%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU715^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 03:29:25 EDT 2024
% Result : Theorem 63.95s 11.18s
% Output : CNFRefutation 63.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 563
% Syntax : Number of formulae : 641 ( 10 unt; 331 typ; 0 def)
% Number of atoms : 2784 ( 452 equ; 0 cnn)
% Maximal formula atoms : 840 ( 8 avg)
% Number of connectives : 10533 ( 657 ~; 682 |; 459 &;7063 @)
% ( 318 <=>;1354 =>; 0 <=; 0 <~>)
% Maximal formula depth : 986 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 497 ( 497 >; 0 *; 0 +; 0 <<)
% Number of symbols : 335 ( 331 usr; 240 con; 0-4 aty)
% Number of variables : 2423 ( 156 ^2187 !; 80 ?;2423 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_40,type,
descr: ( $i > $o ) > $i ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
notdexE: $o ).
thf(decl_93,type,
notdallE: $o ).
thf(decl_94,type,
exuI1: $o ).
thf(decl_95,type,
exuI3: $o ).
thf(decl_96,type,
exuI2: $o ).
thf(decl_97,type,
inCongP: $o ).
thf(decl_98,type,
in__Cong: $o ).
thf(decl_99,type,
exuE3u: $o ).
thf(decl_100,type,
exu__Cong: $o ).
thf(decl_101,type,
emptyset__Cong: $o ).
thf(decl_102,type,
setadjoin__Cong: $o ).
thf(decl_103,type,
powerset__Cong: $o ).
thf(decl_104,type,
setunion__Cong: $o ).
thf(decl_105,type,
omega__Cong: $o ).
thf(decl_106,type,
exuEu: $o ).
thf(decl_107,type,
descr__Cong: $o ).
thf(decl_108,type,
dsetconstr__Cong: $o ).
thf(decl_109,type,
subset: $i > $i > $o ).
thf(decl_112,type,
subsetI1: $o ).
thf(decl_113,type,
eqimpsubset2: $o ).
thf(decl_114,type,
eqimpsubset1: $o ).
thf(decl_115,type,
subsetI2: $o ).
thf(decl_116,type,
emptysetsubset: $o ).
thf(decl_117,type,
subsetE: $o ).
thf(decl_118,type,
subsetE2: $o ).
thf(decl_119,type,
notsubsetI: $o ).
thf(decl_120,type,
notequalI1: $o ).
thf(decl_121,type,
notequalI2: $o ).
thf(decl_122,type,
subsetRefl: $o ).
thf(decl_123,type,
subsetTrans: $o ).
thf(decl_124,type,
setadjoinSub: $o ).
thf(decl_125,type,
setadjoinSub2: $o ).
thf(decl_126,type,
subset2powerset: $o ).
thf(decl_127,type,
setextsub: $o ).
thf(decl_128,type,
subsetemptysetimpeq: $o ).
thf(decl_129,type,
powersetI1: $o ).
thf(decl_130,type,
powersetE1: $o ).
thf(decl_131,type,
inPowerset: $o ).
thf(decl_132,type,
powersetsubset: $o ).
thf(decl_133,type,
sepInPowerset: $o ).
thf(decl_134,type,
sepSubset: $o ).
thf(decl_135,type,
binunion: $i > $i > $i ).
thf(decl_136,type,
binunionIL: $o ).
thf(decl_137,type,
upairset2IR: $o ).
thf(decl_138,type,
binunionIR: $o ).
thf(decl_139,type,
binunionEcases: $o ).
thf(decl_140,type,
binunionE: $o ).
thf(decl_141,type,
binunionLsub: $o ).
thf(decl_142,type,
binunionRsub: $o ).
thf(decl_143,type,
binintersect: $i > $i > $i ).
thf(decl_144,type,
binintersectI: $o ).
thf(decl_145,type,
binintersectSubset5: $o ).
thf(decl_146,type,
binintersectEL: $o ).
thf(decl_147,type,
binintersectLsub: $o ).
thf(decl_148,type,
binintersectSubset2: $o ).
thf(decl_149,type,
binintersectSubset3: $o ).
thf(decl_150,type,
binintersectER: $o ).
thf(decl_151,type,
disjointsetsI1: $o ).
thf(decl_152,type,
binintersectRsub: $o ).
thf(decl_153,type,
binintersectSubset4: $o ).
thf(decl_154,type,
binintersectSubset1: $o ).
thf(decl_155,type,
bs114d: $o ).
thf(decl_157,type,
setminus: $i > $i > $i ).
thf(decl_158,type,
setminusI: $o ).
thf(decl_159,type,
setminusEL: $o ).
thf(decl_160,type,
setminusER: $o ).
thf(decl_161,type,
setminusSubset2: $o ).
thf(decl_162,type,
setminusERneg: $o ).
thf(decl_163,type,
setminusELneg: $o ).
thf(decl_164,type,
setminusILneg: $o ).
thf(decl_165,type,
setminusIRneg: $o ).
thf(decl_166,type,
setminusLsub: $o ).
thf(decl_167,type,
setminusSubset1: $o ).
thf(decl_168,type,
symdiff: $i > $i > $i ).
thf(decl_169,type,
symdiffE: $o ).
thf(decl_170,type,
symdiffI1: $o ).
thf(decl_171,type,
symdiffI2: $o ).
thf(decl_172,type,
symdiffIneg1: $o ).
thf(decl_173,type,
symdiffIneg2: $o ).
thf(decl_174,type,
iskpair: $i > $o ).
thf(decl_175,type,
secondinupair: $o ).
thf(decl_176,type,
setukpairIL: $o ).
thf(decl_177,type,
setukpairIR: $o ).
thf(decl_178,type,
kpairiskpair: $o ).
thf(decl_179,type,
kpair: $i > $i > $i ).
thf(decl_180,type,
kpairp: $o ).
thf(decl_181,type,
cartprod: $i > $i > $i ).
thf(decl_182,type,
singletonsubset: $o ).
thf(decl_183,type,
singletoninpowerset: $o ).
thf(decl_184,type,
singletoninpowunion: $o ).
thf(decl_185,type,
upairset2E: $o ).
thf(decl_186,type,
upairsubunion: $o ).
thf(decl_187,type,
upairinpowunion: $o ).
thf(decl_188,type,
ubforcartprodlem1: $o ).
thf(decl_189,type,
ubforcartprodlem2: $o ).
thf(decl_190,type,
ubforcartprodlem3: $o ).
thf(decl_191,type,
cartprodpairin: $o ).
thf(decl_192,type,
cartprodmempair1: $o ).
thf(decl_193,type,
cartprodmempair: $o ).
thf(decl_194,type,
setunionE2: $o ).
thf(decl_195,type,
setunionsingleton1: $o ).
thf(decl_196,type,
setunionsingleton2: $o ).
thf(decl_197,type,
setunionsingleton: $o ).
thf(decl_198,type,
singleton: $i > $o ).
thf(decl_199,type,
singletonprop: $o ).
thf(decl_200,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_201,type,
ex1E1: $o ).
thf(decl_202,type,
ex1I: $o ).
thf(decl_203,type,
ex1I2: $o ).
thf(decl_204,type,
singletonsuniq: $o ).
thf(decl_209,type,
setukpairinjL1: $o ).
thf(decl_210,type,
kfstsingleton: $o ).
thf(decl_211,type,
theprop: $o ).
thf(decl_212,type,
kfst: $i > $i ).
thf(decl_213,type,
kfstpairEq: $o ).
thf(decl_214,type,
cartprodfstin: $o ).
thf(decl_215,type,
setukpairinjL2: $o ).
thf(decl_216,type,
setukpairinjL: $o ).
thf(decl_217,type,
setukpairinjR11: $o ).
thf(decl_218,type,
setukpairinjR12: $o ).
thf(decl_219,type,
setukpairinjR1: $o ).
thf(decl_220,type,
upairequniteq: $o ).
thf(decl_221,type,
setukpairinjR2: $o ).
thf(decl_222,type,
setukpairinjR: $o ).
thf(decl_223,type,
ksndsingleton: $o ).
thf(decl_224,type,
ksnd: $i > $i ).
thf(decl_225,type,
ksndpairEq: $o ).
thf(decl_226,type,
kpairsurjEq: $o ).
thf(decl_227,type,
cartprodsndin: $o ).
thf(decl_228,type,
cartprodpairmemEL: $o ).
thf(decl_229,type,
cartprodpairmemER: $o ).
thf(decl_230,type,
cartprodmempaircEq: $o ).
thf(decl_231,type,
cartprodfstpairEq: $o ).
thf(decl_232,type,
cartprodsndpairEq: $o ).
thf(decl_233,type,
cartprodpairsurjEq: $o ).
thf(decl_234,type,
breln: $i > $i > $i > $o ).
thf(decl_235,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_236,type,
dpsetconstrI: $o ).
thf(decl_237,type,
dpsetconstrSub: $o ).
thf(decl_238,type,
setOfPairsIsBReln: $o ).
thf(decl_239,type,
dpsetconstrERa: $o ).
thf(decl_240,type,
dpsetconstrEL1: $o ).
thf(decl_241,type,
dpsetconstrEL2: $o ).
thf(decl_242,type,
dpsetconstrER: $o ).
thf(decl_243,type,
func: $i > $i > $i > $o ).
thf(decl_244,type,
funcSet: $i > $i > $i ).
thf(decl_245,type,
funcImageSingleton: $o ).
thf(decl_246,type,
apProp: $o ).
thf(decl_247,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_248,type,
app: $o ).
thf(decl_249,type,
infuncsetfunc: $o ).
thf(decl_250,type,
ap2p: $o ).
thf(decl_251,type,
funcinfuncset: $o ).
thf(decl_252,type,
lamProp: $o ).
thf(decl_253,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_254,type,
lamp: $o ).
thf(decl_255,type,
lam2p: $o ).
thf(decl_256,type,
brelnall1: $o ).
thf(decl_257,type,
brelnall2: $o ).
thf(decl_258,type,
ex1E2: $o ).
thf(decl_259,type,
funcGraphProp1: $o ).
thf(decl_260,type,
funcGraphProp3: $o ).
thf(decl_261,type,
funcGraphProp2: $o ).
thf(decl_262,type,
funcextLem: $o ).
thf(decl_263,type,
funcGraphProp4: $o ).
thf(decl_264,type,
subbreln: $o ).
thf(decl_265,type,
eqbreln: $o ).
thf(decl_266,type,
funcext: $o ).
thf(decl_267,type,
funcext2: $o ).
thf(decl_268,type,
ap2apEq1: $o ).
thf(decl_269,type,
ap2apEq2: $o ).
thf(decl_270,type,
beta1: $o ).
thf(decl_271,type,
eta1: $o ).
thf(decl_272,type,
lam2lamEq: $o ).
thf(decl_273,type,
beta2: $o ).
thf(decl_274,type,
eta2: $o ).
thf(decl_275,type,
iffalseProp1: $o ).
thf(decl_276,type,
iffalseProp2: $o ).
thf(decl_277,type,
iftrueProp1: $o ).
thf(decl_278,type,
iftrueProp2: $o ).
thf(decl_279,type,
ifSingleton: $o ).
thf(decl_280,type,
if: $i > $o > $i > $i > $i ).
thf(decl_281,type,
ifp: $o ).
thf(decl_282,type,
theeq: $o ).
thf(decl_283,type,
iftrue: $o ).
thf(decl_284,type,
iffalse: $o ).
thf(decl_285,type,
iftrueorfalse: $o ).
thf(decl_286,type,
binintersectT_lem: $o ).
thf(decl_287,type,
binunionT_lem: $o ).
thf(decl_288,type,
powersetT_lem: $o ).
thf(decl_289,type,
setminusT_lem: $o ).
thf(decl_290,type,
complementT_lem: $o ).
thf(decl_291,type,
epred1_0: $o ).
thf(decl_292,type,
esk1_2: $i > $i > $i ).
thf(decl_293,type,
esk2_2: $i > $i > $i ).
thf(decl_294,type,
esk3_2: $i > $i > $i ).
thf(decl_295,type,
esk4_1: $i > $i ).
thf(decl_296,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_297,type,
esk6_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_298,type,
esk7_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_299,type,
esk8_1: $i > $i ).
thf(decl_300,type,
esk9_1: ( $i > $o ) > $i ).
thf(decl_301,type,
esk10_1: ( $i > $o ) > $i ).
thf(decl_302,type,
esk11_2: $i > $i > $i ).
thf(decl_303,type,
esk12_2: $i > $i > $i ).
thf(decl_304,type,
esk13_1: $i > $i ).
thf(decl_305,type,
esk14_1: $i > $i ).
thf(decl_306,type,
esk15_1: $i > $i ).
thf(decl_307,type,
esk16_2: $i > $i > $i ).
thf(decl_308,type,
esk17_3: $i > $i > $o > $i ).
thf(decl_309,type,
esk18_1: ( $i > $o ) > $i ).
thf(decl_310,type,
esk19_1: $i > $i ).
thf(decl_311,type,
esk20_2: $i > ( $i > $o ) > $i ).
thf(decl_312,type,
esk21_2: $i > ( $i > $o ) > $i ).
thf(decl_313,type,
esk22_2: $i > ( $i > $o ) > $i ).
thf(decl_314,type,
esk23_2: $i > ( $i > $o ) > $i ).
thf(decl_315,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_316,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_317,type,
esk26_2: ( $i > $o ) > $i > $i ).
thf(decl_318,type,
esk27_1: ( $i > $o ) > $i ).
thf(decl_319,type,
esk28_1: ( $i > $o ) > $i ).
thf(decl_320,type,
esk29_2: ( $i > $o ) > $i > $i ).
thf(decl_321,type,
esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_322,type,
esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_323,type,
esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_324,type,
esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_325,type,
esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_326,type,
esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_327,type,
esk36_2: $i > $i > $i ).
thf(decl_328,type,
esk37_2: $i > $i > $i ).
thf(decl_329,type,
esk38_2: $i > $i > $i ).
thf(decl_330,type,
esk39_3: $i > $i > $i > $i ).
thf(decl_331,type,
esk40_3: $i > $i > $i > $i ).
thf(decl_332,type,
esk41_2: $i > $i > $i ).
thf(decl_333,type,
esk42_2: $i > ( $i > $o ) > $i ).
thf(decl_334,type,
esk43_2: $i > ( $i > $o ) > $i ).
thf(decl_335,type,
esk44_2: $i > ( $i > $o ) > $i ).
thf(decl_336,type,
esk45_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_337,type,
esk46_2: $i > ( $i > $o ) > $i ).
thf(decl_338,type,
esk47_2: $i > ( $i > $o ) > $i ).
thf(decl_339,type,
esk48_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_340,type,
esk49_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_341,type,
esk50_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_342,type,
esk51_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_343,type,
esk52_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_344,type,
esk53_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_345,type,
esk54_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_346,type,
esk55_4: $i > $i > $i > $i > $i ).
thf(decl_347,type,
esk56_4: $i > $i > $i > $i > $i ).
thf(decl_348,type,
esk57_4: $i > $i > $i > $i > $i ).
thf(decl_349,type,
esk58_4: $i > $i > $i > $i > $i ).
thf(decl_350,type,
esk59_4: $i > $i > $i > $i > $i ).
thf(decl_351,type,
esk60_4: $i > $i > $i > $i > $i ).
thf(decl_352,type,
esk61_4: $i > $i > $i > $i > $i ).
thf(decl_353,type,
esk62_4: $i > $i > $i > $i > $i ).
thf(decl_354,type,
esk63_4: $i > $i > $i > $i > $i ).
thf(decl_355,type,
esk64_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_356,type,
esk65_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_357,type,
esk66_3: $i > $i > ( $i > $i ) > $i ).
thf(decl_358,type,
esk67_0: $i ).
thf(decl_359,type,
esk68_0: $i ).
thf(decl_360,type,
esk69_0: $i ).
thf(dpsetconstrEL2,axiom,
( dpsetconstrEL2
<=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
=> ( X28 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( singleton
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( dsetconstr @ X5
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(apProp,axiom,
( apProp
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X5
@ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
@ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(lamProp,axiom,
( lamProp
<=> ! [X4: $i,X5: $i,X30: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X30 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] :
( ( X30 @ X2 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,axiom,
( lamp
<=> ! [X4: $i,X5: $i,X31: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X31 @ X2 ) @ X5 ) )
=> ( func @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(lam2p,axiom,
( lam2p
<=> ! [X4: $i,X5: $i,X32: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X32 @ X2 ) @ X5 ) )
=> ( in
@ ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X32 @ X2 ) )
@ ( funcSet @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(ex1E2,axiom,
( ex1E2
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(beta1,axiom,
( beta1
<=> ! [X4: $i,X5: $i,X36: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X36 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X36 @ X3 ) )
@ X2 )
= ( X36 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(eta1,axiom,
( eta1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(lam2lamEq,axiom,
( lam2lamEq
<=> ! [X4: $i,X5: $i,X37: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X37 @ X2 ) @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) )
= ( lam @ X4 @ X5
@ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(beta2,axiom,
( beta2
<=> ! [X4: $i,X5: $i,X38: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( X38 @ X2 ) @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5
@ ( lam @ X4 @ X5
@ ^ [X3: $i] : ( X38 @ X3 ) )
@ X2 )
= ( X38 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(eta2,axiom,
( eta2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( ( lam @ X4 @ X5
@ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
= X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(iffalseProp1,axiom,
( iffalseProp1
<=> ! [X4: $i,X39: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X39
=> ( in @ X3
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X39
& ( X14 = X2 ) )
| ( ~ X39
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,axiom,
( iffalseProp2
<=> ! [X4: $i,X40: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X40
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X40
& ( X14 = X2 ) )
| ( ~ X40
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(iftrueProp1,axiom,
( iftrueProp1
<=> ! [X4: $i,X41: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X41
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X41
& ( X14 = X2 ) )
| ( ~ X41
& ( X14 = X3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,axiom,
( iftrueProp2
<=> ! [X4: $i,X42: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( X42
=> ( ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X42
& ( X14 = X2 ) )
| ( ~ X42
& ( X14 = X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(ifSingleton,axiom,
( ifSingleton
<=> ! [X4: $i,X43: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X14: $i] :
( ( X43
& ( X14 = X2 ) )
| ( ~ X43
& ( X14 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(sepInPowerset,axiom,
( sepInPowerset
<=> ! [X4: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,axiom,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(exuEu,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(descr__Cong,axiom,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(singletonprop,axiom,
( singletonprop
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(ex1E1,axiom,
( ex1E1
<=> ! [X4: $i,X1: $i > $o] :
( ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,axiom,
( ex1I
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X3 )
=> ( X3 = X2 ) ) )
=> ( ex1 @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,axiom,
( ex1I2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X18 )
@ ^ [X2: $i] :
( X18
= ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( X22 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
@ ( cartprod @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
<=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(dpsetconstrERa,axiom,
( dpsetconstrERa
<=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
=> ( X25 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrEL1,axiom,
( dpsetconstrEL1
<=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ X4 @ X5
@ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(exu__Cong,axiom,
( exu__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(exuE3u,axiom,
( exuE3u
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI2,axiom,
( exuI2
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,axiom,
( exuI3
<=> ! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exuI1,axiom,
( exuI1
<=> ! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(setextT,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(notequalI1,axiom,
( notequalI1
<=> ! [X4: $i,X5: $i] :
( ~ ( subset @ X4 @ X5 )
=> ( X4 != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(funcext,axiom,
( funcext
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(app,axiom,
( app
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(infuncsetfunc,axiom,
( infuncsetfunc
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ( func @ X4 @ X5 @ X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(ap2p,axiom,
( ap2p
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(eqimpsubset2,axiom,
( eqimpsubset2
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(eqimpsubset1,axiom,
( eqimpsubset1
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,axiom,
( brelnall2
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X33 )
=> ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(funcGraphProp3,axiom,
( funcGraphProp3
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(subsetE2,axiom,
( subsetE2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( subset @ X4 @ X5 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(funcextLem,axiom,
( funcextLem
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X34: $i] :
( ( func @ X4 @ X5 @ X34 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcGraphProp4,axiom,
( funcGraphProp4
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( subset @ X33 @ X35 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(notsubsetI,axiom,
( notsubsetI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( subset @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X4: $i,X5: $i,X33: $i] :
( ( breln @ X4 @ X5 @ X33 )
=> ! [X35: $i] :
( ( breln @ X4 @ X5 @ X35 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
=> ( X33 = X35 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(binunionEcases,axiom,
( binunionEcases
<=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( ( in @ X2 @ X4 )
=> X19 )
=> ( ( ( in @ X2 @ X5 )
=> X19 )
=> X19 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(funcext2,axiom,
( funcext2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X34: $i] :
( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
=> ( X29 = X34 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(ap2apEq1,axiom,
( ap2apEq1
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,axiom,
( ap2apEq2
<=> ! [X4: $i,X5: $i,X29: $i] :
( ( func @ X4 @ X5 @ X29 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( ap @ X4 @ X5 @ X29 @ X2 )
= ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(notequalI2,axiom,
( notequalI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( X4 != X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(subsetRefl,axiom,
( subsetRefl
<=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,axiom,
( subsetTrans
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X7 )
=> ( subset @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(setadjoinSub,axiom,
( setadjoinSub
<=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,axiom,
( setadjoinSub2
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(ifp,axiom,
( ifp
<=> ! [X4: $i,X44: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(theeq,axiom,
( theeq
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ! [X2: $i] :
( ( in @ X2 @ X21 )
=> ( ( setunion @ X21 )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(subset2powerset,axiom,
( subset2powerset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( in @ X4 @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X4: $i,X46: $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X4 )
=> ( ~ X46
=> ( ( if @ X4 @ X46 @ X2 @ X3 )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( subset @ X5 @ X4 )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(powersetT_lem,axiom,
( powersetT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powersetI1,axiom,
( powersetI1
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(setminusT_lem,axiom,
( setminusT_lem
<=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(inPowerset,axiom,
( inPowerset
<=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(powersetsubset,axiom,
( powersetsubset
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(binunionIL,axiom,
( binunionIL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(binunionIR,axiom,
( binunionIR
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(singletonsubset,axiom,
( singletonsubset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletoninpowerset,axiom,
( singletoninpowerset
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,axiom,
( singletoninpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
| ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionLsub,axiom,
( binunionLsub
<=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,axiom,
( binunionRsub
<=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( subset @ X7 @ X4 )
=> ( ( subset @ X7 @ X5 )
=> ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectLsub,axiom,
( binintersectLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectSubset2,axiom,
( binintersectSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( binintersect @ X4 @ X5 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,axiom,
( binintersectSubset3
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X5 )
=> ( subset @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X4: $i,X5: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( in @ X2 @ X5 ) )
=> ( ( binintersect @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(binintersectRsub,axiom,
( binintersectRsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset4,axiom,
( binintersectSubset4
<=> ! [X4: $i,X5: $i] :
( ( subset @ X5 @ X4 )
=> ( ( binintersect @ X4 @ X5 )
= X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset1,axiom,
( binintersectSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( binintersect @ X4 @ X5 )
= X4 )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(bs114d,axiom,
( bs114d
<=> ! [X4: $i,X5: $i,X7: $i] :
( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
= ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ~ ( in @ X2 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusSubset2,axiom,
( setminusSubset2
<=> ! [X4: $i,X5: $i] :
( ( subset @ X4 @ X5 )
=> ( ( setminus @ X4 @ X5 )
= emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusERneg,axiom,
( setminusERneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusELneg,axiom,
( setminusELneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusILneg,axiom,
( setminusILneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( setunion @ X4 )
= ( setunion @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setminusIRneg,axiom,
( setminusIRneg
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,axiom,
( setminusLsub
<=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,axiom,
( setminusSubset1
<=> ! [X4: $i,X5: $i] :
( ( ( setminus @ X4 @ X5 )
= emptyset )
=> ( subset @ X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(symdiffE,axiom,
( symdiffE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
=> ! [X20: $o] :
( ( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> X20 ) )
=> ( ( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> X20 ) )
=> X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,axiom,
( symdiffI1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,axiom,
( symdiffI2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,axiom,
( symdiffIneg1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,axiom,
( symdiffIneg2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ~ ( in @ X2 @ X4 )
=> ( ~ ( in @ X2 @ X5 )
=> ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(omega__Cong,axiom,
( omega__Cong
<=> ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(upairset2E,axiom,
( upairset2E
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairsubunion,axiom,
( upairsubunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(upairinpowunion,axiom,
( upairinpowunion
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(ubforcartprodlem1,axiom,
( ubforcartprodlem1
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,axiom,
( ubforcartprodlem2
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,axiom,
( ubforcartprodlem3
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(cartprodpairin,axiom,
( cartprodpairin
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ? [X3: $i] :
( ( in @ X3 @ X5 )
& ( X18
= ( kpair @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempair,axiom,
( cartprodmempair
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( iskpair @ X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ? [X21: $i] :
( ( in @ X21 @ X4 )
& ( in @ X2 @ X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singletonsuniq,axiom,
( singletonsuniq
<=> ! [X2: $i,X3: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(theprop,axiom,
( theprop
<=> ! [X21: $i] :
( ( singleton @ X21 )
=> ( in @ ( setunion @ X21 ) @ X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(cartprodfstin,axiom,
( cartprodfstin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( kfst @ X18 ) @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X2 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR11,axiom,
( setukpairinjR11
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR1,axiom,
( setukpairinjR1
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X14 = X18 )
=> ( X3 = X18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,axiom,
( upairequniteq
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= ( setadjoin @ X14 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(setukpairinjR2,axiom,
( setukpairinjR2
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
( ( ( kpair @ X2 @ X3 )
= ( kpair @ X14 @ X18 ) )
=> ( X3 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(kpairsurjEq,axiom,
( kpairsurjEq
<=> ! [X18: $i] :
( ( iskpair @ X18 )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(cartprodsndin,axiom,
( cartprodsndin
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,axiom,
( cartprodpairmemER
<=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
=> ( in @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodmempaircEq,axiom,
( cartprodmempaircEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ! [X3: $i] :
( ( in @ X3 @ X5 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(cartprodpairsurjEq,axiom,
( cartprodpairsurjEq
<=> ! [X4: $i,X5: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
=> ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
= X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(powerset__Cong,axiom,
( powerset__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ( ( powerset @ X4 )
= ( powerset @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ! [X14: $i,X18: $i] :
( ( X14 = X18 )
=> ( ( setadjoin @ X2 @ X14 )
= ( setadjoin @ X3 @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(emptyset__Cong,axiom,
( emptyset__Cong
<=> ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(inCongP,axiom,
( inCongP
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(notdallE,axiom,
( notdallE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,axiom,
( notdexE
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(c_0_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,plain,
( sepSubset
<=> ! [X4: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
@ X4 ) ),
inference(fof_simplification,[status(thm)],[sepSubset]) ).
thf(c_0_252,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_253,plain,
( descr__Cong
<=> ! [X1: $i > $o,X17: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X17 @ X3 ) ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( ( exu
@ ^ [Z0: $i] : ( X17 @ Z0 ) )
=> ( ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descr__Cong]) ).
thf(c_0_254,plain,
( 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,
( 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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_273,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_274,plain,
( 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_275,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_276,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_277,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_278,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_279,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_280,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_281,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_282,plain,
( epred1_0
<=> ! [X789: $i] :
? [X790: $i] :
( ! [X791: $i] :
( ( in @ X791 @ X790 )
=> ! [X792: $i] :
( ( in @ X792 @ X791 )
=> ( in @ X792 @ X789 ) ) )
& ! [X793: $i,X794: $i] :
( ( ( in @ X793 @ X789 )
& ( in @ X794 @ X789 ) )
=> ( ! [X795: $i] :
( ( in @ X795 @ X790 )
=> ( ( in @ X793 @ X795 )
<=> ( in @ X794 @ X795 ) ) )
=> ( X793 = X794 ) ) )
& ! [X796: $i,X797: $i] :
( ( ( in @ X796 @ X790 )
& ( in @ X797 @ X790 ) )
=> ( ! [X798: $i] :
( ( in @ X798 @ X796 )
=> ( in @ X798 @ X797 ) )
| ! [X799: $i] :
( ( in @ X799 @ X797 )
=> ( in @ X799 @ X796 ) ) ) )
& ! [X800: $i] :
( ( ! [X801: $i] :
( ( in @ X801 @ X800 )
=> ( in @ X801 @ X789 ) )
& ? [X802: $i] : ( in @ X802 @ X800 ) )
=> ? [X803: $i,X804: $i] :
( ( in @ X803 @ X790 )
& ( in @ X804 @ X800 )
& ~ ? [X805: $i] :
( ( in @ X805 @ X803 )
& ( in @ X805 @ X800 ) )
& ! [X806: $i] :
( ( in @ X806 @ X790 )
=> ( ! [X807: $i] :
( ( in @ X807 @ X806 )
=> ( in @ X807 @ X803 ) )
| ( in @ X804 @ X806 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_283,negated_conjecture,
~ ( ! [X762: $i,X763: $i] :
( ! [X764: $i] :
( ( in @ X764 @ X762 )
<=> ( in @ X764 @ X763 ) )
=> ( X762 = X763 ) )
=> ( ! [X765: $i] :
~ ( in @ X765 @ emptyset )
=> ( ! [X766: $i,X767: $i,X768: $i] :
( ( in @ X768 @ ( setadjoin @ X766 @ X767 ) )
<=> ( ( X768 = X766 )
| ( in @ X768 @ X767 ) ) )
=> ( ! [X769: $i,X770: $i] :
( ( in @ X770 @ ( powerset @ X769 ) )
<=> ! [X771: $i] :
( ( in @ X771 @ X770 )
=> ( in @ X771 @ X769 ) ) )
=> ( ! [X772: $i,X773: $i] :
( ( in @ X773 @ ( setunion @ X772 ) )
<=> ? [X774: $i] :
( ( in @ X773 @ X774 )
& ( in @ X774 @ X772 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X775: $i] :
( ( in @ X775 @ omega )
=> ( in @ ( setadjoin @ X775 @ X775 ) @ omega ) )
=> ( ! [X776: $i] :
( ( ( in @ emptyset @ X776 )
& ! [X777: $i] :
( ( ( in @ X777 @ omega )
& ( in @ X777 @ X776 ) )
=> ( in @ ( setadjoin @ X777 @ X777 ) @ X776 ) ) )
=> ! [X778: $i] :
( ( in @ X778 @ omega )
=> ( in @ X778 @ X776 ) ) )
=> ( ! [X779: $i > $i > $o,X780: $i] :
( ! [X781: $i] :
( ( in @ X781 @ X780 )
=> ( exu @ ( X779 @ X781 ) ) )
=> ? [X782: $i] :
! [X783: $i] :
( ( in @ X783 @ X782 )
<=> ? [X784: $i] :
( ( in @ X784 @ X780 )
& ( X779 @ X784 @ X783 ) ) ) )
=> ( ! [X785: $i] :
( ? [X786: $i] : ( in @ X786 @ X785 )
=> ? [X787: $i] :
( ( in @ X787 @ X785 )
& ~ ? [X788: $i] :
( ( in @ X788 @ X787 )
& ( in @ X788 @ X785 ) ) ) )
=> ( epred1_0
=> ( ! [X808: $i > $o] :
( ( exu @ X808 )
=> ( X808
@ ( descr
@ ^ [Z0: $i] : ( X808 @ Z0 ) ) ) )
=> ( ! [X809: $i,X810: $i > $o,X811: $i] :
( ( in @ X811 @ X809 )
=> ( ( X810 @ X811 )
=> ( in @ X811 @ ( dsetconstr @ X809 @ X810 ) ) ) )
=> ( ! [X812: $i,X813: $i > $o,X814: $i] :
( ( in @ X814 @ ( dsetconstr @ X812 @ X813 ) )
=> ( in @ X814 @ X812 ) )
=> ( ! [X815: $i,X816: $i > $o,X817: $i] :
( ( in @ X817 @ ( dsetconstr @ X815 @ X816 ) )
=> ( X816 @ X817 ) )
=> ( ! [X818: $i > $o] :
( ( exu @ X818 )
=> ? [X819: $i] :
( ( X818 @ X819 )
& ! [X820: $i] :
( ( X818 @ X820 )
=> ( X819 = X820 ) ) ) )
=> ( ! [X821: $o,X822: $i] :
( ( in @ X822 @ ( prop2set @ X821 ) )
=> X821 )
=> ( ! [X823: $i] :
( ( in @ X823 @ emptyset )
=> ! [X824: $o] : X824 )
=> ( ! [X825: $i] :
( ( in @ X825 @ emptyset )
=> ~ $true )
=> ( ! [X826: $i] :
~ ( in @ X826 @ emptyset )
=> ( ! [X827: $i > $o] :
( ( exu @ X827 )
=> ? [X828: $i] : ( X827 @ X828 ) )
=> ( ! [X829: $i,X830: $i] :
( ! [X831: $i] :
( ( in @ X831 @ X829 )
=> ( in @ X831 @ X830 ) )
=> ( ! [X832: $i] :
( ( in @ X832 @ X830 )
=> ( in @ X832 @ X829 ) )
=> ( X829 = X830 ) ) )
=> ( ! [X833: $i] :
( ! [X834: $i] :
~ ( in @ X834 @ X833 )
=> ( X833 = emptyset ) )
=> ( ! [X835: $i] :
( ! [X836: $i] :
~ ( in @ X836 @ X835 )
=> ( X835 = emptyset ) )
=> ( ! [X837: $i,X838: $i > $o,X839: $i] :
( ( in @ X839 @ X837 )
=> ( ( in @ X839 @ ( dsetconstr @ X837 @ X838 ) )
<=> ( X838 @ X839 ) ) )
=> ( ! [X840: $i] :
( ( nonempty @ X840 )
=> ? [X841: $i] : ( in @ X841 @ X840 ) )
=> ( ! [X842: $i,X843: $i > $o,X844: $i] :
( ( in @ X844 @ X842 )
=> ( ( X843 @ X844 )
=> ( nonempty @ ( dsetconstr @ X842 @ X843 ) ) ) )
=> ( ! [X845: $i] :
( ? [X846: $i] : ( in @ X846 @ X845 )
=> ( nonempty @ X845 ) )
=> ( ! [X847: $i,X848: $i] : ( in @ X847 @ ( setadjoin @ X847 @ X848 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X849: $i,X850: $i,X851: $i] :
( ( in @ X851 @ X850 )
=> ( in @ X851 @ ( setadjoin @ X849 @ X850 ) ) )
=> ( ! [X852: $i,X853: $i,X854: $i] :
( ( in @ X854 @ ( setadjoin @ X852 @ X853 ) )
=> ! [X855: $o] :
( ( ( X854 = X852 )
=> X855 )
=> ( ( ( in @ X854 @ X853 )
=> X855 )
=> X855 ) ) )
=> ( ! [X856: $i,X857: $i,X858: $i] :
( ( in @ X858 @ ( setadjoin @ X856 @ X857 ) )
=> ( ( X858 = X856 )
| ( in @ X858 @ X857 ) ) )
=> ( ! [X859: $i] :
( ( dsetconstr @ X859
@ ^ [Z0: $i] : $true )
= X859 )
=> ( ! [X860: $i,X861: $i] :
( ! [X862: $i] :
( ( in @ X862 @ X861 )
=> ( in @ X862 @ X860 ) )
=> ( in @ X861 @ ( powerset @ X860 ) ) )
=> ( ! [X863: $i] : ( in @ emptyset @ ( powerset @ X863 ) )
=> ( ! [X864: $i] : ( in @ emptyset @ ( powerset @ X864 ) )
=> ( ! [X865: $i,X866: $i,X867: $i] :
( ( in @ X866 @ ( powerset @ X865 ) )
=> ( ( in @ X867 @ X866 )
=> ( in @ X867 @ X865 ) ) )
=> ( ! [X868: $i,X869: $i,X870: $i] :
( ( in @ X869 @ X870 )
=> ( ( in @ X870 @ X868 )
=> ( in @ X869 @ ( setunion @ X868 ) ) ) )
=> ( ! [X871: $i,X872: $i] :
( ( in @ X872 @ ( setunion @ X871 ) )
=> ! [X873: $o] :
( ! [X874: $i] :
( ( in @ X872 @ X874 )
=> ( ( in @ X874 @ X871 )
=> X873 ) )
=> X873 ) )
=> ( ! [X875: $i,X876: $i] :
( ( in @ X876 @ X875 )
=> ( in @ X876 @ ( powerset @ ( setunion @ X875 ) ) ) )
=> ( ! [X877: $i > $o] :
( ( exu @ X877 )
=> ? [X878: $i] :
! [X879: $i] :
( ( X877 @ X879 )
<=> ( X879 = X878 ) ) )
=> ( ! [X880: $i] :
( ( nonempty @ X880 )
=> ? [X881: $i] :
( ( in @ X881 @ X880 )
& $true ) )
=> ( ! [X882: $i,X883: $i] :
( ( in @ X882 @ ( setadjoin @ X883 @ emptyset ) )
=> ( X882 = X883 ) )
=> ( ! [X884: $i,X885: $i] :
( ( X884 != X885 )
=> ~ ( in @ X885 @ ( setadjoin @ X884 @ emptyset ) ) )
=> ( ! [X886: $i,X887: $i] :
( ( X886 = X887 )
=> ( in @ X886 @ ( setadjoin @ X887 @ emptyset ) ) )
=> ( ! [X888: $i,X889: $i] :
( ( in @ X888 @ ( setadjoin @ X889 @ emptyset ) )
=> ( in @ X889 @ ( setadjoin @ X888 @ emptyset ) ) )
=> ( ! [X890: $i,X891: $i,X892: $i] :
( ( in @ X892 @ ( setadjoin @ X890 @ ( setadjoin @ X891 @ emptyset ) ) )
=> ( ( X892 = X890 )
| ( X892 = X891 ) ) )
=> ( ! [X893: $i,X894: $i] : ( in @ X893 @ ( setadjoin @ X893 @ ( setadjoin @ X894 @ emptyset ) ) )
=> ( ! [X895: $i,X896: $i] : ( in @ X896 @ ( setadjoin @ X895 @ ( setadjoin @ X896 @ emptyset ) ) )
=> ( ! [X897: $i,X898: $i > $o] :
( ? [X899: $i] :
( ( in @ X899 @ X897 )
& ( X898 @ X899 ) )
=> ( ( ( dsetconstr @ X897 @ X898 )
= emptyset )
=> ~ $true ) )
=> ( ! [X900: $i > $o,X901: $i] :
( ( in @ X901 @ emptyset )
=> ( X900 @ X901 ) )
=> ( ! [X902: $i,X903: $i > $o] :
( ~ ! [X904: $i] :
( ( in @ X904 @ X902 )
=> ( X903 @ X904 ) )
=> ? [X905: $i] :
( ( in @ X905 @ X902 )
& ~ ( X903 @ X905 ) ) )
=> ( ! [X906: $i,X907: $i > $o] :
( ! [X908: $i] :
( ( in @ X908 @ X906 )
=> ~ ( X907 @ X908 ) )
=> ~ ? [X909: $i] :
( ( in @ X909 @ X906 )
& ( X907 @ X909 ) ) )
=> ( ! [X910: $i,X911: $i > $o] :
( ~ ? [X912: $i] :
( ( in @ X912 @ X910 )
& ( X911 @ X912 ) )
=> ! [X913: $i] :
( ( in @ X913 @ X910 )
=> ~ ( X911 @ X913 ) ) )
=> ( ! [X914: $i,X915: $i > $o] :
( ? [X916: $i] :
( ( in @ X916 @ X914 )
& ~ ( X915 @ X916 ) )
=> ~ ! [X917: $i] :
( ( in @ X917 @ X914 )
=> ( X915 @ X917 ) ) )
=> ( ! [X918: $o] :
( X918
=> ( in @ emptyset @ ( prop2set @ X918 ) ) )
=> ( prop2set2propI
=> ( ! [X919: $i,X920: $i > $o] :
( ~ ? [X921: $i] :
( ( in @ X921 @ X919 )
& ( X920 @ X921 ) )
=> ! [X922: $i] :
( ( in @ X922 @ X919 )
=> ~ ( X920 @ X922 ) ) )
=> ( ! [X923: $i,X924: $i > $o] :
( ~ ! [X925: $i] :
( ( in @ X925 @ X923 )
=> ( X924 @ X925 ) )
=> ? [X926: $i] :
( ( in @ X926 @ X923 )
& ~ ( X924 @ X926 ) ) )
=> ( ! [X927: $i > $o] :
( ? [X928: $i] :
( ( X927 @ X928 )
& ! [X929: $i] :
( ( X927 @ X929 )
=> ( X928 = X929 ) ) )
=> ( exu @ X927 ) )
=> ( ! [X930: $i > $o] :
( ? [X931: $i] : ( X930 @ X931 )
=> ( ! [X932: $i,X933: $i] :
( ( X930 @ X932 )
=> ( ( X930 @ X933 )
=> ( X932 = X933 ) ) )
=> ( exu @ X930 ) ) )
=> ( ! [X934: $i > $o] :
( ? [X935: $i] :
! [X936: $i] :
( ( X934 @ X936 )
<=> ( X936 = X935 ) )
=> ( exu @ X934 ) )
=> ( ! [X937: $i,X938: $i] :
( ( X937 = X938 )
=> ! [X939: $i,X940: $i] :
( ( X939 = X940 )
=> ( ( in @ X939 @ X937 )
=> ( in @ X940 @ X938 ) ) ) )
=> ( ! [X941: $i,X942: $i] :
( ( X941 = X942 )
=> ! [X943: $i,X944: $i] :
( ( X943 = X944 )
=> ( ( in @ X943 @ X941 )
<=> ( in @ X944 @ X942 ) ) ) )
=> ( ! [X945: $i > $o] :
( ( exu @ X945 )
=> ! [X946: $i,X947: $i] :
( ( X945 @ X946 )
=> ( ( X945 @ X947 )
=> ( X946 = X947 ) ) ) )
=> ( ! [X948: $i > $o,X949: $i > $o] :
( ! [X950: $i,X951: $i] :
( ( X950 = X951 )
=> ( ( X948 @ X950 )
<=> ( X949 @ X951 ) ) )
=> ( ( exu @ X948 )
<=> ( exu @ X949 ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [X952: $i,X953: $i] :
( ( X952 = X953 )
=> ! [X954: $i,X955: $i] :
( ( X954 = X955 )
=> ( ( setadjoin @ X952 @ X954 )
= ( setadjoin @ X953 @ X955 ) ) ) )
=> ( ! [X956: $i,X957: $i] :
( ( X956 = X957 )
=> ( ( powerset @ X956 )
= ( powerset @ X957 ) ) )
=> ( ! [X958: $i,X959: $i] :
( ( X958 = X959 )
=> ( ( setunion @ X958 )
= ( setunion @ X959 ) ) )
=> ( ( omega = omega )
=> ( ! [X960: $i > $o] :
( ( exu @ X960 )
=> ! [X961: $i,X962: $i] :
( ( X960 @ X961 )
=> ( ( X960 @ X962 )
=> ( X961 = X962 ) ) ) )
=> ( ! [X963: $i > $o,X964: $i > $o] :
( ! [X965: $i,X966: $i] :
( ( X965 = X966 )
=> ( ( X963 @ X965 )
<=> ( X964 @ X966 ) ) )
=> ( ( exu @ X963 )
=> ( ( exu @ X964 )
=> ( ( descr @ X963 )
= ( descr @ X964 ) ) ) ) )
=> ( ! [X967: $i,X968: $i] :
( ( X967 = X968 )
=> ! [X969: $i > $o,X970: $i > $o] :
( ! [X971: $i] :
( ( in @ X971 @ X967 )
=> ! [X972: $i] :
( ( in @ X972 @ X968 )
=> ( ( X971 = X972 )
=> ( ( X969 @ X971 )
<=> ( X970 @ X972 ) ) ) ) )
=> ( ( dsetconstr @ X967 @ X969 )
= ( dsetconstr @ X968 @ X970 ) ) ) )
=> ( ! [X973: $i,X974: $i] :
( ! [X975: $i] :
( ( in @ X975 @ X973 )
=> ( in @ X975 @ X974 ) )
=> ( subset @ X973 @ X974 ) )
=> ( ! [X976: $i,X977: $i] :
( ( X976 = X977 )
=> ( subset @ X977 @ X976 ) )
=> ( ! [X978: $i,X979: $i] :
( ( X978 = X979 )
=> ( subset @ X978 @ X979 ) )
=> ( ! [X980: $i,X981: $i] :
( ! [X982: $i] :
( ( in @ X982 @ X980 )
=> ( in @ X982 @ X981 ) )
=> ( subset @ X980 @ X981 ) )
=> ( ! [X983: $i] : ( subset @ emptyset @ X983 )
=> ( ! [X984: $i,X985: $i,X986: $i] :
( ( subset @ X984 @ X985 )
=> ( ( in @ X986 @ X984 )
=> ( in @ X986 @ X985 ) ) )
=> ( ! [X987: $i,X988: $i,X989: $i] :
( ( subset @ X987 @ X988 )
=> ( ~ ( in @ X989 @ X988 )
=> ~ ( in @ X989 @ X987 ) ) )
=> ( ! [X990: $i,X991: $i,X992: $i] :
( ( in @ X992 @ X990 )
=> ( ~ ( in @ X992 @ X991 )
=> ~ ( subset @ X990 @ X991 ) ) )
=> ( ! [X993: $i,X994: $i] :
( ~ ( subset @ X993 @ X994 )
=> ( X993 != X994 ) )
=> ( ! [X995: $i,X996: $i,X997: $i] :
( ( in @ X997 @ X995 )
=> ( ~ ( in @ X997 @ X996 )
=> ( X995 != X996 ) ) )
=> ( ! [X998: $i] : ( subset @ X998 @ X998 )
=> ( ! [X999: $i,X1000: $i,X1001: $i] :
( ( subset @ X999 @ X1000 )
=> ( ( subset @ X1000 @ X1001 )
=> ( subset @ X999 @ X1001 ) ) )
=> ( ! [X1002: $i,X1003: $i] : ( subset @ X1003 @ ( setadjoin @ X1002 @ X1003 ) )
=> ( ! [X1004: $i,X1005: $i,X1006: $i] :
( ( subset @ X1004 @ X1006 )
=> ( subset @ X1004 @ ( setadjoin @ X1005 @ X1006 ) ) )
=> ( ! [X1007: $i,X1008: $i] :
( ( subset @ X1007 @ X1008 )
=> ( in @ X1007 @ ( powerset @ X1008 ) ) )
=> ( ! [X1009: $i,X1010: $i] :
( ( subset @ X1009 @ X1010 )
=> ( ( subset @ X1010 @ X1009 )
=> ( X1009 = X1010 ) ) )
=> ( ! [X1011: $i] :
( ( subset @ X1011 @ emptyset )
=> ( X1011 = emptyset ) )
=> ( ! [X1012: $i,X1013: $i] :
( ( subset @ X1013 @ X1012 )
=> ( in @ X1013 @ ( powerset @ X1012 ) ) )
=> ( ! [X1014: $i,X1015: $i] :
( ( in @ X1015 @ ( powerset @ X1014 ) )
=> ( subset @ X1015 @ X1014 ) )
=> ( ! [X1016: $i] : ( in @ X1016 @ ( powerset @ X1016 ) )
=> ( ! [X1017: $i,X1018: $i] :
( ( subset @ X1017 @ X1018 )
=> ( subset @ ( powerset @ X1017 ) @ ( powerset @ X1018 ) ) )
=> ( ! [X1019: $i,X1020: $i > $o] : ( in @ ( dsetconstr @ X1019 @ X1020 ) @ ( powerset @ X1019 ) )
=> ( ! [X1021: $i,X1022: $i > $o] : ( subset @ ( dsetconstr @ X1021 @ X1022 ) @ X1021 )
=> ( ! [X1023: $i,X1024: $i,X1025: $i] :
( ( in @ X1025 @ X1023 )
=> ( in @ X1025 @ ( binunion @ X1023 @ X1024 ) ) )
=> ( ! [X1026: $i,X1027: $i] : ( in @ X1027 @ ( setadjoin @ X1026 @ ( setadjoin @ X1027 @ emptyset ) ) )
=> ( ! [X1028: $i,X1029: $i,X1030: $i] :
( ( in @ X1030 @ X1029 )
=> ( in @ X1030 @ ( binunion @ X1028 @ X1029 ) ) )
=> ( ! [X1031: $i,X1032: $i,X1033: $i,X1034: $o] :
( ( in @ X1033 @ ( binunion @ X1031 @ X1032 ) )
=> ( ( ( in @ X1033 @ X1031 )
=> X1034 )
=> ( ( ( in @ X1033 @ X1032 )
=> X1034 )
=> X1034 ) ) )
=> ( ! [X1035: $i,X1036: $i,X1037: $i] :
( ( in @ X1037 @ ( binunion @ X1035 @ X1036 ) )
=> ( ( in @ X1037 @ X1035 )
| ( in @ X1037 @ X1036 ) ) )
=> ( ! [X1038: $i,X1039: $i] : ( subset @ X1038 @ ( binunion @ X1038 @ X1039 ) )
=> ( ! [X1040: $i,X1041: $i] : ( subset @ X1041 @ ( binunion @ X1040 @ X1041 ) )
=> ( ! [X1042: $i,X1043: $i,X1044: $i] :
( ( in @ X1044 @ X1042 )
=> ( ( in @ X1044 @ X1043 )
=> ( in @ X1044 @ ( binintersect @ X1042 @ X1043 ) ) ) )
=> ( ! [X1045: $i,X1046: $i,X1047: $i] :
( ( subset @ X1047 @ X1045 )
=> ( ( subset @ X1047 @ X1046 )
=> ( subset @ X1047 @ ( binintersect @ X1045 @ X1046 ) ) ) )
=> ( ! [X1048: $i,X1049: $i,X1050: $i] :
( ( in @ X1050 @ ( binintersect @ X1048 @ X1049 ) )
=> ( in @ X1050 @ X1048 ) )
=> ( ! [X1051: $i,X1052: $i] : ( subset @ ( binintersect @ X1051 @ X1052 ) @ X1051 )
=> ( ! [X1053: $i,X1054: $i] :
( ( subset @ X1053 @ X1054 )
=> ( ( binintersect @ X1053 @ X1054 )
= X1053 ) )
=> ( ! [X1055: $i,X1056: $i] :
( ( ( binintersect @ X1055 @ X1056 )
= X1056 )
=> ( subset @ X1056 @ X1055 ) )
=> ( ! [X1057: $i,X1058: $i,X1059: $i] :
( ( in @ X1059 @ ( binintersect @ X1057 @ X1058 ) )
=> ( in @ X1059 @ X1058 ) )
=> ( ! [X1060: $i,X1061: $i] :
( ~ ? [X1062: $i] :
( ( in @ X1062 @ X1060 )
& ( in @ X1062 @ X1061 ) )
=> ( ( binintersect @ X1060 @ X1061 )
= emptyset ) )
=> ( ! [X1063: $i,X1064: $i] : ( subset @ ( binintersect @ X1063 @ X1064 ) @ X1064 )
=> ( ! [X1065: $i,X1066: $i] :
( ( subset @ X1066 @ X1065 )
=> ( ( binintersect @ X1065 @ X1066 )
= X1066 ) )
=> ( ! [X1067: $i,X1068: $i] :
( ( ( binintersect @ X1067 @ X1068 )
= X1067 )
=> ( subset @ X1067 @ X1068 ) )
=> ( ! [X1069: $i,X1070: $i,X1071: $i] :
( ( binintersect @ X1069 @ ( binunion @ X1070 @ X1071 ) )
= ( binunion @ ( binintersect @ X1069 @ X1070 ) @ ( binintersect @ X1069 @ X1071 ) ) )
=> ( ! [X1072: $i,X1073: $i,X1074: $i] :
( ( in @ X1074 @ X1072 )
=> ( ~ ( in @ X1074 @ X1073 )
=> ( in @ X1074 @ ( setminus @ X1072 @ X1073 ) ) ) )
=> ( ! [X1075: $i,X1076: $i,X1077: $i] :
( ( in @ X1077 @ ( setminus @ X1075 @ X1076 ) )
=> ( in @ X1077 @ X1075 ) )
=> ( ! [X1078: $i,X1079: $i,X1080: $i] :
( ( in @ X1080 @ ( setminus @ X1078 @ X1079 ) )
=> ~ ( in @ X1080 @ X1079 ) )
=> ( ! [X1081: $i,X1082: $i] :
( ( subset @ X1081 @ X1082 )
=> ( ( setminus @ X1081 @ X1082 )
= emptyset ) )
=> ( ! [X1083: $i,X1084: $i,X1085: $i] :
( ~ ( in @ X1085 @ ( setminus @ X1083 @ X1084 ) )
=> ( ( in @ X1085 @ X1083 )
=> ( in @ X1085 @ X1084 ) ) )
=> ( ! [X1086: $i,X1087: $i,X1088: $i] :
( ~ ( in @ X1088 @ ( setminus @ X1086 @ X1087 ) )
=> ( ~ ( in @ X1088 @ X1087 )
=> ~ ( in @ X1088 @ X1086 ) ) )
=> ( ! [X1089: $i,X1090: $i,X1091: $i] :
( ~ ( in @ X1091 @ X1089 )
=> ~ ( in @ X1091 @ ( setminus @ X1089 @ X1090 ) ) )
=> ( ! [X1092: $i,X1093: $i,X1094: $i] :
( ( in @ X1094 @ X1093 )
=> ~ ( in @ X1094 @ ( setminus @ X1092 @ X1093 ) ) )
=> ( ! [X1095: $i,X1096: $i] : ( subset @ ( setminus @ X1095 @ X1096 ) @ X1095 )
=> ( ! [X1097: $i,X1098: $i] :
( ( ( setminus @ X1097 @ X1098 )
= emptyset )
=> ( subset @ X1097 @ X1098 ) )
=> ( ! [X1099: $i,X1100: $i,X1101: $i] :
( ( in @ X1101 @ ( symdiff @ X1099 @ X1100 ) )
=> ! [X1102: $o] :
( ( ( in @ X1101 @ X1099 )
=> ( ~ ( in @ X1101 @ X1100 )
=> X1102 ) )
=> ( ( ~ ( in @ X1101 @ X1099 )
=> ( ( in @ X1101 @ X1100 )
=> X1102 ) )
=> X1102 ) ) )
=> ( ! [X1103: $i,X1104: $i,X1105: $i] :
( ( in @ X1105 @ X1103 )
=> ( ~ ( in @ X1105 @ X1104 )
=> ( in @ X1105 @ ( symdiff @ X1103 @ X1104 ) ) ) )
=> ( ! [X1106: $i,X1107: $i,X1108: $i] :
( ~ ( in @ X1108 @ X1106 )
=> ( ( in @ X1108 @ X1107 )
=> ( in @ X1108 @ ( symdiff @ X1106 @ X1107 ) ) ) )
=> ( ! [X1109: $i,X1110: $i,X1111: $i] :
( ( in @ X1111 @ X1109 )
=> ( ( in @ X1111 @ X1110 )
=> ~ ( in @ X1111 @ ( symdiff @ X1109 @ X1110 ) ) ) )
=> ( ! [X1112: $i,X1113: $i,X1114: $i] :
( ~ ( in @ X1114 @ X1112 )
=> ( ~ ( in @ X1114 @ X1113 )
=> ~ ( in @ X1114 @ ( symdiff @ X1112 @ X1113 ) ) ) )
=> ( ! [X1115: $i,X1116: $i] : ( in @ X1116 @ ( setadjoin @ X1115 @ ( setadjoin @ X1116 @ emptyset ) ) )
=> ( ! [X1117: $i,X1118: $i] : ( in @ X1117 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1117 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1117 @ ( setadjoin @ X1118 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1119: $i,X1120: $i] : ( in @ X1120 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1119 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1119 @ ( setadjoin @ X1120 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X1121: $i,X1122: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1121 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1121 @ ( setadjoin @ X1122 @ emptyset ) ) @ emptyset ) ) )
=> ( ! [X1123: $i,X1124: $i] : ( iskpair @ ( kpair @ X1123 @ X1124 ) )
=> ( ! [X1125: $i,X1126: $i] :
( ( in @ X1126 @ X1125 )
=> ( subset @ ( setadjoin @ X1126 @ emptyset ) @ X1125 ) )
=> ( ! [X1127: $i,X1128: $i] :
( ( in @ X1128 @ X1127 )
=> ( in @ ( setadjoin @ X1128 @ emptyset ) @ ( powerset @ X1127 ) ) )
=> ( ! [X1129: $i,X1130: $i,X1131: $i] :
( ( in @ X1131 @ X1129 )
=> ( in @ ( setadjoin @ X1131 @ emptyset ) @ ( powerset @ ( binunion @ X1129 @ X1130 ) ) ) )
=> ( ! [X1132: $i,X1133: $i,X1134: $i] :
( ( in @ X1134 @ ( setadjoin @ X1132 @ ( setadjoin @ X1133 @ emptyset ) ) )
=> ( ( X1134 = X1132 )
| ( X1134 = X1133 ) ) )
=> ( ! [X1135: $i,X1136: $i,X1137: $i] :
( ( in @ X1137 @ X1135 )
=> ! [X1138: $i] :
( ( in @ X1138 @ X1136 )
=> ( subset @ ( setadjoin @ X1137 @ ( setadjoin @ X1138 @ emptyset ) ) @ ( binunion @ X1135 @ X1136 ) ) ) )
=> ( ! [X1139: $i,X1140: $i,X1141: $i] :
( ( in @ X1141 @ X1139 )
=> ! [X1142: $i] :
( ( in @ X1142 @ X1140 )
=> ( in @ ( setadjoin @ X1141 @ ( setadjoin @ X1142 @ emptyset ) ) @ ( powerset @ ( binunion @ X1139 @ X1140 ) ) ) ) )
=> ( ! [X1143: $i,X1144: $i,X1145: $i] :
( ( in @ X1145 @ X1143 )
=> ! [X1146: $i] :
( ( in @ X1146 @ X1144 )
=> ( subset @ ( setadjoin @ ( setadjoin @ X1145 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1145 @ ( setadjoin @ X1146 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1143 @ X1144 ) ) ) ) )
=> ( ! [X1147: $i,X1148: $i,X1149: $i] :
( ( in @ X1149 @ X1147 )
=> ! [X1150: $i] :
( ( in @ X1150 @ X1148 )
=> ( in @ ( setadjoin @ ( setadjoin @ X1149 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1149 @ ( setadjoin @ X1150 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1147 @ X1148 ) ) ) ) ) )
=> ( ! [X1151: $i,X1152: $i,X1153: $i] :
( ( in @ X1153 @ X1151 )
=> ! [X1154: $i] :
( ( in @ X1154 @ X1152 )
=> ( in @ ( kpair @ X1153 @ X1154 ) @ ( powerset @ ( powerset @ ( binunion @ X1151 @ X1152 ) ) ) ) ) )
=> ( ! [X1155: $i,X1156: $i,X1157: $i] :
( ( in @ X1157 @ X1155 )
=> ! [X1158: $i] :
( ( in @ X1158 @ X1156 )
=> ( in @ ( kpair @ X1157 @ X1158 ) @ ( cartprod @ X1155 @ X1156 ) ) ) )
=> ( ! [X1159: $i,X1160: $i,X1161: $i] :
( ( in @ X1161 @ ( cartprod @ X1159 @ X1160 ) )
=> ? [X1162: $i] :
( ( in @ X1162 @ X1159 )
& ? [X1163: $i] :
( ( in @ X1163 @ X1160 )
& ( X1161
= ( kpair @ X1162 @ X1163 ) ) ) ) )
=> ( ! [X1164: $i,X1165: $i,X1166: $i] :
( ( in @ X1166 @ ( cartprod @ X1164 @ X1165 ) )
=> ( iskpair @ X1166 ) )
=> ( ! [X1167: $i,X1168: $i] :
( ( in @ X1168 @ ( setunion @ X1167 ) )
=> ? [X1169: $i] :
( ( in @ X1169 @ X1167 )
& ( in @ X1168 @ X1169 ) ) )
=> ( ! [X1170: $i] : ( subset @ ( setunion @ ( setadjoin @ X1170 @ emptyset ) ) @ X1170 )
=> ( ! [X1171: $i] : ( subset @ X1171 @ ( setunion @ ( setadjoin @ X1171 @ emptyset ) ) )
=> ( ! [X1172: $i] :
( ( setunion @ ( setadjoin @ X1172 @ emptyset ) )
= X1172 )
=> ( ! [X1173: $i,X1174: $i > $o] :
( ! [X1175: $i] :
( ( in @ X1175 @ X1173 )
=> ! [X1176: $i] :
( ( in @ X1176 @ X1173 )
=> ( ( X1174 @ X1175 )
=> ( ( X1174 @ X1176 )
=> ( X1175 = X1176 ) ) ) ) )
=> ( ? [X1177: $i] :
( ( in @ X1177 @ X1173 )
& ( X1174 @ X1177 ) )
=> ( singleton @ ( dsetconstr @ X1173 @ X1174 ) ) ) )
=> ( ! [X1178: $i,X1179: $i > $o] :
( ( ex1 @ X1178 @ X1179 )
=> ? [X1180: $i] :
( ( in @ X1180 @ X1178 )
& ( X1179 @ X1180 ) ) )
=> ( ! [X1181: $i,X1182: $i > $o,X1183: $i] :
( ( in @ X1183 @ X1181 )
=> ( ( X1182 @ X1183 )
=> ( ! [X1184: $i] :
( ( in @ X1184 @ X1181 )
=> ( ( X1182 @ X1184 )
=> ( X1184 = X1183 ) ) )
=> ( ex1 @ X1181 @ X1182 ) ) ) )
=> ( ! [X1185: $i,X1186: $i > $o] :
( ! [X1187: $i] :
( ( in @ X1187 @ X1185 )
=> ! [X1188: $i] :
( ( in @ X1188 @ X1185 )
=> ( ( X1186 @ X1187 )
=> ( ( X1186 @ X1188 )
=> ( X1187 = X1188 ) ) ) ) )
=> ( ? [X1189: $i] :
( ( in @ X1189 @ X1185 )
& ( X1186 @ X1189 ) )
=> ( ex1 @ X1185 @ X1186 ) ) )
=> ( ! [X1190: $i,X1191: $i] :
( ( ( setadjoin @ X1190 @ emptyset )
= ( setadjoin @ X1191 @ emptyset ) )
=> ( X1190 = X1191 ) )
=> ( ! [X1192: $i,X1193: $i,X1194: $i] :
( ( in @ ( setadjoin @ X1194 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1192 @ ( setadjoin @ X1193 @ emptyset ) ) @ emptyset ) ) )
=> ( X1192 = X1194 ) )
=> ( ! [X1195: $i] :
( ( iskpair @ X1195 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1195 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1195 ) ) ) )
=> ( ! [X1196: $i] :
( ( singleton @ X1196 )
=> ( in @ ( setunion @ X1196 ) @ X1196 ) )
=> ( ! [X1197: $i,X1198: $i] :
( ( kfst @ ( kpair @ X1197 @ X1198 ) )
= X1197 )
=> ( ! [X1199: $i,X1200: $i,X1201: $i] :
( ( in @ X1201 @ ( cartprod @ X1199 @ X1200 ) )
=> ( in @ ( kfst @ X1201 ) @ X1199 ) )
=> ( ! [X1202: $i,X1203: $i,X1204: $i,X1205: $i] :
( ( ( setadjoin @ ( setadjoin @ X1202 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1202 @ ( setadjoin @ X1203 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1204 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1204 @ ( setadjoin @ X1205 @ emptyset ) ) @ emptyset ) ) )
=> ( X1202 = X1204 ) )
=> ( ! [X1206: $i,X1207: $i,X1208: $i,X1209: $i] :
( ( ( kpair @ X1206 @ X1207 )
= ( kpair @ X1208 @ X1209 ) )
=> ( X1206 = X1208 ) )
=> ( ! [X1210: $i,X1211: $i] :
( ( X1210 = X1211 )
=> ( ( setadjoin @ X1210 @ ( setadjoin @ X1211 @ emptyset ) )
= ( setadjoin @ X1210 @ emptyset ) ) )
=> ( ! [X1212: $i,X1213: $i] :
( ( X1212 = X1213 )
=> ( ( setadjoin @ ( setadjoin @ X1212 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1212 @ ( setadjoin @ X1213 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1212 @ emptyset ) @ emptyset ) ) )
=> ( ! [X1214: $i,X1215: $i,X1216: $i,X1217: $i] :
( ( ( setadjoin @ ( setadjoin @ X1214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1214 @ ( setadjoin @ X1215 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1216 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1216 @ ( setadjoin @ X1217 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1216 = X1217 )
=> ( X1215 = X1217 ) ) )
=> ( ! [X1218: $i,X1219: $i,X1220: $i] :
( ( ( setadjoin @ X1218 @ ( setadjoin @ X1219 @ emptyset ) )
= ( setadjoin @ X1220 @ emptyset ) )
=> ( X1218 = X1219 ) )
=> ( ! [X1221: $i,X1222: $i,X1223: $i,X1224: $i] :
( ( ( setadjoin @ ( setadjoin @ X1221 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1221 @ ( setadjoin @ X1222 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1223 @ ( setadjoin @ X1224 @ emptyset ) ) @ emptyset ) ) )
=> ( X1222 = X1224 ) )
=> ( ! [X1225: $i,X1226: $i,X1227: $i,X1228: $i] :
( ( ( kpair @ X1225 @ X1226 )
= ( kpair @ X1227 @ X1228 ) )
=> ( X1226 = X1228 ) )
=> ( ! [X1229: $i] :
( ( iskpair @ X1229 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1229 )
@ ^ [Z0: $i] :
( X1229
= ( kpair @ ( kfst @ X1229 ) @ Z0 ) ) ) ) )
=> ( ! [X1230: $i,X1231: $i] :
( ( ksnd @ ( kpair @ X1230 @ X1231 ) )
= X1231 )
=> ( ! [X1232: $i] :
( ( iskpair @ X1232 )
=> ( ( kpair @ ( kfst @ X1232 ) @ ( ksnd @ X1232 ) )
= X1232 ) )
=> ( ! [X1233: $i,X1234: $i,X1235: $i] :
( ( in @ X1235 @ ( cartprod @ X1233 @ X1234 ) )
=> ( in @ ( ksnd @ X1235 ) @ X1234 ) )
=> ( ! [X1236: $i,X1237: $i,X1238: $i,X1239: $i] :
( ( in @ ( kpair @ X1238 @ X1239 ) @ ( cartprod @ X1236 @ X1237 ) )
=> ( in @ X1238 @ X1236 ) )
=> ( ! [X1240: $i,X1241: $i,X1242: $i,X1243: $i] :
( ( in @ ( kpair @ X1242 @ X1243 ) @ ( cartprod @ X1240 @ X1241 ) )
=> ( in @ X1243 @ X1241 ) )
=> ( ! [X1244: $i,X1245: $i,X1246: $i] :
( ( in @ X1246 @ X1244 )
=> ! [X1247: $i] :
( ( in @ X1247 @ X1245 )
=> ( ( kpair @ X1246 @ X1247 )
= ( kpair @ X1246 @ X1247 ) ) ) )
=> ( ! [X1248: $i,X1249: $i,X1250: $i] :
( ( in @ X1250 @ X1248 )
=> ! [X1251: $i] :
( ( in @ X1251 @ X1249 )
=> ( ( kfst @ ( kpair @ X1250 @ X1251 ) )
= X1250 ) ) )
=> ( ! [X1252: $i,X1253: $i,X1254: $i] :
( ( in @ X1254 @ X1252 )
=> ! [X1255: $i] :
( ( in @ X1255 @ X1253 )
=> ( ( ksnd @ ( kpair @ X1254 @ X1255 ) )
= X1255 ) ) )
=> ( ! [X1256: $i,X1257: $i,X1258: $i] :
( ( in @ X1258 @ ( cartprod @ X1256 @ X1257 ) )
=> ( ( kpair @ ( kfst @ X1258 ) @ ( ksnd @ X1258 ) )
= X1258 ) )
=> ( ! [X1259: $i,X1260: $i,X1261: $i > $i > $o,X1262: $i] :
( ( in @ X1262 @ X1259 )
=> ! [X1263: $i] :
( ( in @ X1263 @ X1260 )
=> ( ( X1261 @ X1262 @ X1263 )
=> ( in @ ( kpair @ X1262 @ X1263 ) @ ( dpsetconstr @ X1259 @ X1260 @ X1261 ) ) ) ) )
=> ( ! [X1264: $i,X1265: $i,X1266: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1264 @ X1265 @ X1266 ) @ ( cartprod @ X1264 @ X1265 ) )
=> ( ! [X1267: $i,X1268: $i,X1269: $i > $i > $o] : ( breln @ X1267 @ X1268 @ ( dpsetconstr @ X1267 @ X1268 @ X1269 ) )
=> ( ! [X1270: $i,X1271: $i,X1272: $i > $i > $o,X1273: $i] :
( ( in @ X1273 @ X1270 )
=> ! [X1274: $i] :
( ( in @ X1274 @ X1271 )
=> ( ( in @ ( kpair @ X1273 @ X1274 ) @ ( dpsetconstr @ X1270 @ X1271 @ X1272 ) )
=> ( X1272 @ X1273 @ X1274 ) ) ) )
=> ( ! [X1275: $i,X1276: $i,X1277: $i > $i > $o,X1278: $i,X1279: $i] :
( ( in @ ( kpair @ X1278 @ X1279 ) @ ( dpsetconstr @ X1275 @ X1276 @ X1277 ) )
=> ( in @ X1278 @ X1275 ) )
=> ( ! [X1280: $i,X1281: $i,X1282: $i > $i > $o,X1283: $i,X1284: $i] :
( ( in @ ( kpair @ X1283 @ X1284 ) @ ( dpsetconstr @ X1280 @ X1281 @ X1282 ) )
=> ( in @ X1284 @ X1281 ) )
=> ( ! [X1285: $i,X1286: $i,X1287: $i > $i > $o,X1288: $i,X1289: $i] :
( ( in @ ( kpair @ X1288 @ X1289 ) @ ( dpsetconstr @ X1285 @ X1286 @ X1287 ) )
=> ( X1287 @ X1288 @ X1289 ) )
=> ( ! [X1290: $i,X1291: $i,X1292: $i] :
( ( func @ X1290 @ X1291 @ X1292 )
=> ! [X1293: $i] :
( ( in @ X1293 @ X1290 )
=> ( singleton
@ ( dsetconstr @ X1291
@ ^ [Z0: $i] : ( in @ ( kpair @ X1293 @ Z0 ) @ X1292 ) ) ) ) )
=> ( ! [X1294: $i,X1295: $i,X1296: $i] :
( ( func @ X1294 @ X1295 @ X1296 )
=> ! [X1297: $i] :
( ( in @ X1297 @ X1294 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1295
@ ^ [Z0: $i] : ( in @ ( kpair @ X1297 @ Z0 ) @ X1296 ) ) )
@ X1295 ) ) )
=> ( ! [X1298: $i,X1299: $i,X1300: $i] :
( ( func @ X1298 @ X1299 @ X1300 )
=> ! [X1301: $i] :
( ( in @ X1301 @ X1298 )
=> ( in @ ( ap @ X1298 @ X1299 @ X1300 @ X1301 ) @ X1299 ) ) )
=> ( ! [X1302: $i,X1303: $i,X1304: $i] :
( ( in @ X1304 @ ( funcSet @ X1302 @ X1303 ) )
=> ( func @ X1302 @ X1303 @ X1304 ) )
=> ( ! [X1305: $i,X1306: $i,X1307: $i] :
( ( in @ X1307 @ ( funcSet @ X1305 @ X1306 ) )
=> ! [X1308: $i] :
( ( in @ X1308 @ X1305 )
=> ( in @ ( ap @ X1305 @ X1306 @ X1307 @ X1308 ) @ X1306 ) ) )
=> ( ! [X1309: $i,X1310: $i,X1311: $i] :
( ( func @ X1309 @ X1310 @ X1311 )
=> ( in @ X1311 @ ( funcSet @ X1309 @ X1310 ) ) )
=> ( ! [X1312: $i,X1313: $i,X1314: $i > $i] :
( ! [X1315: $i] :
( ( in @ X1315 @ X1312 )
=> ( in @ ( X1314 @ X1315 ) @ X1313 ) )
=> ( func @ X1312 @ X1313
@ ( dpsetconstr @ X1312 @ X1313
@ ^ [Z0: $i] : ( $eq @ ( X1314 @ Z0 ) ) ) ) )
=> ( ! [X1316: $i,X1317: $i,X1318: $i > $i] :
( ! [X1319: $i] :
( ( in @ X1319 @ X1316 )
=> ( in @ ( X1318 @ X1319 ) @ X1317 ) )
=> ( func @ X1316 @ X1317 @ ( lam @ X1316 @ X1317 @ X1318 ) ) )
=> ( ! [X1320: $i,X1321: $i,X1322: $i > $i] :
( ! [X1323: $i] :
( ( in @ X1323 @ X1320 )
=> ( in @ ( X1322 @ X1323 ) @ X1321 ) )
=> ( in @ ( lam @ X1320 @ X1321 @ X1322 ) @ ( funcSet @ X1320 @ X1321 ) ) )
=> ( ! [X1324: $i,X1325: $i,X1326: $i] :
( ( breln @ X1324 @ X1325 @ X1326 )
=> ! [X1327: $i > $o] :
( ! [X1328: $i] :
( ( in @ X1328 @ X1324 )
=> ! [X1329: $i] :
( ( in @ X1329 @ X1325 )
=> ( ( in @ ( kpair @ X1328 @ X1329 ) @ X1326 )
=> ( X1327 @ ( kpair @ X1328 @ X1329 ) ) ) ) )
=> ! [X1330: $i] :
( ( in @ X1330 @ X1326 )
=> ( X1327 @ X1330 ) ) ) )
=> ( ! [X1331: $i,X1332: $i,X1333: $i] :
( ( breln @ X1331 @ X1332 @ X1333 )
=> ! [X1334: $i > $o] :
( ! [X1335: $i] :
( ( in @ X1335 @ X1331 )
=> ! [X1336: $i] :
( ( in @ X1336 @ X1332 )
=> ( ( in @ ( kpair @ X1335 @ X1336 ) @ X1333 )
=> ( X1334 @ ( kpair @ X1335 @ X1336 ) ) ) ) )
=> ! [X1337: $i] :
( ( in @ X1337 @ X1333 )
=> ( X1334 @ X1337 ) ) ) )
=> ( ! [X1338: $i,X1339: $i > $o] :
( ( ex1 @ X1338 @ X1339 )
=> ! [X1340: $i] :
( ( in @ X1340 @ X1338 )
=> ! [X1341: $i] :
( ( in @ X1341 @ X1338 )
=> ( ( X1339 @ X1340 )
=> ( ( X1339 @ X1341 )
=> ( X1340 = X1341 ) ) ) ) ) )
=> ( ! [X1342: $i,X1343: $i,X1344: $i] :
( ( func @ X1342 @ X1343 @ X1344 )
=> ! [X1345: $i] :
( ( in @ X1345 @ X1342 )
=> ( in @ ( kpair @ X1345 @ ( ap @ X1342 @ X1343 @ X1344 @ X1345 ) ) @ X1344 ) ) )
=> ( ! [X1346: $i,X1347: $i,X1348: $i] :
( ( in @ X1348 @ ( funcSet @ X1346 @ X1347 ) )
=> ! [X1349: $i] :
( ( in @ X1349 @ X1346 )
=> ( in @ ( kpair @ X1349 @ ( ap @ X1346 @ X1347 @ X1348 @ X1349 ) ) @ X1348 ) ) )
=> ( ! [X1350: $i,X1351: $i,X1352: $i] :
( ( func @ X1350 @ X1351 @ X1352 )
=> ! [X1353: $i] :
( ( in @ X1353 @ X1350 )
=> ! [X1354: $i] :
( ( in @ X1354 @ X1351 )
=> ( ( in @ ( kpair @ X1353 @ X1354 ) @ X1352 )
=> ( ( ap @ X1350 @ X1351 @ X1352 @ X1353 )
= X1354 ) ) ) ) )
=> ( ! [X1355: $i,X1356: $i,X1357: $i] :
( ( func @ X1355 @ X1356 @ X1357 )
=> ! [X1358: $i] :
( ( func @ X1355 @ X1356 @ X1358 )
=> ( ! [X1359: $i] :
( ( in @ X1359 @ X1355 )
=> ( ( ap @ X1355 @ X1356 @ X1357 @ X1359 )
= ( ap @ X1355 @ X1356 @ X1358 @ X1359 ) ) )
=> ! [X1360: $i] :
( ( in @ X1360 @ X1355 )
=> ! [X1361: $i] :
( ( in @ X1361 @ X1356 )
=> ( ( in @ ( kpair @ X1360 @ X1361 ) @ X1358 )
=> ( in @ ( kpair @ X1360 @ X1361 ) @ X1357 ) ) ) ) ) ) )
=> ( ! [X1362: $i,X1363: $i,X1364: $i] :
( ( in @ X1364 @ ( funcSet @ X1362 @ X1363 ) )
=> ! [X1365: $i] :
( ( in @ X1365 @ X1362 )
=> ! [X1366: $i] :
( ( in @ X1366 @ X1363 )
=> ( ( in @ ( kpair @ X1365 @ X1366 ) @ X1364 )
=> ( ( ap @ X1362 @ X1363 @ X1364 @ X1365 )
= X1366 ) ) ) ) )
=> ( ! [X1367: $i,X1368: $i,X1369: $i] :
( ( breln @ X1367 @ X1368 @ X1369 )
=> ! [X1370: $i] :
( ( breln @ X1367 @ X1368 @ X1370 )
=> ( ! [X1371: $i] :
( ( in @ X1371 @ X1367 )
=> ! [X1372: $i] :
( ( in @ X1372 @ X1368 )
=> ( ( in @ ( kpair @ X1371 @ X1372 ) @ X1369 )
=> ( in @ ( kpair @ X1371 @ X1372 ) @ X1370 ) ) ) )
=> ( subset @ X1369 @ X1370 ) ) ) )
=> ( ! [X1373: $i,X1374: $i,X1375: $i] :
( ( breln @ X1373 @ X1374 @ X1375 )
=> ! [X1376: $i] :
( ( breln @ X1373 @ X1374 @ X1376 )
=> ( ! [X1377: $i] :
( ( in @ X1377 @ X1373 )
=> ! [X1378: $i] :
( ( in @ X1378 @ X1374 )
=> ( ( in @ ( kpair @ X1377 @ X1378 ) @ X1375 )
=> ( in @ ( kpair @ X1377 @ X1378 ) @ X1376 ) ) ) )
=> ( ! [X1379: $i] :
( ( in @ X1379 @ X1373 )
=> ! [X1380: $i] :
( ( in @ X1380 @ X1374 )
=> ( ( in @ ( kpair @ X1379 @ X1380 ) @ X1376 )
=> ( in @ ( kpair @ X1379 @ X1380 ) @ X1375 ) ) ) )
=> ( X1375 = X1376 ) ) ) ) )
=> ( ! [X1381: $i,X1382: $i,X1383: $i] :
( ( func @ X1381 @ X1382 @ X1383 )
=> ! [X1384: $i] :
( ( func @ X1381 @ X1382 @ X1384 )
=> ( ! [X1385: $i] :
( ( in @ X1385 @ X1381 )
=> ( ( ap @ X1381 @ X1382 @ X1383 @ X1385 )
= ( ap @ X1381 @ X1382 @ X1384 @ X1385 ) ) )
=> ( X1383 = X1384 ) ) ) )
=> ( ! [X1386: $i,X1387: $i,X1388: $i] :
( ( in @ X1388 @ ( funcSet @ X1386 @ X1387 ) )
=> ! [X1389: $i] :
( ( in @ X1389 @ ( funcSet @ X1386 @ X1387 ) )
=> ( ! [X1390: $i] :
( ( in @ X1390 @ X1386 )
=> ( ( ap @ X1386 @ X1387 @ X1388 @ X1390 )
= ( ap @ X1386 @ X1387 @ X1389 @ X1390 ) ) )
=> ( X1388 = X1389 ) ) ) )
=> ( ! [X1391: $i,X1392: $i,X1393: $i] :
( ( in @ X1393 @ ( funcSet @ X1391 @ X1392 ) )
=> ! [X1394: $i] :
( ( in @ X1394 @ X1391 )
=> ( ( ap @ X1391 @ X1392 @ X1393 @ X1394 )
= ( ap @ X1391 @ X1392 @ X1393 @ X1394 ) ) ) )
=> ( ! [X1395: $i,X1396: $i,X1397: $i] :
( ( func @ X1395 @ X1396 @ X1397 )
=> ! [X1398: $i] :
( ( in @ X1398 @ X1395 )
=> ( ( ap @ X1395 @ X1396 @ X1397 @ X1398 )
= ( ap @ X1395 @ X1396 @ X1397 @ X1398 ) ) ) )
=> ( ! [X1399: $i,X1400: $i,X1401: $i > $i] :
( ! [X1402: $i] :
( ( in @ X1402 @ X1399 )
=> ( in @ ( X1401 @ X1402 ) @ X1400 ) )
=> ! [X1403: $i] :
( ( in @ X1403 @ X1399 )
=> ( ( ap @ X1399 @ X1400 @ ( lam @ X1399 @ X1400 @ X1401 ) @ X1403 )
= ( X1401 @ X1403 ) ) ) )
=> ( ! [X1404: $i,X1405: $i,X1406: $i] :
( ( func @ X1404 @ X1405 @ X1406 )
=> ( ( lam @ X1404 @ X1405 @ ( ap @ X1404 @ X1405 @ X1406 ) )
= X1406 ) )
=> ( ! [X1407: $i,X1408: $i,X1409: $i > $i] :
( ! [X1410: $i] :
( ( in @ X1410 @ X1407 )
=> ( in @ ( X1409 @ X1410 ) @ X1408 ) )
=> ( ( lam @ X1407 @ X1408 @ X1409 )
= ( lam @ X1407 @ X1408 @ X1409 ) ) )
=> ( ! [X1411: $i,X1412: $i,X1413: $i > $i] :
( ! [X1414: $i] :
( ( in @ X1414 @ X1411 )
=> ( in @ ( X1413 @ X1414 ) @ X1412 ) )
=> ! [X1415: $i] :
( ( in @ X1415 @ X1411 )
=> ( ( ap @ X1411 @ X1412 @ ( lam @ X1411 @ X1412 @ X1413 ) @ X1415 )
= ( X1413 @ X1415 ) ) ) )
=> ( ! [X1416: $i,X1417: $i,X1418: $i] :
( ( in @ X1418 @ ( funcSet @ X1416 @ X1417 ) )
=> ( ( lam @ X1416 @ X1417 @ ( ap @ X1416 @ X1417 @ X1418 ) )
= X1418 ) )
=> ( ! [X1419: $i,X1420: $o,X1421: $i] :
( ( in @ X1421 @ X1419 )
=> ! [X1422: $i] :
( ( in @ X1422 @ X1419 )
=> ( ~ X1420
=> ( in @ X1422
@ ( dsetconstr @ X1419
@ ^ [Z0: $i] :
( ( X1420
& ( Z0 = X1421 ) )
| ( ~ X1420
& ( Z0 = X1422 ) ) ) ) ) ) ) )
=> ( ! [X1423: $i,X1424: $o,X1425: $i] :
( ( in @ X1425 @ X1423 )
=> ! [X1426: $i] :
( ( in @ X1426 @ X1423 )
=> ( ~ X1424
=> ( ( dsetconstr @ X1423
@ ^ [Z0: $i] :
( ( X1424
& ( Z0 = X1425 ) )
| ( ~ X1424
& ( Z0 = X1426 ) ) ) )
= ( setadjoin @ X1426 @ emptyset ) ) ) ) )
=> ( ! [X1427: $i,X1428: $o,X1429: $i] :
( ( in @ X1429 @ X1427 )
=> ! [X1430: $i] :
( ( in @ X1430 @ X1427 )
=> ( X1428
=> ( in @ X1429
@ ( dsetconstr @ X1427
@ ^ [Z0: $i] :
( ( X1428
& ( Z0 = X1429 ) )
| ( ~ X1428
& ( Z0 = X1430 ) ) ) ) ) ) ) )
=> ( ! [X1431: $i,X1432: $o,X1433: $i] :
( ( in @ X1433 @ X1431 )
=> ! [X1434: $i] :
( ( in @ X1434 @ X1431 )
=> ( X1432
=> ( ( dsetconstr @ X1431
@ ^ [Z0: $i] :
( ( X1432
& ( Z0 = X1433 ) )
| ( ~ X1432
& ( Z0 = X1434 ) ) ) )
= ( setadjoin @ X1433 @ emptyset ) ) ) ) )
=> ( ! [X1435: $i,X1436: $o,X1437: $i] :
( ( in @ X1437 @ X1435 )
=> ! [X1438: $i] :
( ( in @ X1438 @ X1435 )
=> ( singleton
@ ( dsetconstr @ X1435
@ ^ [Z0: $i] :
( ( X1436
& ( Z0 = X1437 ) )
| ( ~ X1436
& ( Z0 = X1438 ) ) ) ) ) ) )
=> ( ! [X1439: $i,X1440: $o,X1441: $i] :
( ( in @ X1441 @ X1439 )
=> ! [X1442: $i] :
( ( in @ X1442 @ X1439 )
=> ( in @ ( if @ X1439 @ X1440 @ X1441 @ X1442 ) @ X1439 ) ) )
=> ( ! [X1443: $i] :
( ( singleton @ X1443 )
=> ! [X1444: $i] :
( ( in @ X1444 @ X1443 )
=> ( ( setunion @ X1443 )
= X1444 ) ) )
=> ( ! [X1445: $i,X1446: $o,X1447: $i] :
( ( in @ X1447 @ X1445 )
=> ! [X1448: $i] :
( ( in @ X1448 @ X1445 )
=> ( X1446
=> ( ( if @ X1445 @ X1446 @ X1447 @ X1448 )
= X1447 ) ) ) )
=> ( ! [X1449: $i,X1450: $o,X1451: $i] :
( ( in @ X1451 @ X1449 )
=> ! [X1452: $i] :
( ( in @ X1452 @ X1449 )
=> ( ~ X1450
=> ( ( if @ X1449 @ X1450 @ X1451 @ X1452 )
= X1452 ) ) ) )
=> ( ! [X1453: $i,X1454: $o,X1455: $i] :
( ( in @ X1455 @ X1453 )
=> ! [X1456: $i] :
( ( in @ X1456 @ X1453 )
=> ( in @ ( if @ X1453 @ X1454 @ X1455 @ X1456 ) @ ( setadjoin @ X1455 @ ( setadjoin @ X1456 @ emptyset ) ) ) ) )
=> ( ! [X1457: $i,X1458: $i] :
( ( in @ X1458 @ ( powerset @ X1457 ) )
=> ! [X1459: $i] :
( ( in @ X1459 @ ( powerset @ X1457 ) )
=> ( in @ ( binintersect @ X1458 @ X1459 ) @ ( powerset @ X1457 ) ) ) )
=> ( ! [X1460: $i,X1461: $i] :
( ( in @ X1461 @ ( powerset @ X1460 ) )
=> ! [X1462: $i] :
( ( in @ X1462 @ ( powerset @ X1460 ) )
=> ( in @ ( binunion @ X1461 @ X1462 ) @ ( powerset @ X1460 ) ) ) )
=> ( ! [X1463: $i,X1464: $i] :
( ( in @ X1464 @ ( powerset @ X1463 ) )
=> ( in @ ( powerset @ X1464 ) @ ( powerset @ ( powerset @ X1463 ) ) ) )
=> ( ! [X1465: $i,X1466: $i] :
( ( in @ X1466 @ ( powerset @ X1465 ) )
=> ! [X1467: $i] :
( ( in @ X1467 @ ( powerset @ X1465 ) )
=> ( in @ ( setminus @ X1466 @ X1467 ) @ ( powerset @ X1465 ) ) ) )
=> ( ! [X1468: $i,X1469: $i] :
( ( in @ X1469 @ ( powerset @ X1468 ) )
=> ( in @ ( setminus @ X1468 @ X1469 ) @ ( powerset @ X1468 ) ) )
=> ! [X4: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X4 ) )
=> ! [X48: $i] :
( ( in @ X48 @ ( powerset @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X21 )
=> ( in @ X2 @ X48 ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2 @ X48 )
=> ( in @ X2 @ X21 ) ) )
=> ( X21 = X48 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setextT]),notequalI1]),funcext]),complementT_lem]),c_0_231]),c_0_232]),c_0_233]),c_0_234]),c_0_235]),app]),subsetI1]),infuncsetfunc]),ap2p]),eqimpsubset2]),funcinfuncset]),c_0_236]),eqimpsubset1]),c_0_237]),c_0_238]),subsetI2]),brelnall1]),brelnall2]),emptysetsubset]),c_0_239]),funcGraphProp1]),subsetE]),funcGraphProp3]),funcGraphProp2]),subsetE2]),funcextLem]),funcGraphProp4]),subbreln]),notsubsetI]),eqbreln]),binunionEcases]),funcext2]),ap2apEq1]),ap2apEq2]),notequalI2]),c_0_240]),c_0_241]),subsetRefl]),c_0_242]),c_0_243]),subsetTrans]),c_0_244]),c_0_245]),c_0_246]),c_0_247]),setadjoinSub]),c_0_248]),c_0_249]),setadjoinSub2]),ifp]),theeq]),subset2powerset]),iftrue]),iffalse]),setextsub]),iftrueorfalse]),binintersectT_lem]),subsetemptysetimpeq]),binunionT_lem]),powersetT_lem]),powersetI1]),setminusT_lem]),powersetE1]),inPowerset]),powersetsubset]),c_0_250]),c_0_251]),binunionIL]),upairset2IR]),binunionIR]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setunion__Cong]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),omega__Cong]),secondinupair]),c_0_252]),setukpairIL]),c_0_253]),setukpairIR]),kpairiskpair]),kpairp]),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]),c_0_262]),c_0_263]),c_0_264]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_265]),c_0_266]),in__Cong]),inCongP]),c_0_267]),c_0_268]),c_0_269]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_270]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_271]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_272]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_273]),nonemptyE1]),c_0_274]),noeltsimpempty]),emptyI]),setext]),c_0_275]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_276]),c_0_277]),c_0_278]),c_0_279]),c_0_280]),wellorderingAx]),foundationAx]),c_0_281]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_282]) ).
thf(c_0_284,negated_conjecture,
! 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$i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i > $i,X2014: $i,X2015: $i,X2016: $i > $i,X2018: $i,X2019: $i,X2020: $i > $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i > $o,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i > $o,X2035: $i,X2036: $i,X2037: $i > $o,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $i,X2054: $i,X2055: $i,X2056: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i,X2095: $i,X2096: $i,X2097: $i,X2098: $i,X2099: $i > $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i > $i,X2109: $i,X2110: $i,X2111: $i > $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $o,X2119: $i,X2120: $i,X2121: $i,X2122: $o,X2123: $i,X2124: $i,X2125: $i,X2126: $o,X2127: $i,X2128: $i,X2129: $i,X2130: $o,X2131: $i,X2132: $i,X2133: $i,X2134: $o,X2135: $i,X2136: $i,X2137: $i,X2138: $o,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $o,X2145: $i,X2146: $i,X2147: $i,X2148: $o,X2149: $i,X2150: $i,X2151: $i,X2152: $o,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2171: $i,X2172: $i] :
( ( ~ ( in @ ( esk1_2 @ X1470 @ X1471 ) @ X1470 )
| ~ ( in @ ( esk1_2 @ X1470 @ X1471 ) @ X1471 )
| ( X1470 = X1471 ) )
& ( ( in @ ( esk1_2 @ X1470 @ X1471 ) @ X1470 )
| ( in @ ( esk1_2 @ X1470 @ X1471 ) @ X1471 )
| ( X1470 = X1471 ) )
& ~ ( in @ X1473 @ emptyset )
& ( ~ ( in @ X1476 @ ( setadjoin @ X1474 @ X1475 ) )
| ( X1476 = X1474 )
| ( in @ X1476 @ X1475 ) )
& ( ( X1476 != X1474 )
| ( in @ X1476 @ ( setadjoin @ X1474 @ X1475 ) ) )
& ( ~ ( in @ X1476 @ X1475 )
| ( in @ X1476 @ ( setadjoin @ X1474 @ X1475 ) ) )
& ( ~ ( in @ X1478 @ ( powerset @ X1477 ) )
| ~ ( in @ X1479 @ X1478 )
| ( in @ X1479 @ X1477 ) )
& ( ( in @ ( esk2_2 @ X1480 @ X1481 ) @ X1481 )
| ( in @ X1481 @ ( powerset @ X1480 ) ) )
& ( ~ ( in @ ( esk2_2 @ X1480 @ X1481 ) @ X1480 )
| ( in @ X1481 @ ( powerset @ X1480 ) ) )
& ( ( in @ X1484 @ ( esk3_2 @ X1483 @ X1484 ) )
| ~ ( in @ X1484 @ ( setunion @ X1483 ) ) )
& ( ( in @ ( esk3_2 @ X1483 @ X1484 ) @ X1483 )
| ~ ( in @ X1484 @ ( setunion @ X1483 ) ) )
& ( ~ ( in @ X1487 @ X1488 )
| ~ ( in @ X1488 @ X1486 )
| ( in @ X1487 @ ( setunion @ X1486 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X1489 @ omega )
| ( in @ ( setadjoin @ X1489 @ X1489 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X1490 ) @ omega )
| ~ ( in @ emptyset @ X1490 )
| ~ ( in @ X1492 @ omega )
| ( in @ X1492 @ X1490 ) )
& ( ( in @ ( esk4_1 @ X1490 ) @ X1490 )
| ~ ( in @ emptyset @ X1490 )
| ~ ( in @ X1492 @ omega )
| ( in @ X1492 @ X1490 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1490 ) @ ( esk4_1 @ X1490 ) ) @ X1490 )
| ~ ( in @ emptyset @ X1490 )
| ~ ( in @ X1492 @ omega )
| ( in @ X1492 @ X1490 ) )
& ( ( in @ ( esk7_3 @ X1493 @ X1494 @ X1497 ) @ X1494 )
| ~ ( in @ X1497 @ ( esk6_2 @ X1493 @ X1494 ) )
| ( in @ ( esk5_2 @ X1493 @ X1494 ) @ X1494 ) )
& ( ( X1493 @ ( esk7_3 @ X1493 @ X1494 @ X1497 ) @ X1497 )
| ~ ( in @ X1497 @ ( esk6_2 @ X1493 @ X1494 ) )
| ( in @ ( esk5_2 @ X1493 @ X1494 ) @ X1494 ) )
& ( ~ ( in @ X1500 @ X1494 )
| ~ ( X1493 @ X1500 @ X1499 )
| ( in @ X1499 @ ( esk6_2 @ X1493 @ X1494 ) )
| ( in @ ( esk5_2 @ X1493 @ X1494 ) @ X1494 ) )
& ( ( in @ ( esk7_3 @ X1493 @ X1494 @ X1497 ) @ X1494 )
| ~ ( in @ X1497 @ ( esk6_2 @ X1493 @ X1494 ) )
| ~ ( exu @ ( X1493 @ ( esk5_2 @ X1493 @ X1494 ) ) ) )
& ( ( X1493 @ ( esk7_3 @ X1493 @ X1494 @ X1497 ) @ X1497 )
| ~ ( in @ X1497 @ ( esk6_2 @ X1493 @ X1494 ) )
| ~ ( exu @ ( X1493 @ ( esk5_2 @ X1493 @ X1494 ) ) ) )
& ( ~ ( in @ X1500 @ X1494 )
| ~ ( X1493 @ X1500 @ X1499 )
| ( in @ X1499 @ ( esk6_2 @ X1493 @ X1494 ) )
| ~ ( exu @ ( X1493 @ ( esk5_2 @ X1493 @ X1494 ) ) ) )
& ( ( in @ ( esk8_1 @ X1501 ) @ X1501 )
| ~ ( in @ X1502 @ X1501 ) )
& ( ~ ( in @ X1504 @ ( esk8_1 @ X1501 ) )
| ~ ( in @ X1504 @ X1501 )
| ~ ( in @ X1502 @ X1501 ) )
& epred1_0
& ( ~ ( exu @ X1505 )
| ( X1505 @ ( descr @ X1505 ) ) )
& ( ~ ( in @ X1508 @ X1506 )
| ~ ( X1507 @ X1508 )
| ( in @ X1508 @ ( dsetconstr @ X1506 @ X1507 ) ) )
& ( ~ ( in @ X1511 @ ( dsetconstr @ X1509 @ X1510 ) )
| ( in @ X1511 @ X1509 ) )
& ( ~ ( in @ X1514 @ ( dsetconstr @ X1512 @ X1513 ) )
| ( X1513 @ X1514 ) )
& ( ( X1515 @ ( esk9_1 @ X1515 ) )
| ~ ( exu @ X1515 ) )
& ( ~ ( X1515 @ X1517 )
| ( ( esk9_1 @ X1515 )
= X1517 )
| ~ ( exu @ X1515 ) )
& ( ~ ( in @ X1519 @ ( prop2set @ X1518 ) )
| X1518 )
& ( ~ ( in @ X1520 @ emptyset )
| X1521 )
& ( ~ ( in @ X1522 @ emptyset )
| ~ $true )
& ~ ( in @ X1523 @ emptyset )
& ( ~ ( exu @ X1524 )
| ( X1524 @ ( esk10_1 @ X1524 ) ) )
& ( ( in @ ( esk12_2 @ X1526 @ X1527 ) @ X1527 )
| ( X1526 = X1527 )
| ( in @ ( esk11_2 @ X1526 @ X1527 ) @ X1526 ) )
& ( ~ ( in @ ( esk12_2 @ X1526 @ X1527 ) @ X1526 )
| ( X1526 = X1527 )
| ( in @ ( esk11_2 @ X1526 @ X1527 ) @ X1526 ) )
& ( ( in @ ( esk12_2 @ X1526 @ X1527 ) @ X1527 )
| ( X1526 = X1527 )
| ~ ( in @ ( esk11_2 @ X1526 @ X1527 ) @ X1527 ) )
& ( ~ ( in @ ( esk12_2 @ X1526 @ X1527 ) @ X1526 )
| ( X1526 = X1527 )
| ~ ( in @ ( esk11_2 @ X1526 @ X1527 ) @ X1527 ) )
& ( ( in @ ( esk13_1 @ X1530 ) @ X1530 )
| ( X1530 = emptyset ) )
& ( ( in @ ( esk14_1 @ X1532 ) @ X1532 )
| ( X1532 = emptyset ) )
& ( ~ ( in @ X1536 @ ( dsetconstr @ X1534 @ X1535 ) )
| ( X1535 @ X1536 )
| ~ ( in @ X1536 @ X1534 ) )
& ( ~ ( X1535 @ X1536 )
| ( in @ X1536 @ ( dsetconstr @ X1534 @ X1535 ) )
| ~ ( in @ X1536 @ X1534 ) )
& ( ~ ( nonempty @ X1537 )
| ( in @ ( esk15_1 @ X1537 ) @ X1537 ) )
& ( ~ ( in @ X1541 @ X1539 )
| ~ ( X1540 @ X1541 )
| ( nonempty @ ( dsetconstr @ X1539 @ X1540 ) ) )
& ( ~ ( in @ X1543 @ X1542 )
| ( nonempty @ X1542 ) )
& ( in @ X1544 @ ( setadjoin @ X1544 @ X1545 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X1548 @ X1547 )
| ( in @ X1548 @ ( setadjoin @ X1546 @ X1547 ) ) )
& ( ( in @ X1551 @ X1550 )
| X1552
| ( X1551 = X1549 )
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ X1552
| X1552
| ( X1551 = X1549 )
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ( in @ X1551 @ X1550 )
| X1552
| ~ X1552
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ X1552
| X1552
| ~ X1552
| ~ ( in @ X1551 @ ( setadjoin @ X1549 @ X1550 ) ) )
& ( ~ ( in @ X1555 @ ( setadjoin @ X1553 @ X1554 ) )
| ( X1555 = X1553 )
| ( in @ X1555 @ X1554 ) )
& ( ( dsetconstr @ X1556
@ ^ [Z0: $i] : $true )
= X1556 )
& ( ( in @ ( esk16_2 @ X1557 @ X1558 ) @ X1558 )
| ( in @ X1558 @ ( powerset @ X1557 ) ) )
& ( ~ ( in @ ( esk16_2 @ X1557 @ X1558 ) @ X1557 )
| ( in @ X1558 @ ( powerset @ X1557 ) ) )
& ( in @ emptyset @ ( powerset @ X1560 ) )
& ( in @ emptyset @ ( powerset @ X1561 ) )
& ( ~ ( in @ X1563 @ ( powerset @ X1562 ) )
| ~ ( in @ X1564 @ X1563 )
| ( in @ X1564 @ X1562 ) )
& ( ~ ( in @ X1566 @ X1567 )
| ~ ( in @ X1567 @ X1565 )
| ( in @ X1566 @ ( setunion @ X1565 ) ) )
& ( ( in @ X1569 @ ( esk17_3 @ X1568 @ X1569 @ X1570 ) )
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ( in @ ( esk17_3 @ X1568 @ X1569 @ X1570 ) @ X1568 )
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ~ X1570
| X1570
| ~ ( in @ X1569 @ ( setunion @ X1568 ) ) )
& ( ~ ( in @ X1573 @ X1572 )
| ( in @ X1573 @ ( powerset @ ( setunion @ X1572 ) ) ) )
& ( ~ ( X1574 @ X1576 )
| ( X1576
= ( esk18_1 @ X1574 ) )
| ~ ( exu @ X1574 ) )
& ( ( X1577
!= ( esk18_1 @ X1574 ) )
| ( X1574 @ X1577 )
| ~ ( exu @ X1574 ) )
& ( ( in @ ( esk19_1 @ X1578 ) @ X1578 )
| ~ ( nonempty @ X1578 ) )
& ( $true
| ~ ( nonempty @ X1578 ) )
& ( ~ ( in @ X1580 @ ( setadjoin @ X1581 @ emptyset ) )
| ( X1580 = X1581 ) )
& ( ( X1582 = X1583 )
| ~ ( in @ X1583 @ ( setadjoin @ X1582 @ emptyset ) ) )
& ( ( X1584 != X1585 )
| ( in @ X1584 @ ( setadjoin @ X1585 @ emptyset ) ) )
& ( ~ ( in @ X1586 @ ( setadjoin @ X1587 @ emptyset ) )
| ( in @ X1587 @ ( setadjoin @ X1586 @ emptyset ) ) )
& ( ~ ( in @ X1590 @ ( setadjoin @ X1588 @ ( setadjoin @ X1589 @ emptyset ) ) )
| ( X1590 = X1588 )
| ( X1590 = X1589 ) )
& ( in @ X1591 @ ( setadjoin @ X1591 @ ( setadjoin @ X1592 @ emptyset ) ) )
& ( in @ X1594 @ ( setadjoin @ X1593 @ ( setadjoin @ X1594 @ emptyset ) ) )
& ( ~ ( in @ X1597 @ X1595 )
| ~ ( X1596 @ X1597 )
| ( ( dsetconstr @ X1595 @ X1596 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X1599 @ emptyset )
| ( X1598 @ X1599 ) )
& ( ( in @ ( esk20_2 @ X1600 @ X1601 ) @ X1600 )
| ~ ( in @ X1602 @ X1600 )
| ( X1601 @ X1602 ) )
& ( ~ ( X1601 @ ( esk20_2 @ X1600 @ X1601 ) )
| ~ ( in @ X1602 @ X1600 )
| ( X1601 @ X1602 ) )
& ( ( in @ ( esk21_2 @ X1604 @ X1605 ) @ X1604 )
| ~ ( in @ X1607 @ X1604 )
| ~ ( X1605 @ X1607 ) )
& ( ( X1605 @ ( esk21_2 @ X1604 @ X1605 ) )
| ~ ( in @ X1607 @ X1604 )
| ~ ( X1605 @ X1607 ) )
& ( ( in @ ( esk22_2 @ X1608 @ X1609 ) @ X1608 )
| ~ ( in @ X1611 @ X1608 )
| ~ ( X1609 @ X1611 ) )
& ( ( X1609 @ ( esk22_2 @ X1608 @ X1609 ) )
| ~ ( in @ X1611 @ X1608 )
| ~ ( X1609 @ X1611 ) )
& ( ( in @ ( esk23_2 @ X1612 @ X1613 ) @ X1612 )
| ~ ( in @ X1614 @ X1612 )
| ( X1613 @ X1614 ) )
& ( ~ ( X1613 @ ( esk23_2 @ X1612 @ X1613 ) )
| ~ ( in @ X1614 @ X1612 )
| ( X1613 @ X1614 ) )
& ( ~ X1616
| ( in @ emptyset @ ( prop2set @ X1616 ) ) )
& prop2set2propI
& ( ( in @ ( esk24_2 @ X1617 @ X1618 ) @ X1617 )
| ~ ( in @ X1620 @ X1617 )
| ~ ( X1618 @ X1620 ) )
& ( ( X1618 @ ( esk24_2 @ X1617 @ X1618 ) )
| ~ ( in @ X1620 @ X1617 )
| ~ ( X1618 @ X1620 ) )
& ( ( in @ ( esk25_2 @ X1621 @ X1622 ) @ X1621 )
| ~ ( in @ X1623 @ X1621 )
| ( X1622 @ X1623 ) )
& ( ~ ( X1622 @ ( esk25_2 @ X1621 @ X1622 ) )
| ~ ( in @ X1623 @ X1621 )
| ( X1622 @ X1623 ) )
& ( ( X1625 @ ( esk26_2 @ X1625 @ X1626 ) )
| ~ ( X1625 @ X1626 )
| ( exu @ X1625 ) )
& ( ( X1626
!= ( esk26_2 @ X1625 @ X1626 ) )
| ~ ( X1625 @ X1626 )
| ( exu @ X1625 ) )
& ( ( X1628 @ ( esk27_1 @ X1628 ) )
| ( exu @ X1628 )
| ~ ( X1628 @ X1629 ) )
& ( ( X1628 @ ( esk28_1 @ X1628 ) )
| ( exu @ X1628 )
| ~ ( X1628 @ X1629 ) )
& ( ( ( esk27_1 @ X1628 )
!= ( esk28_1 @ X1628 ) )
| ( exu @ X1628 )
| ~ ( X1628 @ X1629 ) )
& ( ~ ( X1632 @ ( esk29_2 @ X1632 @ X1633 ) )
| ( ( esk29_2 @ X1632 @ X1633 )
!= X1633 )
| ( exu @ X1632 ) )
& ( ( X1632 @ ( esk29_2 @ X1632 @ X1633 ) )
| ( ( esk29_2 @ X1632 @ X1633 )
= X1633 )
| ( exu @ X1632 ) )
& ( ( X1635 != X1636 )
| ( X1637 != X1638 )
| ~ ( in @ X1637 @ X1635 )
| ( in @ X1638 @ X1636 ) )
& ( ~ ( in @ X1641 @ X1639 )
| ( in @ X1642 @ X1640 )
| ( X1641 != X1642 )
| ( X1639 != X1640 ) )
& ( ~ ( in @ X1642 @ X1640 )
| ( in @ X1641 @ X1639 )
| ( X1641 != X1642 )
| ( X1639 != X1640 ) )
& ( ~ ( exu @ X1643 )
| ~ ( X1643 @ X1644 )
| ~ ( X1643 @ X1645 )
| ( X1644 = X1645 ) )
& ( ~ ( exu @ X1646 )
| ( exu @ X1647 )
| ( ( esk30_2 @ X1646 @ X1647 )
= ( esk31_2 @ X1646 @ X1647 ) ) )
& ( ~ ( exu @ X1647 )
| ( exu @ X1646 )
| ( ( esk30_2 @ X1646 @ X1647 )
= ( esk31_2 @ X1646 @ X1647 ) ) )
& ( ~ ( exu @ X1646 )
| ( exu @ X1647 )
| ~ ( X1646 @ ( esk30_2 @ X1646 @ X1647 ) )
| ~ ( X1647 @ ( esk31_2 @ X1646 @ X1647 ) ) )
& ( ~ ( exu @ X1647 )
| ( exu @ X1646 )
| ~ ( X1646 @ ( esk30_2 @ X1646 @ X1647 ) )
| ~ ( X1647 @ ( esk31_2 @ X1646 @ X1647 ) ) )
& ( ~ ( exu @ X1646 )
| ( exu @ X1647 )
| ( X1646 @ ( esk30_2 @ X1646 @ X1647 ) )
| ( X1647 @ ( esk31_2 @ X1646 @ X1647 ) ) )
& ( ~ ( exu @ X1647 )
| ( exu @ X1646 )
| ( X1646 @ ( esk30_2 @ X1646 @ X1647 ) )
| ( X1647 @ ( esk31_2 @ X1646 @ X1647 ) ) )
& ( emptyset = emptyset )
& ( ( X1650 != X1651 )
| ( X1652 != X1653 )
| ( ( setadjoin @ X1650 @ X1652 )
= ( setadjoin @ X1651 @ X1653 ) ) )
& ( ( X1654 != X1655 )
| ( ( powerset @ X1654 )
= ( powerset @ X1655 ) ) )
& ( ( X1656 != X1657 )
| ( ( setunion @ X1656 )
= ( setunion @ X1657 ) ) )
& ( omega = omega )
& ( ~ ( exu @ X1658 )
| ~ ( X1658 @ X1659 )
| ~ ( X1658 @ X1660 )
| ( X1659 = X1660 ) )
& ( ( ( esk32_2 @ X1661 @ X1662 )
= ( esk33_2 @ X1661 @ X1662 ) )
| ~ ( exu @ X1661 )
| ~ ( exu @ X1662 )
| ( ( descr @ X1661 )
= ( descr @ X1662 ) ) )
& ( ~ ( X1661 @ ( esk32_2 @ X1661 @ X1662 ) )
| ~ ( X1662 @ ( esk33_2 @ X1661 @ X1662 ) )
| ~ ( exu @ X1661 )
| ~ ( exu @ X1662 )
| ( ( descr @ X1661 )
= ( descr @ X1662 ) ) )
& ( ( X1661 @ ( esk32_2 @ X1661 @ X1662 ) )
| ( X1662 @ ( esk33_2 @ X1661 @ X1662 ) )
| ~ ( exu @ X1661 )
| ~ ( exu @ X1662 )
| ( ( descr @ X1661 )
= ( descr @ X1662 ) ) )
& ( ( in @ ( esk34_4 @ X1665 @ X1666 @ X1667 @ X1668 ) @ X1665 )
| ( ( dsetconstr @ X1665 @ X1667 )
= ( dsetconstr @ X1666 @ X1668 ) )
| ( X1665 != X1666 ) )
& ( ( in @ ( esk35_4 @ X1665 @ X1666 @ X1667 @ X1668 ) @ X1666 )
| ( ( dsetconstr @ X1665 @ X1667 )
= ( dsetconstr @ X1666 @ X1668 ) )
| ( X1665 != X1666 ) )
& ( ( ( esk34_4 @ X1665 @ X1666 @ X1667 @ X1668 )
= ( esk35_4 @ X1665 @ X1666 @ X1667 @ X1668 ) )
| ( ( dsetconstr @ X1665 @ X1667 )
= ( dsetconstr @ X1666 @ X1668 ) )
| ( X1665 != X1666 ) )
& ( ~ ( X1667 @ ( esk34_4 @ X1665 @ X1666 @ X1667 @ X1668 ) )
| ~ ( X1668 @ ( esk35_4 @ X1665 @ X1666 @ X1667 @ X1668 ) )
| ( ( dsetconstr @ X1665 @ X1667 )
= ( dsetconstr @ X1666 @ X1668 ) )
| ( X1665 != X1666 ) )
& ( ( X1667 @ ( esk34_4 @ X1665 @ X1666 @ X1667 @ X1668 ) )
| ( X1668 @ ( esk35_4 @ X1665 @ X1666 @ X1667 @ X1668 ) )
| ( ( dsetconstr @ X1665 @ X1667 )
= ( dsetconstr @ X1666 @ X1668 ) )
| ( X1665 != X1666 ) )
& ( ( in @ ( esk36_2 @ X1671 @ X1672 ) @ X1671 )
| ( subset @ X1671 @ X1672 ) )
& ( ~ ( in @ ( esk36_2 @ X1671 @ X1672 ) @ X1672 )
| ( subset @ X1671 @ X1672 ) )
& ( ( X1674 != X1675 )
| ( subset @ X1675 @ X1674 ) )
& ( ( X1676 != X1677 )
| ( subset @ X1676 @ X1677 ) )
& ( ( in @ ( esk37_2 @ X1678 @ X1679 ) @ X1678 )
| ( subset @ X1678 @ X1679 ) )
& ( ~ ( in @ ( esk37_2 @ X1678 @ X1679 ) @ X1679 )
| ( subset @ X1678 @ X1679 ) )
& ( subset @ emptyset @ X1681 )
& ( ~ ( subset @ X1682 @ X1683 )
| ~ ( in @ X1684 @ X1682 )
| ( in @ X1684 @ X1683 ) )
& ( ~ ( subset @ X1685 @ X1686 )
| ( in @ X1687 @ X1686 )
| ~ ( in @ X1687 @ X1685 ) )
& ( ~ ( in @ X1690 @ X1688 )
| ( in @ X1690 @ X1689 )
| ~ ( subset @ X1688 @ X1689 ) )
& ( ( subset @ X1691 @ X1692 )
| ( X1691 != X1692 ) )
& ( ~ ( in @ X1695 @ X1693 )
| ( in @ X1695 @ X1694 )
| ( X1693 != X1694 ) )
& ( subset @ X1696 @ X1696 )
& ( ~ ( subset @ X1697 @ X1698 )
| ~ ( subset @ X1698 @ X1699 )
| ( subset @ X1697 @ X1699 ) )
& ( subset @ X1701 @ ( setadjoin @ X1700 @ X1701 ) )
& ( ~ ( subset @ X1702 @ X1704 )
| ( subset @ X1702 @ ( setadjoin @ X1703 @ X1704 ) ) )
& ( ~ ( subset @ X1705 @ X1706 )
| ( in @ X1705 @ ( powerset @ X1706 ) ) )
& ( ~ ( subset @ X1707 @ X1708 )
| ~ ( subset @ X1708 @ X1707 )
| ( X1707 = X1708 ) )
& ( ~ ( subset @ X1709 @ emptyset )
| ( X1709 = emptyset ) )
& ( ~ ( subset @ X1711 @ X1710 )
| ( in @ X1711 @ ( powerset @ X1710 ) ) )
& ( ~ ( in @ X1713 @ ( powerset @ X1712 ) )
| ( subset @ X1713 @ X1712 ) )
& ( in @ X1714 @ ( powerset @ X1714 ) )
& ( ~ ( subset @ X1715 @ X1716 )
| ( subset @ ( powerset @ X1715 ) @ ( powerset @ X1716 ) ) )
& ( in @ ( dsetconstr @ X1717 @ X1718 ) @ ( powerset @ X1717 ) )
& ( subset @ ( dsetconstr @ X1719 @ X1720 ) @ X1719 )
& ( ~ ( in @ X1723 @ X1721 )
| ( in @ X1723 @ ( binunion @ X1721 @ X1722 ) ) )
& ( in @ X1725 @ ( setadjoin @ X1724 @ ( setadjoin @ X1725 @ emptyset ) ) )
& ( ~ ( in @ X1728 @ X1727 )
| ( in @ X1728 @ ( binunion @ X1726 @ X1727 ) ) )
& ( ( in @ X1731 @ X1730 )
| X1732
| ( in @ X1731 @ X1729 )
| ~ ( in @ X1731 @ ( binunion @ X1729 @ X1730 ) ) )
& ( ~ X1732
| X1732
| ( in @ X1731 @ X1729 )
| ~ ( in @ X1731 @ ( binunion @ X1729 @ X1730 ) ) )
& ( ( in @ X1731 @ X1730 )
| X1732
| ~ X1732
| ~ ( in @ X1731 @ ( binunion @ X1729 @ X1730 ) ) )
& ( ~ X1732
| X1732
| ~ X1732
| ~ ( in @ X1731 @ ( binunion @ X1729 @ X1730 ) ) )
& ( ~ ( in @ X1735 @ ( binunion @ X1733 @ X1734 ) )
| ( in @ X1735 @ X1733 )
| ( in @ X1735 @ X1734 ) )
& ( subset @ X1736 @ ( binunion @ X1736 @ X1737 ) )
& ( subset @ X1739 @ ( binunion @ X1738 @ X1739 ) )
& ( ~ ( in @ X1742 @ X1740 )
| ~ ( in @ X1742 @ X1741 )
| ( in @ X1742 @ ( binintersect @ X1740 @ X1741 ) ) )
& ( ~ ( subset @ X1745 @ X1743 )
| ~ ( subset @ X1745 @ X1744 )
| ( subset @ X1745 @ ( binintersect @ X1743 @ X1744 ) ) )
& ( ~ ( in @ X1748 @ ( binintersect @ X1746 @ X1747 ) )
| ( in @ X1748 @ X1746 ) )
& ( subset @ ( binintersect @ X1749 @ X1750 ) @ X1749 )
& ( ~ ( subset @ X1751 @ X1752 )
| ( ( binintersect @ X1751 @ X1752 )
= X1751 ) )
& ( ( ( binintersect @ X1753 @ X1754 )
!= X1754 )
| ( subset @ X1754 @ X1753 ) )
& ( ~ ( in @ X1757 @ ( binintersect @ X1755 @ X1756 ) )
| ( in @ X1757 @ X1756 ) )
& ( ( in @ ( esk38_2 @ X1758 @ X1759 ) @ X1758 )
| ( ( binintersect @ X1758 @ X1759 )
= emptyset ) )
& ( ( in @ ( esk38_2 @ X1758 @ X1759 ) @ X1759 )
| ( ( binintersect @ X1758 @ X1759 )
= emptyset ) )
& ( subset @ ( binintersect @ X1761 @ X1762 ) @ X1762 )
& ( ~ ( subset @ X1764 @ X1763 )
| ( ( binintersect @ X1763 @ X1764 )
= X1764 ) )
& ( ( ( binintersect @ X1765 @ X1766 )
!= X1765 )
| ( subset @ X1765 @ X1766 ) )
& ( ( binintersect @ X1767 @ ( binunion @ X1768 @ X1769 ) )
= ( binunion @ ( binintersect @ X1767 @ X1768 ) @ ( binintersect @ X1767 @ X1769 ) ) )
& ( ~ ( in @ X1772 @ X1770 )
| ( in @ X1772 @ X1771 )
| ( in @ X1772 @ ( setminus @ X1770 @ X1771 ) ) )
& ( ~ ( in @ X1775 @ ( setminus @ X1773 @ X1774 ) )
| ( in @ X1775 @ X1773 ) )
& ( ~ ( in @ X1778 @ ( setminus @ X1776 @ X1777 ) )
| ~ ( in @ X1778 @ X1777 ) )
& ( ~ ( subset @ X1779 @ X1780 )
| ( ( setminus @ X1779 @ X1780 )
= emptyset ) )
& ( ( in @ X1783 @ ( setminus @ X1781 @ X1782 ) )
| ~ ( in @ X1783 @ X1781 )
| ( in @ X1783 @ X1782 ) )
& ( ( in @ X1786 @ ( setminus @ X1784 @ X1785 ) )
| ( in @ X1786 @ X1785 )
| ~ ( in @ X1786 @ X1784 ) )
& ( ( in @ X1789 @ X1787 )
| ~ ( in @ X1789 @ ( setminus @ X1787 @ X1788 ) ) )
& ( ~ ( in @ X1792 @ X1791 )
| ~ ( in @ X1792 @ ( setminus @ X1790 @ X1791 ) ) )
& ( subset @ ( setminus @ X1793 @ X1794 ) @ X1793 )
& ( ( ( setminus @ X1795 @ X1796 )
!= emptyset )
| ( subset @ X1795 @ X1796 ) )
& ( ~ ( in @ X1799 @ X1797 )
| X1800
| ( in @ X1799 @ X1797 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ( in @ X1799 @ X1798 )
| X1800
| ( in @ X1799 @ X1797 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ X1800
| X1800
| ( in @ X1799 @ X1797 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ ( in @ X1799 @ X1797 )
| X1800
| ~ ( in @ X1799 @ X1798 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ( in @ X1799 @ X1798 )
| X1800
| ~ ( in @ X1799 @ X1798 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ X1800
| X1800
| ~ ( in @ X1799 @ X1798 )
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ ( in @ X1799 @ X1797 )
| X1800
| ~ X1800
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ( in @ X1799 @ X1798 )
| X1800
| ~ X1800
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ X1800
| X1800
| ~ X1800
| ~ ( in @ X1799 @ ( symdiff @ X1797 @ X1798 ) ) )
& ( ~ ( in @ X1803 @ X1801 )
| ( in @ X1803 @ X1802 )
| ( in @ X1803 @ ( symdiff @ X1801 @ X1802 ) ) )
& ( ( in @ X1806 @ X1804 )
| ~ ( in @ X1806 @ X1805 )
| ( in @ X1806 @ ( symdiff @ X1804 @ X1805 ) ) )
& ( ~ ( in @ X1809 @ X1807 )
| ~ ( in @ X1809 @ X1808 )
| ~ ( in @ X1809 @ ( symdiff @ X1807 @ X1808 ) ) )
& ( ( in @ X1812 @ X1810 )
| ( in @ X1812 @ X1811 )
| ~ ( in @ X1812 @ ( symdiff @ X1810 @ X1811 ) ) )
& ( in @ X1814 @ ( setadjoin @ X1813 @ ( setadjoin @ X1814 @ emptyset ) ) )
& ( in @ X1815 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1815 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1815 @ ( setadjoin @ X1816 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X1818 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1817 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1817 @ ( setadjoin @ X1818 @ emptyset ) ) @ emptyset ) ) ) )
& ( iskpair @ ( setadjoin @ ( setadjoin @ X1819 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1819 @ ( setadjoin @ X1820 @ emptyset ) ) @ emptyset ) ) )
& ( iskpair @ ( kpair @ X1821 @ X1822 ) )
& ( ~ ( in @ X1824 @ X1823 )
| ( subset @ ( setadjoin @ X1824 @ emptyset ) @ X1823 ) )
& ( ~ ( in @ X1826 @ X1825 )
| ( in @ ( setadjoin @ X1826 @ emptyset ) @ ( powerset @ X1825 ) ) )
& ( ~ ( in @ X1829 @ X1827 )
| ( in @ ( setadjoin @ X1829 @ emptyset ) @ ( powerset @ ( binunion @ X1827 @ X1828 ) ) ) )
& ( ~ ( in @ X1832 @ ( setadjoin @ X1830 @ ( setadjoin @ X1831 @ emptyset ) ) )
| ( X1832 = X1830 )
| ( X1832 = X1831 ) )
& ( ~ ( in @ X1835 @ X1833 )
| ~ ( in @ X1836 @ X1834 )
| ( subset @ ( setadjoin @ X1835 @ ( setadjoin @ X1836 @ emptyset ) ) @ ( binunion @ X1833 @ X1834 ) ) )
& ( ~ ( in @ X1839 @ X1837 )
| ~ ( in @ X1840 @ X1838 )
| ( in @ ( setadjoin @ X1839 @ ( setadjoin @ X1840 @ emptyset ) ) @ ( powerset @ ( binunion @ X1837 @ X1838 ) ) ) )
& ( ~ ( in @ X1843 @ X1841 )
| ~ ( in @ X1844 @ X1842 )
| ( subset @ ( setadjoin @ ( setadjoin @ X1843 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1843 @ ( setadjoin @ X1844 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1841 @ X1842 ) ) ) )
& ( ~ ( in @ X1847 @ X1845 )
| ~ ( in @ X1848 @ X1846 )
| ( in @ ( setadjoin @ ( setadjoin @ X1847 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1847 @ ( setadjoin @ X1848 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1845 @ X1846 ) ) ) ) )
& ( ~ ( in @ X1851 @ X1849 )
| ~ ( in @ X1852 @ X1850 )
| ( in @ ( kpair @ X1851 @ X1852 ) @ ( powerset @ ( powerset @ ( binunion @ X1849 @ X1850 ) ) ) ) )
& ( ~ ( in @ X1855 @ X1853 )
| ~ ( in @ X1856 @ X1854 )
| ( in @ ( kpair @ X1855 @ X1856 ) @ ( cartprod @ X1853 @ X1854 ) ) )
& ( ( in @ ( esk39_3 @ X1857 @ X1858 @ X1859 ) @ X1857 )
| ~ ( in @ X1859 @ ( cartprod @ X1857 @ X1858 ) ) )
& ( ( in @ ( esk40_3 @ X1857 @ X1858 @ X1859 ) @ X1858 )
| ~ ( in @ X1859 @ ( cartprod @ X1857 @ X1858 ) ) )
& ( ( X1859
= ( kpair @ ( esk39_3 @ X1857 @ X1858 @ X1859 ) @ ( esk40_3 @ X1857 @ X1858 @ X1859 ) ) )
| ~ ( in @ X1859 @ ( cartprod @ X1857 @ X1858 ) ) )
& ( ~ ( in @ X1864 @ ( cartprod @ X1862 @ X1863 ) )
| ( iskpair @ X1864 ) )
& ( ( in @ ( esk41_2 @ X1865 @ X1866 ) @ X1865 )
| ~ ( in @ X1866 @ ( setunion @ X1865 ) ) )
& ( ( in @ X1866 @ ( esk41_2 @ X1865 @ X1866 ) )
| ~ ( in @ X1866 @ ( setunion @ X1865 ) ) )
& ( subset @ ( setunion @ ( setadjoin @ X1868 @ emptyset ) ) @ X1868 )
& ( subset @ X1869 @ ( setunion @ ( setadjoin @ X1869 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ X1870 @ emptyset ) )
= X1870 )
& ( ( in @ ( esk42_2 @ X1871 @ X1872 ) @ X1871 )
| ~ ( in @ X1875 @ X1871 )
| ~ ( X1872 @ X1875 )
| ( singleton @ ( dsetconstr @ X1871 @ X1872 ) ) )
& ( ( in @ ( esk43_2 @ X1871 @ X1872 ) @ X1871 )
| ~ ( in @ X1875 @ X1871 )
| ~ ( X1872 @ X1875 )
| ( singleton @ ( dsetconstr @ X1871 @ X1872 ) ) )
& ( ( X1872 @ ( esk42_2 @ X1871 @ X1872 ) )
| ~ ( in @ X1875 @ X1871 )
| ~ ( X1872 @ X1875 )
| ( singleton @ ( dsetconstr @ X1871 @ X1872 ) ) )
& ( ( X1872 @ ( esk43_2 @ X1871 @ X1872 ) )
| ~ ( in @ X1875 @ X1871 )
| ~ ( X1872 @ X1875 )
| ( singleton @ ( dsetconstr @ X1871 @ X1872 ) ) )
& ( ( ( esk42_2 @ X1871 @ X1872 )
!= ( esk43_2 @ X1871 @ X1872 ) )
| ~ ( in @ X1875 @ X1871 )
| ~ ( X1872 @ X1875 )
| ( singleton @ ( dsetconstr @ X1871 @ X1872 ) ) )
& ( ( in @ ( esk44_2 @ X1876 @ X1877 ) @ X1876 )
| ~ ( ex1 @ X1876 @ X1877 ) )
& ( ( X1877 @ ( esk44_2 @ X1876 @ X1877 ) )
| ~ ( ex1 @ X1876 @ X1877 ) )
& ( ( in @ ( esk45_3 @ X1879 @ X1880 @ X1881 ) @ X1879 )
| ( ex1 @ X1879 @ X1880 )
| ~ ( X1880 @ X1881 )
| ~ ( in @ X1881 @ X1879 ) )
& ( ( X1880 @ ( esk45_3 @ X1879 @ X1880 @ X1881 ) )
| ( ex1 @ X1879 @ X1880 )
| ~ ( X1880 @ X1881 )
| ~ ( in @ X1881 @ X1879 ) )
& ( ( ( esk45_3 @ X1879 @ X1880 @ X1881 )
!= X1881 )
| ( ex1 @ X1879 @ X1880 )
| ~ ( X1880 @ X1881 )
| ~ ( in @ X1881 @ X1879 ) )
& ( ( in @ ( esk46_2 @ X1883 @ X1884 ) @ X1883 )
| ~ ( in @ X1887 @ X1883 )
| ~ ( X1884 @ X1887 )
| ( ex1 @ X1883 @ X1884 ) )
& ( ( in @ ( esk47_2 @ X1883 @ X1884 ) @ X1883 )
| ~ ( in @ X1887 @ X1883 )
| ~ ( X1884 @ X1887 )
| ( ex1 @ X1883 @ X1884 ) )
& ( ( X1884 @ ( esk46_2 @ X1883 @ X1884 ) )
| ~ ( in @ X1887 @ X1883 )
| ~ ( X1884 @ X1887 )
| ( ex1 @ X1883 @ X1884 ) )
& ( ( X1884 @ ( esk47_2 @ X1883 @ X1884 ) )
| ~ ( in @ X1887 @ X1883 )
| ~ ( X1884 @ X1887 )
| ( ex1 @ X1883 @ X1884 ) )
& ( ( ( esk46_2 @ X1883 @ X1884 )
!= ( esk47_2 @ X1883 @ X1884 ) )
| ~ ( in @ X1887 @ X1883 )
| ~ ( X1884 @ X1887 )
| ( ex1 @ X1883 @ X1884 ) )
& ( ( ( setadjoin @ X1888 @ emptyset )
!= ( setadjoin @ X1889 @ emptyset ) )
| ( X1888 = X1889 ) )
& ( ~ ( in @ ( setadjoin @ X1892 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1890 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1890 @ ( setadjoin @ X1891 @ emptyset ) ) @ emptyset ) ) )
| ( X1890 = X1892 ) )
& ( ~ ( iskpair @ X1893 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1893 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1893 ) ) ) )
& ( ~ ( singleton @ X1894 )
| ( in @ ( setunion @ X1894 ) @ X1894 ) )
& ( ( kfst @ ( kpair @ X1895 @ X1896 ) )
= X1895 )
& ( ~ ( in @ X1899 @ ( cartprod @ X1897 @ X1898 ) )
| ( in @ ( kfst @ X1899 ) @ X1897 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1900 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1900 @ ( setadjoin @ X1901 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1902 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1902 @ ( setadjoin @ X1903 @ emptyset ) ) @ emptyset ) ) )
| ( X1900 = X1902 ) )
& ( ( ( kpair @ X1904 @ X1905 )
!= ( kpair @ X1906 @ X1907 ) )
| ( X1904 = X1906 ) )
& ( ( X1908 != X1909 )
| ( ( setadjoin @ X1908 @ ( setadjoin @ X1909 @ emptyset ) )
= ( setadjoin @ X1908 @ emptyset ) ) )
& ( ( X1910 != X1911 )
| ( ( setadjoin @ ( setadjoin @ X1910 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1910 @ ( setadjoin @ X1911 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1910 @ emptyset ) @ emptyset ) ) )
& ( ( ( setadjoin @ ( setadjoin @ X1912 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1912 @ ( setadjoin @ X1913 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1914 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1914 @ ( setadjoin @ X1915 @ emptyset ) ) @ emptyset ) ) )
| ( X1914 != X1915 )
| ( X1913 = X1915 ) )
& ( ( ( setadjoin @ X1916 @ ( setadjoin @ X1917 @ emptyset ) )
!= ( setadjoin @ X1918 @ emptyset ) )
| ( X1916 = X1917 ) )
& ( ( ( setadjoin @ ( setadjoin @ X1919 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1919 @ ( setadjoin @ X1920 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1921 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1921 @ ( setadjoin @ X1922 @ emptyset ) ) @ emptyset ) ) )
| ( X1920 = X1922 ) )
& ( ( ( kpair @ X1923 @ X1924 )
!= ( kpair @ X1925 @ X1926 ) )
| ( X1924 = X1926 ) )
& ( ~ ( iskpair @ X1927 )
| ( singleton
@ ( dsetconstr @ ( setunion @ X1927 )
@ ^ [Z0: $i] :
( X1927
= ( kpair @ ( kfst @ X1927 ) @ Z0 ) ) ) ) )
& ( ( ksnd @ ( kpair @ X1928 @ X1929 ) )
= X1929 )
& ( ~ ( iskpair @ X1930 )
| ( ( kpair @ ( kfst @ X1930 ) @ ( ksnd @ X1930 ) )
= X1930 ) )
& ( ~ ( in @ X1933 @ ( cartprod @ X1931 @ X1932 ) )
| ( in @ ( ksnd @ X1933 ) @ X1932 ) )
& ( ~ ( in @ ( kpair @ X1936 @ X1937 ) @ ( cartprod @ X1934 @ X1935 ) )
| ( in @ X1936 @ X1934 ) )
& ( ~ ( in @ ( kpair @ X1940 @ X1941 ) @ ( cartprod @ X1938 @ X1939 ) )
| ( in @ X1941 @ X1939 ) )
& ( ~ ( in @ X1944 @ X1942 )
| ~ ( in @ X1945 @ X1943 )
| ( ( kpair @ X1944 @ X1945 )
= ( kpair @ X1944 @ X1945 ) ) )
& ( ~ ( in @ X1948 @ X1946 )
| ~ ( in @ X1949 @ X1947 )
| ( ( kfst @ ( kpair @ X1948 @ X1949 ) )
= X1948 ) )
& ( ~ ( in @ X1952 @ X1950 )
| ~ ( in @ X1953 @ X1951 )
| ( ( ksnd @ ( kpair @ X1952 @ X1953 ) )
= X1953 ) )
& ( ~ ( in @ X1956 @ ( cartprod @ X1954 @ X1955 ) )
| ( ( kpair @ ( kfst @ X1956 ) @ ( ksnd @ X1956 ) )
= X1956 ) )
& ( ~ ( in @ X1960 @ X1957 )
| ~ ( in @ X1961 @ X1958 )
| ~ ( X1959 @ X1960 @ X1961 )
| ( in @ ( kpair @ X1960 @ X1961 ) @ ( dpsetconstr @ X1957 @ X1958 @ X1959 ) ) )
& ( subset @ ( dpsetconstr @ X1962 @ X1963 @ X1964 ) @ ( cartprod @ X1962 @ X1963 ) )
& ( breln @ X1965 @ X1966 @ ( dpsetconstr @ X1965 @ X1966 @ X1967 ) )
& ( ~ ( in @ X1971 @ X1968 )
| ~ ( in @ X1972 @ X1969 )
| ~ ( in @ ( kpair @ X1971 @ X1972 ) @ ( dpsetconstr @ X1968 @ X1969 @ X1970 ) )
| ( X1970 @ X1971 @ X1972 ) )
& ( ~ ( in @ ( kpair @ X1976 @ X1977 ) @ ( dpsetconstr @ X1973 @ X1974 @ X1975 ) )
| ( in @ X1976 @ X1973 ) )
& ( ~ ( in @ ( kpair @ X1981 @ X1982 ) @ ( dpsetconstr @ X1978 @ X1979 @ X1980 ) )
| ( in @ X1982 @ X1979 ) )
& ( ~ ( in @ ( kpair @ X1986 @ X1987 ) @ ( dpsetconstr @ X1983 @ X1984 @ X1985 ) )
| ( X1985 @ X1986 @ X1987 ) )
& ( ~ ( func @ X1988 @ X1989 @ X1990 )
| ~ ( in @ X1991 @ X1988 )
| ( singleton
@ ( dsetconstr @ X1989
@ ^ [Z0: $i] : ( in @ ( kpair @ X1991 @ Z0 ) @ X1990 ) ) ) )
& ( ~ ( func @ X1992 @ X1993 @ X1994 )
| ~ ( in @ X1995 @ X1992 )
| ( in
@ ( setunion
@ ( dsetconstr @ X1993
@ ^ [Z0: $i] : ( in @ ( kpair @ X1995 @ Z0 ) @ X1994 ) ) )
@ X1993 ) )
& ( ~ ( func @ X1996 @ X1997 @ X1998 )
| ~ ( in @ X1999 @ X1996 )
| ( in @ ( ap @ X1996 @ X1997 @ X1998 @ X1999 ) @ X1997 ) )
& ( ~ ( in @ X2002 @ ( funcSet @ X2000 @ X2001 ) )
| ( func @ X2000 @ X2001 @ X2002 ) )
& ( ~ ( in @ X2005 @ ( funcSet @ X2003 @ X2004 ) )
| ~ ( in @ X2006 @ X2003 )
| ( in @ ( ap @ X2003 @ X2004 @ X2005 @ X2006 ) @ X2004 ) )
& ( ~ ( func @ X2007 @ X2008 @ X2009 )
| ( in @ X2009 @ ( funcSet @ X2007 @ X2008 ) ) )
& ( ( in @ ( esk48_3 @ X2010 @ X2011 @ X2012 ) @ X2010 )
| ( func @ X2010 @ X2011
@ ( dpsetconstr @ X2010 @ X2011
@ ^ [Z0: $i] : ( $eq @ ( X2012 @ Z0 ) ) ) ) )
& ( ~ ( in @ ( X2012 @ ( esk48_3 @ X2010 @ X2011 @ X2012 ) ) @ X2011 )
| ( func @ X2010 @ X2011
@ ( dpsetconstr @ X2010 @ X2011
@ ^ [Z0: $i] : ( $eq @ ( X2012 @ Z0 ) ) ) ) )
& ( ( in @ ( esk49_3 @ X2014 @ X2015 @ X2016 ) @ X2014 )
| ( func @ X2014 @ X2015 @ ( lam @ X2014 @ X2015 @ X2016 ) ) )
& ( ~ ( in @ ( X2016 @ ( esk49_3 @ X2014 @ X2015 @ X2016 ) ) @ X2015 )
| ( func @ X2014 @ X2015 @ ( lam @ X2014 @ X2015 @ X2016 ) ) )
& ( ( in @ ( esk50_3 @ X2018 @ X2019 @ X2020 ) @ X2018 )
| ( in @ ( lam @ X2018 @ X2019 @ X2020 ) @ ( funcSet @ X2018 @ X2019 ) ) )
& ( ~ ( in @ ( X2020 @ ( esk50_3 @ X2018 @ X2019 @ X2020 ) ) @ X2019 )
| ( in @ ( lam @ X2018 @ X2019 @ X2020 ) @ ( funcSet @ X2018 @ X2019 ) ) )
& ( ( in @ ( esk51_4 @ X2022 @ X2023 @ X2024 @ X2025 ) @ X2022 )
| ~ ( in @ X2028 @ X2024 )
| ( X2025 @ X2028 )
| ~ ( breln @ X2022 @ X2023 @ X2024 ) )
& ( ( in @ ( esk52_4 @ X2022 @ X2023 @ X2024 @ X2025 ) @ X2023 )
| ~ ( in @ X2028 @ X2024 )
| ( X2025 @ X2028 )
| ~ ( breln @ X2022 @ X2023 @ X2024 ) )
& ( ( in @ ( kpair @ ( esk51_4 @ X2022 @ X2023 @ X2024 @ X2025 ) @ ( esk52_4 @ X2022 @ X2023 @ X2024 @ X2025 ) ) @ X2024 )
| ~ ( in @ X2028 @ X2024 )
| ( X2025 @ X2028 )
| ~ ( breln @ X2022 @ X2023 @ X2024 ) )
& ( ~ ( X2025 @ ( kpair @ ( esk51_4 @ X2022 @ X2023 @ X2024 @ X2025 ) @ ( esk52_4 @ X2022 @ X2023 @ X2024 @ X2025 ) ) )
| ~ ( in @ X2028 @ X2024 )
| ( X2025 @ X2028 )
| ~ ( breln @ X2022 @ X2023 @ X2024 ) )
& ( ( in @ ( esk53_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ X2029 )
| ~ ( in @ X2035 @ X2031 )
| ( X2032 @ X2035 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ( in @ ( esk54_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ X2030 )
| ~ ( in @ X2035 @ X2031 )
| ( X2032 @ X2035 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ( in @ ( kpair @ ( esk53_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ ( esk54_4 @ X2029 @ X2030 @ X2031 @ X2032 ) ) @ X2031 )
| ~ ( in @ X2035 @ X2031 )
| ( X2032 @ X2035 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ~ ( X2032 @ ( kpair @ ( esk53_4 @ X2029 @ X2030 @ X2031 @ X2032 ) @ ( esk54_4 @ X2029 @ X2030 @ X2031 @ X2032 ) ) )
| ~ ( in @ X2035 @ X2031 )
| ( X2032 @ X2035 )
| ~ ( breln @ X2029 @ X2030 @ X2031 ) )
& ( ~ ( ex1 @ X2036 @ X2037 )
| ~ ( in @ X2038 @ X2036 )
| ~ ( in @ X2039 @ X2036 )
| ~ ( X2037 @ X2038 )
| ~ ( X2037 @ X2039 )
| ( X2038 = X2039 ) )
& ( ~ ( func @ X2040 @ X2041 @ X2042 )
| ~ ( in @ X2043 @ X2040 )
| ( in @ ( kpair @ X2043 @ ( ap @ X2040 @ X2041 @ X2042 @ X2043 ) ) @ X2042 ) )
& ( ~ ( in @ X2046 @ ( funcSet @ X2044 @ X2045 ) )
| ~ ( in @ X2047 @ X2044 )
| ( in @ ( kpair @ X2047 @ ( ap @ X2044 @ X2045 @ X2046 @ X2047 ) ) @ X2046 ) )
& ( ~ ( func @ X2048 @ X2049 @ X2050 )
| ~ ( in @ X2051 @ X2048 )
| ~ ( in @ X2052 @ X2049 )
| ~ ( in @ ( kpair @ X2051 @ X2052 ) @ X2050 )
| ( ( ap @ X2048 @ X2049 @ X2050 @ X2051 )
= X2052 ) )
& ( ( in @ ( esk55_4 @ X2053 @ X2054 @ X2055 @ X2056 ) @ X2053 )
| ~ ( in @ X2058 @ X2053 )
| ~ ( in @ X2059 @ X2054 )
| ~ ( in @ ( kpair @ X2058 @ X2059 ) @ X2056 )
| ( in @ ( kpair @ X2058 @ X2059 ) @ X2055 )
| ~ ( func @ X2053 @ X2054 @ X2056 )
| ~ ( func @ X2053 @ X2054 @ X2055 ) )
& ( ( ( ap @ X2053 @ X2054 @ X2055 @ ( esk55_4 @ X2053 @ X2054 @ X2055 @ X2056 ) )
!= ( ap @ X2053 @ X2054 @ X2056 @ ( esk55_4 @ X2053 @ X2054 @ X2055 @ X2056 ) ) )
| ~ ( in @ X2058 @ X2053 )
| ~ ( in @ X2059 @ X2054 )
| ~ ( in @ ( kpair @ X2058 @ X2059 ) @ X2056 )
| ( in @ ( kpair @ X2058 @ X2059 ) @ X2055 )
| ~ ( func @ X2053 @ X2054 @ X2056 )
| ~ ( func @ X2053 @ X2054 @ X2055 ) )
& ( ~ ( in @ X2062 @ ( funcSet @ X2060 @ X2061 ) )
| ~ ( in @ X2063 @ X2060 )
| ~ ( in @ X2064 @ X2061 )
| ~ ( in @ ( kpair @ X2063 @ X2064 ) @ X2062 )
| ( ( ap @ X2060 @ X2061 @ X2062 @ X2063 )
= X2064 ) )
& ( ( in @ ( esk56_4 @ X2065 @ X2066 @ X2067 @ X2068 ) @ X2065 )
| ( subset @ X2067 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2067 ) )
& ( ( in @ ( esk57_4 @ X2065 @ X2066 @ X2067 @ X2068 ) @ X2066 )
| ( subset @ X2067 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2067 ) )
& ( ( in @ ( kpair @ ( esk56_4 @ X2065 @ X2066 @ X2067 @ X2068 ) @ ( esk57_4 @ X2065 @ X2066 @ X2067 @ X2068 ) ) @ X2067 )
| ( subset @ X2067 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2067 ) )
& ( ~ ( in @ ( kpair @ ( esk56_4 @ X2065 @ X2066 @ X2067 @ X2068 ) @ ( esk57_4 @ X2065 @ X2066 @ X2067 @ X2068 ) ) @ X2068 )
| ( subset @ X2067 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2068 )
| ~ ( breln @ X2065 @ X2066 @ X2067 ) )
& ( ( in @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ( X2073 = X2074 )
| ( in @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ( X2073 = X2074 )
| ( in @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ( X2073 = X2074 )
| ( in @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ( X2073 = X2074 )
| ( in @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ( X2073 = X2074 )
| ( in @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ( X2073 = X2074 )
| ( in @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ( X2073 = X2074 )
| ( in @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ( X2073 = X2074 )
| ( in @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ( X2073 = X2074 )
| ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ( X2073 = X2074 )
| ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ( X2073 = X2074 )
| ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ( X2073 = X2074 )
| ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2071 )
| ( X2073 = X2074 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ X2072 )
| ( X2073 = X2074 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ( X2073 = X2074 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ~ ( in @ ( kpair @ ( esk60_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk61_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
| ( X2073 = X2074 )
| ~ ( in @ ( kpair @ ( esk58_4 @ X2071 @ X2072 @ X2073 @ X2074 ) @ ( esk59_4 @ X2071 @ X2072 @ X2073 @ X2074 ) ) @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2074 )
| ~ ( breln @ X2071 @ X2072 @ X2073 ) )
& ( ( in @ ( esk62_4 @ X2079 @ X2080 @ X2081 @ X2082 ) @ X2079 )
| ( X2081 = X2082 )
| ~ ( func @ X2079 @ X2080 @ X2082 )
| ~ ( func @ X2079 @ X2080 @ X2081 ) )
& ( ( ( ap @ X2079 @ X2080 @ X2081 @ ( esk62_4 @ X2079 @ X2080 @ X2081 @ X2082 ) )
!= ( ap @ X2079 @ X2080 @ X2082 @ ( esk62_4 @ X2079 @ X2080 @ X2081 @ X2082 ) ) )
| ( X2081 = X2082 )
| ~ ( func @ X2079 @ X2080 @ X2082 )
| ~ ( func @ X2079 @ X2080 @ X2081 ) )
& ( ( in @ ( esk63_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ X2084 )
| ( X2086 = X2087 )
| ~ ( in @ X2087 @ ( funcSet @ X2084 @ X2085 ) )
| ~ ( in @ X2086 @ ( funcSet @ X2084 @ X2085 ) ) )
& ( ( ( ap @ X2084 @ X2085 @ X2086 @ ( esk63_4 @ X2084 @ X2085 @ X2086 @ X2087 ) )
!= ( ap @ X2084 @ X2085 @ X2087 @ ( esk63_4 @ X2084 @ X2085 @ X2086 @ X2087 ) ) )
| ( X2086 = X2087 )
| ~ ( in @ X2087 @ ( funcSet @ X2084 @ X2085 ) )
| ~ ( in @ X2086 @ ( funcSet @ X2084 @ X2085 ) ) )
& ( ~ ( in @ X2091 @ ( funcSet @ X2089 @ X2090 ) )
| ~ ( in @ X2092 @ X2089 )
| ( ( ap @ X2089 @ X2090 @ X2091 @ X2092 )
= ( ap @ X2089 @ X2090 @ X2091 @ X2092 ) ) )
& ( ~ ( func @ X2093 @ X2094 @ X2095 )
| ~ ( in @ X2096 @ X2093 )
| ( ( ap @ X2093 @ X2094 @ X2095 @ X2096 )
= ( ap @ X2093 @ X2094 @ X2095 @ X2096 ) ) )
& ( ( in @ ( esk64_3 @ X2097 @ X2098 @ X2099 ) @ X2097 )
| ~ ( in @ X2101 @ X2097 )
| ( ( ap @ X2097 @ X2098 @ ( lam @ X2097 @ X2098 @ X2099 ) @ X2101 )
= ( X2099 @ X2101 ) ) )
& ( ~ ( in @ ( X2099 @ ( esk64_3 @ X2097 @ X2098 @ X2099 ) ) @ X2098 )
| ~ ( in @ X2101 @ X2097 )
| ( ( ap @ X2097 @ X2098 @ ( lam @ X2097 @ X2098 @ X2099 ) @ X2101 )
= ( X2099 @ X2101 ) ) )
& ( ~ ( func @ X2102 @ X2103 @ X2104 )
| ( ( lam @ X2102 @ X2103 @ ( ap @ X2102 @ X2103 @ X2104 ) )
= X2104 ) )
& ( ( in @ ( esk65_3 @ X2105 @ X2106 @ X2107 ) @ X2105 )
| ( ( lam @ X2105 @ X2106 @ X2107 )
= ( lam @ X2105 @ X2106 @ X2107 ) ) )
& ( ~ ( in @ ( X2107 @ ( esk65_3 @ X2105 @ X2106 @ X2107 ) ) @ X2106 )
| ( ( lam @ X2105 @ X2106 @ X2107 )
= ( lam @ X2105 @ X2106 @ X2107 ) ) )
& ( ( in @ ( esk66_3 @ X2109 @ X2110 @ X2111 ) @ X2109 )
| ~ ( in @ X2113 @ X2109 )
| ( ( ap @ X2109 @ X2110 @ ( lam @ X2109 @ X2110 @ X2111 ) @ X2113 )
= ( X2111 @ X2113 ) ) )
& ( ~ ( in @ ( X2111 @ ( esk66_3 @ X2109 @ X2110 @ X2111 ) ) @ X2110 )
| ~ ( in @ X2113 @ X2109 )
| ( ( ap @ X2109 @ X2110 @ ( lam @ X2109 @ X2110 @ X2111 ) @ X2113 )
= ( X2111 @ X2113 ) ) )
& ( ~ ( in @ X2116 @ ( funcSet @ X2114 @ X2115 ) )
| ( ( lam @ X2114 @ X2115 @ ( ap @ X2114 @ X2115 @ X2116 ) )
= X2116 ) )
& ( ~ ( in @ X2119 @ X2117 )
| ~ ( in @ X2120 @ X2117 )
| X2118
| ( in @ X2120
@ ( dsetconstr @ X2117
@ ^ [Z0: $i] :
( ( X2118
& ( Z0 = X2119 ) )
| ( ~ X2118
& ( Z0 = X2120 ) ) ) ) ) )
& ( ~ ( in @ X2123 @ X2121 )
| ~ ( in @ X2124 @ X2121 )
| X2122
| ( ( dsetconstr @ X2121
@ ^ [Z0: $i] :
( ( X2122
& ( Z0 = X2123 ) )
| ( ~ X2122
& ( Z0 = X2124 ) ) ) )
= ( setadjoin @ X2124 @ emptyset ) ) )
& ( ~ ( in @ X2127 @ X2125 )
| ~ ( in @ X2128 @ X2125 )
| ~ X2126
| ( in @ X2127
@ ( dsetconstr @ X2125
@ ^ [Z0: $i] :
( ( X2126
& ( Z0 = X2127 ) )
| ( ~ X2126
& ( Z0 = X2128 ) ) ) ) ) )
& ( ~ ( in @ X2131 @ X2129 )
| ~ ( in @ X2132 @ X2129 )
| ~ X2130
| ( ( dsetconstr @ X2129
@ ^ [Z0: $i] :
( ( X2130
& ( Z0 = X2131 ) )
| ( ~ X2130
& ( Z0 = X2132 ) ) ) )
= ( setadjoin @ X2131 @ emptyset ) ) )
& ( ~ ( in @ X2135 @ X2133 )
| ~ ( in @ X2136 @ X2133 )
| ( singleton
@ ( dsetconstr @ X2133
@ ^ [Z0: $i] :
( ( X2134
& ( Z0 = X2135 ) )
| ( ~ X2134
& ( Z0 = X2136 ) ) ) ) ) )
& ( ~ ( in @ X2139 @ X2137 )
| ~ ( in @ X2140 @ X2137 )
| ( in @ ( if @ X2137 @ X2138 @ X2139 @ X2140 ) @ X2137 ) )
& ( ~ ( singleton @ X2141 )
| ~ ( in @ X2142 @ X2141 )
| ( ( setunion @ X2141 )
= X2142 ) )
& ( ~ ( in @ X2145 @ X2143 )
| ~ ( in @ X2146 @ X2143 )
| ~ X2144
| ( ( if @ X2143 @ X2144 @ X2145 @ X2146 )
= X2145 ) )
& ( ~ ( in @ X2149 @ X2147 )
| ~ ( in @ X2150 @ X2147 )
| X2148
| ( ( if @ X2147 @ X2148 @ X2149 @ X2150 )
= X2150 ) )
& ( ~ ( in @ X2153 @ X2151 )
| ~ ( in @ X2154 @ X2151 )
| ( in @ ( if @ X2151 @ X2152 @ X2153 @ X2154 ) @ ( setadjoin @ X2153 @ ( setadjoin @ X2154 @ emptyset ) ) ) )
& ( ~ ( in @ X2156 @ ( powerset @ X2155 ) )
| ~ ( in @ X2157 @ ( powerset @ X2155 ) )
| ( in @ ( binintersect @ X2156 @ X2157 ) @ ( powerset @ X2155 ) ) )
& ( ~ ( in @ X2159 @ ( powerset @ X2158 ) )
| ~ ( in @ X2160 @ ( powerset @ X2158 ) )
| ( in @ ( binunion @ X2159 @ X2160 ) @ ( powerset @ X2158 ) ) )
& ( ~ ( in @ X2162 @ ( powerset @ X2161 ) )
| ( in @ ( powerset @ X2162 ) @ ( powerset @ ( powerset @ X2161 ) ) ) )
& ( ~ ( in @ X2164 @ ( powerset @ X2163 ) )
| ~ ( in @ X2165 @ ( powerset @ X2163 ) )
| ( in @ ( setminus @ X2164 @ X2165 ) @ ( powerset @ X2163 ) ) )
& ( ~ ( in @ X2167 @ ( powerset @ X2166 ) )
| ( in @ ( setminus @ X2166 @ X2167 ) @ ( powerset @ X2166 ) ) )
& ( in @ esk68_0 @ ( powerset @ esk67_0 ) )
& ( in @ esk69_0 @ ( powerset @ esk67_0 ) )
& ( ~ ( in @ X2171 @ esk67_0 )
| ~ ( in @ X2171 @ esk68_0 )
| ( in @ X2171 @ esk69_0 ) )
& ( ~ ( in @ X2172 @ esk67_0 )
| ~ ( in @ X2172 @ esk69_0 )
| ( in @ X2172 @ esk68_0 ) )
& ( esk68_0 != esk69_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_283])])])])])])]) ).
thf(c_0_285,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_286,negated_conjecture,
in @ esk68_0 @ ( powerset @ esk67_0 ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_287,negated_conjecture,
! [X3: $i,X2: $i] :
( ( X2 = X3 )
| ( in @ ( esk11_2 @ X2 @ X3 ) @ X2 )
| ~ ( in @ ( esk12_2 @ X2 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_288,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk69_0 )
| ~ ( in @ X2 @ esk67_0 )
| ~ ( in @ X2 @ esk68_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_289,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk67_0 )
| ~ ( in @ X2 @ esk68_0 ) ),
inference(spm,[status(thm)],[c_0_285,c_0_286]) ).
thf(c_0_290,negated_conjecture,
in @ esk69_0 @ ( powerset @ esk67_0 ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_291,negated_conjecture,
! [X2: $i] :
( ( esk69_0 = X2 )
| ( in @ ( esk11_2 @ esk69_0 @ X2 ) @ esk69_0 )
| ~ ( in @ ( esk12_2 @ esk69_0 @ X2 ) @ esk68_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_289]) ).
thf(c_0_292,negated_conjecture,
! [X3: $i,X2: $i] :
( ( in @ ( esk12_2 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 )
| ( in @ ( esk11_2 @ X2 @ X3 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_293,negated_conjecture,
esk68_0 != esk69_0,
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_294,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk67_0 )
| ~ ( in @ X2 @ esk69_0 ) ),
inference(spm,[status(thm)],[c_0_285,c_0_290]) ).
thf(c_0_295,negated_conjecture,
in @ ( esk11_2 @ esk69_0 @ esk68_0 ) @ esk69_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_292]),c_0_293]) ).
thf(c_0_296,negated_conjecture,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk36_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_297,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk68_0 )
| ~ ( in @ X2 @ esk67_0 )
| ~ ( in @ X2 @ esk69_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_298,negated_conjecture,
in @ ( esk11_2 @ esk69_0 @ esk68_0 ) @ esk67_0,
inference(spm,[status(thm)],[c_0_294,c_0_295]) ).
thf(c_0_299,negated_conjecture,
! [X2: $i] :
( ( subset @ X2 @ esk69_0 )
| ~ ( in @ ( esk36_2 @ X2 @ esk69_0 ) @ esk68_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_288]),c_0_289]) ).
thf(c_0_300,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk36_2 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_301,negated_conjecture,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ ( in @ ( esk12_2 @ X2 @ X3 ) @ X2 )
| ~ ( in @ ( esk11_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_302,negated_conjecture,
in @ ( esk11_2 @ esk69_0 @ esk68_0 ) @ esk68_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_295]),c_0_298])]) ).
thf(c_0_303,negated_conjecture,
! [X4: $i,X3: $i,X2: $i] :
( ( in @ X4 @ X3 )
| ~ ( subset @ X2 @ X3 )
| ~ ( in @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_304,negated_conjecture,
subset @ esk68_0 @ esk69_0,
inference(spm,[status(thm)],[c_0_299,c_0_300]) ).
thf(c_0_305,negated_conjecture,
~ ( in @ ( esk12_2 @ esk69_0 @ esk68_0 ) @ esk69_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_302]),c_0_293]) ).
thf(c_0_306,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ esk69_0 )
| ~ ( in @ X2 @ esk68_0 ) ),
inference(spm,[status(thm)],[c_0_303,c_0_304]) ).
thf(c_0_307,negated_conjecture,
~ ( in @ ( esk12_2 @ esk69_0 @ esk68_0 ) @ esk68_0 ),
inference(spm,[status(thm)],[c_0_305,c_0_306]) ).
thf(c_0_308,negated_conjecture,
! [X2: $i,X3: $i] :
( ( in @ ( esk12_2 @ X2 @ X3 ) @ X3 )
| ( X2 = X3 )
| ~ ( in @ ( esk11_2 @ X2 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
thf(c_0_309,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_308]),c_0_302])]),c_0_293]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU715^1 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 18:20:52 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.43 Running higher-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.95/11.18 # Version: 3.1.0-ho
% 63.95/11.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 63.95/11.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 63.95/11.18 # Starting ehoh_best5 with 300s (1) cores
% 63.95/11.18 # Starting almost_fo_3_lam with 300s (1) cores
% 63.95/11.18 # Starting new_bool_5 with 300s (1) cores
% 63.95/11.18 # Starting pre_casc_3 with 300s (1) cores
% 63.95/11.18 # Starting ho_unfolding_8 with 300s (1) cores
% 63.95/11.18 # Starting new_ho_10_cnf2 with 300s (1) cores
% 63.95/11.18 # Starting new_bool_3 with 300s (1) cores
% 63.95/11.18 # Starting new_ho_5 with 300s (1) cores
% 63.95/11.18 # pre_casc_3 with pid 28221 completed with status 8
% 63.95/11.18 # new_ho_5 with pid 28225 completed with status 8
% 63.95/11.18 # new_bool_5 with pid 28220 completed with status 0
% 63.95/11.18 # Result found by new_bool_5
% 63.95/11.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 63.95/11.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 63.95/11.18 # Starting ehoh_best5 with 300s (1) cores
% 63.95/11.18 # Starting almost_fo_3_lam with 300s (1) cores
% 63.95/11.18 # Starting new_bool_5 with 300s (1) cores
% 63.95/11.18 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 63.95/11.18 # Search class: HGHSM-FSLM32-MHFMMSBN
% 63.95/11.18 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 63.95/11.18 # Starting ho_unfolding_8 with 55s (1) cores
% 63.95/11.18 # ho_unfolding_8 with pid 28244 completed with status 0
% 63.95/11.18 # Result found by ho_unfolding_8
% 63.95/11.18 # Preprocessing class: HSLMSLSSLLLCHFA.
% 63.95/11.18 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 63.95/11.18 # Starting ehoh_best5 with 300s (1) cores
% 63.95/11.18 # Starting almost_fo_3_lam with 300s (1) cores
% 63.95/11.18 # Starting new_bool_5 with 300s (1) cores
% 63.95/11.18 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 63.95/11.18 # Search class: HGHSM-FSLM32-MHFMMSBN
% 63.95/11.18 # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 63.95/11.18 # Starting ho_unfolding_8 with 55s (1) cores
% 63.95/11.18 # Preprocessing time : 0.052 s
% 63.95/11.18 # Presaturation interreduction done
% 63.95/11.18
% 63.95/11.18 # Proof found!
% 63.95/11.18 # SZS status Theorem
% 63.95/11.18 # SZS output start CNFRefutation
% See solution above
% 63.95/11.18 # Parsed axioms : 505
% 63.95/11.18 # Removed by relevancy pruning/SinE : 274
% 63.95/11.18 # Initial clauses : 381
% 63.95/11.18 # Removed in clause preprocessing : 34
% 63.95/11.18 # Initial clauses in saturation : 347
% 63.95/11.18 # Processed clauses : 8618
% 63.95/11.18 # ...of these trivial : 59
% 63.95/11.18 # ...subsumed : 4631
% 63.95/11.18 # ...remaining for further processing : 3928
% 63.95/11.18 # Other redundant clauses eliminated : 131
% 63.95/11.18 # Clauses deleted for lack of memory : 0
% 63.95/11.18 # Backward-subsumed : 749
% 63.95/11.18 # Backward-rewritten : 214
% 63.95/11.18 # Generated clauses : 363329
% 63.95/11.18 # ...of the previous two non-redundant : 360705
% 63.95/11.18 # ...aggressively subsumed : 0
% 63.95/11.18 # Contextual simplify-reflections : 83
% 63.95/11.18 # Paramodulations : 363048
% 63.95/11.18 # Factorizations : 74
% 63.95/11.18 # NegExts : 40
% 63.95/11.18 # Equation resolutions : 139
% 63.95/11.18 # Disequality decompositions : 0
% 63.95/11.18 # Total rewrite steps : 9460
% 63.95/11.18 # ...of those cached : 8906
% 63.95/11.18 # Propositional unsat checks : 0
% 63.95/11.18 # Propositional check models : 0
% 63.95/11.18 # Propositional check unsatisfiable : 0
% 63.95/11.18 # Propositional clauses : 0
% 63.95/11.18 # Propositional clauses after purity: 0
% 63.95/11.18 # Propositional unsat core size : 0
% 63.95/11.18 # Propositional preprocessing time : 0.000
% 63.95/11.18 # Propositional encoding time : 0.000
% 63.95/11.18 # Propositional solver time : 0.000
% 63.95/11.18 # Success case prop preproc time : 0.000
% 63.95/11.18 # Success case prop encoding time : 0.000
% 63.95/11.18 # Success case prop solver time : 0.000
% 63.95/11.18 # Current number of processed clauses : 2641
% 63.95/11.18 # Positive orientable unit clauses : 90
% 63.95/11.18 # Positive unorientable unit clauses: 0
% 63.95/11.18 # Negative unit clauses : 239
% 63.95/11.18 # Non-unit-clauses : 2312
% 63.95/11.18 # Current number of unprocessed clauses: 351959
% 63.95/11.18 # ...number of literals in the above : 1362511
% 63.95/11.18 # Current number of archived formulas : 0
% 63.95/11.18 # Current number of archived clauses : 1271
% 63.95/11.18 # Clause-clause subsumption calls (NU) : 914438
% 63.95/11.18 # Rec. Clause-clause subsumption calls : 472026
% 63.95/11.18 # Non-unit clause-clause subsumptions : 3695
% 63.95/11.18 # Unit Clause-clause subsumption calls : 45654
% 63.95/11.18 # Rewrite failures with RHS unbound : 0
% 63.95/11.18 # BW rewrite match attempts : 50
% 63.95/11.18 # BW rewrite match successes : 18
% 63.95/11.18 # Condensation attempts : 0
% 63.95/11.18 # Condensation successes : 0
% 63.95/11.18 # Termbank termtop insertions : 7104597
% 63.95/11.18 # Search garbage collected termcells : 22379
% 63.95/11.18
% 63.95/11.18 # -------------------------------------------------
% 63.95/11.18 # User time : 10.187 s
% 63.95/11.18 # System time : 0.283 s
% 63.95/11.18 # Total time : 10.470 s
% 63.95/11.18 # Maximum resident set size: 7428 pages
% 63.95/11.18
% 63.95/11.18 # -------------------------------------------------
% 63.95/11.18 # User time : 10.385 s
% 63.95/11.18 # System time : 0.360 s
% 63.95/11.18 # Total time : 10.744 s
% 63.95/11.18 # Maximum resident set size: 2356 pages
% 63.95/11.18 % E---3.1 exiting
% 63.95/11.19 % E exiting
%------------------------------------------------------------------------------