam @ X1310 @ X1311 @ X1312 ) @ ( funcSet @ X1310 @ X1311 ) ) )
=> ( ! [X1314: $i,X1315: $i,X1316: $i] :
( ( breln @ X1314 @ X1315 @ X1316 )
=> ! [X1317: $i > $o] :
( ! [X1318: $i] :
( ( in @ X1318 @ X1314 )
=> ! [X1319: $i] :
( ( in @ X1319 @ X1315 )
=> ( ( in @ ( kpair @ X1318 @ X1319 ) @ X1316 )
=> ( X1317 @ ( kpair @ X1318 @ X1319 ) ) ) ) )
=> ! [X1320: $i] :
( ( in @ X1320 @ X1316 )
=> ( X1317 @ X1320 ) ) ) )
=> ( ! [X1321: $i,X1322: $i,X1323: $i] :
( ( breln @ X1321 @ X1322 @ X1323 )
=> ! [X1324: $i > $o] :
( ! [X1325: $i] :
( ( in @ X1325 @ X1321 )
=> ! [X1326: $i] :
( ( in @ X1326 @ X1322 )
=> ( ( in @ ( kpair @ X1325 @ X1326 ) @ X1323 )
=> ( X1324 @ ( kpair @ X1325 @ X1326 ) ) ) ) )
=> ! [X1327: $i] :
( ( in @ X1327 @ X1323 )
=> ( X1324 @ X1327 ) ) ) )
=> ( ! [X1328: $i,X1329: $i > $o] :
( ( ex1 @ X1328 @ X1329 )
=> ! [X1330: $i] :
( ( in @ X1330 @ X1328 )
=> ! [X1331: $i] :
( ( in @ X1331 @ X1328 )
=> ( ( X1329 @ X1330 )
=> ( ( X1329 @ X1331 )
=> ( X1330 = X1331 ) ) ) ) ) )
=> ( ! [X1332: $i,X1333: $i,X1334: $i] :
( ( func @ X1332 @ X1333 @ X1334 )
=> ! [X1335: $i] :
( ( in @ X1335 @ X1332 )
=> ( in @ ( kpair @ X1335 @ ( ap @ X1332 @ X1333 @ X1334 @ X1335 ) ) @ X1334 ) ) )
=> ( ! [X1336: $i,X1337: $i,X1338: $i] :
( ( in @ X1338 @ ( funcSet @ X1336 @ X1337 ) )
=> ! [X1339: $i] :
( ( in @ X1339 @ X1336 )
=> ( in @ ( kpair @ X1339 @ ( ap @ X1336 @ X1337 @ X1338 @ X1339 ) ) @ X1338 ) ) )
=> ( ! [X1340: $i,X1341: $i,X1342: $i] :
( ( func @ X1340 @ X1341 @ X1342 )
=> ! [X1343: $i] :
( ( in @ X1343 @ X1340 )
=> ! [X1344: $i] :
( ( in @ X1344 @ X1341 )
=> ( ( in @ ( kpair @ X1343 @ X1344 ) @ X1342 )
=> ( ( ap @ X1340 @ X1341 @ X1342 @ X1343 )
= X1344 ) ) ) ) )
=> ( ! [X1345: $i,X1346: $i,X1347: $i] :
( ( func @ X1345 @ X1346 @ X1347 )
=> ! [X1348: $i] :
( ( func @ X1345 @ X1346 @ X1348 )
=> ( ! [X1349: $i] :
( ( in @ X1349 @ X1345 )
=> ( ( ap @ X1345 @ X1346 @ X1347 @ X1349 )
= ( ap @ X1345 @ X1346 @ X1348 @ X1349 ) ) )
=> ! [X1350: $i] :
( ( in @ X1350 @ X1345 )
=> ! [X1351: $i] :
( ( in @ X1351 @ X1346 )
=> ( ( in @ ( kpair @ X1350 @ X1351 ) @ X1348 )
=> ( in @ ( kpair @ X1350 @ X1351 ) @ X1347 ) ) ) ) ) ) )
=> ( ! [X1352: $i,X1353: $i,X1354: $i] :
( ( in @ X1354 @ ( funcSet @ X1352 @ X1353 ) )
=> ! [X1355: $i] :
( ( in @ X1355 @ X1352 )
=> ! [X1356: $i] :
( ( in @ X1356 @ X1353 )
=> ( ( in @ ( kpair @ X1355 @ X1356 ) @ X1354 )
=> ( ( ap @ X1352 @ X1353 @ X1354 @ X1355 )
= X1356 ) ) ) ) )
=> ( ! [X1357: $i,X1358: $i,X1359: $i] :
( ( breln @ X1357 @ X1358 @ X1359 )
=> ! [X1360: $i] :
( ( breln @ X1357 @ X1358 @ X1360 )
=> ( ! [X1361: $i] :
( ( in @ X1361 @ X1357 )
=> ! [X1362: $i] :
( ( in @ X1362 @ X1358 )
=> ( ( in @ ( kpair @ X1361 @ X1362 ) @ X1359 )
=> ( in @ ( kpair @ X1361 @ X1362 ) @ X1360 ) ) ) )
=> ( subset @ X1359 @ X1360 ) ) ) )
=> ( ! [X1363: $i,X1364: $i,X1365: $i] :
( ( breln @ X1363 @ X1364 @ X1365 )
=> ! [X1366: $i] :
( ( breln @ X1363 @ X1364 @ X1366 )
=> ( ! [X1367: $i] :
( ( in @ X1367 @ X1363 )
=> ! [X1368: $i] :
( ( in @ X1368 @ X1364 )
=> ( ( in @ ( kpair @ X1367 @ X1368 ) @ X1365 )
=> ( in @ ( kpair @ X1367 @ X1368 ) @ X1366 ) ) ) )
=> ( ! [X1369: $i] :
( ( in @ X1369 @ X1363 )
=> ! [X1370: $i] :
( ( in @ X1370 @ X1364 )
=> ( ( in @ ( kpair @ X1369 @ X1370 ) @ X1366 )
=> ( in @ ( kpair @ X1369 @ X1370 ) @ X1365 ) ) ) )
=> ( X1365 = X1366 ) ) ) ) )
=> ( ! [X1371: $i,X1372: $i,X1373: $i] :
( ( func @ X1371 @ X1372 @ X1373 )
=> ! [X1374: $i] :
( ( func @ X1371 @ X1372 @ X1374 )
=> ( ! [X1375: $i] :
( ( in @ X1375 @ X1371 )
=> ( ( ap @ X1371 @ X1372 @ X1373 @ X1375 )
= ( ap @ X1371 @ X1372 @ X1374 @ X1375 ) ) )
=> ( X1373 = X1374 ) ) ) )
=> ( ! [X1376: $i,X1377: $i,X1378: $i] :
( ( in @ X1378 @ ( funcSet @ X1376 @ X1377 ) )
=> ! [X1379: $i] :
( ( in @ X1379 @ ( funcSet @ X1376 @ X1377 ) )
=> ( ! [X1380: $i] :
( ( in @ X1380 @ X1376 )
=> ( ( ap @ X1376 @ X1377 @ X1378 @ X1380 )
= ( ap @ X1376 @ X1377 @ X1379 @ X1380 ) ) )
=> ( X1378 = X1379 ) ) ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i] :
( ( in @ X1383 @ ( funcSet @ X1381 @ X1382 ) )
=> ! [X1384: $i] :
( ( in @ X1384 @ X1381 )
=> ( ( ap @ X1381 @ X1382 @ X1383 @ X1384 )
= ( ap @ X1381 @ X1382 @ X1383 @ X1384 ) ) ) )
=> ( ! [X1385: $i,X1386: $i,X1387: $i] :
( ( func @ X1385 @ X1386 @ X1387 )
=> ! [X1388: $i] :
( ( in @ X1388 @ X1385 )
=> ( ( ap @ X1385 @ X1386 @ X1387 @ X1388 )
= ( ap @ X1385 @ X1386 @ X1387 @ X1388 ) ) ) )
=> ( ! [X1389: $i,X1390: $i,X1391: $i > $i] :
( ! [X1392: $i] :
( ( in @ X1392 @ X1389 )
=> ( in @ ( X1391 @ X1392 ) @ X1390 ) )
=> ! [X1393: $i] :
( ( in @ X1393 @ X1389 )
=> ( ( ap @ X1389 @ X1390 @ ( lam @ X1389 @ X1390 @ X1391 ) @ X1393 )
= ( X1391 @ X1393 ) ) ) )
=> ( ! [X1394: $i,X1395: $i,X1396: $i] :
( ( func @ X1394 @ X1395 @ X1396 )
=> ( ( lam @ X1394 @ X1395 @ ( ap @ X1394 @ X1395 @ X1396 ) )
= X1396 ) )
=> ( ! [X1397: $i,X1398: $i,X1399: $i > $i] :
( ! [X1400: $i] :
( ( in @ X1400 @ X1397 )
=> ( in @ ( X1399 @ X1400 ) @ X1398 ) )
=> ( ( lam @ X1397 @ X1398 @ X1399 )
= ( lam @ X1397 @ X1398 @ X1399 ) ) )
=> ( ! [X1401: $i,X1402: $i,X1403: $i > $i] :
( ! [X1404: $i] :
( ( in @ X1404 @ X1401 )
=> ( in @ ( X1403 @ X1404 ) @ X1402 ) )
=> ! [X1405: $i] :
( ( in @ X1405 @ X1401 )
=> ( ( ap @ X1401 @ X1402 @ ( lam @ X1401 @ X1402 @ X1403 ) @ X1405 )
= ( X1403 @ X1405 ) ) ) )
=> ( ! [X1406: $i,X1407: $i,X1408: $i] :
( ( in @ X1408 @ ( funcSet @ X1406 @ X1407 ) )
=> ( ( lam @ X1406 @ X1407 @ ( ap @ X1406 @ X1407 @ X1408 ) )
= X1408 ) )
=> ( ! [X1409: $i,X1410: $o,X1411: $i] :
( ( in @ X1411 @ X1409 )
=> ! [X1412: $i] :
( ( in @ X1412 @ X1409 )
=> ( ~ X1410
=> ( in @ X1412
@ ( dsetconstr @ X1409
@ ^ [Z0: $i] :
( ( X1410
& ( Z0 = X1411 ) )
| ( ~ X1410
& ( Z0 = X1412 ) ) ) ) ) ) ) )
=> ( ! [X1413: $i,X1414: $o,X1415: $i] :
( ( in @ X1415 @ X1413 )
=> ! [X1416: $i] :
( ( in @ X1416 @ X1413 )
=> ( ~ X1414
=> ( ( dsetconstr @ X1413
@ ^ [Z0: $i] :
( ( X1414
& ( Z0 = X1415 ) )
| ( ~ X1414
& ( Z0 = X1416 ) ) ) )
= ( setadjoin @ X1416 @ emptyset ) ) ) ) )
=> ( ! [X1417: $i,X1418: $o,X1419: $i] :
( ( in @ X1419 @ X1417 )
=> ! [X1420: $i] :
( ( in @ X1420 @ X1417 )
=> ( X1418
=> ( in @ X1419
@ ( dsetconstr @ X1417
@ ^ [Z0: $i] :
( ( X1418
& ( Z0 = X1419 ) )
| ( ~ X1418
& ( Z0 = X1420 ) ) ) ) ) ) ) )
=> ( ! [X1421: $i,X1422: $o,X1423: $i] :
( ( in @ X1423 @ X1421 )
=> ! [X1424: $i] :
( ( in @ X1424 @ X1421 )
=> ( X1422
=> ( ( dsetconstr @ X1421
@ ^ [Z0: $i] :
( ( X1422
& ( Z0 = X1423 ) )
| ( ~ X1422
& ( Z0 = X1424 ) ) ) )
= ( setadjoin @ X1423 @ emptyset ) ) ) ) )
=> ( ! [X1425: $i,X1426: $o,X1427: $i] :
( ( in @ X1427 @ X1425 )
=> ! [X1428: $i] :
( ( in @ X1428 @ X1425 )
=> ( singleton
@ ( dsetconstr @ X1425
@ ^ [Z0: $i] :
( ( X1426
& ( Z0 = X1427 ) )
| ( ~ X1426
& ( Z0 = X1428 ) ) ) ) ) ) )
=> ( ! [X1429: $i,X1430: $o,X1431: $i] :
( ( in @ X1431 @ X1429 )
=> ! [X1432: $i] :
( ( in @ X1432 @ X1429 )
=> ( in @ ( if @ X1429 @ X1430 @ X1431 @ X1432 ) @ X1429 ) ) )
=> ( ! [X1433: $i] :
( ( singleton @ X1433 )
=> ! [X1434: $i] :
( ( in @ X1434 @ X1433 )
=> ( ( setunion @ X1433 )
= X1434 ) ) )
=> ( ! [X1435: $i,X1436: $o,X1437: $i] :
( ( in @ X1437 @ X1435 )
=> ! [X1438: $i] :
( ( in @ X1438 @ X1435 )
=> ( X1436
=> ( ( if @ X1435 @ X1436 @ X1437 @ X1438 )
= X1437 ) ) ) )
=> ( ! [X1439: $i,X1440: $o,X1441: $i] :
( ( in @ X1441 @ X1439 )
=> ! [X1442: $i] :
( ( in @ X1442 @ X1439 )
=> ( ~ X1440
=> ( ( if @ X1439 @ X1440 @ X1441 @ X1442 )
= X1442 ) ) ) )
=> ( ! [X1443: $i,X1444: $o,X1445: $i] :
( ( in @ X1445 @ X1443 )
=> ! [X1446: $i] :
( ( in @ X1446 @ X1443 )
=> ( in @ ( if @ X1443 @ X1444 @ X1445 @ X1446 ) @ ( setadjoin @ X1445 @ ( setadjoin @ X1446 @ emptyset ) ) ) ) )
=> ( ! [X1447: $i,X1448: $i] :
( ( in @ X1448 @ ( powerset @ X1447 ) )
=> ! [X1449: $i] :
( ( in @ X1449 @ ( powerset @ X1447 ) )
=> ( in @ ( binintersect @ X1448 @ X1449 ) @ ( powerset @ X1447 ) ) ) )
=> ( ! [X1450: $i,X1451: $i] :
( ( in @ X1451 @ ( powerset @ X1450 ) )
=> ! [X1452: $i] :
( ( in @ X1452 @ ( powerset @ X1450 ) )
=> ( in @ ( binunion @ X1451 @ X1452 ) @ ( powerset @ X1450 ) ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[powersetT_lem]),funcGraphProp4]),binunionT_lem]),c_0_228]),c_0_229]),c_0_230]),c_0_231]),c_0_232]),c_0_233]),c_0_234]),c_0_235]),c_0_236]),c_0_237]),app]),subsetI1]),infuncsetfunc]),ap2p]),eqimpsubset2]),funcinfuncset]),c_0_238]),eqimpsubset1]),c_0_239]),c_0_240]),subsetI2]),brelnall1]),emptysetsubset]),brelnall2]),c_0_241]),funcGraphProp1]),subsetE]),funcGraphProp3]),funcGraphProp2]),funcextLem]),subsetE2]),binunionIR]),subbreln]),eqbreln]),notsubsetI]),funcext]),funcext2]),notequalI1]),ap2apEq1]),ap2apEq2]),notequalI2]),c_0_242]),c_0_243]),c_0_244]),c_0_245]),subsetRefl]),c_0_246]),c_0_247]),subsetTrans]),c_0_248]),c_0_249]),setadjoinSub]),c_0_250]),c_0_251]),setadjoinSub2]),ifp]),theeq]),subset2powerset]),iftrue]),iffalse]),setextsub]),iftrueorfalse]),binintersectT_lem]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_252]),c_0_253]),binunionIL]),upairset2IR]),kpairp]),singletonsubset]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),powerset__Cong]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),setunion__Cong]),symdiffIneg1]),omega__Cong]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_254]),c_0_255]),c_0_256]),c_0_257]),singletonsuniq]),setukpairinjL1]),c_0_258]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_259]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_260]),c_0_261]),setadjoin__Cong]),emptyset__Cong]),c_0_262]),c_0_263]),in__Cong]),inCongP]),c_0_264]),c_0_265]),c_0_266]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_267]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_268]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_269]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_270]),nonemptyE1]),c_0_271]),noeltsimpempty]),emptyI]),setext]),c_0_272]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_273]),c_0_274]),c_0_275]),c_0_276]),c_0_277]),wellorderingAx]),foundationAx]),c_0_278]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_279]) ).
thf(c_0_281,negated_conjecture,
! [X1453: $i,X1454: $i,X1456: $i,X1457: $i,X1458: $i,X1459: $i,X1460: $i,X1461: $i,X1462: $i,X1463: $i,X1464: $i,X1466: $i,X1467: $i,X1469: $i,X1470: $i,X1471: $i,X1472: $i,X1473: $i,X1475: $i,X1476: $i > $i > $o,X1477: $i,X1480: $i,X1482: $i,X1483: $i,X1484: $i,X1485: $i,X1487: $i,X1488: $i > $o,X1489: $i,X1490: $i > $o,X1491: $i,X1492: $i,X1493: $i > $o,X1494: $i,X1495: $i,X1496: $i > $o,X1497: $i,X1498: $i > $o,X1500: $i,X1501: $o,X1502: $i,X1503: $i,X1504: $o,X1505: $i,X1506: $i,X1507: $i > $o,X1509: $i,X1510: $i,X1513: $i,X1515: $i,X1517: $i,X1518: $i > $o,X1519: $i,X1520: $i,X1522: $i,X1523: $i > $o,X1524: $i,X1525: $i,X1526: $i,X1527: $i,X1528: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1533: $i,X1534: $i,X1535: $o,X1536: $i,X1537: $i,X1538: $i,X1539: $i,X1540: $i,X1541: $i,X1543: $i,X1544: $i,X1545: $i,X1546: $i,X1547: $i,X1548: $i,X1549: $i,X1550: $i,X1551: $i,X1552: $i,X1553: $o,X1555: $i,X1556: $i,X1557: $i > $o,X1559: $i,X1560: $i,X1561: $i,X1563: $i,X1564: $i,X1565: $i,X1566: $i,X1567: $i,X1568: $i,X1569: $i,X1570: $i,X1571: $i,X1572: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $i > $o,X1580: $i,X1581: $i > $o,X1582: $i,X1583: $i,X1584: $i > $o,X1585: $i,X1587: $i,X1588: $i > $o,X1590: $i,X1591: $i,X1592: $i > $o,X1594: $i,X1595: $i,X1596: $i > $o,X1597: $i,X1599: $o,X1600: $i,X1601: $i > $o,X1603: $i,X1604: $i,X1605: $i > $o,X1606: $i,X1608: $i > $o,X1609: $i,X1611: $i > $o,X1612: $i,X1615: $i > $o,X1616: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1626: $i > $o,X1627: $i,X1628: $i,X1629: $i > $o,X1630: $i > $o,X1633: $i,X1634: $i,X1635: $i,X1636: $i,X1637: $i,X1638: $i,X1639: $i,X1640: $i,X1641: $i > $o,X1642: $i,X1643: $i,X1644: $i > $o,X1645: $i > $o,X1648: $i,X1649: $i,X1650: $i > $o,X1651: $i > $o,X1654: $i,X1655: $i,X1657: $i,X1658: $i,X1659: $i,X1660: $i,X1661: $i,X1662: $i,X1664: $i,X1665: $i,X1666: $i,X1667: $i,X1668: $i,X1669: $i,X1670: $i,X1671: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1692: $i,X1693: $i,X1694: $i,X1695: $i,X1696: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i > $o,X1702: $i,X1703: $i > $o,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1713: $i,X1714: $i,X1715: $o,X1716: $i,X1717: $i,X1718: $i,X1719: $i,X1720: $i,X1721: $i,X1722: $i,X1723: $i,X1724: $i,X1725: $i,X1726: $i,X1727: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1734: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i,X1772: $i,X1773: $i,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $o,X1784: $i,X1785: $i,X1786: $i,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $i,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $i,X1855: $i > $o,X1858: $i,X1859: $i,X1860: $i > $o,X1862: $i,X1863: $i > $o,X1864: $i,X1866: $i,X1867: $i > $o,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1914: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $i,X1929: $i,X1930: $i,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $i > $i > $o,X1943: $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i > $i > $o,X1948: $i,X1949: $i,X1950: $i > $i > $o,X1951: $i,X1952: $i,X1953: $i > $i > $o,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i > $i > $o,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i > $i > $o,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i > $i > $o,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i,X1988: $i,X1989: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i > $i,X1997: $i,X1998: $i,X1999: $i > $i,X2001: $i,X2002: $i,X2003: $i > $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i > $o,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i > $o,X2018: $i,X2019: $i,X2020: $i > $o,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,X2038: $i,X2039: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2077: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i > $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2088: $i,X2089: $i,X2090: $i > $i,X2092: $i,X2093: $i,X2094: $i > $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i,X2100: $i,X2101: $o,X2102: $i,X2103: $i,X2104: $i,X2105: $o,X2106: $i,X2107: $i,X2108: $i,X2109: $o,X2110: $i,X2111: $i,X2112: $i,X2113: $o,X2114: $i,X2115: $i,X2116: $i,X2117: $o,X2118: $i,X2119: $i,X2120: $i,X2121: $o,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $o,X2128: $i,X2129: $i,X2130: $i,X2131: $o,X2132: $i,X2133: $i,X2134: $i,X2135: $o,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i] :
( ( ~ ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1453 )
| ~ ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1454 )
| ( X1453 = X1454 ) )
& ( ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1453 )
| ( in @ ( esk1_2 @ X1453 @ X1454 ) @ X1454 )
| ( X1453 = X1454 ) )
& ~ ( in @ X1456 @ emptyset )
& ( ~ ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) )
| ( X1459 = X1457 )
| ( in @ X1459 @ X1458 ) )
& ( ( X1459 != X1457 )
| ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) ) )
& ( ~ ( in @ X1459 @ X1458 )
| ( in @ X1459 @ ( setadjoin @ X1457 @ X1458 ) ) )
& ( ~ ( in @ X1461 @ ( powerset @ X1460 ) )
| ~ ( in @ X1462 @ X1461 )
| ( in @ X1462 @ X1460 ) )
& ( ( in @ ( esk2_2 @ X1463 @ X1464 ) @ X1464 )
| ( in @ X1464 @ ( powerset @ X1463 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1463 @ X1464 ) @ X1463 )
| ( in @ X1464 @ ( powerset @ X1463 ) ) )
& ( ( in @ X1467 @ ( esk3_2 @ X1466 @ X1467 ) )
| ~ ( in @ X1467 @ ( setunion @ X1466 ) ) )
& ( ( in @ ( esk3_2 @ X1466 @ X1467 ) @ X1466 )
| ~ ( in @ X1467 @ ( setunion @ X1466 ) ) )
& ( ~ ( in @ X1470 @ X1471 )
| ~ ( in @ X1471 @ X1469 )
| ( in @ X1470 @ ( setunion @ X1469 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1472 @ omega )
| ( in @ ( setadjoin @ X1472 @ X1472 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1473 ) @ omega )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ( in @ ( esk4_1 @ X1473 ) @ X1473 )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1473 ) @ ( esk4_1 @ X1473 ) ) @ X1473 )
| ~ ( in @ emptyset @ X1473 )
| ~ ( in @ X1475 @ omega )
| ( in @ X1475 @ X1473 ) )
& ( ( in @ ( esk7_3 @ X1476 @ X1477 @ X1480 ) @ X1477 )
| ~ ( in @ X1480 @ ( esk6_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ( X1476 @ ( esk7_3 @ X1476 @ X1477 @ X1480 ) @ X1480 )
| ~ ( in @ X1480 @ ( esk6_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ~ ( in @ X1483 @ X1477 )
| ~ ( X1476 @ X1483 @ X1482 )
| ( in @ X1482 @ ( esk6_2 @ X1476 @ X1477 ) )
| ( in @ ( esk5_2 @ X1476 @ X1477 ) @ X1477 ) )
& ( ( in @ ( esk7_3 @ X1476 @ X1477 @ X1480 ) @ X1477 )
| ~ ( in @ X1480 @ ( esk6_2 @ X1476 @ X1477 ) )
| ~ ( exu @ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) ) ) )
& ( ( X1476 @ ( esk7_3 @ X1476 @ X1477 @ X1480 ) @ X1480 )
| ~ ( in @ X1480 @ ( esk6_2 @ X1476 @ X1477 ) )
| ~ ( exu @ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) ) ) )
& ( ~ ( in @ X1483 @ X1477 )
| ~ ( X1476 @ X1483 @ X1482 )
| ( in @ X1482 @ ( esk6_2 @ X1476 @ X1477 ) )
| ~ ( exu @ ( X1476 @ ( esk5_2 @ X1476 @ X1477 ) ) ) )
& ( ( in @ ( esk8_1 @ X1484 ) @ X1484 )
| ~ ( in @ X1485 @ X1484 ) )
& ( ~ ( in @ X1487 @ ( esk8_1 @ X1484 ) )
| ~ ( in @ X1487 @ X1484 )
| ~ ( in @ X1485 @ X1484 ) )
& epred1_0
& ( ~ ( exu @ X1488 )
| ( X1488 @ ( descr @ X1488 ) ) )
& ( ~ ( in @ X1491 @ X1489 )
| ~ ( X1490 @ X1491 )
| ( in @ X1491 @ ( dsetconstr @ X1489 @ X1490 ) ) )
& ( ~ ( in @ X1494 @ ( dsetconstr @ X1492 @ X1493 ) )
| ( in @ X1494 @ X1492 ) )
& ( ~ ( in @ X1497 @ ( dsetconstr @ X1495 @ X1496 ) )
| ( X1496 @ X1497 ) )
& ( ( X1498 @ ( esk9_1 @ X1498 ) )
| ~ ( exu @ X1498 ) )
& ( ~ ( X1498 @ X1500 )
| ( ( esk9_1 @ X1498 )
= X1500 )
| ~ ( exu @ X1498 ) )
& ( ~ ( in @ X1502 @ ( prop2set @ X1501 ) )
| X1501 )
& ( ~ ( in @ X1503 @ emptyset )
| X1504 )
& ( ~ ( in @ X1505 @ emptyset )
| ~ $true )
& ~ ( in @ X1506 @ emptyset )
& ( ~ ( exu @ X1507 )
| ( X1507 @ ( esk10_1 @ X1507 ) ) )
& ( ( in @ ( esk12_2 @ X1509 @ X1510 ) @ X1510 )
| ( X1509 = X1510 )
| ( in @ ( esk11_2 @ X1509 @ X1510 ) @ X1509 ) )
& ( ~ ( in @ ( esk12_2 @ X1509 @ X1510 ) @ X1509 )
| ( X1509 = X1510 )
| ( in @ ( esk11_2 @ X1509 @ X1510 ) @ X1509 ) )
& ( ( in @ ( esk12_2 @ X1509 @ X1510 ) @ X1510 )
| ( X1509 = X1510 )
| ~ ( in @ ( esk11_2 @ X1509 @ X1510 ) @ X1510 ) )
& ( ~ ( in @ ( esk12_2 @ X1509 @ X1510 ) @ X1509 )
| ( X1509 = X1510 )
| ~ ( in @ ( esk11_2 @ X1509 @ X1510 ) @ X1510 ) )
& ( ( in @ ( esk13_1 @ X1513 ) @ X1513 )
| ( X1513 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1515 ) @ X1515 )
| ( X1515 = emptyset ) )
& ( ~ ( in @ X1519 @ ( dsetconstr @ X1517 @ X1518 ) )
| ( X1518 @ X1519 )
| ~ ( in @ X1519 @ X1517 ) )
& ( ~ ( X1518 @ X1519 )
| ( in @ X1519 @ ( dsetconstr @ X1517 @ X1518 ) )
| ~ ( in @ X1519 @ X1517 ) )
& ( ~ ( nonempty @ X1520 )
| ( in @ ( esk15_1 @ X1520 ) @ X1520 ) )
& ( ~ ( in @ X1524 @ X1522 )
| ~ ( X1523 @ X1524 )
| ( nonempty @ ( dsetconstr @ X1522 @ X1523 ) ) )
& ( ~ ( in @ X1526 @ X1525 )
| ( nonempty @ X1525 ) )
& ( in @ X1527 @ ( setadjoin @ X1527 @ X1528 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1531 @ X1530 )
| ( in @ X1531 @ ( setadjoin @ X1529 @ X1530 ) ) )
& ( ( in @ X1534 @ X1533 )
| X1535
| ( X1534 = X1532 )
| ~ ( in @ X1534 @ ( setadjoin @ X1532 @ X1533 ) ) )
& ( ~ X1535
| X1535
| ( X1534 = X1532 )
| ~ ( in @ X1534 @ ( setadjoin @ X1532 @ X1533 ) ) )
& ( ( in @ X1534 @ X1533 )
| X1535
| ~ X1535
| ~ ( in @ X1534 @ ( setadjoin @ X1532 @ X1533 ) ) )
& ( ~ X1535
| X1535
| ~ X1535
| ~ ( in @ X1534 @ ( setadjoin @ X1532 @ X1533 ) ) )
& ( ~ ( in @ X1538 @ ( setadjoin @ X1536 @ X1537 ) )
| ( X1538 = X1536 )
| ( in @ X1538 @ X1537 ) )
& ( ( dsetconstr @ X1539
@ ^ [Z0: $i] : $true )
= X1539 )
& ( ( in @ ( esk16_2 @ X1540 @ X1541 ) @ X1541 )
| ( in @ X1541 @ ( powerset @ X1540 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1540 @ X1541 ) @ X1540 )
| ( in @ X1541 @ ( powerset @ X1540 ) ) )
& ( in @ emptyset @ ( powerset @ X1543 ) )
& ( in @ emptyset @ ( powerset @ X1544 ) )
& ( ~ ( in @ X1546 @ ( powerset @ X1545 ) )
| ~ ( in @ X1547 @ X1546 )
| ( in @ X1547 @ X1545 ) )
& ( ~ ( in @ X1549 @ X1550 )
| ~ ( in @ X1550 @ X1548 )
| ( in @ X1549 @ ( setunion @ X1548 ) ) )
& ( ( in @ X1552 @ ( esk17_3 @ X1551 @ X1552 @ X1553 ) )
| X1553
| ~ ( in @ X1552 @ ( setunion @ X1551 ) ) )
& ( ( in @ ( esk17_3 @ X1551 @ X1552 @ X1553 ) @ X1551 )
| X1553
| ~ ( in @ X1552 @ ( setunion @ X1551 ) ) )
& ( ~ X1553
| X1553
| ~ ( in @ X1552 @ ( setunion @ X1551 ) ) )
& ( ~ ( in @ X1556 @ X1555 )
| ( in @ X1556 @ ( powerset @ ( setunion @ X1555 ) ) ) )
& ( ~ ( X1557 @ X1559 )
| ( X1559
= ( esk18_1 @ X1557 ) )
| ~ ( exu @ X1557 ) )
& ( ( X1560
!= ( esk18_1 @ X1557 ) )
| ( X1557 @ X1560 )
| ~ ( exu @ X1557 ) )
& ( ( in @ ( esk19_1 @ X1561 ) @ X1561 )
| ~ ( nonempty @ X1561 ) )
& ( $true
| ~ ( nonempty @ X1561 ) )
& ( ~ ( in @ X1563 @ ( setadjoin @ X1564 @ emptyset ) )
| ( X1563 = X1564 ) )
& ( ( X1565 = X1566 )
| ~ ( in @ X1566 @ ( setadjoin @ X1565 @ emptyset ) ) )
& ( ( X1567 != X1568 )
| ( in @ X1567 @ ( setadjoin @ X1568 @ emptyset ) ) )
& ( ~ ( in @ X1569 @ ( setadjoin @ X1570 @ emptyset ) )
| ( in @ X1570 @ ( setadjoin @ X1569 @ emptyset ) ) )
& ( ~ ( in @ X1573 @ ( setadjoin @ X1571 @ ( setadjoin @ X1572 @ emptyset ) ) )
| ( X1573 = X1571 )
| ( X1573 = X1572 ) )
& ( in @ X1574 @ ( setadjoin @ X1574 @ ( setadjoin @ X1575 @ emptyset ) ) )
& ( in @ X1577 @ ( setadjoin @ X1576 @ ( setadjoin @ X1577 @ emptyset ) ) )
& ( ~ ( in @ X1580 @ X1578 )
| ~ ( X1579 @ X1580 )
| ( ( dsetconstr @ X1578 @ X1579 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1582 @ emptyset )
| ( X1581 @ X1582 ) )
& ( ( in @ ( esk20_2 @ X1583 @ X1584 ) @ X1583 )
| ~ ( in @ X1585 @ X1583 )
| ( X1584 @ X1585 ) )
& ( ~ ( X1584 @ ( esk20_2 @ X1583 @ X1584 ) )
| ~ ( in @ X1585 @ X1583 )
| ( X1584 @ X1585 ) )
& ( ( in @ ( esk21_2 @ X1587 @ X1588 ) @ X1587 )
| ~ ( in @ X1590 @ X1587 )
| ~ ( X1588 @ X1590 ) )
& ( ( X1588 @ ( esk21_2 @ X1587 @ X1588 ) )
| ~ ( in @ X1590 @ X1587 )
| ~ ( X1588 @ X1590 ) )
& ( ( in @ ( esk22_2 @ X1591 @ X1592 ) @ X1591 )
| ~ ( in @ X1594 @ X1591 )
| ~ ( X1592 @ X1594 ) )
& ( ( X1592 @ ( esk22_2 @ X1591 @ X1592 ) )
| ~ ( in @ X1594 @ X1591 )
| ~ ( X1592 @ X1594 ) )
& ( ( in @ ( esk23_2 @ X1595 @ X1596 ) @ X1595 )
| ~ ( in @ X1597 @ X1595 )
| ( X1596 @ X1597 ) )
& ( ~ ( X1596 @ ( esk23_2 @ X1595 @ X1596 ) )
| ~ ( in @ X1597 @ X1595 )
| ( X1596 @ X1597 ) )
& ( ~ X1599
| ( in @ emptyset @ ( prop2set @ X1599 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1600 @ X1601 ) @ X1600 )
| ~ ( in @ X1603 @ X1600 )
| ~ ( X1601 @ X1603 ) )
& ( ( X1601 @ ( esk24_2 @ X1600 @ X1601 ) )
| ~ ( in @ X1603 @ X1600 )
| ~ ( X1601 @ X1603 ) )
& ( ( in @ ( esk25_2 @ X1604 @ X1605 ) @ X1604 )
| ~ ( in @ X1606 @ X1604 )
| ( X1605 @ X1606 ) )
& ( ~ ( X1605 @ ( esk25_2 @ X1604 @ X1605 ) )
| ~ ( in @ X1606 @ X1604 )
| ( X1605 @ X1606 ) )
& ( ( X1608 @ ( esk26_2 @ X1608 @ X1609 ) )
| ~ ( X1608 @ X1609 )
| ( exu @ X1608 ) )
& ( ( X1609
!= ( esk26_2 @ X1608 @ X1609 ) )
| ~ ( X1608 @ X1609 )
| ( exu @ X1608 ) )
& ( ( X1611 @ ( esk27_1 @ X1611 ) )
| ( exu @ X1611 )
| ~ ( X1611 @ X1612 ) )
& ( ( X1611 @ ( esk28_1 @ X1611 ) )
| ( exu @ X1611 )
| ~ ( X1611 @ X1612 ) )
& ( ( ( esk27_1 @ X1611 )
!= ( esk28_1 @ X1611 ) )
| ( exu @ X1611 )
| ~ ( X1611 @ X1612 ) )
& ( ~ ( X1615 @ ( esk29_2 @ X1615 @ X1616 ) )
| ( ( esk29_2 @ X1615 @ X1616 )
!= X1616 )
| ( exu @ X1615 ) )
& ( ( X1615 @ ( esk29_2 @ X1615 @ X1616 ) )
| ( ( esk29_2 @ X1615 @ X1616 )
= X1616 )
| ( exu @ X1615 ) )
& ( ( X1618 != X1619 )
| ( X1620 != X1621 )
| ~ ( in @ X1620 @ X1618 )
| ( in @ X1621 @ X1619 ) )
& ( ~ ( in @ X1624 @ X1622 )
| ( in @ X1625 @ X1623 )
| ( X1624 != X1625 )
| ( X1622 != X1623 ) )
& ( ~ ( in @ X1625 @ X1623 )
| ( in @ X1624 @ X1622 )
| ( X1624 != X1625 )
| ( X1622 != X1623 ) )
& ( ~ ( exu @ X1626 )
| ~ ( X1626 @ X1627 )
| ~ ( X1626 @ X1628 )
| ( X1627 = X1628 ) )
& ( ~ ( exu @ X1629 )
| ( exu @ X1630 )
| ( ( esk30_2 @ X1629 @ X1630 )
= ( esk31_2 @ X1629 @ X1630 ) ) )
& ( ~ ( exu @ X1630 )
| ( exu @ X1629 )
| ( ( esk30_2 @ X1629 @ X1630 )
= ( esk31_2 @ X1629 @ X1630 ) ) )
& ( ~ ( exu @ X1629 )
| ( exu @ X1630 )
| ~ ( X1629 @ ( esk30_2 @ X1629 @ X1630 ) )
| ~ ( X1630 @ ( esk31_2 @ X1629 @ X1630 ) ) )
& ( ~ ( exu @ X1630 )
| ( exu @ X1629 )
| ~ ( X1629 @ ( esk30_2 @ X1629 @ X1630 ) )
| ~ ( X1630 @ ( esk31_2 @ X1629 @ X1630 ) ) )
& ( ~ ( exu @ X1629 )
| ( exu @ X1630 )
| ( X1629 @ ( esk30_2 @ X1629 @ X1630 ) )
| ( X1630 @ ( esk31_2 @ X1629 @ X1630 ) ) )
& ( ~ ( exu @ X1630 )
| ( exu @ X1629 )
| ( X1629 @ ( esk30_2 @ X1629 @ X1630 ) )
| ( X1630 @ ( esk31_2 @ X1629 @ X1630 ) ) )
& ( emptyset = emptyset )
& ( ( X1633 != X1634 )
| ( X1635 != X1636 )
| ( ( setadjoin @ X1633 @ X1635 )
= ( setadjoin @ X1634 @ X1636 ) ) )
& ( ( X1637 != X1638 )
| ( ( powerset @ X1637 )
= ( powerset @ X1638 ) ) )
& ( ( X1639 != X1640 )
| ( ( setunion @ X1639 )
= ( setunion @ X1640 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1641 )
| ~ ( X1641 @ X1642 )
| ~ ( X1641 @ X1643 )
| ( X1642 = X1643 ) )
& ( ( ( esk32_2 @ X1644 @ X1645 )
= ( esk33_2 @ X1644 @ X1645 ) )
| ~ ( exu @ X1644 )
| ~ ( exu @ X1645 )
| ( ( descr @ X1644 )
= ( descr @ X1645 ) ) )
& ( ~ ( X1644 @ ( esk32_2 @ X1644 @ X1645 ) )
| ~ ( X1645 @ ( esk33_2 @ X1644 @ X1645 ) )
| ~ ( exu @ X1644 )
| ~ ( exu @ X1645 )
| ( ( descr @ X1644 )
= ( descr @ X1645 ) ) )
& ( ( X1644 @ ( esk32_2 @ X1644 @ X1645 ) )
| ( X1645 @ ( esk33_2 @ X1644 @ X1645 ) )
| ~ ( exu @ X1644 )
| ~ ( exu @ X1645 )
| ( ( descr @ X1644 )
= ( descr @ X1645 ) ) )
& ( ( in @ ( esk34_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ X1648 )
| ( ( dsetconstr @ X1648 @ X1650 )
= ( dsetconstr @ X1649 @ X1651 ) )
| ( X1648 != X1649 ) )
& ( ( in @ ( esk35_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ X1649 )
| ( ( dsetconstr @ X1648 @ X1650 )
= ( dsetconstr @ X1649 @ X1651 ) )
| ( X1648 != X1649 ) )
& ( ( ( esk34_4 @ X1648 @ X1649 @ X1650 @ X1651 )
= ( esk35_4 @ X1648 @ X1649 @ X1650 @ X1651 ) )
| ( ( dsetconstr @ X1648 @ X1650 )
= ( dsetconstr @ X1649 @ X1651 ) )
| ( X1648 != X1649 ) )
& ( ~ ( X1650 @ ( esk34_4 @ X1648 @ X1649 @ X1650 @ X1651 ) )
| ~ ( X1651 @ ( esk35_4 @ X1648 @ X1649 @ X1650 @ X1651 ) )
| ( ( dsetconstr @ X1648 @ X1650 )
= ( dsetconstr @ X1649 @ X1651 ) )
| ( X1648 != X1649 ) )
& ( ( X1650 @ ( esk34_4 @ X1648 @ X1649 @ X1650 @ X1651 ) )
| ( X1651 @ ( esk35_4 @ X1648 @ X1649 @ X1650 @ X1651 ) )
| ( ( dsetconstr @ X1648 @ X1650 )
= ( dsetconstr @ X1649 @ X1651 ) )
| ( X1648 != X1649 ) )
& ( ( in @ ( esk36_2 @ X1654 @ X1655 ) @ X1654 )
| ( subset @ X1654 @ X1655 ) )
& ( ~ ( in @ ( esk36_2 @ X1654 @ X1655 ) @ X1655 )
| ( subset @ X1654 @ X1655 ) )
& ( ( X1657 != X1658 )
| ( subset @ X1658 @ X1657 ) )
& ( ( X1659 != X1660 )
| ( subset @ X1659 @ X1660 ) )
& ( ( in @ ( esk37_2 @ X1661 @ X1662 ) @ X1661 )
| ( subset @ X1661 @ X1662 ) )
& ( ~ ( in @ ( esk37_2 @ X1661 @ X1662 ) @ X1662 )
| ( subset @ X1661 @ X1662 ) )
& ( subset @ emptyset @ X1664 )
& ( ~ ( subset @ X1665 @ X1666 )
| ~ ( in @ X1667 @ X1665 )
| ( in @ X1667 @ X1666 ) )
& ( ~ ( subset @ X1668 @ X1669 )
| ( in @ X1670 @ X1669 )
| ~ ( in @ X1670 @ X1668 ) )
& ( ~ ( in @ X1673 @ X1671 )
| ( in @ X1673 @ X1672 )
| ~ ( subset @ X1671 @ X1672 ) )
& ( ( subset @ X1674 @ X1675 )
| ( X1674 != X1675 ) )
& ( ~ ( in @ X1678 @ X1676 )
| ( in @ X1678 @ X1677 )
| ( X1676 != X1677 ) )
& ( subset @ X1679 @ X1679 )
& ( ~ ( subset @ X1680 @ X1681 )
| ~ ( subset @ X1681 @ X1682 )
| ( subset @ X1680 @ X1682 ) )
& ( subset @ X1684 @ ( setadjoin @ X1683 @ X1684 ) )
& ( ~ ( subset @ X1685 @ X1687 )
| ( subset @ X1685 @ ( setadjoin @ X1686 @ X1687 ) ) )
& ( ~ ( subset @ X1688 @ X1689 )
| ( in @ X1688 @ ( powerset @ X1689 ) ) )
& ( ~ ( subset @ X1690 @ X1691 )
| ~ ( subset @ X1691 @ X1690 )
| ( X1690 = X1691 ) )
& ( ~ ( subset @ X1692 @ emptyset )
| ( X1692 = emptyset ) )
& ( ~ ( subset @ X1694 @ X1693 )
| ( in @ X1694 @ ( powerset @ X1693 ) ) )
& ( ~ ( in @ X1696 @ ( powerset @ X1695 ) )
| ( subset @ X1696 @ X1695 ) )
& ( in @ X1697 @ ( powerset @ X1697 ) )
& ( ~ ( subset @ X1698 @ X1699 )
| ( subset @ ( powerset @ X1698 ) @ ( powerset @ X1699 ) ) )
& ( in @ ( dsetconstr @ X1700 @ X1701 ) @ ( powerset @ X1700 ) )
& ( subset @ ( dsetconstr @ X1702 @ X1703 ) @ X1702 )
& ( ~ ( in @ X1706 @ X1704 )
| ( in @ X1706 @ ( binunion @ X1704 @ X1705 ) ) )
& ( in @ X1708 @ ( setadjoin @ X1707 @ ( setadjoin @ X1708 @ emptyset ) ) )
& ( ~ ( in @ X1711 @ X1710 )
| ( in @ X1711 @ ( binunion @ X1709 @ X1710 ) ) )
& ( ( in @ X1714 @ X1713 )
| X1715
| ( in @ X1714 @ X1712 )
| ~ ( in @ X1714 @ ( binunion @ X1712 @ X1713 ) ) )
& ( ~ X1715
| X1715
| ( in @ X1714 @ X1712 )
| ~ ( in @ X1714 @ ( binunion @ X1712 @ X1713 ) ) )
& ( ( in @ X1714 @ X1713 )
| X1715
| ~ X1715
| ~ ( in @ X1714 @ ( binunion @ X1712 @ X1713 ) ) )
& ( ~ X1715
| X1715
| ~ X1715
| ~ ( in @ X1714 @ ( binunion @ X1712 @ X1713 ) ) )
& ( ~ ( in @ X1718 @ ( binunion @ X1716 @ X1717 ) )
| ( in @ X1718 @ X1716 )
| ( in @ X1718 @ X1717 ) )
& ( subset @ X1719 @ ( binunion @ X1719 @ X1720 ) )
& ( subset @ X1722 @ ( binunion @ X1721 @ X1722 ) )
& ( ~ ( in @ X1725 @ X1723 )
| ~ ( in @ X1725 @ X1724 )
| ( in @ X1725 @ ( binintersect @ X1723 @ X1724 ) ) )
& ( ~ ( subset @ X1728 @ X1726 )
| ~ ( subset @ X1728 @ X1727 )
| ( subset @ X1728 @ ( binintersect @ X1726 @ X1727 ) ) )
& ( ~ ( in @ X1731 @ ( binintersect @ X1729 @ X1730 ) )
| ( in @ X1731 @ X1729 ) )
& ( subset @ ( binintersect @ X1732 @ X1733 ) @ X1732 )
& ( ~ ( subset @ X1734 @ X1735 )
| ( ( binintersect @ X1734 @ X1735 )
= X1734 ) )
& ( ( ( binintersect @ X1736 @ X1737 )
!= X1737 )
| ( subset @ X1737 @ X1736 ) )
& ( ~ ( in @ X1740 @ ( binintersect @ X1738 @ X1739 ) )
| ( in @ X1740 @ X1739 ) )
& ( ( in @ ( esk38_2 @ X1741 @ X1742 ) @ X1741 )
| ( ( binintersect @ X1741 @ X1742 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1741 @ X1742 ) @ X1742 )
| ( ( binintersect @ X1741 @ X1742 )
= emptyset ) )
& ( subset @ ( binintersect @ X1744 @ X1745 ) @ X1745 )
& ( ~ ( subset @ X1747 @ X1746 )
| ( ( binintersect @ X1746 @ X1747 )
= X1747 ) )
& ( ( ( binintersect @ X1748 @ X1749 )
!= X1748 )
| ( subset @ X1748 @ X1749 ) )
& ( ( binintersect @ X1750 @ ( binunion @ X1751 @ X1752 ) )
= ( binunion @ ( binintersect @ X1750 @ X1751 ) @ ( binintersect @ X1750 @ X1752 ) ) )
& ( ~ ( in @ X1755 @ X1753 )
| ( in @ X1755 @ X1754 )
| ( in @ X1755 @ ( setminus @ X1753 @ X1754 ) ) )
& ( ~ ( in @ X1758 @ ( setminus @ X1756 @ X1757 ) )
| ( in @ X1758 @ X1756 ) )
& ( ~ ( in @ X1761 @ ( setminus @ X1759 @ X1760 ) )
| ~ ( in @ X1761 @ X1760 ) )
& ( ~ ( subset @ X1762 @ X1763 )
| ( ( setminus @ X1762 @ X1763 )
= emptyset ) )
& ( ( in @ X1766 @ ( setminus @ X1764 @ X1765 ) )
| ~ ( in @ X1766 @ X1764 )
| ( in @ X1766 @ X1765 ) )
& ( ( in @ X1769 @ ( setminus @ X1767 @ X1768 ) )
| ( in @ X1769 @ X1768 )
| ~ ( in @ X1769 @ X1767 ) )
& ( ( in @ X1772 @ X1770 )
| ~ ( in @ X1772 @ ( setminus @ X1770 @ X1771 ) ) )
& ( ~ ( in @ X1775 @ X1774 )
| ~ ( in @ X1775 @ ( setminus @ X1773 @ X1774 ) ) )
& ( subset @ ( setminus @ X1776 @ X1777 ) @ X1776 )
& ( ( ( setminus @ X1778 @ X1779 )
!= emptyset )
| ( subset @ X1778 @ X1779 ) )
& ( ~ ( in @ X1782 @ X1780 )
| X1783
| ( in @ X1782 @ X1780 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ( in @ X1782 @ X1781 )
| X1783
| ( in @ X1782 @ X1780 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ X1783
| X1783
| ( in @ X1782 @ X1780 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ ( in @ X1782 @ X1780 )
| X1783
| ~ ( in @ X1782 @ X1781 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ( in @ X1782 @ X1781 )
| X1783
| ~ ( in @ X1782 @ X1781 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ X1783
| X1783
| ~ ( in @ X1782 @ X1781 )
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ ( in @ X1782 @ X1780 )
| X1783
| ~ X1783
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ( in @ X1782 @ X1781 )
| X1783
| ~ X1783
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ X1783
| X1783
| ~ X1783
| ~ ( in @ X1782 @ ( symdiff @ X1780 @ X1781 ) ) )
& ( ~ ( in @ X1786 @ X1784 )
| ( in @ X1786 @ X1785 )
| ( in @ X1786 @ ( symdiff @ X1784 @ X1785 ) ) )
& ( ( in @ X1789 @ X1787 )
| ~ ( in @ X1789 @ X1788 )
| ( in @ X1789 @ ( symdiff @ X1787 @ X1788 ) ) )
& ( ~ ( in @ X1792 @ X1790 )
| ~ ( in @ X1792 @ X1791 )
| ~ ( in @ X1792 @ ( symdiff @ X1790 @ X1791 ) ) )
& ( ( in @ X1795 @ X1793 )
| ( in @ X1795 @ X1794 )
| ~ ( in @ X1795 @ ( symdiff @ X1793 @ X1794 ) ) )
& ( in @ X1797 @ ( setadjoin @ X1796 @ ( setadjoin @ X1797 @ emptyset ) ) )
& ( in @ X1798 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1798 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1798 @ ( setadjoin @ X1799 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1801 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1800 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1800 @ ( setadjoin @ X1801 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1802 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1802 @ ( setadjoin @ X1803 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1804 @ X1805 ) )
& ( ~ ( in @ X1807 @ X1806 )
| ( subset @ ( setadjoin @ X1807 @ emptyset ) @ X1806 ) )
& ( ~ ( in @ X1809 @ X1808 )
| ( in @ ( setadjoin @ X1809 @ emptyset ) @ ( powerset @ X1808 ) ) )
& ( ~ ( in @ X1812 @ X1810 )
| ( in @ ( setadjoin @ X1812 @ emptyset ) @ ( powerset @ ( binunion @ X1810 @ X1811 ) ) ) )
& ( ~ ( in @ X1815 @ ( setadjoin @ X1813 @ ( setadjoin @ X1814 @ emptyset ) ) )
| ( X1815 = X1813 )
| ( X1815 = X1814 ) )
& ( ~ ( in @ X1818 @ X1816 )
| ~ ( in @ X1819 @ X1817 )
| ( subset @ ( setadjoin @ X1818 @ ( setadjoin @ X1819 @ emptyset ) ) @ ( binunion @ X1816 @ X1817 ) ) )
& ( ~ ( in @ X1822 @ X1820 )
| ~ ( in @ X1823 @ X1821 )
| ( in @ ( setadjoin @ X1822 @ ( setadjoin @ X1823 @ emptyset ) ) @ ( powerset @ ( binunion @ X1820 @ X1821 ) ) ) )
& ( ~ ( in @ X1826 @ X1824 )
| ~ ( in @ X1827 @ X1825 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1826 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1826 @ ( setadjoin @ X1827 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1824 @ X1825 ) ) ) )
& ( ~ ( in @ X1830 @ X1828 )
| ~ ( in @ X1831 @ X1829 )
| ( in @ ( setadjoin @ ( setadjoin @ X1830 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1830 @ ( setadjoin @ X1831 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1828 @ X1829 ) ) ) ) )
& ( ~ ( in @ X1834 @ X1832 )
| ~ ( in @ X1835 @ X1833 )
| ( in @ ( kpair @ X1834 @ X1835 ) @ ( powerset @ ( powerset @ ( binunion @ X1832 @ X1833 ) ) ) ) )
& ( ~ ( in @ X1838 @ X1836 )
| ~ ( in @ X1839 @ X1837 )
| ( in @ ( kpair @ X1838 @ X1839 ) @ ( cartprod @ X1836 @ X1837 ) ) )
& ( ( in @ ( esk39_3 @ X1840 @ X1841 @ X1842 ) @ X1840 )
| ~ ( in @ X1842 @ ( cartprod @ X1840 @ X1841 ) ) )
& ( ( in @ ( esk40_3 @ X1840 @ X1841 @ X1842 ) @ X1841 )
| ~ ( in @ X1842 @ ( cartprod @ X1840 @ X1841 ) ) )
& ( ( X1842
= ( kpair @ ( esk39_3 @ X1840 @ X1841 @ X1842 ) @ ( esk40_3 @ X1840 @ X1841 @ X1842 ) ) )
| ~ ( in @ X1842 @ ( cartprod @ X1840 @ X1841 ) ) )
& ( ~ ( in @ X1847 @ ( cartprod @ X1845 @ X1846 ) )
| ( iskpair @ X1847 ) )
& ( ( in @ ( esk41_2 @ X1848 @ X1849 ) @ X1848 )
| ~ ( in @ X1849 @ ( setunion @ X1848 ) ) )
& ( ( in @ X1849 @ ( esk41_2 @ X1848 @ X1849 ) )
| ~ ( in @ X1849 @ ( setunion @ X1848 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1851 @ emptyset ) ) @ X1851 )
& ( subset @ X1852 @ ( setunion @ ( setadjoin @ X1852 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1853 @ emptyset ) )
= X1853 )
& ( ( in @ ( esk42_2 @ X1854 @ X1855 ) @ X1854 )
| ~ ( in @ X1858 @ X1854 )
| ~ ( X1855 @ X1858 )
| ( singleton @ ( dsetconstr @ X1854 @ X1855 ) ) )
& ( ( in @ ( esk43_2 @ X1854 @ X1855 ) @ X1854 )
| ~ ( in @ X1858 @ X1854 )
| ~ ( X1855 @ X1858 )
| ( singleton @ ( dsetconstr @ X1854 @ X1855 ) ) )
& ( ( X1855 @ ( esk42_2 @ X1854 @ X1855 ) )
| ~ ( in @ X1858 @ X1854 )
| ~ ( X1855 @ X1858 )
| ( singleton @ ( dsetconstr @ X1854 @ X1855 ) ) )
& ( ( X1855 @ ( esk43_2 @ X1854 @ X1855 ) )
| ~ ( in @ X1858 @ X1854 )
| ~ ( X1855 @ X1858 )
| ( singleton @ ( dsetconstr @ X1854 @ X1855 ) ) )
& ( ( ( esk42_2 @ X1854 @ X1855 )
!= ( esk43_2 @ X1854 @ X1855 ) )
| ~ ( in @ X1858 @ X1854 )
| ~ ( X1855 @ X1858 )
| ( singleton @ ( dsetconstr @ X1854 @ X1855 ) ) )
& ( ( in @ ( esk44_2 @ X1859 @ X1860 ) @ X1859 )
| ~ ( ex1 @ X1859 @ X1860 ) )
& ( ( X1860 @ ( esk44_2 @ X1859 @ X1860 ) )
| ~ ( ex1 @ X1859 @ X1860 ) )
& ( ( in @ ( esk45_3 @ X1862 @ X1863 @ X1864 ) @ X1862 )
| ( ex1 @ X1862 @ X1863 )
| ~ ( X1863 @ X1864 )
| ~ ( in @ X1864 @ X1862 ) )
& ( ( X1863 @ ( esk45_3 @ X1862 @ X1863 @ X1864 ) )
| ( ex1 @ X1862 @ X1863 )
| ~ ( X1863 @ X1864 )
| ~ ( in @ X1864 @ X1862 ) )
& ( ( ( esk45_3 @ X1862 @ X1863 @ X1864 )
!= X1864 )
| ( ex1 @ X1862 @ X1863 )
| ~ ( X1863 @ X1864 )
| ~ ( in @ X1864 @ X1862 ) )
& ( ( in @ ( esk46_2 @ X1866 @ X1867 ) @ X1866 )
| ~ ( in @ X1870 @ X1866 )
| ~ ( X1867 @ X1870 )
| ( ex1 @ X1866 @ X1867 ) )
& ( ( in @ ( esk47_2 @ X1866 @ X1867 ) @ X1866 )
| ~ ( in @ X1870 @ X1866 )
| ~ ( X1867 @ X1870 )
| ( ex1 @ X1866 @ X1867 ) )
& ( ( X1867 @ ( esk46_2 @ X1866 @ X1867 ) )
| ~ ( in @ X1870 @ X1866 )
| ~ ( X1867 @ X1870 )
| ( ex1 @ X1866 @ X1867 ) )
& ( ( X1867 @ ( esk47_2 @ X1866 @ X1867 ) )
| ~ ( in @ X1870 @ X1866 )
| ~ ( X1867 @ X1870 )
| ( ex1 @ X1866 @ X1867 ) )
& ( ( ( esk46_2 @ X1866 @ X1867 )
!= ( esk47_2 @ X1866 @ X1867 ) )
| ~ ( in @ X1870 @ X1866 )
| ~ ( X1867 @ X1870 )
| ( ex1 @ X1866 @ X1867 ) )
& ( ( ( setadjoin @ X1871 @ emptyset )
!= ( setadjoin @ X1872 @ emptyset ) )
| ( X1871 = X1872 ) )
& ( ~ ( in @ ( setadjoin @ X1875 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1873 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1873 @ ( setadjoin @ X1874 @ emptyset ) ) @ emptyset ) ) )
| ( X1873 = X1875 ) )
& ( ~ ( iskpair @ X1876 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1876 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1876 ) ) ) )
& ( ~ ( singleton @ X1877 )
| ( in @ ( setunion @ X1877 ) @ X1877 ) )
& ( ( kfst @ ( kpair @ X1878 @ X1879 ) )
= X1878 )
& ( ~ ( in @ X1882 @ ( cartprod @ X1880 @ X1881 ) )
| ( in @ ( kfst @ X1882 ) @ X1880 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1883 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1883 @ ( setadjoin @ X1884 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1885 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1885 @ ( setadjoin @ X1886 @ emptyset ) ) @ emptyset ) ) )
| ( X1883 = X1885 ) )
& ( ( ( kpair @ X1887 @ X1888 )
!= ( kpair @ X1889 @ X1890 ) )
| ( X1887 = X1889 ) )
& ( ( X1891 != X1892 )
| ( ( setadjoin @ X1891 @ ( setadjoin @ X1892 @ emptyset ) )
= ( setadjoin @ X1891 @ emptyset ) ) )
& ( ( X1893 != X1894 )
| ( ( setadjoin @ ( setadjoin @ X1893 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1893 @ ( setadjoin @ X1894 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1893 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1895 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1895 @ ( setadjoin @ X1896 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1897 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1897 @ ( setadjoin @ X1898 @ emptyset ) ) @ emptyset ) ) )
| ( X1897 != X1898 )
| ( X1896 = X1898 ) )
& ( ( ( setadjoin @ X1899 @ ( setadjoin @ X1900 @ emptyset ) )
!= ( setadjoin @ X1901 @ emptyset ) )
| ( X1899 = X1900 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1902 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1902 @ ( setadjoin @ X1903 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1904 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1904 @ ( setadjoin @ X1905 @ emptyset ) ) @ emptyset ) ) )
| ( X1903 = X1905 ) )
& ( ( ( kpair @ X1906 @ X1907 )
!= ( kpair @ X1908 @ X1909 ) )
| ( X1907 = X1909 ) )
& ( ~ ( iskpair @ X1910 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1910 )
@ ^ [Z0: $i] :
( X1910
= ( kpair @ ( kfst @ X1910 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1911 @ X1912 ) )
= X1912 )
& ( ~ ( iskpair @ X1913 )
| ( ( kpair @ ( kfst @ X1913 ) @ ( ksnd @ X1913 ) )
= X1913 ) )
& ( ~ ( in @ X1916 @ ( cartprod @ X1914 @ X1915 ) )
| ( in @ ( ksnd @ X1916 ) @ X1915 ) )
& ( ~ ( in @ ( kpair @ X1919 @ X1920 ) @ ( cartprod @ X1917 @ X1918 ) )
| ( in @ X1919 @ X1917 ) )
& ( ~ ( in @ ( kpair @ X1923 @ X1924 ) @ ( cartprod @ X1921 @ X1922 ) )
| ( in @ X1924 @ X1922 ) )
& ( ~ ( in @ X1927 @ X1925 )
| ~ ( in @ X1928 @ X1926 )
| ( ( kpair @ X1927 @ X1928 )
= ( kpair @ X1927 @ X1928 ) ) )
& ( ~ ( in @ X1931 @ X1929 )
| ~ ( in @ X1932 @ X1930 )
| ( ( kfst @ ( kpair @ X1931 @ X1932 ) )
= X1931 ) )
& ( ~ ( in @ X1935 @ X1933 )
| ~ ( in @ X1936 @ X1934 )
| ( ( ksnd @ ( kpair @ X1935 @ X1936 ) )
= X1936 ) )
& ( ~ ( in @ X1939 @ ( cartprod @ X1937 @ X1938 ) )
| ( ( kpair @ ( kfst @ X1939 ) @ ( ksnd @ X1939 ) )
= X1939 ) )
& ( ~ ( in @ X1943 @ X1940 )
| ~ ( in @ X1944 @ X1941 )
| ~ ( X1942 @ X1943 @ X1944 )
| ( in @ ( kpair @ X1943 @ X1944 ) @ ( dpsetconstr @ X1940 @ X1941 @ X1942 ) ) )
& ( subset @ ( dpsetconstr @ X1945 @ X1946 @ X1947 ) @ ( cartprod @ X1945 @ X1946 ) )
& ( breln @ X1948 @ X1949 @ ( dpsetconstr @ X1948 @ X1949 @ X1950 ) )
& ( ~ ( in @ X1954 @ X1951 )
| ~ ( in @ X1955 @ X1952 )
| ~ ( in @ ( kpair @ X1954 @ X1955 ) @ ( dpsetconstr @ X1951 @ X1952 @ X1953 ) )
| ( X1953 @ X1954 @ X1955 ) )
& ( ~ ( in @ ( kpair @ X1959 @ X1960 ) @ ( dpsetconstr @ X1956 @ X1957 @ X1958 ) )
| ( in @ X1959 @ X1956 ) )
& ( ~ ( in @ ( kpair @ X1964 @ X1965 ) @ ( dpsetconstr @ X1961 @ X1962 @ X1963 ) )
| ( in @ X1965 @ X1962 ) )
& ( ~ ( in @ ( kpair @ X1969 @ X1970 ) @ ( dpsetconstr @ X1966 @ X1967 @ X1968 ) )
| ( X1968 @ X1969 @ X1970 ) )
& ( ~ ( func @ X1971 @ X1972 @ X1973 )
| ~ ( in @ X1974 @ X1971 )
| ( singleton
@ ( dsetconstr @ X1972
@ ^ [Z0: $i] : ( in @ ( kpair @ X1974 @ Z0 ) @ X1973 ) ) ) )
& ( ~ ( func @ X1975 @ X1976 @ X1977 )
| ~ ( in @ X1978 @ X1975 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1976
@ ^ [Z0: $i] : ( in @ ( kpair @ X1978 @ Z0 ) @ X1977 ) ) )
@ X1976 ) )
& ( ~ ( func @ X1979 @ X1980 @ X1981 )
| ~ ( in @ X1982 @ X1979 )
| ( in @ ( ap @ X1979 @ X1980 @ X1981 @ X1982 ) @ X1980 ) )
& ( ~ ( in @ X1985 @ ( funcSet @ X1983 @ X1984 ) )
| ( func @ X1983 @ X1984 @ X1985 ) )
& ( ~ ( in @ X1988 @ ( funcSet @ X1986 @ X1987 ) )
| ~ ( in @ X1989 @ X1986 )
| ( in @ ( ap @ X1986 @ X1987 @ X1988 @ X1989 ) @ X1987 ) )
& ( ~ ( func @ X1990 @ X1991 @ X1992 )
| ( in @ X1992 @ ( funcSet @ X1990 @ X1991 ) ) )
& ( ( in @ ( esk48_3 @ X1993 @ X1994 @ X1995 ) @ X1993 )
| ( func @ X1993 @ X1994
@ ( dpsetconstr @ X1993 @ X1994
@ ^ [Z0: $i] : ( $eq @ ( X1995 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X1995 @ ( esk48_3 @ X1993 @ X1994 @ X1995 ) ) @ X1994 )
| ( func @ X1993 @ X1994
@ ( dpsetconstr @ X1993 @ X1994
@ ^ [Z0: $i] : ( $eq @ ( X1995 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X1997 @ X1998 @ X1999 ) @ X1997 )
| ( func @ X1997 @ X1998 @ ( lam @ X1997 @ X1998 @ X1999 ) ) )
& ( ~ ( in @ ( X1999 @ ( esk49_3 @ X1997 @ X1998 @ X1999 ) ) @ X1998 )
| ( func @ X1997 @ X1998 @ ( lam @ X1997 @ X1998 @ X1999 ) ) )
& ( ( in @ ( esk50_3 @ X2001 @ X2002 @ X2003 ) @ X2001 )
| ( in @ ( lam @ X2001 @ X2002 @ X2003 ) @ ( funcSet @ X2001 @ X2002 ) ) )
& ( ~ ( in @ ( X2003 @ ( esk50_3 @ X2001 @ X2002 @ X2003 ) ) @ X2002 )
| ( in @ ( lam @ X2001 @ X2002 @ X2003 ) @ ( funcSet @ X2001 @ X2002 ) ) )
& ( ( in @ ( esk51_4 @ X2005 @ X2006 @ X2007 @ X2008 ) @ X2005 )
| ~ ( in @ X2011 @ X2007 )
| ( X2008 @ X2011 )
| ~ ( breln @ X2005 @ X2006 @ X2007 ) )
& ( ( in @ ( esk52_4 @ X2005 @ X2006 @ X2007 @ X2008 ) @ X2006 )
| ~ ( in @ X2011 @ X2007 )
| ( X2008 @ X2011 )
| ~ ( breln @ X2005 @ X2006 @ X2007 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2005 @ X2006 @ X2007 @ X2008 ) @ ( esk52_4 @ X2005 @ X2006 @ X2007 @ X2008 ) ) @ X2007 )
| ~ ( in @ X2011 @ X2007 )
| ( X2008 @ X2011 )
| ~ ( breln @ X2005 @ X2006 @ X2007 ) )
& ( ~ ( X2008 @ ( kpair @ ( esk51_4 @ X2005 @ X2006 @ X2007 @ X2008 ) @ ( esk52_4 @ X2005 @ X2006 @ X2007 @ X2008 ) ) )
| ~ ( in @ X2011 @ X2007 )
| ( X2008 @ X2011 )
| ~ ( breln @ X2005 @ X2006 @ X2007 ) )
& ( ( in @ ( esk53_4 @ X2012 @ X2013 @ X2014 @ X2015 ) @ X2012 )
| ~ ( in @ X2018 @ X2014 )
| ( X2015 @ X2018 )
| ~ ( breln @ X2012 @ X2013 @ X2014 ) )
& ( ( in @ ( esk54_4 @ X2012 @ X2013 @ X2014 @ X2015 ) @ X2013 )
| ~ ( in @ X2018 @ X2014 )
| ( X2015 @ X2018 )
| ~ ( breln @ X2012 @ X2013 @ X2014 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2012 @ X2013 @ X2014 @ X2015 ) @ ( esk54_4 @ X2012 @ X2013 @ X2014 @ X2015 ) ) @ X2014 )
| ~ ( in @ X2018 @ X2014 )
| ( X2015 @ X2018 )
| ~ ( breln @ X2012 @ X2013 @ X2014 ) )
& ( ~ ( X2015 @ ( kpair @ ( esk53_4 @ X2012 @ X2013 @ X2014 @ X2015 ) @ ( esk54_4 @ X2012 @ X2013 @ X2014 @ X2015 ) ) )
| ~ ( in @ X2018 @ X2014 )
| ( X2015 @ X2018 )
| ~ ( breln @ X2012 @ X2013 @ X2014 ) )
& ( ~ ( ex1 @ X2019 @ X2020 )
| ~ ( in @ X2021 @ X2019 )
| ~ ( in @ X2022 @ X2019 )
| ~ ( X2020 @ X2021 )
| ~ ( X2020 @ X2022 )
| ( X2021 = X2022 ) )
& ( ~ ( func @ X2023 @ X2024 @ X2025 )
| ~ ( in @ X2026 @ X2023 )
| ( in @ ( kpair @ X2026 @ ( ap @ X2023 @ X2024 @ X2025 @ X2026 ) ) @ X2025 ) )
& ( ~ ( in @ X2029 @ ( funcSet @ X2027 @ X2028 ) )
| ~ ( in @ X2030 @ X2027 )
| ( in @ ( kpair @ X2030 @ ( ap @ X2027 @ X2028 @ X2029 @ X2030 ) ) @ X2029 ) )
& ( ~ ( func @ X2031 @ X2032 @ X2033 )
| ~ ( in @ X2034 @ X2031 )
| ~ ( in @ X2035 @ X2032 )
| ~ ( in @ ( kpair @ X2034 @ X2035 ) @ X2033 )
| ( ( ap @ X2031 @ X2032 @ X2033 @ X2034 )
= X2035 ) )
& ( ( in @ ( esk55_4 @ X2036 @ X2037 @ X2038 @ X2039 ) @ X2036 )
| ~ ( in @ X2041 @ X2036 )
| ~ ( in @ X2042 @ X2037 )
| ~ ( in @ ( kpair @ X2041 @ X2042 ) @ X2039 )
| ( in @ ( kpair @ X2041 @ X2042 ) @ X2038 )
| ~ ( func @ X2036 @ X2037 @ X2039 )
| ~ ( func @ X2036 @ X2037 @ X2038 ) )
& ( ( ( ap @ X2036 @ X2037 @ X2038 @ ( esk55_4 @ X2036 @ X2037 @ X2038 @ X2039 ) )
!= ( ap @ X2036 @ X2037 @ X2039 @ ( esk55_4 @ X2036 @ X2037 @ X2038 @ X2039 ) ) )
| ~ ( in @ X2041 @ X2036 )
| ~ ( in @ X2042 @ X2037 )
| ~ ( in @ ( kpair @ X2041 @ X2042 ) @ X2039 )
| ( in @ ( kpair @ X2041 @ X2042 ) @ X2038 )
| ~ ( func @ X2036 @ X2037 @ X2039 )
| ~ ( func @ X2036 @ X2037 @ X2038 ) )
& ( ~ ( in @ X2045 @ ( funcSet @ X2043 @ X2044 ) )
| ~ ( in @ X2046 @ X2043 )
| ~ ( in @ X2047 @ X2044 )
| ~ ( in @ ( kpair @ X2046 @ X2047 ) @ X2045 )
| ( ( ap @ X2043 @ X2044 @ X2045 @ X2046 )
= X2047 ) )
& ( ( in @ ( esk56_4 @ X2048 @ X2049 @ X2050 @ X2051 ) @ X2048 )
| ( subset @ X2050 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2050 ) )
& ( ( in @ ( esk57_4 @ X2048 @ X2049 @ X2050 @ X2051 ) @ X2049 )
| ( subset @ X2050 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2050 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2048 @ X2049 @ X2050 @ X2051 ) @ ( esk57_4 @ X2048 @ X2049 @ X2050 @ X2051 ) ) @ X2050 )
| ( subset @ X2050 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2050 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2048 @ X2049 @ X2050 @ X2051 ) @ ( esk57_4 @ X2048 @ X2049 @ X2050 @ X2051 ) ) @ X2051 )
| ( subset @ X2050 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2051 )
| ~ ( breln @ X2048 @ X2049 @ X2050 ) )
& ( ( in @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ( X2056 = X2057 )
| ( in @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ( X2056 = X2057 )
| ( in @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ( X2056 = X2057 )
| ( in @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ( X2056 = X2057 )
| ( in @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ( X2056 = X2057 )
| ( in @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ( X2056 = X2057 )
| ( in @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ( X2056 = X2057 )
| ( in @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ( X2056 = X2057 )
| ( in @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ( X2056 = X2057 )
| ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ( X2056 = X2057 )
| ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ( X2056 = X2057 )
| ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ( X2056 = X2057 )
| ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2054 )
| ( X2056 = X2057 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ X2055 )
| ( X2056 = X2057 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ( X2056 = X2057 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk61_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2056 )
| ( X2056 = X2057 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2054 @ X2055 @ X2056 @ X2057 ) @ ( esk59_4 @ X2054 @ X2055 @ X2056 @ X2057 ) ) @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2057 )
| ~ ( breln @ X2054 @ X2055 @ X2056 ) )
& ( ( in @ ( esk62_4 @ X2062 @ X2063 @ X2064 @ X2065 ) @ X2062 )
| ( X2064 = X2065 )
| ~ ( func @ X2062 @ X2063 @ X2065 )
| ~ ( func @ X2062 @ X2063 @ X2064 ) )
& ( ( ( ap @ X2062 @ X2063 @ X2064 @ ( esk62_4 @ X2062 @ X2063 @ X2064 @ X2065 ) )
!= ( ap @ X2062 @ X2063 @ X2065 @ ( esk62_4 @ X2062 @ X2063 @ X2064 @ X2065 ) ) )
| ( X2064 = X2065 )
| ~ ( func @ X2062 @ X2063 @ X2065 )
| ~ ( func @ X2062 @ X2063 @ X2064 ) )
& ( ( in @ ( esk63_4 @ X2067 @ X2068 @ X2069 @ X2070 ) @ X2067 )
| ( X2069 = X2070 )
| ~ ( in @ X2070 @ ( funcSet @ X2067 @ X2068 ) )
| ~ ( in @ X2069 @ ( funcSet @ X2067 @ X2068 ) ) )
& ( ( ( ap @ X2067 @ X2068 @ X2069 @ ( esk63_4 @ X2067 @ X2068 @ X2069 @ X2070 ) )
!= ( ap @ X2067 @ X2068 @ X2070 @ ( esk63_4 @ X2067 @ X2068 @ X2069 @ X2070 ) ) )
| ( X2069 = X2070 )
| ~ ( in @ X2070 @ ( funcSet @ X2067 @ X2068 ) )
| ~ ( in @ X2069 @ ( funcSet @ X2067 @ X2068 ) ) )
& ( ~ ( in @ X2074 @ ( funcSet @ X2072 @ X2073 ) )
| ~ ( in @ X2075 @ X2072 )
| ( ( ap @ X2072 @ X2073 @ X2074 @ X2075 )
= ( ap @ X2072 @ X2073 @ X2074 @ X2075 ) ) )
& ( ~ ( func @ X2076 @ X2077 @ X2078 )
| ~ ( in @ X2079 @ X2076 )
| ( ( ap @ X2076 @ X2077 @ X2078 @ X2079 )
= ( ap @ X2076 @ X2077 @ X2078 @ X2079 ) ) )
& ( ( in @ ( esk64_3 @ X2080 @ X2081 @ X2082 ) @ X2080 )
| ~ ( in @ X2084 @ X2080 )
| ( ( ap @ X2080 @ X2081 @ ( lam @ X2080 @ X2081 @ X2082 ) @ X2084 )
= ( X2082 @ X2084 ) ) )
& ( ~ ( in @ ( X2082 @ ( esk64_3 @ X2080 @ X2081 @ X2082 ) ) @ X2081 )
| ~ ( in @ X2084 @ X2080 )
| ( ( ap @ X2080 @ X2081 @ ( lam @ X2080 @ X2081 @ X2082 ) @ X2084 )
= ( X2082 @ X2084 ) ) )
& ( ~ ( func @ X2085 @ X2086 @ X2087 )
| ( ( lam @ X2085 @ X2086 @ ( ap @ X2085 @ X2086 @ X2087 ) )
= X2087 ) )
& ( ( in @ ( esk65_3 @ X2088 @ X2089 @ X2090 ) @ X2088 )
| ( ( lam @ X2088 @ X2089 @ X2090 )
= ( lam @ X2088 @ X2089 @ X2090 ) ) )
& ( ~ ( in @ ( X2090 @ ( esk65_3 @ X2088 @ X2089 @ X2090 ) ) @ X2089 )
| ( ( lam @ X2088 @ X2089 @ X2090 )
= ( lam @ X2088 @ X2089 @ X2090 ) ) )
& ( ( in @ ( esk66_3 @ X2092 @ X2093 @ X2094 ) @ X2092 )
| ~ ( in @ X2096 @ X2092 )
| ( ( ap @ X2092 @ X2093 @ ( lam @ X2092 @ X2093 @ X2094 ) @ X2096 )
= ( X2094 @ X2096 ) ) )
& ( ~ ( in @ ( X2094 @ ( esk66_3 @ X2092 @ X2093 @ X2094 ) ) @ X2093 )
| ~ ( in @ X2096 @ X2092 )
| ( ( ap @ X2092 @ X2093 @ ( lam @ X2092 @ X2093 @ X2094 ) @ X2096 )
= ( X2094 @ X2096 ) ) )
& ( ~ ( in @ X2099 @ ( funcSet @ X2097 @ X2098 ) )
| ( ( lam @ X2097 @ X2098 @ ( ap @ X2097 @ X2098 @ X2099 ) )
= X2099 ) )
& ( ~ ( in @ X2102 @ X2100 )
| ~ ( in @ X2103 @ X2100 )
| X2101
| ( in @ X2103
@ ( dsetconstr @ X2100
@ ^ [Z0: $i] :
( ( X2101
& ( Z0 = X2102 ) )
| ( ~ X2101
& ( Z0 = X2103 ) ) ) ) ) )
& ( ~ ( in @ X2106 @ X2104 )
| ~ ( in @ X2107 @ X2104 )
| X2105
| ( ( dsetconstr @ X2104
@ ^ [Z0: $i] :
( ( X2105
& ( Z0 = X2106 ) )
| ( ~ X2105
& ( Z0 = X2107 ) ) ) )
= ( setadjoin @ X2107 @ emptyset ) ) )
& ( ~ ( in @ X2110 @ X2108 )
| ~ ( in @ X2111 @ X2108 )
| ~ X2109
| ( in @ X2110
@ ( dsetconstr @ X2108
@ ^ [Z0: $i] :
( ( X2109
& ( Z0 = X2110 ) )
| ( ~ X2109
& ( Z0 = X2111 ) ) ) ) ) )
& ( ~ ( in @ X2114 @ X2112 )
| ~ ( in @ X2115 @ X2112 )
| ~ X2113
| ( ( dsetconstr @ X2112
@ ^ [Z0: $i] :
( ( X2113
& ( Z0 = X2114 ) )
| ( ~ X2113
& ( Z0 = X2115 ) ) ) )
= ( setadjoin @ X2114 @ emptyset ) ) )
& ( ~ ( in @ X2118 @ X2116 )
| ~ ( in @ X2119 @ X2116 )
| ( singleton
@ ( dsetconstr @ X2116
@ ^ [Z0: $i] :
( ( X2117
& ( Z0 = X2118 ) )
| ( ~ X2117
& ( Z0 = X2119 ) ) ) ) ) )
& ( ~ ( in @ X2122 @ X2120 )
| ~ ( in @ X2123 @ X2120 )
| ( in @ ( if @ X2120 @ X2121 @ X2122 @ X2123 ) @ X2120 ) )
& ( ~ ( singleton @ X2124 )
| ~ ( in @ X2125 @ X2124 )
| ( ( setunion @ X2124 )
= X2125 ) )
& ( ~ ( in @ X2128 @ X2126 )
| ~ ( in @ X2129 @ X2126 )
| ~ X2127
| ( ( if @ X2126 @ X2127 @ X2128 @ X2129 )
= X2128 ) )
& ( ~ ( in @ X2132 @ X2130 )
| ~ ( in @ X2133 @ X2130 )
| X2131
| ( ( if @ X2130 @ X2131 @ X2132 @ X2133 )
= X2133 ) )
& ( ~ ( in @ X2136 @ X2134 )
| ~ ( in @ X2137 @ X2134 )
| ( in @ ( if @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( setadjoin @ X2136 @ ( setadjoin @ X2137 @ emptyset ) ) ) )
& ( ~ ( in @ X2139 @ ( powerset @ X2138 ) )
| ~ ( in @ X2140 @ ( powerset @ X2138 ) )
| ( in @ ( binintersect @ X2139 @ X2140 ) @ ( powerset @ X2138 ) ) )
& ( ~ ( in @ X2142 @ ( powerset @ X2141 ) )
| ~ ( in @ X2143 @ ( powerset @ X2141 ) )
| ( in @ ( binunion @ X2142 @ X2143 ) @ ( powerset @ X2141 ) ) )
& ( in @ esk68_0 @ ( powerset @ esk67_0 ) )
& ~ ( in @ ( powerset @ esk68_0 ) @ ( powerset @ ( powerset @ esk67_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_280])])])])])])]) ).
thf(c_0_282,negated_conjecture,
~ ( in @ ( powerset @ esk68_0 ) @ ( powerset @ ( powerset @ esk67_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
thf(c_0_283,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
thf(c_0_284,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
thf(c_0_285,negated_conjecture,
in @ esk68_0 @ ( powerset @ esk67_0 ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
thf(c_0_286,negated_conjecture,
~ ( subset @ ( powerset @ esk68_0 ) @ ( powerset @ esk67_0 ) ),
inference(spm,[status(thm)],[c_0_282,c_0_283]) ).
thf(c_0_287,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ ( powerset @ X2 ) @ ( powerset @ X3 ) )
| ~ ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
thf(c_0_288,negated_conjecture,
subset @ esk68_0 @ esk67_0,
inference(spm,[status(thm)],[c_0_284,c_0_285]) ).
thf(c_0_289,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_287]),c_0_288])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEU712^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 16:12:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 Running higher-order theorem proving
% 0.21/0.51 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.11/0.97 # Version: 3.1.0-ho
% 2.11/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.11/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.11/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.11/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.11/0.97 # Starting pre_casc_3 with 300s (1) cores
% 2.11/0.97 # Starting ho_unfolding_8 with 300s (1) cores
% 2.11/0.97 # Starting new_ho_10_cnf2 with 300s (1) cores
% 2.11/0.97 # Starting new_bool_3 with 300s (1) cores
% 2.11/0.97 # Starting new_ho_5 with 300s (1) cores
% 2.11/0.97 # new_ho_5 with pid 15086 completed with status 8
% 2.11/0.97 # pre_casc_3 with pid 15082 completed with status 8
% 2.11/0.97 # new_bool_5 with pid 15081 completed with status 0
% 2.11/0.97 # Result found by new_bool_5
% 2.11/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.11/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.11/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.11/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.11/0.97 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.11/0.97 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.11/0.97 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.11/0.97 # Starting ho_unfolding_8 with 55s (1) cores
% 2.11/0.97 # ho_unfolding_8 with pid 15113 completed with status 0
% 2.11/0.97 # Result found by ho_unfolding_8
% 2.11/0.97 # Preprocessing class: HSLMSLSSLLLCHFA.
% 2.11/0.97 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 2.11/0.97 # Starting ehoh_best5 with 300s (1) cores
% 2.11/0.97 # Starting almost_fo_3_lam with 300s (1) cores
% 2.11/0.97 # Starting new_bool_5 with 300s (1) cores
% 2.11/0.97 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 2.11/0.97 # Search class: HGHSM-FSLM32-MHFMMSBN
% 2.11/0.97 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 2.11/0.97 # Starting ho_unfolding_8 with 55s (1) cores
% 2.11/0.97 # Preprocessing time : 0.069 s
% 2.11/0.97 # Presaturation interreduction done
% 2.11/0.97
% 2.11/0.97 # Proof found!
% 2.11/0.97 # SZS status Theorem
% 2.11/0.97 # SZS output start CNFRefutation
% See solution above
% 2.11/0.97 # Parsed axioms : 499
% 2.11/0.97 # Removed by relevancy pruning/SinE : 271
% 2.11/0.97 # Initial clauses : 375
% 2.11/0.97 # Removed in clause preprocessing : 34
% 2.11/0.97 # Initial clauses in saturation : 341
% 2.11/0.97 # Processed clauses : 667
% 2.11/0.97 # ...of these trivial : 9
% 2.11/0.97 # ...subsumed : 31
% 2.11/0.97 # ...remaining for further processing : 627
% 2.11/0.97 # Other redundant clauses eliminated : 53
% 2.11/0.97 # Clauses deleted for lack of memory : 0
% 2.11/0.97 # Backward-subsumed : 0
% 2.11/0.97 # Backward-rewritten : 3
% 2.11/0.97 # Generated clauses : 6242
% 2.11/0.97 # ...of the previous two non-redundant : 6036
% 2.11/0.97 # ...aggressively subsumed : 0
% 2.11/0.97 # Contextual simplify-reflections : 0
% 2.11/0.97 # Paramodulations : 6154
% 2.11/0.97 # Factorizations : 2
% 2.11/0.97 # NegExts : 0
% 2.11/0.97 # Equation resolutions : 60
% 2.11/0.97 # Disequality decompositions : 0
% 2.11/0.97 # Total rewrite steps : 169
% 2.11/0.97 # ...of those cached : 113
% 2.11/0.97 # Propositional unsat checks : 0
% 2.11/0.97 # Propositional check models : 0
% 2.11/0.97 # Propositional check unsatisfiable : 0
% 2.11/0.97 # Propositional clauses : 0
% 2.11/0.97 # Propositional clauses after purity: 0
% 2.11/0.97 # Propositional unsat core size : 0
% 2.11/0.97 # Propositional preprocessing time : 0.000
% 2.11/0.97 # Propositional encoding time : 0.000
% 2.11/0.97 # Propositional solver time : 0.000
% 2.11/0.97 # Success case prop preproc time : 0.000
% 2.11/0.97 # Success case prop encoding time : 0.000
% 2.11/0.97 # Success case prop solver time : 0.000
% 2.11/0.97 # Current number of processed clauses : 308
% 2.11/0.97 # Positive orientable unit clauses : 40
% 2.11/0.97 # Positive unorientable unit clauses: 0
% 2.11/0.97 # Negative unit clauses : 4
% 2.11/0.97 # Non-unit-clauses : 264
% 2.11/0.97 # Current number of unprocessed clauses: 6007
% 2.11/0.97 # ...number of literals in the above : 24163
% 2.11/0.97 # Current number of archived formulas : 0
% 2.11/0.97 # Current number of archived clauses : 303
% 2.11/0.97 # Clause-clause subsumption calls (NU) : 34666
% 2.11/0.97 # Rec. Clause-clause subsumption calls : 15750
% 2.11/0.97 # Non-unit clause-clause subsumptions : 24
% 2.11/0.97 # Unit Clause-clause subsumption calls : 583
% 2.11/0.97 # Rewrite failures with RHS unbound : 0
% 2.11/0.97 # BW rewrite match attempts : 33
% 2.11/0.97 # BW rewrite match successes : 2
% 2.11/0.97 # Condensation attempts : 0
% 2.11/0.97 # Condensation successes : 0
% 2.11/0.97 # Termbank termtop insertions : 152641
% 2.11/0.97 # Search garbage collected termcells : 22044
% 2.11/0.97
% 2.11/0.97 # -------------------------------------------------
% 2.11/0.97 # User time : 0.406 s
% 2.11/0.97 # System time : 0.019 s
% 2.11/0.97 # Total time : 0.425 s
% 2.11/0.97 # Maximum resident set size: 7388 pages
% 2.11/0.97
% 2.11/0.97 # -------------------------------------------------
% 2.11/0.97 # User time : 0.595 s
% 2.11/0.97 # System time : 0.095 s
% 2.11/0.97 # Total time : 0.690 s
% 2.11/0.97 # Maximum resident set size: 2356 pages
% 2.11/0.97 % E---3.1 exiting
% 2.11/0.97 % E exiting
%------------------------------------------------------------------------------